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Concentration and costs in Canadian food manufacturing industries, 1961-1982 Cahill, Sean Andrew 1986

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CONCENTRATION AND COSTS IN CANADIAN FOOD MANUFACTURING INDUSTRIES: 1961-1982 by SEAN ANDREW CAHILL A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES A g r i c u l t u r a l Economics We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA June 1986 © Sean Andrew C a h i l l , 1986 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the The University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Agricultural Economics The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: June. 1986 t ABSTRACT This study is concerned with- the effects of changes in industrial concentration • on average • costs of production in 17 Canadian 4—digit food manufacturing industries over the period 1961-1982. The model employed is a dual Translog cost function adapted to include a concentration variable (Herfindahl index) and technical change, , and is estimated using pooling techniques to allow simultaneous analysis of all 17 industries. The results indicate that there was a significant relationship between concentration and average costs for this sample. In particular, there appears to have been a decrease in average costs for low-concentration industries as concentration increased, ceteris paribus, while in high-concentration industries, increases in concentration led to increases in costs. Concentration changes have also had an effect on the relative shares of factors of production for these industries. An evaluation of employment effects across industries indicates that the benefits in efficiency due to increases in concentration in low-concentration industries must be weighed against apparent decreases in the overall employment (of labour) - f o r these industries. Alternatively, the efficiency losses in high-concentration industries appear to have been offset by increases in overall employment as concentration has increased. Thus, depending on the criterion used, relative concentration effects may have been beneficial or detremental to social welfare; the outcome is not unequivocal. l l Table of Contents A B S T R A C T , i i LIST O F TABLES -Vii. A C K N O W L E D G E M E N T S i x 1. I N T R O D U C T I O N 1 1.1 The General Problem .-. 1 1.2 The Gisser Model of the Productivity/Concentration Relationship 2 1.3 Applying an Alternative Specification to Gisser's Data 4 1.4 The Case for Canadian Food Manufacturing 5 2. C O N C E N T R A T I O N A N D COSTS: S O M E ESTABL I SHED VIEWS 8 2.1 The Concentration-Profits Literature 8 2.2 The Concentration-Profits Debate: Collusion versus Efficiency 9 2.2.1 The Demsetz Hypothesis 9 2.2.2 Other Tests of the Efficiency Hypothesis at the Industry Level 11 2.2.3 Intra-Industry(Firm Level) Analyses 12. 2.3 Models That Directly Measure Concentration-Cost Effects 14 2.3.1 The Peltzman/Lustgarten Models 15 2.3.2 Gisser Revisited 20 2.4 The Need for an Integrated Theory 21 3. A N I N T E G R A T E D M E T H O D O L O G Y F O R M E A S U R I N G C O N C E N T R A T I O N - C O S T EFFECTS .._ 22 » 3.1 Assumptions about F i rm-level Behaviour 22 3.2 The Conceptual Model 25 3.3 Specifying a Cost Function 27 4. PROPERTIES O F T H E C O N C E P T U A L D U A L COST F U N C T I O N 29 4.1 Regularity Conditions Necessary for Duality 29 4.2 Measuring Returns to Scale 31 4.3 Homogeneity : 33 4.4 Homotheticity 34 4;5 Elasticities of Factor Demands .« , 35 4.6 Elasticities of Substitution 36 4.7 Technical Change 37 4.7.1 The Elements of Technical Change 37 4.7.2 The Bias of Technical Change 39 4.8 Measuring the Effects of Concentration on. Costs ... .....41 4.8.1 Returns to Concentration . , 42 4.8:2 The Bias of Concentration 42 4.9 Optimal Scale , 43 4.10 Aggregation and Dynamics 44 4.11 The Issue of Output Exogeneity : 45 MODELLING CANADIAN FOOD MANUFACTURING INDUSTRIES: FUNCTIONAL FORM AND COST FUNCTION SPECIFICATION 48 5.1 Introduction 48 5.2 Choice of Functional Form 48 5.3 The Canadian Food and Beverage Industry: Previous Studies 52 5.4 Stochastic Specification of the Total Cost Function 56 5.4.1 The Translog Cost Function: Integrating the Concentration Variable , 56 5.4.2 Stochastic Specification of the Model 60 5.5 Specification, Regularity and Structural Tests for the TL Cost Function 66 5.5.1 Specification Testing 66 5.5.1.1 Concentration Effects: Specification Tests 66 5.5.1.2 Implementation of Specification Tests: the Wald and Likelihood Ratio Methods 68 5.5.1.3 Specification Tests for form of Production Technology: Homogeneity and Homotheticity 70 5.5.2 Misspecification Tests: Autocorrelation, Hetroscedasticity, and Diagonality of the Covariance Matrix 71 iv 5.5.3 Regularity of the Cost Function: Testing for Concavity 73 • 5.5.4 Structural Tests with the TL .- , 74 5.5.4.1 Elasticities of Factor Demands 74 5.5.4.2 Elasticities of Substitution 75 5.5.4.3 Returns to Concentration and Concentration Bias 75 5.5.4.4 Returns to Scale 76 5.5.4.5 Measuring Technical Change '. 76 5.5.4.6 Finding the Optimal Level of Output 77 6. D A T A DESCR IPT ION A N D S O U R C E S 78 6.1 Introduction 78 6.2 The Raw Data 78 6.2.1 Capital Cost and Price :. 78 6.2.2 Labour Cost and Prices 86 6.2.3 Energy Cost and Price 87 6.2.4 Materials Cost and Price 89 6.2.5 Output Quantity 89 6.2.6 Concentration (Herfindahl) Index 89 6.2.7 The Trend Variable !.90 6.3 Estimating Total Costs of Production and Cost Shares 91 7. RE SULTS F R O M T H E F I N A L M O D E L A N D S T R U C T U R A L TESTS 94 7.1 Introduction 94 7.1.1 Specification Tests with the Share Equations 94 7.1.2 Misspecification Tests: Concentration and Technical Change 94 7.1.3 Preliminary Specification Tests with the Cost/Share System 95 7.1.3.1 First-Order Concentration Effects 97 7.1.3.2 First-Order (neutral) Technological Change 99 7.1.3.3 Other F irst-Order Hypothesis Tests 99 v. -7.2 Results from the Converged Cost/Share System 100 7.2.1 The Final 'Specification of the Cost/Share System: General Results , .- . . . v - - 1 0 0 . 7.2.2 Cross-Industry and Production Technology Hypothesis Tests 106, -7.2.3- Residual .Analysis and Diagonality ..110 7.2.4 Concavity Test Results - 114 7.2.5 Estimated Elasticities of Factor Demands 117 7.2.6 Estimated Elasticities o f Substitution 121 7.2.7 Estimated Returns to Concentration and Concentration Bias 123 7.2.8 Estimated Returns to Scale 132 7.2.9 Estimated Technical Change and Bias 132 7.2.10 Testing for Optimal Output Levels , 135 8. CONCLUS IONS , CAVEATS . A N D R E C O M M M E N D A T I O N S 139 F O O T N O T E S 146 B I B L I O G R A P H Y 157 A P P E N D I X 1: C A P I T A L S T O C K D A T A DER IVAT IONS 163 A P P E N D I X 2: D A T A U S E D IN E & M A T I O N O F COST A N D S H A R E EQUAT IONS ., A P P E N D I X 3: R E S I D U A L P L O T F O R T H E COST F U N C T I O N A N D R E S I D U A L STATISTICS F O R T H E COST/SHARE S Y S T E M .' KM Vi List of Tables Table 1 Estimated Price Elasticities of Factor Demand for the Canadian Food Manufacturing Industry, Previous Studies 53 Table 2 Estimated Minimum Efficient Scale (MES) as a Percentage of Industry Size, Canadian Food Manufacturing Industries, 1965-1970 57 Table 3 AII-of-Manufacturing Rate of Return Data, Canada, 1961-1982 81 Table 4 Estimation of Depreciation Rates for All-Components Capital Stocks: Canadian Food Manufacturing (3-digit) Industries 83 Table 5 Sources of Energy Data: Canadian Food Manufacturing Industries, 1961 88 Table 6 Canadian Food Manufacturing Industries: Numbers, S.I.C.'s and Names of Industries Studied 92 Table 7 Average Cost Shares, Herfindahl Indices and Output Indices, Canadian Food Manufacturing Industries, 1961-1982 93 Table 8 Concentration and Technical Change Misspecification Tests with the T L Share System, Canadian Food Manufacturing Industries, 1961-1982 96 Table 9 Cross-Industry Wald Specification Tests with the T L Cost/Share System al One Iteration, Canadian Food Manufacturing Industries, 1961-1982 98 Table 10 T L Cost Function Estimated Coefficients and Summary Statistics, Final Model, Canadian Food Manufacturing Industries, 1961-1982 . . . 101 Table 11 Production Labour Share Equation Estimated Coefficients and Summary Statistics, Final Model, Canadian Food Manufacturing Industries, 1961-1982 104 Table 12 Non-Production Labour Share Equation Estimated Coefficients and Summary Statistics, Final Model, Canadian Food Manufacturing Industries, 1961-1982 104 Table 13 Energy Share Equation Estimated Coefficients and Summary Statistics, Final Model, Canadian Food Manufacturing Industries, 1961-1982 105 Table 14 Materials Share Equation Estimated Coefficients and Summary Statistics, Final Model, Canadian Food Manufacturing Industries, 1961-1982. 105 Table 15 Cross-Industry Hypothesis Tests with Final Cost Function Specification, Canadian Food Manufacturing Industries, 1961-1982 107 Table 16 Wald Specification Tests for Concentration and Technical Change Effects and Form of Production Technology, Final Model, Canadian Food Manufacturing Industries, 1961-1982 109 Table 17 Concavity Violations by Industry, Final Model, Canadian Food Manufacturing Industries, 1961-1982 115 Table 18 Estimated Own and Selected Cross Price Elasticities of Factor Demands, Canadian Food Manufacturing Industries, 1961-1982 118 Tabic 19 Estimated Elasticities of Substitution, Canadian Food Manufacturing Industries, 1961-1982 122 vii Table 20 Estimated Returns to Concentration, Canadian Food Manufacturing Industries, 1961-1982 124 Table 21 Estimated Returns to Concentration, Canadian Food Manufacturing Industries, 1961-1982 (Ranked by Average Concentration Level) 126 Table 22 Estimated Bias of Concentration by Input, Canadian Food Manufacturing Industries, 1961-1982 128 Table 23 Simulated Average Employment Effects of Increases in Concentration, Canadian Food Manufacturing Industries, 1961-1982 130 Table 24 Estimated Dual Returns to Scale, Canadian Food Manufacturing Industries, 1961-1982 133 Table 25 Estimated Bias of Technical Change, Canadian Food Manufacturing Industries, 1961-1982 136 Table 26 Estimated Optimal and Actual Output, Canadian Food Manufacturing Industries, 1961-1982 137 Table A l . l Capital Stock and Related Data, Canadian 4-digit Food Manufacturing Industries, 1947-1971/1975 172 Table A1.2 Capital Stock Data, Canadian 3-digit Food Manufacturing Industries, 1955-1982 184 Table A 1.3 All-Components Capital Expenditures (Investment), Canadian 4-digit Food Manufacturing Industries, 1972-1981 193 Table A1.4 Implicit Price Index (pcap) for Capital Expenditure on Total Components, Canadian Food Manufacturing, 1960-1982 194 Table A 1.5 Observed, Revised and Imputed End-Year Capital Stock Series, Canadian Food Manufacturing Industries, 1961-1982 195 Table A2.1 Data Used in Estimation of Final Model, Canadian Food Manufacturing Industries, 1961-1982 197 Table A3.1 Estimated Residuals from Total Cost Function Equation, Final Model, Canadian Food Manufacturing Industries, 1961-1982 205 Table A3.2 Residual Summary Statistics for the Final Model, Canadian Food Manufacturing Industries, 1961-1982 212 viii ACKNOWLEDGEMENTS During the development of this thesis, I have been assisted by many people, if only by their interest in my work. To name all would take up alot of space and risk tedium, but I would like to acknowledge those who were most influential. In particular, I must thank Tim Hazledine, whose observations instigated this research and who provided support of various kinds during what was sometimes a frustrating project The other members of my committee, Rick Barichello and Terence Wales, were both very helpful in identifying some of the subtleties I would have otherwise missed; it must also be said that it was largely through Rick's persistent encouragement and guidance over the years that I undertook this degree. Others I should mention are: Robert Avery, who provided some stimulating econometric insights; Luis (^ nstantino; Dan Gordon, whose all-too-short series of lectures provided me with a valuable theoretical groundwork to start from; John Graham; Margaret Slade; and Ken White. In all, I was given an enormous amount of freedom to follow numerous, always enlightening, but sometimes directly unproductive paths. It would be hard to place a firm value on that ix Chapter 1 INTRODUCTION 1.1 THE GENERAL PROBLEM - -' One of-the most widely researched topics in the field of industrial organization is the relationship between concentration and profitability. Although most studies have found a-positive correlation between profits and concentration, very little has been done to separate the overall profit effect into its respective components of price and costs. In a relatively recent study, Peltzman (1977) attempted to document these effects explicidy and his initiative has generated at least two studies focussing on the connection between - changes in concentration and changes in costs (or total factor productivity (TFP)). In an analysis of the U.S. food manufacturing industry, Gisser (1982) drew upon some earlier work on productivity change, and in the spirit of Peltzman's study, obtained some rather curious empirical results. In particular, his estimates indicated that both increases and decreases in industrial concentration had a positive influence on productivity over the period of his analysis. What made these results more surprising was that Gisser did not acknowledge the apparently similar effects of increases and decreases in concentration. Thus, since a generally rrionotonic relationship between concentration and productivity was postulated by Gisser, the question which arose was whether his results had been tabled incorrectly or the model mis-specified. As we will see below, however, Gisser's results do in fact appear to have been correct A brief discussion of Gisser's model follows in the next part of this Introduction. The third part will provide a summary of a test of Gisser's data with an alternative specification. Finally, an argument for the development and estimation of a more refined model of the concentration/cost relationship with Canadian food manufacturing industry data will be presented. 1 2 1.2 T H E GISSER M O D E L O F T H E PRODUCT IV I TY / C O N C E N T R A T I O N RELAT IONSH IP ' " • ' " Rather than relate changes - in concentration to changes in costs, Gisser uses an alternative method, relating changes in concentration to changes in TFE. If it is kept in mind that the change in productivity is equivalent to the change in costs which would have occurred had there been no change in factor prices, (i.e. the change in costs holding factor prices constant), it can be seen that either characterization is valid. The two approaches may not yield identical results i f the respective specifications do not assume the same functional form or production technology, but i f there is a strong relationship between concentration and costs, the conclusions should be the same. Gisser's study is limited to the period 1963 to 1972 for 40 subindustries within the U.S. food manufacturing industry. His approach to T F P measurement follows Solow (1957) and incorporates the assumption that the change in productivity is due to a neutral shift in technology. Thus, Solow's general relationship using a discrete approximation to relate changes in output to changes in inputs over time is specified, with only capital and labour inputs considered. In order to test the hypothesis that productivity is related to concentration, Gisser proposes the following relationship: (1) A / A = F (Q/Q, D l C , D,c, c) where: A/A is the annual percentage change in productivity over the period studied Q/Q is the annual percentage change in output c is the average annual percentage change in concentration (with concentration defined as the 4 - f i rm concentration ratio) c is the average level of concentration D j = l for increases in concentration, 0 otherwise, and D 2 = l for decreases in concentration, 0 otherwise. 3 •By applying'the dummy variables D! and D2 to c, the relative effects of increases" versus decreases, in concentration on productivity can be determined. The linear model'specified is-a simple .application of-(1), namely:. (2) (A/A). = a + B1(Q/Q)i + 0,(0,1:), + /3,(D2c)/ + 0 « C / + e. : i =1.2 40 where: a is some constant, and e. is a random error term. As noted earlier, Gisser's results show 0 2 to be positive and 0 3 to be negative, with both results significant at the 95% level (although 0 2 is more significant). Moreover, |03|>|02|, suggesting not only that both increases and decreases in concentration have positive effects on TFP, but also that decreases have a larger influence than increases. A re-estimation of this model with Gisser's data yielded almost identical results to those obtained by Gisser. It can be concluded from this that Gisser's results are valid and thus have not been tabled incorrectly. Hence, they are either the product of poorly defined data or a misspecified model. Alternatively, they could reflect the true relationship between TFP and concentratioa So the comment that "the results for decreasing concentration have the expected negative sign" (Gisser 1982, p. 618) implies that decreases in concentration have a positive effect on productivity. It appears, by the way in which the claim is made, however, that Gisser believes the opposite. His conclusion that "increased concentration leads to a fall in the production costs of the food industry..." (ibid, p. 620) is thus a misleading one since the results show that decreases in concentration are actually more important (see Hazledine and Cahill (1986), Gisser (1986)) 4 1.3 A P P L Y I N G - A N .ALTERNAT IVE SPEC IF ICAT ION TO GISSER 'S D A T A Given the conclusions reached above on the asymmetric effects of increases, and decreases in concentratipn on TFP, it was-felt-.that some, further confirmation of these results" would be useful,, considering the unexpected nature of the relationship. Although a re-examination of the data and re-specification of the aggregated variables' used by Gisser would have been one way to check his results, the simpler route of applying an alternative specification to his data was chosen instead. A simplified version of Peltzman's model proposed by Lustgarten (1979)J seemed to be an obvious candidate. Lustgarten's model is of the form: (3) (A/A). = 6 + 7 l (Q/Q),- + 7 : [ D , c 2 /c ( l - c ) ]( + 7 3 [D 2 c 2 /c ( l - c ) ] ( + e,. ; / =1.2, 40 where: 8 is some constant Estimation of (3) upheld the original results: both increases and decreases in concentration positively affected productivity in U.S. food manufacturing over the sample period. Thus, both 7 2 and 7 3 are positive, since the c variable is squared for both terms, in this way eliminating the sign distinction between increases and decreases (i.e. positive coefficients for 7 2 and 7 , in (3) are equivalent to j3 2 in (2) being positive and 03 being negative). In addition, decreases in concentration again had a larger impact on T F P than increases ( 7 3 was about four times larger than 7 2 , although the effect was less statistically significant by the t-ratios: see Hazledine and Cahil l (1986, fn.2)). This result, then, reinforces the notion that decreases in concentration are more desirable, i f increases in T F P is the criterion being used. 5 1.4 T H E C A S E F O R C A N A D I A N F O O D M A N U F A C T U R I N G ' . -• It is apparent from the above alternative test with-.Gisser's data-that the whole "issue deserves some additional analysis. As noted,, one approach would be to re-examine .the data used-by Gisser to determine whether, his, derivations of TFP, the growth variable Q/Q and concentration are consistent, w i th . standard practice and, perhaps, to apply other specifications than those already estimated with the resulting (possibly improved) data set . A more appealing and novel approach, however, would be to estimate the effects of concentration on costs with Canadian food manufacturing data. Such an effort would clearly be enlightening, not only in an academic sense, but also, from the perspective of government policy towards the food manufacturing industry. The food and beverage industry in Canada represents a significant sector: in 1982, total value-added amounted to S10.2B and accounted for about 2.9 percent and 14.7 percent of Canada's G N P and total value-added of all manufacturers respectively (Statistics Canada, Catalogue 31-203). Therefore, given its importance to the Canadian economy, a greater understanding of this industry would seem worthwhile, especially i f it were to make policy applications more effective. It is evident from Gisser's analysis that aside from the possibility of misspecified variables, a considerable amount of information is disguised by his simple model. In particular, although it yields some interesting results, his model cannot be used to determine why the growth of both concentrated and unconcentrated sub-industries would lead to a TFP increase in each case. Thus, it is very uninformative when questions are asked about the results it offers. There are numerous reasons which could be found for Gisser's results. Presumably, i f both concentrated and unconcentrated industries are minimizing costs, the differential in T F P effects is caused by differences in the respective technologies of each group of industries, the existence of (biased) technical change, differences in 6 substitution responses, • economies of scale, and so on. These diverse factors, when coupled with output growth, lead to' an equivalent (but not necessarily equal) effect of "concentration on TFP for the two groups, Gisser's -model doesn't account for any of these possibilities, .first because, it is a grossly oversimplified version-of reality, and second because. it really. has no sound theoretical structure. -The lack of microeconomic theory underlying the models of Gisser and -Lustgarten. is troubling. As we will see in the next chapter, the Peltzman model and most of the concentration-profits studies considered also fail to provide rigorous theoretical foundations. Rather, most of the approaches suffer from ad hoc specifications or rely on overly simple OLS techniques to determine causality. The proposition here is to build a model which both satisfies the neoclassical paradigm of cost minimization, but which is flexible to the effects of collusion, entry barriers, and particularly, industrial concentration. With this model, the effects of levels and changes of concentration on costs of production will be estimated for 17 4-digit industries within the Canadian food manufacturing (2- digit) industry over the period 1961-1982. It is believed that the results obtained will help to answer a question occasionally asked by economists outside the industrial organization enclave, namely: why might concentration affect costs or efficiency and how might this effect come about? Given a theoretically sound conceptual model of cost and concentration effects, an obvious vehicle for implementing estimation is the dual cost function. While providing much of the necessary information about the concentration-costs relationship, it can also be used to test inferences about the underlying technological differences of the industries, and the interaction between concentration and types of production technologies. The 'family' of flexible forms currently employed in empirical microeconomics provides significant potential for the identification of the types of technological factors which might lead to differences (and similarities) between industries 7 as their relative levels of concentration-change. In addition, there are numerous benefits from the use of duality, many of which-should be familiar, but which will be discussed briefly in subsequent chapters. . The outline of" this' thesis is as follows. The next, chapter will provide a -detailed analysis of the Peltzman and Lustgarten, models and a critique, of their methods, since these are by far the most advanced studies of the effects of concentration on costs. In addition, some prominent papers dealing with the concentration-profits debate (i.e. whether the generally observed positive concentration-profits effect is due to collusion or efficiency) will be reviewed. The purpose of this survey is to provide an understanding both of the now-accepted positive relationship between profits and concentration, and the efforts of a number of researchers other than Peltzman and Lustgarten to measure the relative importance of collusion as opposed to efficiency in the concentration-profits relationship. The results of these studies have some bearing on the way in which the eventual model is constructed. In Chapter 3, an integrated concentration-cost model is developed; the properties of the conceptual cost function are outlined in Chapter 4. In Chapter 5, the empirical model is developed and specified, while Chapter 6 provides a discussion of the data used in estimation, how they are derived and their properties and shortcomings. Chapter 7 presents the results of the specification tests and the final model chosen. Finally, Chapter 8 offers conclusions, caveats and recommendations. . ..• Chapter 2 C O N C E N T R A T I O N A N D COSTS: S O M E ESTABL I SHED .VIEWS. .- The purpose of this chapter is to-briefly survey some previous studies which investigate •the concentration- efficiency hypothesis. The reasoning for this is twofold; first, it is useful, to understand the general nature of this .debate in order to grasp its importance, and second, this survey should serve to illustrate how little structure is given to the problem - . i t wi l l prove the need, for a more fully integrated model and approach. Since the debate has emanated from within the concentration-profits literature, it seems logical to begin with a brief description of some generally accepted views on this relationship and from there proceed into the area where the real disagreement lies. 2.1 T H E C O N C E N T R A T I O N - PROFITS L I T E R A T U R E As noted in the Introduction, the relationship between concentration and profits has been studied extensively; in fact, complete papers have been devoted simply to surveying this mainly empirical literature. Waterson (1984) makes reference to two of these surveys, and on the basis of them notes that "the overwhelming majority of these [profit-concentration] studies have some measure of statistical success in relating the basic structural variables to profitability. Concentration, in one form or another, very commonly features a significant positive influence" (p.200). Thus, there is considerable evidence that increases in concentration increase profits or profitability. There have been some rather serious attacks made on the validity of this overall conclusion, however. For example, Fisher and McGowan (1983) indicate that many profits-concentration studies yield spurious results due to the use of accounting as opposed to economic rates of return. Cooley (1982) focusses on the econometric issues of these models and notes the "concern that the final results are heavily influenced by the process of ad hoc specification searching... "(p. 114). He also observes that "those 8 9 not familiar ' "with--this literature may regard the links and the direction of causality between [seller concentration] and profit rates to be vague at best" (ibid, p. 115). Cobley hereby identifies two major flaws, in this literature: the use of ad hoc, overly simplistic models of profit" determination, and implicit use of the questionable assumption that concentration is exogenous, to the industry. It. is not clear, he infers,, whether higher profits lead to higher concentration or vice versa. The former issue will be directly addressed later - this has already been mentioned - but the latter , issue is one which shall not be dealt with here since it suggests the need for simultaneous equation systems including an equation for profit determination and one for concentration determination. Analysis of this sort is beyond the scope of this effort 3 Even though such objections exist, there is. still a widespread belief that the positive concentration-profits result is a relatively robust one (see, for example, Long and Ravenscraft (1984) and other comments on the article by Fisher and McGowan (1983)). The real issue, then, is whether this result indicates collusion (since it is generally believed that increased concentration facilitates price-fixing), or higher efficiency on the part Of more concentrated industries. Opinion as to which effect exists or persists "is the area where most the controversy resides at present" (Waterson 1984, p. 201), and the topic to which we wil l now turn. 2.2 T H E C O N C E N T R A T I O N - PROFITS DEBATE : C O L L U S I O N VERSUS E F F I C I E N C Y 2.2.1 T H E D E M S E T Z HYPOTHES IS The basic hypothesis behind the empirical concentration-profits studies, as noted, is that more concentrated industries are able to price above average costs. Most researchers finding a positive result have attributed this to collusion and therefore, the weight of the empirical evidence has been that high concentration is a bad thing since 10 it lead's to higher prices than under perfect competition and therefore causes welfare -losses. In a long overdue article, Demsetz (1973) observed that this need not be the case", -pointing out that higher profits -call .-.also come- from lower costs; highly concentrated' industries m a y have higher profits because the firms in them with high market share are relatively-more efficient He provides empirical ' p r oo f of his argument by ranking groups of firms within industries according to size and compares rates of return for these groups, doing this for a number, of groups of industries ranging from low to high concentration. He concludes that "the data do not seem to support the notion that concentration and collusion are closely related" (Demsetz 1973, p. 6). Although Demsetz's challenge of the almost naive assumption that only collusion accounts for positive profits-concentration result is.val id, his "tests are rather too blunt-edged a tool to allocate acclaim or blame" (Waterson 1984, p. 310) and he admits that his data set is rather small. In other words, his results do not tell us much more than before: other than alerting us to the fact that efficiency might also be an important effect to measure. They certainly don't rule out the possibility of collusion, or for that matter, collusive losses eliminating any efficiency gains in a welfare sense. Nevertheless, Demsetz's initiative has led to a small but' growing body of literature dealing with the concerns he raised. Round (1975) carried out a similar analysis to Demsetz's for an Australian data set, and observed similar results. Carter (1978) refined Demsetz's methodology and employed regression analysis instead to a separate data set He divided his sample into leading versus secondary firms and found evidence of both collusion and efficiency effects for high concentration industries (i.e. both effects are important as opposed to the na'ive (structuralist) view that only collusion is important or the pure Demsetz view that only efficiency is important). Another observation which he makes which will have some bearing on the model 11 developed for this study is that ' " the degree to which price exceeds, leading-firm costs ii i concentrated industries is- l imited to the extent of the cost advantage over secondary firms" _(p. 441). This empirical evidence. suggests that the leading firms in a concentrated industry may set a price which yields them profits, but which discourages expansion of secondary .firms. . . . 2.2.2 O T H E R TESTS O F T H E E F F I C I E N C Y HYPOTHES I S A T T H E I N D U S T R Y L E V E L There are a number of other studies which attempt to measure the importance of efficiency and yet do not fall directly into the Demsetz style of analysis. Two of these will be reviewed here; both provide useful insights and round out the efficiency view described above. Rather than focus only on efficiency, Al len (1983) tries to determine the relative impacts of collusion and efficiency on price-cost margins (profits) in his sample, noting that the Demsetz and Carter approaches .preclude such relative quantification. He finds that although both collusion and efficiency effects are important, the former dominates, noting that "collusion appears to be the more important influence, viewed statistically and economically. Thus the results are at odds with the view that efficiency is the primary factor in the concentration-profits relationship" (Allen 1983, p. 934). While the collusion hypothesis is supported for his sample, Allen's results show that efficiency effects cannot be ruled out Rather, it is necessary to have a model flexible enough to measure both, or at the very least to acknowledge the possibility of both effects occurring simultaneously. His conclusion, that "this study finds little support for the view of Demsetz and others that high concentration and high profits largely reflect the superior efficiency of large firms..." (ibid., p. 939) is a bit bold, but does suggest that the Demsetz view, like the pure collusion view, hardly tells the whole story, and therefore must be considered with equal caution. Moreover, it reinforces the observation that Demsetz's methodology is 12 rather blunt, and. indicates that it is not very robust to challenge with different data and techniques. - -r The second' study of interest, Smiley (1982), carries the Demsetz hypothesis r further, suggesting" tha t some firms which., are. more efficient than others within an industry are likely to. have larger market,shares and .therefore concentration will be associated with higher profits. Smiley's model is based on what he terms the 'learning ef fect ' , essentially a scale measure. He claims that as firms.grow, their average costs decrease through 'learning by do ing ' . The advantage o f -h i s approach is that it does provide more structure to the problem of measuring efficiency, and is particularly useful in that it focusses on scale effects on the average cost curve. His simulation results indicate that while concentration is positively associated with profits, once again, efficiency effects cannot be ruled out as a factor, in this relationship. 2.2.3 I N T R A - I N D U S T R Y ( F I R M L E V E L ) A N A L Y S E S -So far, the discussion has been limited to industry-level analyses, with only occasional allusions to firm-level behaviour. Since properties displayed at the industry level are merely a reflection of inter-f irm relationships, it would seem that it is important to investigate such interactions. F i rm- leve l analysis has been limited until recently by data availability, but the development of 'L ine of Business' data sets has encouraged both a more microeconomic interest in the concentration-profits debate, and as a result, a reassessment of industry-level research with regards to its relevance to and consistency with the behaviour of firms. Some valuable insights can be gained by once more turning briefly to a couple of studies in this field. Although a good deal about industry-level concerns has been outlined, formulation of an industry model consistent with a model of the firm is crucial i f it is to be at all useful. One of the more detailed analyses of intra-industry structure is that of Porter (1979). His perspective is somewhat different, since he doesn't deal with the 13 profits-concentration or concentration-efficiency hypotheses directly. Rather, the main . - point of the paper is to illustrate the importance of intra- industry structural differences •"' ' when looking at intra-industry performance. "His theory is. based on-the notion of -'strategic groups' of .firms within an industry; firms within each group follow .similar strategies. Moreover,, these groups of firms ..display, systematic differences in behaviour which may change or persist over time. Thus, Porter suggests that the presence of structure within industries serves as an explanation, for the existence of relationships between firm size and profits or costs. His 'empirical' test of the theory tends to confirm his hypothesis, and suggests that any industry-level analysis should at least keep in mind the likelihood of significant inter-firm differences, particularly in the case of this study, differences in costs. The importance of inter-firm differences is, also emphasized in Martin and Ravenscraft (1982). This paper is unlike Porter (1979), however, in that it deals with the possibility of errors in concentration-profits studies if firm-level share effects are not considered explicitly. The authors observe that it is generally accepted that market share will have an impact on firm profitability which is independent of the effect of market concentration. In particular, market share may represent either market power or. the realization of economies of scale; the latter view is the one held by Demsetz (1973) and is consistent with efficiency hypothesis. Given this interpretation, then, Martin and Ravenscraft postulate a firm-level profit equation of the form: ( 4 ) n.. = a + B S.. + 7 h. + .... ij ij J where: II ~ is the profit/sales ratio or similar measure of profitability for firm / in industry j S.j is the market share of firm / in industry j hj is the Herfindahl index of concentration in industry j ( .2^  (S„ )J), and n is the number of firms in industry j . 14 In • this case, 0.. measures, the scale or efficiency effect and 7 , the collusion effect on profits. • • • ~ . To perform an industry-level analysis, equation (4) may be "aggregated from the division of the firm level- to the industry level by multiplying both sides of the equation by [ S „ ] and summing over all firms in the industry" (Martin and Ravenscraft 1982, p. 162). From (4) this yields: "' (5) IT. = a +r(/3 + 7 ) h y +  where: I I. = H II.. S.. . J /=i u ij They note that the problem with (5) is that it cannot accurately reflect firm-level influences since it is impossible to "distinguish between market concentration effects (the coefficient 0) and firm specific market share effects (the coefficient «r). The most that can be estimated is the industry-level combination of the two effects" (ibid.) Thus, their observations indicate the dangers of performing industry-level analyses without considering first what might be happening to the firms within the industry and emphasize the importance of at least acknowledging aggregation problems when industry models are being bui l t 2.3 M O D E L S T H A T D I R E C T L Y M E A S U R E C O N C E N T R A T I O N - C O S T E F F E C T S Although the preceding section has provided a number of insights into the important elements of the concentration-efficiency hypothesis, none of the studies surveyed has attempted to measure directly the effects of industrial concentration on costs. A notable exception to this apparent rule is the model developed and estimated by Peltzman (1977), who tried to measure independently the direct effects of concentration on unit costs and prices respectively. Since the concern of this study is the former, only his cost model will be outlined here. The primary purpose of the detailed illustration of this which follows wil l be to indicate the restrictiveness of his 15 approach"and to. justify the development of a different, more flejuble, specification which can integrate many of the elements discussed. so far without imposing too many unnecessary restrictions on .the underlying properties of the firms/industries being considered. •• 2.3.1 T H E P E L T Z M A N / L U S T G A R T E N M O D E L S Peltzman begins, his formulation by noting that the., firms of any industry can be divided into two groups: type ' L ' firms are the largest in the industry, and type ' M ' are all the others. The industry's unit costs (total costs per unit of output) at any point in time may be defined, then, as: (6) C = sL + ( l - s ) M where: C is unit cost for the industry s is the share of industry output produced by type ' L ' firms (eg. the four- f i rm concentration ratio), and L and M are unit costs for type ' L ' and ' M ' firms respectively. Since he is most interested in the dynamics of (6), Peltzman differentiates this with respect to time, which results in an expression of C in terms of C, s, L, ds/dt, M , and L 4 It is assumed that L and M are not the same, and that these may be divided into two expressions: (7) M = r + m and (8) L = r + 1 where: r is the secular change in costs common to both groups (eg. due to changes in input prices), and 16 1'and m are cost changes peculiar to each group. Insertion of these expressions into the differentiated form of (4) and extensive rearrangement leadsto two. equivalent, characterizations, of cost changes: (9) C = r + 1 + " {[ds/dt + 6(l-s)/D] • (s + 1/D]" 1 J and: (10) C = r + 1 + {[-ds/dt + Sa-sXD'+iyD'l-Kl-s) + 1/D1]"1 } where: D = (L/M) -1 D1 = (M/L) - 1 . and 6 = m - 1. These divided expressions allow us to consider two possibilities. In the case of (9), when D is >0, type 'M' firms have a cost' advantage (since M is <L). If ds/dt is <0 (concentration decreases), industry costs will decrease, an effect which will become more pronounced the greater the cost advantage of type 'M' firms.5 The argument holds similarly for (10) when type 'L' firms have the cost advantage Thus, (9) and (10) measure cost effects in terms of relative (original) cost advantages. A second assumption, and one which turns out to be essential to Peltzman's empirical analysis, is that the group with the cost advantage grows faster over time in proportion to its original advantage. Although this is a rather strong assumption, no clear reason is given for it Incorporation of this growth assumption into (9) and (10) is done by the expressions: (11) z = s(l-s)aaD1 ; for ds/dt >0 and (12) z = s(l-s)a,D ; for ds/dt <0 where: z=| ds/dt | 17 The coefficents a, and a 2 are. both expected to be positive. tea In order - to arrive at estimable expressions for the terms 1, m and 6 in (9) and "(10), Peltzman extends, his growth assumption further. He proposes that a. relative increase in costs^  or-more: specifically the. differential.. 8 .between large and small firm cost • changes, is• directly related to,market growth/ To. capture this effect, the following relationships are specified: (13) 1 = a g (14) m = bg and (15) 5 = m - 1 = (b-a)g where: a and b are constants g = growth of (demand for) output, and (b-a) is assumed to be negative. Substitution of (11)-(15) into (9) and (10) with considerable rearrangement of terms generates, as before, two alternate expressions for C, with both now defined tea purely in terms of the observable or directly estimable variables r, g, s, and ds/dt (or z): (16) C = r +ag + C[-z2/(l-s) + 5(z + a, s(l-s))] • [z + a ^ ] " 1 } and (17) C = r +ag + {[-z2/s + Sa2 (1-s)2 ] • [z + a 2(l-s)]- 1 } Equations (16) and (17) are for ds/dt >0 and ds/dt <0 respectively. Since both (16) and (17) are non-linear in parameters, they cannot be estimated using OLS. Peltzman linearizes these, using a second-order Taylor's-series approximation around (z=0). This yields the penultimate expression: 18 * (18) ' C = r "+ ags + bg(l-s) + (b-a)g[(z 2 UJaf K-.) - (zM./a. ) ] -" " [ z 2 ' /(a. s(l-s)) ] + e-where: / = 1 i f ds/dt is >0 ;' i-2 i f ds/dt is <0 Mj= -1 ; M 2 = Ki= s ; K 2 = (1-s), and e is a remainder, or error term. Although (18) is essentially complete, an empirical counterpart is still needed for r. Peltzman suggests that r is comprised of two effects: secular (neutral) productivity growth, and growth in input prices, with one counteracting, but not necessarily offsetting the other. Since secular productivity growth is merely a constant common to both groups, it simply becomes an intercept term in (18). For the second component of r, Peltzman uses input price changes over the period, weighted by their average cost shares (which are assumed to be constant over time) 7. As a result, r is defined as: (19) r = - 7 ( t ) + where: 7 (1) - secular productivity growth (a constant) th Bj= the (constant) cost share of the j input, and th W^. = the change in price of the j input over the period. Substitution of (19) into (18) yields the final empirical specification: (20) C = - 7 ( 0 + | r A W . ) + a g s + bg(l-s) + (b-a)g[(z 2 M . / a 2 K . ) - (zM./a. ) ] -7 . [ z 2 /(a.s( l -s)) ] + e where: r . is expected to equal 1 V/ , and 7.is expected to equal 1 for / =1,2. 19 There, are a number of features built into equation (20) which deserve comment. T h e - first and perhaps most obvious one is that (20) can only explain . Changes i i i costs .over discrete intervals. So in order to determine the dynamic aspects of concentration and costs (i.e. -how changes in concentration are associated with changes in cost), Peltzman's model obliges us._to consider. only two periods and explains the change over those two periods. Thus, the model is essentially discontinuous and does not allow us. to consider the years in between the two endpoints which,may be equally important as the change between the endpoints. Moreover, Peltzman offers no guide as to how the endpoints should be chosen, but acknowledges that " i f we focus on too short a time period, the market structure^-cost relationship will be unreliable and attenuated. Theory, though, gives no guidance on what is 'too short' concretely" (pp. 250-251). In the case of his sample he suggests that "the underlying process generating the cost reductions takes considerable time indeed - at least two decades - to work itself out or that it can be partly obscured by impermanent changes in market structure" (ibid.p. 251). Such uncertainty implies that the model is probably not easily applied to samples without these properties. A second inherent weakness in (20) is its dependence on market growth; only the first and last terms are free from this variable. An objection to this dependence is raised by Lustgarten (1979), who finds the. interaction between growth and other variables confusing. He proposes a reformulation by substituting Peltzman's assumption of a differential between large and small f irm cost changes (see (13)-(15)) with one of equality of these changes, thus setting a=b in (13) and (14) and thereby eliminating (15). Although this greatly simplifies (20), leading to the expression: (21) - A = 7 ( t ) + ag - y.[z2 /(a,. s(l-s)) ] + e \ the model is really no more realistic, since it seems unlikely that cost changes for both type ' L ' and type ' M ' firms wil l always be the same. 20 A final comment about (20) is with regards to the production structure implied by (19)'. As noted in footnote 7, Peltzman is able to specify (19) only by assuming that the production technology is linearly homogeneous Cobb-Douglas and therefore r -that cost shares are constant over the period studied. Since by any argument.it would be hard to be convinced that cost shares could be constant. over any. period of the length Peltzman notes above, this constraint is particularly bothersome. It is also well-known that Cobb-Douglas technologies are at best rare, and so this objection, along with the other two, would appear to make the model suspect Even though Peltzman's model is flawed enough to suggest that a significant reformulation is in order, it is apparently the only attempt in an extensive body of literature to properly integrate concentration into a measurement of costs. Moreover, by trying to explain the effects of changes in concentration on costs, it not only addresses the question of how absolute concentration levels affect costs but also how increases as opposed to decreases from those levels change costs. This, it seems, is the crux of the concentration- profits/efficiency issue: given existing levels of concentration in any time period, are increases in concentration good or bad, and how does this conclusion differ between high versus low concentration industries? 2.3.2 GISSER REV IS ITED In a recent extension of his 1982 study, Gisser (1984) applies his model (2) to a sample of 314 4-digit manufacturing industries in the U.S.A. over the period 1963-1972. In this case, however, he separates Mow' and ' h i gh ' concentration industries (using plausible cut-off levels to divide his sample) and finds that increases in concentration are associated with rising productivity mainly in low-concentration industries, while in high-concentration industries, decreases in concentration appear to cause increases in productivity.' This result indicates the importance of considering both levels of concentration and changes in these levels, addressing directly the question 21 posed earlier. "14 T H E N E E D F O R A N I N T E G R A T E D T H E O R Y As the preceding survey has indicated, no coherent theory or model exists which can explain the effects-of concentration on costs. Peltzman's. attempt to redress-this imbalance has not really provided us with a workable model, and so, one must be developed. Although the papers cited hardly represent the whole of the . concentration- efficiency literature, they do represent most of the issues which should be considered in such a development These include the importance of returns to scale and market share in explaining inter-f irm cost differences, the possible influence of market growth on costs, the usefulness of a model which, can allow for the possibly quite different effects of increases as opposed to decreases in concentration on costs for high versus low concentration industries, and finally, the necessity of being able to account for continuous changes over time rather than just between discrete time periods. Ghapter 3 • A N I N T E G R A T E D " M E T H O D O L O G Y F O R M E A S U R I N G C O N C E N T R A T I O N - C O S T "-. •. • _. EFFECTS: ; * • On the basis of arguments made in the previous chapter for ,a better-integrated methodology for-measuring the effects of concentration on costs, this chapter will suggest a feasible approach to the problem. Below," the assumptions used about firm-level behaviour are outlined. From this assumed model of behaviour, an industry-level technique meant to measure these effects is given and a brief explanation of a proposed formal specification is offered. 3.1 ASSUMPTIONS A B O U T F I R M - L E V E L B E H A V I O U R The concentration-efficiency literature provides only fragmentary justification for the assumed relationship between concentration and costs of production. To determine a coherent theory from the diverse sources which also deal directly with the issue (i.e. industrial organization references and journals) would be a monumental task, for there seem to be many conflicting views on the subject Given the significance of this task, only a brief but seemingly plausible theory wil l be developed here, borrowing primarily from the essential elements identified in the previous chapter. For the most part, the concentration- cost literature suggests that Firm-level cost and market share differences do indeed exist (which seems reasonable), even though the firms are part of an industry which by and large produces a relatively homogeneous product (which is also a reasonable assumption at the 4-digit level of aggregation). Moreover, there is evidence to suggest that changes in concentration are linked to changes in average costs for the industry; more specifically, changes in the distribution of firm shares in an industry are related to changes in the relative average costs of the firms. The difficulty is in explaining how these two factors are linked. 22 23 Consider an industry where all firms have identical technologies. Given,this assumption, Which - is useful since it allows us to-use the same average cost curve for all' firms, thevquestion arises as to' why Afferent firms would-produce different levels* of output, and therefore have, "different market shares. In-a competitive industry, of course, all firms should have the same market share under this assumption, since they same will all produce the* level of output T©^ pursue this question further, it is helpful to employ the following. diagram: i 1 1 . ; — — ^ In the above diagram, the AC curve represents the cost structure each firm in the industry faces. Nevertheless, the four firms which comprise the industry produce at different levels of output (different scales). Price is set at p by collusion between firms 1 and 2, who have the largest market share, or by some other gwice- setting method. The question noted above is: why don't firms 3 and 4 increase their outputs, thereby increasing their profits? There at least two barriers to this expansion: market share constraints, and price barriers (limit pricing).10 In the first case, it is assumed that, although the technological capability exists for expansion by firms 3 and 4, in order for them to increase production they must be able to sell it If they were to cut prices from p to say p*. not only would 24 firms 1 and 2 still be at an advantage, but a price war could result in a market 'prices below p*. which would surely lead to the exit, of firm 4 and, perhaps, firm 3 (in the long run).- Hence, the 'only practical,, means of- increasing market share is :  through -product differentiation of various sorts and, particularly, advertising (since, the former is seldom.possible without the latter). Both, firms 3 and 4.may not have ; sufficient resources to increase" their advertising expenditures and so are unlikely to be able to increase their market shares.-If they do summon resources to begin a market share increasing advertising campaign, a similar counter-campaign is possible (likely) by the leading firms, if they feel threatened. In the second case, firms 1 and 2, having set a limit price, or price which they believe is close to the average cost of production of their competitors (i.e around p), are able to wage a debilitating price war if firms 3 or 4 begin to erode their (combined) market share. Hence, the price they agree upon effectively limits competition by minimizing the profits of their competitors and maximizing the loss of these firms under a sustained decrease in price. In this way the 'limit' provides not only a barrier to entry but also a barrier to growth by the other firms in the industry. Thus, it seems plausible that large disparities in output could exist between firms in an industry, even though production technologies are the same. Nevertheless, changes in concentration are possible; we would expect such changes to occur rather slowly over time, however. With regards to concentration-cost effects it can also be seen from the diagram above that increases in concentration may in fact increase costs, since if firms 1 and 2 expand from their existing almost-minimum average cost positions, their costs will go up. If we assume that industry output is constant, and so all that changes is the distribution of output between firms, it is clear that the market shares of firms 3 and 4 will drop, and so their costs will be forced up (firm 4 may, in fact, be forced out of business altogether). 25 ••' The figure drawn by no-means exhausts all the possibilities. *For .one, the AC curve could slope downwards much further, indicating returns to scale over a larger span-bf_output In mis case, we would .expect increases in concentration to decrease -costs? assuming the 'fringe' producers, firms 3 and 4^  account for insignificant levels • , of-output relative to 1 and 2. Alternatively, when: firms 1 and 2 are unable to., effectively collude in a price war, expansion of firms 3 and 4 in the absence of other constraints could imply decreases in concentration and decreases in average costs. Other combinations and permutations undoubtedly exist 3.2 THE CONCEPTUAL MODEL The exposition above presents. some plausible examples of the way in which concentration may be related to costs. It indicates, that both the shape of the average cost curve (determined by input prices and output quantities) and market share matters in determining the actual average costs and output of each firm. Even if we were to relax the assumption of homogeneous production technologies (across firms) this would still be true, although the argument would become accordingly more complex. In order to formalize the relationship, we may begin by specifying the average cost function for each firm, / , to be: (22) AC^.= c y / < I y = c ( w > Qy. Sy)/q^. where: Cy is total costs of firm / q^ . is firm /'s output w is a vector of input prices (assumed to be common to all firms) F s, is firm /'s share of total industry output, or s, = q , / L qf , and F is the number of firms in the industry. Ideally, we would have data to estimate an empirical counterpart to (22), as Martin and Ravenscraft (1982) do for profits. However, only industry-level data are 26 available, and so we 'must.estimate an industry average cost function instead, since a firm-level model " i s ruled out Accurate, aggregation of (22) to the industry level is not a simple: task-, and is a complex one beyond the ..scope of this-analysis. 1 1 Instead, an-' industry-level average cost function which exhibits some of the features of „(22). can - be specified, viz.: ... .... . . . . , . (23) A C = Qw,Q4i)/Q where: A C - I ( c r /q - >s, /=1 / V / F Q = I q , , and /=i 7 F h = L ( s , ) J : the Herfindahl index of industrial concentration. Note that C(w,Q,h) in (23) is the total cost function for the industry, the approximate analogue of c(w ,qy ,Sy ), the total cost function for the firm.12 Equation (23) indicates that industry average costs are a weighted (by shares) average of f i rm-level costs and are a function of input prices, industry output, and a weighted average of firm-level market shares (the Herfindahl measure of concentration). The Herfindahl index seems the most appropriate concentration measure to include in (23) since it provides a logical link with firm-level distribution within the industry -something which other indices (such as the four-f i rm concentration ratio) fail to do. This property makes it particularly useful in theoretical work, where it is widely employed, and so its use here should allow better integration of this material with more recent developments in the field of industrial organization. Finally, this index has an advantage in empirical applications since its construction ensures that firm-level shares, although providing its structure, are hard to determine once h is calculated. This means that even in very concentrated industries, missing observations in published data series (i.e. those not reported due to confidentiality rules) are less likely to arise than with, say, the four-f i rm ratio. 27 As noted, there, is. no direct link between (23)' and (22) due to difficulties in •aggregation. Nevertheless," some inferences about firm behaviour can be made with (23). "In particular, i f . industry costs are falling as "-output, rises we would expect to find that •most firms are on the downward-sloping" portion of their average cost curves. And, i f when concentration rises., industry costs rise, we. would .expect to have the sort of firm distribution illustrated in the diagram above. Alternatively i f average costs decrease when- concentration.- increases, we would expect ' leader'- firms to be on the downward-sloping sections of their cost curves as opposed to the flat or upward-sloping portions. The-conceptual model (23) wil l be the kernel of this analysis. Its structure has been kept simple quite deliberately, since technical, detail would have made the above arguments cumbersome. As a result, the preceding, discussion has illustrated how the main elements o f interest can be captured and has provided a useful base from which we can build. Once a more structured model has been specified, details on how to . estimate the effects of increases as opposed to decreases in concentration on costs will be given, as well as tests for other relevant properties. The problem of cost function specification wil l be dealt with generally in the next section, and more detailed testing procedures wil l be outlined in the next chapter. 3.3 S P E C I F Y I N G A COST F U N C T I O N As can be seen from (23), an important facet of this relationship is how C(w,Q,h) is to be specified in a form suitable for estimation. Clearly, an ad hoc specification is undesireable since the weaknesses of such specifications have been well-documented in the discussion of profits-concentration models and the Peltzman model in Chapter 2. Moreover, the cost function should be based on the microeconomic theory of cost-minimization and be consistent with the underlying production technology of the industry. Such consistency is available through the use of the family of flexible dual 28 cost functions. Under certain 'regularity conditions ', such cost functions are able to accurately' represent most of the properties of the industry's production technology withoutv.imposing,-.many restrictions upon i t \ a priori: Hence, through the use of a dual cost function adapted to the structure of (23), we should be able not only to measure the effects of concentration changes on. average costs and the other features of interest. but also elasticities of demand and substitution, returns to scale and so on. Such additional .-information is useful since it could. :possibly provide further, insights as to how concentration might affect costs (i.e. other than through just the relative share/concentration effect emphasized so far). A further attribute of dual cost functions is that there are numerous functional forms to choose from, and therefore not only are they flexible in their representation of production technologies, they are also flexible in how they might be specified. Thus, through use of duality, we can avoid the unrealistic assumptions made by Peltzman (1977) about the underlying production technology of the industries he studied, at the same time increasing our choice of theoretically consistent specifications. Chapter 4 - PROPERTIES O F T H E C O N C E P T U A L D U A L COST F U N C T I O N In this .chapter the regularity conditions needed for duality between C(w,Q,h) defined in (23) -and ' the production. technology are listed and the properties of the conceptual dual cost function. explored. Some disadvantages in using cost functions wil l also be discussed. Throughout, the total cost function will be used to illustrate the properties of interest-since, in numerous cases, .it is irrelevant whether-an average cost or total cost function is used. As noted earlier (see footnote 12) this is primarily a matter of convenience, since most of the theory has been developed to investigate total, and not average costs (except where linear homogeneity is assumed - see below). Where, however, the outcomes .from total cost versus average.cost functions are not the same, methods for adapting total cost effects to average cost effects wil l be illustrated. 4.1 R E G U L A R I T Y COND IT IONS N E C E S S A R Y F O R D U A L I T Y In order for duality to exist, both the production/transformation function being indirectly characterized and the dual cost function must fulfi l l a number of basic behavioural and structural conditions. It should be noted that since it is useful to be as general as possible in the development of the structural model, the cost function defined wi l l include the level of output as an argument, following (23). Thus, linear homogeneity wil l not be a maintained hypothesis (as in the case of the common 'un i t ' cost function). The conceptual cost function wil l be defined in terms of the (single-output) cost minimization problem: ( 23 ' ) C(w,Q,h) = min{ w ' x : f (x) £ Q ; h=h» } x where: w is an n x l vector of (exogenous) input prices (with transpose w ' ) 29 30 Q is output - • •, h* is the concentration level x is an. n x l vector of input'quantities, and -f ( x ) is the production "or transformation function. • .,-For duality-to exist, the production function f(x) must satisfy the following regularity conditions (Diewert 1982, p.553): P I . f ( x > 0 V x » 0 n (f is positive) P2. G X Q M x : f(x)^Q} is a convex set V Q in the range f (f is a quasi-concave function) Assumption P2 rules out increasing returns to scale (in production) but does allow for constant and decreasing returns to scale, the. two cases most likely to be encountered in established industries. The regularity conditions on the cost function are (Diewert 1982, p.554): C I . Q w . Q l i ^ O Vw.Q^O (non-negativity) C2. Wj>Wo implies C(w 1,Q,h)>C(w („Q,h) (increasing in w) C3. Q i > Q 0 implies C(w,Q,,h)>C(w,Qo,h) (increasing in Q) C4. C(Xw,Q,h) = XC(w,Q,h,) (linear homogeneity in w) C5. C(w,Q,h) is concave in input prices w V Q C6. C(w,Q,h) is continuous in w,Q Vw.Q. Properties ( l ) - (4) and (6) need no explanation. Property (5), however, reinforces the behavioural assumption established in (24), and one which is central to duality, namely that all producers are assiduous cost-minimizers (alternatively, profit maximizers). This condition implies negative semi-definiteness of the Hessian matrix (of second-order partial derivatives of C(w,Q,h) with respect to input prices). Invariably, scarcity of data requires that symmetry of the Hessian matrix must be imposed in estimation to allow a test for this condition. 31 " It should be kept in mind that unless cost minimization is in fact occurring (it may, for one reason or- another, not occur), duality may fall short in its ability to model production; no allowance is made for a divergence from assumed behaviour in... the model. Such behavioural restrictivehess is really a weakness of the neoclassical - paradigm, rather than duality itself, but it is essential - that. this assumption hold, in order to exploit the comparative static and optimality properties available through the use of calculus. Having established the general structure of C(w,QJi) we can now explore the measurement of production technology from this starting point, and derive appropriate tests for concentration effects and shape of the average cost curve. Priorization of the tests is not easy, so order of discussion below doesn't necessarily represent relative order of importance. 4.2 M E A S U R I N G R E T U R N S T O S C A L E One factor which has been emphasized in the relationship between concentration and costs is returns to scale. The importance of scale effects, however, was argued at the firm level - the problems of aggregation from firm to industry make it difficult to establish how plant scale effects are related to industry scale effects. No relationship has been posited between concentration levels and output (in fact, the two variables are assumed to be independent of each other) and so we have no prior notions of how scale and concentration wil l be related. Nevertheless, there is some merit in looking into this characteristic of the cost function, since any systematic pattern of scale effects relative to concentration levels might help us understand how concentration affects costs. The method employed here is to determine the existence and form of returns to scale using what is essentially an elasticity measure, giving response of average costs to an increase in output The technique is attributable to Berndt and Khaled (1979, p. 32 1225) and is defined by them in terms of total costs, or: (24) 'r(w,Q,h) = l/e^ where: = [9 Qw,Q,h)/9 Qj • (Q/Q. They observe that i f costs are defined in positive terms as in condition C I , then r(w,Q,h)<0 ( e ^ l ) implies decreasing returns to scale; r(w,QJi)=l ( e ^ l ) implies constant returns to scale; and r(w,Q,h)>l ( e ^ - c l ) implies increasing returns to scale. Returns to scale in costs should not be confused with returns to scale in production (for which increasing returns was ruled out by condition P2 above). In particular, the former refers to the marginal increase in costs when output is increased, as noted, while the latter is really a measure of homogeneity (see below) and represents the increase in output which occurs when all inputs are increased by the same proportion (eg. doubled). The measure (24), however, is an example of a method applied to total costs which is not entirely appropriate in the study of average costs. With regards to the conceptual model (23), we wish to measure the effects on average costs of an increase in output, or the slope of the average cost curve at the level of output observed. Differentiating (23) with respect to Q and multiplying through by (Q/AC), we get: (25) ( 9 A C / 9 Q ) - Q / A C = [9C(w,Q,h)/9Qj • Q/C - 1 = - 1 When (25) is evaluated at the observed level of output (say, the average level of output over the sample period), we would expect it to be <0 i f the industry is on the downward-sloping portion of its average cost curve (i.e. increasing returns prevail), equal to zero i f it is at or very close to the minimum of its average cost curve (this may be a ' f l a t ' section and so constant returns wil l hold), and >0 i f it is on the upward-sloping portion of its cost curve (i.e. decreasing returns prevail). The relationship between (25) and (24) is obvious, and as can be seen, interpretation of results from either leads to equivalent conclusions. 33 4.3 HOMOGENEITY , As suggested in the previous section, - homogeneity of the production function is a quite different way of -viewing 'returns to scale'. If homogeneity (of.-., degree 0.<p<l) in the production technology existsr it may be embodied in the cost function by restricting (23') to the- form: (26) C(w,Q,h) = Q1 / p-A(w,h) 1 3 . •' where: A(wji) is some function, of input prices, w, and h which is linearly homogeneous in w. It follows that if the production function is linearly homogeneous (i.e. p=l), (26) simplifies to: (27) C(w,Q,h) = Q-A(w,h) where A(w,h) is now called the 'unit' cost function. In this case, the average cost 'curve' is horizontal and so concentration changes are unlikely to affect industry average costs. Clearly, if the production function is homogeneous of degree p<l, decreasing returns to scale apply since a proportional increase of all inputs by p leads to a less than proportionate increase in output Similarly, if p= 1, then the technology exhibits constant returns to scale (the long-run competitive case). With an appropriate functional form, we can test for both the existence and degree of homogeneity, simply by imposing the structure (26) or (27) on the cost function, and by measuring 1/p. Again, (26) and (27) must be reinterpreted with respect to the average cost function. As noted, if (27) holds, the average cost ' curve' will be horizontal and so firms are unlikely to have different market shares except by choice. With regards to (26), if p<i, the average cost curve will always be upward-sloping. Both of these cases seem unlikely to hold in practice; not surprisingly, homogeneity is typically rejected in empirical studies (see, for example, Diewert and Wales (1985), who reject 34 linear homogeneity). * •.• • 4.4 HOMOTHFT ICTTY .: . A property- which is less relevant to „ the issue., at hand,, but. related to homogeneity, is..that of homotheticity. Homotheticity. of the production technology means that over any output expansion path, the combination of inputs used remains constant. In other words, i f for.example with a two-input production function, .one considers a ray out of the origin in input space RJ. and isoquants intersecting that ray at various levels of output, the output elasticities of factor demand at each point of intersection wil l be equal. . In the case of a homothetic production technology, the dual cost function may be written as: (28) C(w,Q,h) = f (Q>c(w,h) 1 4 where: c(w,h) is some function linearly homogeneous in w. As can be seen, (26) is a special case o f the homothetic cost function, namely when f(Q) = Qr/p. So it follows that all homogeneous functions are homothetic (i.e. satisfy (28)); the converse is not true, however. Once again, i f C(w,Q,h) is sufficiently ' f l ex ib le ' , we can test for for existence of (28) by imposing a structure consistent with that form and comparing it with a more general structure. A l l this has little to do with concentration, though, simply leading to a more precise understanding of the nature of the production technology. Thus, nothing can be inferred about the concentration/costs relationship by the existence or absence of homotheticity. 1 5 35 4.5 ELASTICITIES O F F A C T O R D E M A N D S The input demand elasticities which can be derived from dual cost functions are .arguably -the most useful information generated by these estimates, and are largely the focal point in assessing- both the reliability o f the model and the sample. If t he , -elasticities are typically far from levels expected from economic theory and knowledge of the sample, the model or data must be reassessed. Thus, although the objective of this study is to investigate concentration effects on costs, the elasticities generated should provide a reasonable guide to the validity and stability of the model. In addition, some further information about structural/behavioural differences between concentrated and unconcentrated industries may be gleaned from a comparison of relative elasticities. Factor demands can be derived from the cost function by invoking Shephard's lemma (Diewert 1982, p. 256) and differentiating it with respect to the relevant input price: (29) X.(w,Q,h) = 9C(w,Q,h)/9w. ; / = 1. 2 n where: X.(w,Q,h) is the cost-minimizing demand for the i ^ input, and th w^ . is the price of the i input. From this result, it is evident that the price elasticities of demand are. obtained by differentiating C(w,Q,h) once again and multiplying through by the relevant ratio Wj/Xj. , or w^./Xj. , viz.: (30) e (w.QJi) = [3 2 QW,Q,h)/3 w. 3 w ] • w /x / = (3 X . (w,Q,h)/9 w )• ( w V x . ) ; / , ; ' = 1, 2 n Note that the elasticities of demand will be the same whether an average cost or total cost function is estimated. 36 4.6 ELASTICITIES O F • SUBST ITUTION ' Another "useful summary measure of production behaviour and technology is the elasticity of substitution ."between inputs. Th i s provides an indication of how 'substitutable'- -one input is for another in the production process, i f output is held . , 'constant Although - this measure offers information similar to the cross-elasticity of demand, "for historical reasons, most economists do not use this cross-elasticity, but instead- use... the elasticity of - substitution" . ;(Varian 1978, p. 45). Whatever the -'historical ' reasons are, both elasticities are typically included in a study of this nature because they do have dissimilarities in construction. -From the perspective of the cost function, Uzawa (1962) has shown that the Al len partial elasticity of substitution between inputs / and j can be expressed as: (31) ai} = C - C < y / C, -C^. V / # ' • ; " " ; / • 1, 2, , n where: C . = 3 C(w,Q,h)/3 w.; C = 3 X , (w,Q,h)/3 w y . It is worth noting that Uzawa (1962) specified (31) in the context of a unit cost function (i.e. with output excluded), thereby limiting his analysis to constant returns to scale technologies. However, Sato and Koizumi (1973) have indicated that (31) is equally valid for more general cost functions (i.e. from non- homogeneous technologies), also showing that a similar measure from the production function plays an exact dual role to (31). Other features of (31) are that a.. is symmetric in the sense that (from Young's theorem), a = Oj. and that when it is positive, factors /' and j are considered substitutes; when it is negative they are complements. Also, given n inputs, among the n(n- l )/2 partial elasticities estimated, there must be at least n-1 substitutes. (Sato and Koizumi 1973, p.51) 37 4.7 T E C H N I C A L C H A N G E One facet of "the production process is that it typically changes over time through the- adoption-1 o f n e w technology. Models which do not account for.this possibility are likely to yield biased estimates, since when- technical change does indeed occur, such models are misspecified. Although-, it is not entirely clear- that technical change has taken place in the Canadian food manufacturing industries, preliminary evidence from previous studies indicates :that it might be a factor (see Chapter 5) and so the model used should at least be able to test for the effects of technical change. Unlike concentration effects, technical change is a peripheral issue, and so it has been excluded from the conceptual discussion up until now. As we wil l see, however, this factor can be incorporated into expressions (22)-(31) with ease, without in any way requiring a reformulation of the results obtained so far. 4.7.1 T H E E L E M E N T S O F T E C H N I C A L C H A N G E Technology is a stock concept indicating the existence of a body of technical expertise and knowledge which can be applied in the production of output Consequently, a change in technology implies a change in this stock. Since, as noted, the cost function's behaviour reflects that of the underlying production technology, it follows it can capture the effects of technical change on production. Yotopoulos and Nugent (1976) have identified four basic elements in the analysis of technical change: (1) the scale of operation; (2) the elasticity of substitution; (3) the technical efficiency of production; and (4) the bias of technical change. The change of one or more of these charateristics over time indicates technical change. Topics (1) and (2) have already been discussed in some detail. A change in scale over time is roughly what is measured by the concentration variable h in (23). With regards to substitution possibilities, the adoption of improved technology is usually 38 reflected by a decrease • in the, elasticity of substitution over time. 1 7 Thus, i f technical - change.were occurring, we would expect a „ to be higher in 1961 (or on average over the early 1960's)... than around 1982JWij. Since investigation of such an effect would be burdensome both computationally, and in interpretation of results, topics (3) and (4), the more ' conventional.' ..measures, w i l l .be stressed here. .The third element increased technical efficiency, refers to a reduction in the quantities of all factors used in producing a un i t ,of output; this behaviour is reflected by a homothetic shift in the production function. Such an effect is commonly referred to as Hicks-neutral technical change, and can be incorporated into the cost function by way of a simple intercept-shifting time-trend variable. 1 ' It is worth noting that the definition of increased technical efficiency used above, although common, is somewhat bold, since, it is obvious that only when at least one or more inputs are increased can the same level of output be produced when all other inputs are reduced. Often, however, the input which is increased is knowledge, management skill, or quality of factors employed; inputs within this class are seldom if ever measured, due to their somewhat intangible nature. Thus, a necessary qualification to the above definition is that it refers only to observable inputs (viz. capital, labour, energy, and materials) and is thus, in some sense a measure of our ignorance of changes in non-quantifiable factors such as those mentioned. There are two popular approaches to the measurement of change in technical efficiency. The first as noted above, presumes Hicks-neutral technical change, which can be incorporated into the production function (and thereby, the cost function) as a disembodied index A(t), or: (32) Q = A ( t ) . f ( x ) This may be done by appending a simple time trend variable to the cost function. Increases in technical efficiency are indicated by a negative coefficient for this variable 39 The second approach, which deals more directly with the efficiency issue, is to measure changes in TFP. .As was suggested in the Introduction, however, some controversy surrounds the appropriate measurement of this index. Moreover, TFP measurement usually implies the -adoption of a number of. restrictive ^assumptions on the form of the production - technology (Yotopoulos..and Nugent 1976, p. 151). For the., latter reason, among others, TFP. measurement is an undesirable technique for the purposes of this study and so the former approach. will be employed instead. Hicks-neutral technical change implies that technology affects all inputs equally; as noted it represents a homothetic shift, which means that factor proportions do not change, ceteris paribus. Hence, (23) becomes: (33) AC = C(w,Q,h.t)/Q where: t is a trend variable which increases in discrete, equal intervals over the period in question (eg. t = 1, 2, .... T ; where T is the number of time periods). Due to the assumption that relative factor demands are unaffected by technical change, the left-hand side of (29) remains unchanged, but C(w,Q,h) is replaced by C(WiQ,h,t) on the right-hand side. In the next section, the assumption of Hicks-neutral technical change is relaxed and the effest of technical change on factor demands (technical bias) is considered. 4.7.2 THE BIAS OF TECHNICAL CHANGE The bias of technical change (or the change in factor intensity due to technical change) is the issue of most concern in the utilization of scarce resources. When a factor becomes generally less obtainable and/or more expensive, technology is often developed to reduce dependence on that factor, or derive greater per-unit returns from it Relative proportions of factors employed, of course, will also change as a 40 result of. changes in relative factor prices, and so it is important to distinguish between such price effects and those due to adoption of technologies with input-specific characteristics. In order to make, this distinction, it is necessary to 'net out' price effects when measuring technical bias. The bias of technical change is often measured in terms of the rate at which the marginal products of inputs change when their relative proportions are held constant Hicks-bias, for example, may be defined as: (34) .' B = dTyVdt ; for given x. / x. 19 where: r„ = (dQ/dx. )«(3Q/3x^. )" 1 = f./f\ (the marginal rate of substitution). If B is >0, there is input / - saving (J - using) bias; if B is <0 there is input / -using (/' - saving) bias; and if B= 0, there is no bias (i.e. if any change in technology has occurred at all, the effect has been Hicks-neutral). Binswanger (1974b) has provided a rather straightforward method to apply an analogous version of the 'primal' measure (34) to the dual cost function. While still in the sprit of the Hicksian notion of bias, his specification is based on changes in cost shares, viz.: (35) B. = (3aV3t)« 1/a. ; holding w^. /w^. constant V i , j ; /" * j where: a. is the cost share or optimal demand for factor L20 Binswanger tests two possible forms for (35), one assuming variable rates of biases over time and the other with constant rates of biases. The much simpler latter model yields results which support its use (ibid., p. 974) and therefore it will be employed here. One troubling aspect of his analysis, however, is that he imposes homotheticity in order to arrive at his results. Since then, a number of studies have measured bias without imposing homotheticity a priori and so, this assumption will also be relaxed in this case.21 41 In-order to measure technical bias, we redefine (29) as: (36) . X.(w,QJi,W) - 3C(w,Q,h,t)/3w. ; ,/ = 1, 2,.« , n The bias of technical change on input i is measured as the partial derivative of (36) with respect to time, or: (37) b. = 3X.(w,Q,h,t)/3t " ; i = 1, 2 n This measure o f bias is not defined as an elasticity and is therefore slightly different from (35). Since X .^ or a. is always positive, this seems a-sensible simplification; the sign of (37) is what we are most concerned with, rather than its size. As Greene (1983) has shown, both (35) and (37) are in any case only partial indicators of the change in factor use over time. In fact, he demonstrates that bias is comprised of three components: a hon-nomothetic (output) effect, an input substitution effect (due to changes in relative factor prices over time), and the technical bias effect given by (37). The distinction between the approach used by Greene and that employed here is that he calculates the total derivative of factor shares with respect to time, while only partial differentiation is used to derive (37). Given the focus of this study, the latter approach provides the information of most interest, but it should be kept in mind that (37) only accounts fo r ' part of the factor share's change over time, namely that portion attributable to the adoption of new (or poor maintenance of old) technology. 4.8 M E A S U R I N G T H E E F F E C T S O F C O N C E N T R A T I O N O N COSTS U p until now, explicit measurement of the effects of concentration on costs has not been addressed. Concentration, though, has implicitly been considered in the other measures described, since the level of concentration has been integrated into all of the properties outlined. Nevertheless, these measures have held concentration constant under ceteris paribus; now that constraint wil l be relaxed. 42 4.8.1 R E T U R N S T O C O N C T N T R A T I O N ^ A measure of the concentration effect which is analagous to returns to scale is returns to concentration. This, of course, is the object of most interest in this study and for which the logic of measurement has been described in some detail in chapter 3. Returns to concentration are defined as: (38) e c h ' = ( 9 A C / 9 h ) - h / A C = (9C(w,Q,h,t)/9h)-h/C As can be seen from (38), the effect on the total cost function is the same as for the average cost function, since Q drops out of the analysis due to the fact that 9Q/9h is presumed to be zero. The reasoning here is that changes in concentration should not have any effect on the magnitude of industry output; rather, we would expect only the way in which firms share the production of industry output to change (i.e. changes in market shares). The trend variable is included in (38), consistent with the technical change material discussed in the previous section. Subsequent expressions and derivations will likewise include this variable. Expressions (22)-(30) can be easily adapted in a similar manner. An interesting means of relating (38) to levels of concentration wil l be to compare the size and sign of e c f l to concentration levels between industries. If a consistent pattern emerges, this would be of particular benefit in policy analysis, since it would indicate where changes in concentration have been beneficial, and where they have been deleterious, in an effeciency sense. 4.8.2 T H E BIAS O F C O N C E N T R A T I O N Another matter of interest is whether increases in concentration affect factor proportions in the production of output As with the returns to concentration measure, it is possible to adapt the technical bias expression (37) for the purposes of measuring concentration effects, viz.: 43 (39) flip. 9X.(w,Q,h,t)/9h ; / = 1, 2, , n We-can interpret (39) in the. same way we did (37): • bh} could be greater than, less than/or equal to. zero, depending on the- direction or existence of bias. If it-is the zero, concentration - increases or decreases have no effect on input levels. In this case, concentration effects, as with technical change, might be 'neutral'. In contrast to (38), we have no' strong prior notions as to why (39) might be anything other than zero, nor would it be easy to explain why it might be positive or negative. Rather, it is of interest just to test for non-neutrality and so it would be useful to have a specification of C(w,Q,h,t) which is flexible enough to do this. 4.9 OPTIMAL SCALE A final effect worthy of measurement is the tendency across industries to diverge from the 'optimal' level of output, or the level of output at which the industry average costs are minimized. It is well-known that perfectly competitive industries produce at this point in long-run equilibrium, and in many regards it is considered socially optimal to produce here (in an efficiency sense). Thus, any divergence from this point suggests inefficiency and so is useful evidence to supplement the other tests noted so. far. In particular, we will be interested in determining whether there is a pattern in such divergences with regards to industrial concentration. The optimal level of output is found by setting (25) to zero, and solving for Q*. The resultant expression is dependent, of course, on how C(w,Q,h,t) is defined and so an explicit solution for Q* cannot be found from the conceptual model until C(w,Q,h,t) is specified. This will be done in the next chapter. 44 4.10 A G G R E G A T I O N A N D D Y N A M I C S Two topics which have been given some attention in the literature but will be neglected in this ' study are those of consistent .aggregation of inputs and dynamic partial adjustment The First topic is of little concern here since, as wil l be seen, most •inputs are only available in-highly, aggregated form from statistical sources, and s o , tests for separability are ruled out from the start; the only inputs with potential for these tests are energy and labour. The former input plays such an unimportant r&le in total costs for Canadian food rnanufacturing that tests for separability and formation of a consistent aggregate for this input would be useful only i f we were interested in substitution possibilites between types of energy (see Fuss (1977)), which is not the case for this analysis. A s ' w e ' w i l l see, a tolerably consistent aggregator is used for this variable in any case. Labour input effects are dissimilar enough in behaviour (i.e. production versus non-production workers) in an empirical sense (see Chapter 7) that a consistent aggregate is unlikely; Thus, aggregation may justifiably be ignored. The other issue, that of dynamic partial adjustment is of more concern, however. In most studies employing duality (including this one), immediate response of factor demands and perfect adjustment to optimal levels is assumed to occur in each, period, no matter how severe the change in relative input prices." Although this could be true in some instances, it is unlikely to be true when severe price shocks occur (as in the case of energy and materials for this sample) and the production technology must be changed (if such price changes are considered likely to persist). Most variable inputs can be changed relatively rapidly, but their employment is often tied to the capital technology chosen, which cannot be changed as rapidly. In fact it is likely that most capital stocks are fixed in the short-run, with investment or liquidation only occurring over a longer period of time. Such static properties mean that, for the capital stock in particular, price elasticities of own and cross- factor demands wil l be subject to bias i f the hypothesis of instantaneous adjustment is violated. Both Denny, 45 Fuss and Waverman (1979, 1981) and Lopez (1984a) stress these weaknesses with static models and propose methods for dealing with the problem. The models which result, however, are complex, non-linear, and have rather severe data requirements.-Aside ' from the" complexity implied by relaxing the perfect adjustment assumption, estimation of a model which allowed for partial adjustment would probably preclude measurement of concentration effects. Given these drawbacks, and the fact that partial adjustment models are still largely unproven, this topic wil l also be neglected. Interpretation of the results from this model must thus be made with the implications of the perfect adjustment assumption kept in mind. 4.11 T H E ISSUE O F O U T P U T E X O G E N E I T Y An additional assumption, explicitly made Ijere but seldom addressed in the literature, is that of output exogeneity. In assuming that output is exogenously determined for the industry, we are assuming that industries take output as given and minimize costs accordingly. In doing so, the possibility that output is in fact a choice variable by firms and at the industry level is ignored. It has been argued in Chapter 3 that firms, particularly followers, do in fact take output as given since this is constrained by market share. At the industry level this argument is harder to apply and other justifications must be found. For i f exogeneity cannot be justified and it is indeed a choice variable, this would mean that simultaneity bias wil l occur and so inferences made from a misspecified model could be spurious. As Nerlove (1972) observes: "the dilemma is that an econometric equation that does not contain output will almost certainly not fit very well. Thus the question seems to be whether or not a coherent theoretical justification can be found for including output... While any such theoretical justification must depend on the specifics of the industry or firm being studied, many types of situations may be envisaged where what is needed is a theory of simultaneous price and output adjustment over time" (p. 242). Since either a fully 46 simultaneous model of output and cost determination is beyond the scope of this study arid since the "use of an instrument for output, the only other option, would be too •technically demanding an^. time-consuming, Nerlove's proposition that justification may . be found in the nature of the sample wil l be pursued. It is generally believed that few manufacturing industries are truly competitive, and even fewer are true monopolies. As a result firm output (and therefore industry output) is not determined in the manner usually thought of for the two extreme cases. In the competitive case,firms solve the problem P=MC, or: A. As can be seen, Q/ can only be chosen when costs (and P) are known; thus, there is a simultaneous solution of both costs and quantity. It is also a decision of the firm to produce Q^. In the monopoly case, the firm/industry solves the problem: M R = M C , or: _ _ _ \ \ 1 1 AC ^ D Again, Q m • can only be chosen once M C is known, and is again an endogenous choice variable. 47 ' A s noted, however, most industries tend to be between these two extremes and that is what is assumed-for this sample. Output price is determined by a mix of -collusion and import competition. Thus, the industry faces the following circumstance: ,. GL9 Q -It has already been suggested in the previous chapter that P ° is likely to be set by the leading firms in the industry. In particular, it will be chosen by some sort of collusive process and wil l probably be somewhere between the competitive and monopolistic price. Moreover, most food manufacturing industries face some sort of import competition which will also have an influence in determining the market price for output Thus, given P ° (which is endogenously or exogenously determined by collusion or import competition, or is a mix of both) and D, the industry must produce at Q ° (or less) since that is the most that consumers wil l demand at price P? Hence, in a way, Q ° is determined exogenously (i.e. by demand conditions as opposed to a profit-maximizing rule). Obviously, the above argument is at best casual, but it seems plausible nevertheless. Given the focus of this thesis, it seems the best way to counter the endogeneity query. Chapter .5 M O D E L L I N G C A N A D I A N F O O D M A N U F A C T U R I N G INDUSTRIES: F U N C T I O N A L F O R M A N D COST F U N C T I O N SPEC IF ICAT ION 5.1 I N T R O D U C T I O N Having outlined the properies of the conceptual dual cost function in the previous chapter, the question now arises as to what form the empirical model will take. Up until now, although it has been shown that input prices, output quantity, concentration levels and time trend are the arguments of the cost function, no comment has been made about empirically measurable functional forms, other than in a paranthetic manner. Thus, this chapter wil l provide a survey of possible candidates which satisfy the analytical demands of the previous section, and adapt the functional form chosen so that it can measure all of the properties discussed so far. The next section of this chapter wil l provide a review of functional forms and justify choice of the form used here. Following that, a brief survey of previous results from other studies of Canadian food manufacturing will be given. In the fourth section, the stochastic specification wil l be established, and in the fifth, structural tests outlined for the conceptual cost function will be applied to the form chosen. 5.2 C H O I C E O F F U N C T I O N A L F O R M Whereas the literature on empirical results of various dual cost functions is substantial, the method of choice between these forms is quite undeveloped, and therefore there is little to guide the analyst in determining which form is most appropriate. In most cases, it is likely that one cost function is able to represent actual behaviour better than others, but without prior knowledge of the technology or actual cost function the procedure of choice becomes largely an ad hoc one. 48 49 Some attempts, have been made- to. assess performance of the various functional forms, using .a variety of performance criteria,* samples, and estimation methods..For -. example, rBerndt, Darrough and Diewert (1977) fitted the Translog (TL), Generalized Leontief (GL), and Generalized .Cobb-Douglas. (GCD ) functions to observed data, using Bayesian. grounds to distinguish between the quality of estimates. They found the T L to be preferred. . . Also using observed (actual) data, both Appelbaum (1979) and Bemdt and^ Khaled (1979) employed the Generalized Box-Cox form to assess, through restrictions and specification tests, the suitability of the Generalized Quadratic, G L and T L forms. The results of these studies where somewhat inconclusive with, regard to the T L and. indicated a slight preference for the G L More recently, Diewert and Wales (1985) have tested a number of coventional and newly developed forms for which concavity is imposed globally either by construction or in estimation." The problem with all four of these studies, however, is that the true functional form and production function was unknown, so that the main performance criterion was whether the forms fit the data well, rather than how well they represented the actual technology. Since the actual technology, as noted, is seldom known a priori, this flaw in the basis of choice presents a serious dilemma. One means.of circumventing this problem is to use data generated from a known technology, or simulated data. Two studies which have employed simulation techniques are Wales (1977) and Guilkey, Lovell and Sickles (1983). Wales tested the T L and G L on data generated from a linearly homogeneous CES production function. Focussing on estimates of the elasticity of substitution (one of the more important summary measures), he found that the T L estimates deteriorated as the true elasticity ( a ~ ) diverged from 1, and that the G L estimates deteriorated as a., diverged from 0. Both forms deteriorated as dispersion (range) of the data increased. Thus, no conclusive basis for choice between the two forms resulted from this study, other than the general notion that no matter 50 which of the two forms are used, extrapolation beyond the range of the observed data . might lead to quite misleading ^conclusions. :... -~."" The results obtained-by Guilkey et al., however, are more enlightening, since . the analysis is carried further: and is somewhat more conclusive. They use sim ulated data generated from a three^ input C R E S - type production function, and test not only for accuracy of the a „ estimates obtained from the dual cost functions employed, but also for-their accuracy in - identifying departures from constant returns to scale and homotheticity, and in measuring the a.j when complementarity between factors exists. The cost function forms tested are the Extended Generalized Cobb-Douglas (EGCD) , the G L , and the T L T h e results of the estimates are outlined in terms of the three criteria mentioned. Economies of scale were represented rather well by all three forms, but with varied results nevertheless. There was a clear preference for the T L over the other two forms on. the basis of this criterion. The T L was also best at accurately measuring the a.. in terms of mean average deviation from actual levels of this elasticity, and along with the E G C D , performed well in identifying divergences of the a .j from unity. The G L was strictly inferior in most cases. In terms of complementarity, the E G C D and T L forms were best in identifying this effect; however, all three forms found nonexistent complementarity a number of times. On the basis of overall estimates of the a.. , the authors conclude that "dominance of [one form over the other] does not imply acceptability; occasionally a dominant form or technique is merely the best of a bad l o t and unacceptable dominance occurs more frequently in estimation of substitution elasticities than in estimation of scale economies" (Guilkey et a l . 1983, pp. 612-613). Thus, accuracy of estimates of a ~ is likely to be low whichever form is chosen, and especially where the a.. diverge from one another (which, of course, is the matter of most interest). It follows that interpretation of any estimates of the a., must be made with a great deal of-caution, which is lamentable, considering that such estimates (along with the ~ generated demand elasticities), should-: provide a useful basis for distinguishing between . models-and technologies, using our prior-notions of .reasonable values for these-elasticities. . . . - . . „ -Aside from these overall reservations about the dual cost functions assessed above, it is clear that the T L is an obvious candidate, since it performs best within this class of functional forms. This probably accounts for its popularity in. empirical work, where it.-is arguably the most extensively used and developed form. „ The G L is less attractive, since results for this form are more heterogeneous in their-quality and accuracy. There, i s ; no strong reason for either accepting or rejecting it, although it has been employed less than die T L in empirical work. Moreover, it is less flexible than the T L in its ability to model a range of homogeneous, homothetic and non-homothetic forms." Thus, the T L is preferred over the G L i f only for this reason, since we do not wish to rule out any possible type of technology a priori. Finally, a previously unmentioned functional form which is rather uncommon in use, but which has been well-developed in all theoretical aspects is the Normalized Quadratic cost function (NQ), first proposed by Lau (1976). This has been adapted to model the dynamic partial adjustment process used by Denny, Fuss and Waverman (1979, 1981) and has a number of attractive features. It suffers from two drawbacks, though. First, since it has been used relatively little, its performance has never been related to that of the more conventional T L and G L forms. Second, it is less flexible in the sense that it cannot realistically represent either a homogeneous or homothetic production technology; it imposes non-homotheticity a priori. Given the apparent weaknesses of other forms, then, the T L is the preferred form and the one which wil l be employed here. 52 5.3 T H E C A N A D I A N F O O D A N D B E V E R A G E I NDUSTRY : PREV IOUS STUDIES A number studies, p r i o r ' t o this, have investigated the• production technology-of-and/or productivity in the,Canadian food manufacturing industry either directly, or as part of larger efforts covering a .number of industries. Probably this survey wil l miss some relevant references; it is believed that the most important ones are covered here, though." The main purpose of this section is to briefly summarize previous results (primarily price elasticities), since these should assist- in assessing the credibility of this effort With the exception of one paper, however, direct comparability wil l be difficult between the 4^ digit analysis performed here and the other results, since these have all been carried out at the 2-digit level of aggregation. . There have been five previous applications of duality to Canadian food manufacturing beginning with Fuss (1975) who applied a non-homothetic T L cost function with an energy price aggregator to food manufacturing disaggregated . into four regions (Quebec, Ontario, Prairies, B.C. and Yukon), over the period 1962-1971. The model included capital, labour, energy and materials ( K L E M ) inputs. He found that "no significant substitution possibilities exist between aggregate energy and other factors" (p. c-2) and so he leaves energy elasticities out of his aggregate model, setting both the own-price and cross-price elasticities to zero.-The average own and cross-price -elasticities (the only useful summary information generated from this study) for the other inputs over the four regions are given in Table 1, along with estimates from the other studies reviewed. Note that since Fuss allows all inputs to be variable, these are ' l ong- run ' estimates. Rather than interpret the elasticity levels obtained from Fuss (1975) here, his results wil l be compared below to those of the other three studies listed in the table. In 1979, Denny, Fuss and Waverman (1979, 1981) applied both a static T L cost function and the dynamic partial adjustment (NQ) cost function mentioned earlier to a variety of industries including food and beverages. The period covered was 53 Table 1. Estimated Price Elasticities of Factor Demand for the Canadian Food Manufacturing Industry1, Previous Studies Input Demand Elasticities Capital Labour Energy Materials Input Study s.r.2 l.r. s.r. l.r. s.r. l.r. s.r. l.r. Capital 4 (I)3 — -0.74 — 0.10 — 0 — 0.63 (2) — -0.74 — 0.22 — 0.01 — 0.52 (3) 0 -0.86 0 — 0 0.08 0 — (4) 0 -1.64 0 0.81 0 -0.71 0 0.62 (5) — -0.07 — 0.05 — -0.02 — 0.04 Labour (1) — 0.12 — -0.37 — 0 — 0.25 (2) — 0.30 — -0.27 — -0.01 — -0.03 (3) — — -0.07 -0.25 0.01 -0.02 — — (4) — — -0.14 -0.54 -0.04 0.31 0.21 -0.10 (5) — 0.06 — -0.31 — 0.28 — -0.04 Energy (1) — 0 — 0 — 0 — 0 (2) — 0.10 — -0.07 — -0.13 — 0.11 (3) — — — — -0.44 -0.51 — — (4) — — -0.03 0.28 -0.38 -0.65 0.31 0.54 (5) — -0.02 — 0.23 — -0.25 — 0.04 Materials (1) — 0.18 — 0.07 — 0 — -0.24 (2) — 0.16 — -0.01 — 0 — -0.16 (3) — — — — — — -0.02 -0.29 (4) — — 0.19 0.08 0.28 0.38 -0.80 -0.90 (5) — 0.04 — 0.03 — 0.05 — -0.12 Al l live studies cilcd provided analysis at the 2-digil S.I.C. level only. 2 "s.r." indicates short-run estimate (capital stock fixed) " l . r ' ' indicates long-run estimate (capital stock quasi-fixed or variable) 1 (I) refers lo Fuss (1975). As with (2) these arc long-run since the model is static (TL). These are also averages of elasticities over four regions. (2) refers to Denny, Fuss and Waverman (1979) static estimates with TL. (3) refers to Denny, Fuss and Waverman (1979) dynamic estimates with NQ. (4) refers to Lopez (1984a) estimates. (5) refers to Lopez (1984b) estimates. 4 The own and cross price elasticities for each input are obtained by reading across the table. Thus, row 1 (capital) column 2 (labour) gives the elasticity of capital demand with respect to an increase in the price of labour. 54 1961-1975 and the model again Included K.LEM with variables defined similarly to Fuss (1975). The price"elasticities, generated from both models-are also given in Table 1. A similar study to- that of Denny, Fuss and Waverman was done, by Lopez (1984a), using instead a N Q profit function but also with partial adjustment for capital. The main objective of this paper was to test for the existence of non-optimal capital stocks in the context of profit maximization, thereby also including output-price effects and responses in the adjustment process. The data covered a slightly longer time period, 1961-1979, and the model again considered four inputs- (K.LEM). The fourth study (Lopez 1984b) lakes an approach which is quite different from the other three, focussing on the existence of non-competitive, oligopolistic output pricing, Using a system of input/output. equations generated from a G L cost function, a market demand (for output) equation, and an output price equation which are estimated simultaneously. N o consideration is made for non-optimal capital stocks (i.e. instantaneous capital adjustment is assumed), and the period covered is 1961-1979. The inputs considered are again K.LEM, and the price elasticities from both his studies are listed as (4) and (5) respectively in Table 1. In the final duality analysis of interest, Freeman (1982) estimates a G L cost function for the food and beverage industry. His sample and approach differs from the other studies in two distinct ways, however: quarterly data covering the period 1968-1978 are used, and energy is not aggregated, being composed of four variables. A l l the elasticities generated are so low that Freeman considers them to be spurious. He attributes part of his lack of success to the fact that his capital data may not be reliable; this will be shown to be a general problem later. Moreover, the use of quarterly data with a static model is probably unrealistic; whereas inputs may adjust perfectly with a year, they are very unlikely to do so in three months. Given the questionable value of his estimates, they are not reported in Table 1. 55 . Turning now to a comparison-of results in Table 1, it is evident that estimates between models, (and; sample periods), are quite ...different, based on the criteria of- price elasticities alone. Own-price elasticities (long-run) are often radically different. The range for e-£ is between -0.07 and -1.64, for e / ^ between -.25 and -.54, for c e between 0 and -.65 and for em, the range is from -.12 to -.90. The labour elasticity seems to be the most stable, while with the exception of the apparently overly high elasticity of .1-1.64 for. capital, - the materials elasticity is the most .unstable. T h e cross-elasticities appear .to be equally unstable, often differing both in sign and .1 magnitude between models and between the short and long-run. Hence, no strong pattern seems to - exist and so it will be relatively difficult to compare estimates generated by this study and those of others. The empirical evidence in Table 1 supports the conclusions reached in the previous section: the estimates obtained will depend to a large extent on the functional form chosen. This is seemingly one disconcerting aspect of duality which cannot easily. be avoided and should be kept in mind when assessing any of the results generated from the sample to be used in this study. . There are two other relevant papers with approaches somewhat peripheral to that taken here, but with some useful conclusions, nevertheless. The first, Johannsen -(1981), is concerned with the measurement of productivity trends in the nine 3-digit food and beverage industries over the period 1962-1977. Johannsen divided the sample into two periods to determine whether any changes in T F P oceurai between 1962-1969 and 1970-1979. He found that from 1962-1977, average annual growth rates ranged from -0.72 percent for fish products to 1.1 percent in the beverage industry, and that in general, T F P growth worsened in the latter period for 6 of the 9 industries studied. In the other analysis, Gupta and Fuss (1979) try to measure minimum efficient scale ( M E S ) " for a number of 4-digit industries, including 14 of the 17 4-digit food 56 . manufacturing industries, using, disaggregated firm group data for these industries for 1965, 1968,-'1969, and 1970. The resulting estimates of ..MES as a .percentage of industry output are particularly; interesting, since these figures, i f high, would seem to justify and -imply high concentration ratios. As can be seen from Table 2, the results suggest that only in the breakfast cereals,; biscuits,, distilleries, breweries and wineries industries ate scale effects a major consideration (i.e. major barrier to entry). 2 ' However, it should be recalled that they-employ a somewhat restrictive homothetic form to arrive at these estimates and therefore- these figures should be considered in light of this. 5.4 STOCHAST IC SPEC IF ICAT ION O F T H E T O T A L COST F U N C T I O N This section is divided into two major parts. In the first part, a general T L specification is derived for the total cost function C(w,Q,h,t) and its regularity properties stated. In the second part, the general specification is adapted to make it consistent with the sample properties. This is achieved by first considering the various feasible estimation procedures available, choosing an appropriate strategy and then accordingly arriving at an appropriate stochastic specification and estimation method for the model which is consistent with the sample to be used. There are numerous subtleties to this latter part of the problem and no attempt wil l be made to address all of these; the objective is to discuss only the most relevant and important econometric issues. 5.4.1 T H E T R A N S L O G COST F U N C T I O N : I N T E G R A T I N G T H E C O N C E N T R A T I O N V A R I A B L E The T L cost function is commonly thought of either as a second-order (differential) approximation to an arbitrary twice-differentiable cost function at a point (Diewert 1982, fn 31) or as an exact representation of the true cost function. The 57 Table 2. Estimated Minimum Efficient Scale (MES) as a percentage of Industry Size from Gupta and Fuss (1979), Canadian Food Manufacturing Industries, 1965-1970. MES 2 as a percentage Industry Industry of industry output S.I.C. (1970) S.I.C. (i960)1 Industry Name (MEPS) 1011 101 Slaughtering & Meat Processing 1.29 1012 103 Poultry Processors 1.96 102 111 Fish Products 0.26 103 112 Fruit & Vegetable Processors 0.53 104 105 Dairy Products 0.02 105 | 124 Flour Mills 1.87 I 125 Breakfast Cereals 13.31 106 123 Feed Manufacturers 0.01 1071 128 Biscuits 3.35 1072 129 Bakeries 0.84 1091 141 Soft Drinks 0.95 1092 143 Distilleries 9.95 1093 145 Breweries 8.85 1094 147 Wineries 7.13 1 Gupta and Fuss used the old (1960) S.I.C.'s. Perfect concordance between these and the 1970 S.I.Cs is not possible for S.I.C.'s (1960) 124 and 125 since after 1970 these industries were combined. 2 See footnote 27 for a definition of MES. •latter definition implies'.that the true cost function is T L in form and therefore the T L cost function ' represents it exactly at--all points, thereby avoiding the econometric . problems associated* with'•. approximation errors (i.e. the-third :and higher order terms f r o m ' the Taylor's series. which are ignored). This is a rather extreme view to take, but it is the one most usually (implicitly) adopted in practice." Although the exactness interpretation wil l be used here, the adapted T L developed below will maintain the features . o f a - second-order differential • approximation, or flexible functional • form, in order to maintain consistency with the theory and to leave open the possibility of allowing explicitly for non-zero approximation errors (perhaps for future analysis). Hence,' rather than introduce the concentration variable in an arbitrary manner to a 'standard' T L cost function (i.e. a non-homothetic form with technical change such as that used by Diewert and Wales (1985, p. 5)), it will be integrated in a manner which conforms to the view of the T L as a second-order Taylor's-series approximation at a point Restricting this form to the notion of exactness above then becomes merely a matter of econometric interest; the structure of the cost function doesn't change in any way as a result of this assumption. The T L specification of C(w,Q,h,t) consistent with approximation theory is: (40) InC(w,Q,h,t) = a + £ a./nw. + a InQ + a, Inh + a t + v ' • >-<'•/ o /=1 i i q h l L I 0..//iw. //iw.+ I 0. Inw. InQ + L p.. Inw. /nh + /=iy=i ry / j /=1 iq i i=\rih i L /3.,/nw. - t + 1/20 (InQ)2 + 0 - . InQ Inh + /=1 'it i 'qq v rqh Pgt InQ-t + 1 / 2 0 M (Inh)2 + $hl /nh - t + 1/20^ t 2 A proof of (40) - that it conforms to the structure of a second-order Taylor's series approximation around the point {w* = [1, 1 1 ] ' ; Q* = 1 ; h* = 1; t* = 1} is not provided, but it is possible to construct one using an approach analogous to that used by Denny and Fuss (1977, pp. 406-407). 59 ~ In order to ensure that (40) to satisfies regularity condition C4 (or linear homogeneity in w)" given' in Chapter 4.:- -all other conditions except concavity .clearly -hold - me* coefficients .must satisfy four adding-^ up conditions, namely: 1 a =0 ; £'B. =0 ; £ =0 ; £ 0. =0 ; and £ 0. =0 V / /=1 t /=i /=1 /A /=i it j=\rij (assuming Young's theorem (By- Bp) applies).30 The optimal" factor shares31 may be derived by "applying Shephard's lemma to - (40), -"viz.: ' ' ' . . • . . . . . . . (41) S.(w,Q,h,t) = 3//jC(w,Q4i,t)/a/nw. = a . + ^ 0„/n w ... + PiqlnQ + Bihlnh + 0-^ t \ t - 1. 2 n As can be seen, both the concentration variable, h, and the trend variable, t, will have an effect on each optimal share.32 There are two main uses for the system of share equations represented by (41). First, as was shown in Chapter 4, they provide the basis for deriving elasticities and other structural results. The second reason is that the system (41) can be estimated independently of (40) if desired; as we will see this is a cheap and efficient way of testing for some of the basic properties of (40). The share system can also be estimated simultaneously with (41); the apparent benefits of doing this will be elaborated upon later. Since equations (41) must both be homogeneous of degree zero in w (Euler's theorem) and sum to one, they must satisfy the same set of restrictions which apply to (40). Note that both (40) and (41) are defined over n inputs. More specific definitions will be given in the next section. 60 5.4:2 STOCHAST IC SPEC IF ICAT ION O F T H E M O D E L . The sample to be employed is a time-rseries of 22 observations for 17 4-digit industr iesfor "the period 1961-1982. Both total cost and input cost and price data f o r , capital, production labour, non-production labour, energy, materials are available, as well as output and Herfindahl index, series, (see Chapter; 6 for details). Given such a sample, the problem becomes how to best estimate the parameters of (40). If data were particularly plentiful, an obvious option would be to estimate (40) separately for,, each industry:. an inspection of (40), however, shows that the number of parameters, (assuming 5 inputs) total 43 per industry whereas the time-series covers only 22 years. Hence, for the purposes of this study, that particular option is ruled out • Whereas estimation of a separate model for each industry means that each is assumed to have a distinctly different production technology and that concentration effects are similarly different for each, the other extreme would be to assume that all industries have the same technology. This is the implicit assumption underlying 2-digit aggregate analyses, but for this sample aggregation over industries would not be necessary; the sample could be 'pooled ' and thus all 374 observations could be used (as opposed to 22 for a 'standard' 2-digit analysis). However, we have no prior justification for such a strong assumption (even though the procedure is common), since there is no reason to believe, for instance, that biscuit manufacturers wil l employ the same technology as, say, sugar refiners, even though both are food manufacturers. A middle ground between the two can be achieved i f we go so far as to assume that some similarities in technologies exist but all 17 industries, for the most part, have different technologies. There is some justification for such an assumption, i f only because it avoids the restrictiveness of the second option given above and therefore carries the perspective of this study to a level of disaggregation never considered up until now. 3 3 Moreover, it seems that food nianufacturing industries may have some behaviour in common since they are al l highly dependent on the 61 agricultural - sector for- their raw materials and since materials costs represent a. large share of total costs {see the: following chapter), So, aside, from being a pragmatic , solution to a data availability problem; this assumption has two fairly, sound bases. In fact, the estimation approach taken, • as a result, has some advantages over even the first option, as. wil l be. shown. Fuss (1977) provides a useful discussion of how best to implement the strategy noted above. Although Fuss's approach is used for-regional variations,in all-of-manufacturing technologies, the technique he uses carries over analogously to the problem being confronted here. He notes that "one approach is to assume that differences in technologies (resulting from [industry] variation) .imply that the parameters of the cost function ..... are [industry] r- specific. In order to conserve degrees of freedom, we would need to restrict [industry] parameter variation to the constant and linear terms of the second-order expansions" (Fuss 1977, p. 98). This technique is adopted here. Fuss also observes that there are two other methods for estimating a model with the above sample properties, limiting his discussion to. single-equation arguments. The two alternatives to the industry-specific parameter approach described above are covariance and error-components estimation. Covariance methods assume that industry differences are stochastic and therefore parameters only diverge randomly from 'mean' levels for each industry; error components methods follow the same assumption, but allow for inter-industry variation in stochastic elements as well. Since it is expected that inter-industry parameter differences are non-stochastic (non-random), but rather deterministic, neither of these two alternative methods are appropriate. Fuss justifies his use of the former method by arguing that inter-regional differences in costs and input demands are primarily a result of differences in product mix and efficiency rather than differences in technologies.3* 62 Another feature of the estimation procedure is the generally acknowledged fact that estimation of the cost-function a s "z system with the n-h^share equations leads to more efficient estimation of me" parameters, thus yielding more reliable hypothesis tests.-One share equation must be dropped to avoid singularity of the covariance matrix. Guilkey, Lovell and Sickles (1983) show the preference for systems estimation in their comparisons of functional forms. The systems procedure most commonly used is Zellner's seemingly unrelated regressions (STJR's).. Zellner (1962) has shown that his iterative SUR ' s method is maximum likelihood so long as the system converges. Moreover, Kmenta and Gilbert (1968) have shown that this result holds whichever share equation is dropped from the system, and that the parameters generated from any one of the possible systems wil l be equally efficient and of the same magnitude. Hence, SUR ' s of the system of equations with the properties suggested by Fuss's first method noted above will be the estimation procedure used. Although, as noted, this does not account for cross-industry variation of the disturbances in estimation, such cross-sectional variations wil l be accounted for by the explicit use of different first-order parameters for each industry and by evaluating the summary measures at each industry's sample means. The stochastic specification of (40) and (41) according to the above structure then, is: (42) /nC(w,Q,h,t) = 2? a + Z I a. Inv/. + ' £ a InQ + v ' ^ ' r =i or i=\ r=\ ir i r =i qr ^ 1 7 1 7 i i Z a . In h + Z a , • t + 1/2 Z Z R I„ W /„ W + r=\ hr r =i tr / = i y ^ i ij i j t 0. Inv/. InQ + t |3.,//iw. Inh + t /3.,/HW. - t + /=i Hiq i /=i 'in i /=i 'it i lWqq (InQ)2 + tqh InQ Inh + 0^ / n Q - t + 1/20^ (Inh)2 + fiht /«h - t + l/20„ t2 + e i r t where: r is the industry index number 63 a , a. ( / = 1,2,3,4,5),. a and a, apply to industry r and are zero otherwise or iry a r nr w ..•= w.J ;-.w„ = w, • ; w, = -w. . ; w -= w ; wc =. w :-and 1 k 2 Ip 3 Inp « • e s m ' "e- n is an-'(independently) normally distributed -error.-..term (see more on its properties below) In order to keep the notation simple in (42), the total cost, price; output and concentration variables have not been subscripted with r and t (for time period) but these do vary over r and l (with the exception-of w^  which is the same for all industries - see Chapter 6). -The four share equations to be estimated with (42) are: (43) S (w,Q,h,t) = ' l a + t B..lnv/.+ B. InQ + 0.. Inh + 0. t + e.w ; / = 2, 3, 4, 5 The subscripts r and t are also dropped from the share equations and other variables for the same reasons. Although the capital share is dropped from estimation, any other share could have been chosen instead; as noted, it is immaterial which is dropped so long as the system converges. The regularity (homogeneity) conditions applied to the system (42) and (43) are imposed to make the cost and share equations homogeneous in w for each industry. Thus, the first-order restrictions are: £ a. =1 ; r = 1, 2, 17 /=i ir i.e. there is one restriction for each industry, a total of 17 in all. Since the four sets of second-order cross-price coefficients are common to all industries, there are eight more of these: 5 Z 7= |0..=O (/= 1, 2,., 5 ) ; | 0.^0 ; . £ 0 .^0; .£ 0., = O Moreover, since the coefficients in equations (43) must conform to those in (42), there are a number of cross-equation restrictions which must be imposed. The 17 intercept 64 terms in each of the 4 share equations must be forced to, equal the 17 respective first-order coefficients for each of the 4 relevant prices in the cost function (a total of 72 restrictions); "the five-price coefficients in each share equation must be forced to, equal their counterparts in the cost function (a total of 20 restrictions); finally, the output, concentration and trend coefficients in the shares must equal those in the cost function (another 12 restrictions). In total, with homogeneity and cross-equation restrictions, there are 128 restrictions which must be imposed in estimatioa" In addition to the fact that the model is being applied to a particularly large-sample (374 observations), these restrictions mean that estimation of the system (42) and (43) is very expensive. With regards to the disturbance (error) terms appended to each equation ,(e. ; / =2,3,4,5), these are assumed to have the following properties: (i) E(e / / t ) =0 ; / = 1, 2 5 ; r = 1, 2, .... 17 = 0 for r * s , t * u where: a2, is the variance of the estimator (not to be confused with the general U notation for the elasticity of substitution (o.jj). Thus, the error terms are assumed to have the usual properties (i) of zero mean and(ii) constant variance (i.e. homoscedasticity) In addition, however, the error terms are contemporaneously correlated (ie. correlated across equations - this is the assumption underlying SUR's) but not across industries or time periods (i.e. they are temporally and cross-sectionally independent). Thus, (ii) implies that there is correlation across equations, but only within industries and time periods. A final comment to be made about the cost/share system (42) and (43) is that although it assumes a priori that the second-order terms are the same across 65 industries, it does have an advantage over the more general procedure of estimating a separate cost function. for each industry. This positive property is that the model as specified provides an ideal environment for testing for cross-industry similarities in technologies. For example, it is possible to formally test the hypothesis that technologies are the same for all industries, or that they are the same within groups of industries. On the other hand, technologies could be allowed to differ even more across industries (say, high versus low concentration industries or within 3— digit groups) by allowing the second-order terms to vary between groups of industries. Although few. such tests will actually be performed in this study due to computational cost constraints, the potential for such extensions exists.. Thus, in some regards this method is more flexible than the more general procedure since the latter imposes complete cross-industry differences in, technology, whereas the former allows us to test for such differences (in a limited way).37 66 5.5 SPECIFICATION, REGULARITY AND STRUCTURAL TESTS FOR THE TL COST FUNCTION •• •5.5.1 SPECIFICATION TESTING 5.5.1.1 Concentration Effects: Specification Tests The cost function defined by (42) is a rather general form: it is non-homothetic and includes the concentration and trend variables within the context of a fully integrated second-order approximation, with price, output, concentration and •trend first-order parameters varying across all industries. As .argued above, however, there is some value in testing formally (in. a statistical sense) the validity of this general model against Various more restrictive (or even less restrictive) alternative specifications. Harvey (1981) stresses the importance of such specification tests, primarily through the classical theory of hypothesis testing, and the construction of tests based on the likelihood ratio and Wald methods. He recommends that all the available a priori knowledge be used "to set up a decision framework before any estimation is carried out Specification testing may then proceed, the starting point being the most general model, or models, under consideration" (p.184). The most systematic manner of doing this testing is to 'nest' hypotheses, beginning with the most general model and sequentially testing subsequently more restrictive specifications. The difficulty in applying Harvey's systematic procedure to (42) is due to the fact that we are concerned with three distinct groups of specifications: (i) restrictions across industries; (ii) restrictions to determine production structure (eg. homotheticity or homogeneity); and (iii) restrictions to determine how concentration affects costs (eg. whether it has an effect on factor shares). The hypotheses which fall into category (iii) are arguably the most important; hypotheses (i) are probably of least interest Given this priorization, hypothesis testing will be conducted primarily on the grounds of appropriate" alternatives for concentration effects and production technologies; cross-industry relations will be explored only peripherally. ' Focussing on concentration effects, the proposed .restrictions to be considered are as follows: . (i) first-order concentration effects are the same for high-concentration •industries and for low-concentration industries but different between the .two • • groups (i.e. a n r - °-ni0^T w ^ a v e r a g e n < n ' (where h <h' is .a 'low' concentration level) and 0.^,= CLhhF1' a v e r a 8 e n )• (ii) first-order concentration effects are the same for all industries (i.e. o., - o., = • • •= a, , or a,, = a, ,.). h i h 2 hi i hlo hhi (iii) second-order cross-price concentration effects are insignificant (i.e. (iv) second-order concentration-scale effects are insignificant (i.e. 0^-0)-(v) all second-order concentration effects are insignificant (i.e. ^ 1 h " Kh =•••= h h " *qhm hh=V-(vi) concentration has no effect at all (i.e. a, = a, =...= / I I tl 2 a A , 7 = * i A = Kh ' " " Bsh - V ^ h ' 0 ^ As can be seen from the ordering above, specifications become increasingly restrictive, with the possible exception of (iii) and (iv) which are 'non-nested' tests. Also note that test (ii) is conditional on the outcome of (i), as are all subsequent tests. Since the production technology specification tests (see section 5.5,$) represent" quite a different set of restrictions from those for concentration effects (and so are not easily 'nested' with the above tests), these will be performed conditionally on the outcome of restrictions (i)-(v). Similarly, the final model will be chosen on the basis of the outcome of the production technology specification tests. 68 5.51.2 Implementation of,Specification Tests:-the Wald and Likelihood Ratio Methods There are two means of implementing the tests outlined above. The first, and most costly procedure is to estimate seven different models, each with the different levels of restrictions applied, from the most general specification (42), to the most restrictive, (42) with restrictions (vi). G iven ' these estimates, and the subsequent values of the' likelihood functions from each, the specifications can be tested using the likelihood ratio (LR) approach, or: (44) L R = -2ln\ « 2lnWi) - 2//zL ( i / / „ ) where: X = L ( \K ) / L W O and is always £ 1 L ( i / / i ) is the value of the likelihood function of the unrestricted model, and U)l>o) is the value of the likelihood function of the restricted model (i.e. under the hypothesis H 0 ) . This statistic is distributed as x 2 under the restricted (null) hypothesis ( H 0 ) , where m m is the number of restrictions needed to define H 0 , (Harvey 1981, p. 163). The null hypothesis is rejected i f L R is greater than some level 6 , chosen to minimize the probability of a Type I error (rejection of H 0 when H 0 is actually correct), or such that: (45) Pr(x2m> S) = a where: a is the nominal size of the test (ibid.). Typically, a is chosen to equal 0.05, or the 95 percent confidence level that rejection of H 0 is correct This will be the usual level of significance chosen here to accept or reject specifications. The problem with the L R procedure is that it is a costly means of making inferences. For this reason, it will only be used in a limited context with the second 69 alternative specification approach noted below. ' Two useful alternatives to the LR approach exist; they are not substitutes for the above procedure, rather they can supplement it of provide a reliable and practical --methbd to arrive at similar conclusions. The first alternative is the Wald test which can be "carried out on the basis of the unrestricted model only" (Harvey 1981, p. 165). Thus, with the Wald test, all six sets of restrictions noted in the previous section can be tested on the basis of only one estimation of (42) (and (43)), as opposed to seven with the LR method This makes it particularly attractive for our purposes, since it means that the specification exercise should be considerably less expensive. The only notable objection to the Wald method is that it is only asymptotically equivalent to the LR test and generally has a higher probability of making a Type I error in small samples, ceteris paribus, than the LR (and so could lead to conflicting results - see Harvey 1981, p. 175). Given that asymptotic properties are assumed for on this model (SUR's are* based asymptotic arguments), this possible inconsistency is unlikely to present problems. As opposed to the LR statistic, the Wald statistic is rather complex and so its specific form won't be illustrated here. Rather, it need only be noted that for a set of m linear restrictions in a linear model such as that used here, the Wald statistic (W) is, like the LR, distributed (asymptotically) as x2m (ibid.). Although the F-distribution is sometimes used with W in small samples, as noted above, it is more approprite to use the x 2 distribution here. As with the LR test, H 0 is rejected, given the nominal size of the test, if x 2 exceeds the level, 6 associated with that size. 171 Again, the 95 percent cut-off value will be used. The second alternative is to perform some tests with the share equation system estimated independently of the cost function. Since this method is relatively cheap, both LR and Wald test procedures can be used. The results from estimates can also be 70 used to choose the correct variables to use in the estimation of. (42),- for example, various rates of return to capital can be checked (see Chapter 6) — and to perform misspecification tests for the inclusion of concentration, and technical change .variables (see Chapter 7 for more details). . -In order to estimate the share equation system independently, restrictions for homogeneity and cross-equation restrictions must be applied to (43), namely 4 homogeneity restrictions (one for each equation) and 6 cross-equation parameter restrictions (on the common B.jcoefficients) for a total of 10. The adding-up restrictions: £ a. =0 Vr ; .£ 0. =0 ; £ 0.,=O ; and £ 0=0 /=i ir /=1 *iq- i=\ 'lh /=1 rU cannot be imposed, due to the fact that the capital share, equation is dropped. These restrictions are assumed, however, in obtaining the parameters of the capital equation. Given the computational cost savings, it is unfortunate that the share-equation estimation procedure cannot be used for anything other than preliminary tests, but since so much cost function information is lost when only this system is estimated, the use of, these estimates alone would defeat the purpose of this study." 5.5.1.3 Specification Tests for form of Production Technology: Homogeneity and Homotheticity In order to test for homogeneity, (42) must be adapted to conform to the relationships implied by (26) and (27), and then these more restrictive specifications can be compared with (42) using the Wald procedure outlined above. For (42) to be of the form (26), it must be a function of output input prices and concentration with no cross-price or cross-concentration output effects, i.e. (46) /nC(w,Q,h,t) = (l/p)./nQ + A(//iw, Inh, t) For this form to hold, we must test the hypothesis that: 71 •0.-0 Vi ; Bn =0 ; 0 , =0 ; and B =0 iq qq qh qt If this holds, l/pr=- aqr; r = l,2,:...,17 . T o test linear homogeneity of the production function, as well as testing" that the 'above restrictions hold, the hypothesis that: a = 1 Vr (or p = 1 Vr ) is also checked. These tests, like those for homotheticity below must be performed simultaneously for-all industries, given the.assumption.of equality of second-order parameters already established. This is an unfortunate consequence of the pooling technique used. The specification test for homotheticity of the production technology is, of course, less demanding than those above, requiring only that: V ° V' • V =0> M d tqt = ° in (42). In fact, this is a further test which can be adequately performed with the share equations since it merely implies a test of the hypothesis that output has no effect on factor shares; if this is indeed the case, it is likely that homotheticity (and possibly homogeneity) applies. 5.5.2 MISSPECIFICATION TESTS: AUTOCORRELATION, HETROSCEDASTICITY, AND DIAGONALITY OF THE COVARIANCE MATRIX This section is concerned with possible violations of the disturbance assumptions of temporal independence, homoscedasticity and contemporaneous correlation made in section 5.4.2. It is well-known that if the first assumption does not hold, autocorrelation may be present and that this leads to biased estimates of the parametric variances, thus reducing the accuracy of hypothesis tests. The presence of heteroscedasticity will tend to do the same thing. Finally, if contemporaneous correlation doesn't exist across equations in the system, these can adequately be estimated using 72 OLS instead of SUR's (i.e there would be no efficiency gain from-using SUR's). To simplify estimation, only autocorrelation and contemporaneous correlation will be tested for: There has seemingly been very little attention given to the issue of heteroscedastieity--in- SUR's (for example,-Breusch .and."Pagan (1979) only mention SUR's parenthetically (see p. 1293)). Since construction of .'an' appropriate- test would certainly. ; be a project in itself, heteroscedastieity will be essentially ignored here; other than an acknowledgement of its possible presence. In order to test for autocorrelation, "arguably the most important test of misspecification in linear regression" (Harvey 1981, p. 155), both the pattern-of residuals will be checked and the formal Durbin- Watson d-statistic will be used for each equation. Even. if autocorrelation exists, however, the complex nature of SUR's (and particularly the singularity feature of the share equations) means that corrections for this problem is difficult Berndt and Savin (1975) provide a methodology for compensating for autocorrelation with SUR's, but implementation of their technique is beyond the scope of this analysis. Hence, no correction of this problem will be made, if in fact it arises. It has been argued previously that because we expect cross-equation correlations of error terms, the SUR's method is the most appropriate estimation procedure. Nevertheless, it is of interest to test for diagonality of the error covariance variance matrix of the system, since it indicates that the efficiency gains on which SUR's estimation is based are also occurring if diagonality is rejected. Such a test based on the Lagrange-Multiplier (LM) technique has been proposed by Breusch and Pagan (1980). Details of their procedure will not be given here except that the test is distributed as x 2 with (1/2 m«(m-l)) degrees of freedom, where m is the number of equations being estimated (Breusch and Pagan 1980, p. 247). The test is against the null-hypothesis of diagonality, and so H 0 is rejected if the statistic exceeds the chosen X 2 value (eg. that which allows us to reject H 0 with 95 percent confidence). 73 5.5.3 REGULARITY OF THE-COST FUNCTION: - TESTING FOR CONCAVITY As opposed to" the other regularity c»nditions on the cost function listed in Chapter 4; concavity *(C5) in prices is not built into the-TL cost function,,nor is*it imposed,Tike linear homogeneity .in prices, in estimation." Thus, it is necessary to test for negative semi-definiteness of.the Hessian, matrix (of second-order partial derivatives with respect to input prices) of the cost function. In particular, the characteristic-'roots, or eigenvalues of this matrix must all be non-positive, and at least one must be zero (Hadley 1961, p. 256). Since symmetry is imposed, all the eigenvalues will be.real (ibid., p. 240); thus, the possibility of imaginary roots is ruled out Unlike the other tests mentioned above, this test has no 'level of significance' ; concavity is either satisfied or violated. There are two ways of testing for concavity. The first is a global test which, if satisfied, indicates that concavity holds for the whole sample. If the former test fails, concavity must be tested for at each observation. Diewert and Wales (1985), provide-a method for making both tests. The Hessian matrix H for the TL cost function is defined as: (47) H = B - S + SS' where: B is the symmetric (5x5) matrix of estimated price coefficients B.. from the cost/share system S is the (1x5) share vector: [S, S2 S3 S4 Sg ]' S' is the transpose of S, and S is a (5x5) diagonal matrix which has the vector S on its diagonal (and zeroes elsewhere) For a global test they show that provided the share vector is non-negative, the matrix - [§ - SS'] is negative semi-definite and therefore a necessary and sufficient condition for concavity is that B be negative semi-definite (Diewert and Wales 1985, 74 p. 9). • If B isn't negative semi-definite then (47) must be evaluated at each,sample point - in this case, 374 such tests must be made - using the 'predicted shares from-(43)' (i.e. those" generated from the model using observed input prices, output, concentration level, and toe period for each industry) rather than the observed -shares.40 Then the eigenvalues are computed for H; the implications of violations at sample points will be discussed in Chapter 7. . 5.5.4 STRUCTURAL TESTS WITH THE TL In this section, the TL analogues to the structural tests described in Chapter 4 will be defined. 5.5.4.1 Elasticities of Factor Demands Berndt and Wood (1975) provide a useful means of estimating own and cross price elasticities for the TL which conform -to (30). The elasticities are expressed as: (48) .e.j = (fitJ+ S r S j ) / S. V/ * j for cross elasticities, and as: (49) « (0..+ (S. )2 - S. ) / S. Vi for own-price elasticities. To facilitate estimation (these must be computed at the average shares for each industry), (48) and (49) are best generalized into matrix form: (50) E = [B + S -S' - S ] / S* v / r r r r r where: E is a (5x5) matrix of own and cross-price elasticities with the first row: K i C 1 2 6 1 3 C 1 « C , 5 ] B, S ,S', and S are defined as in (47) but now each element is the r r r ' average value over the period 75 7 represents'" Hadamard (element -by element) division of the matrix, in square 'brackets by S* : see Horn and Johnson (1985 p. 255) for a more detailed 1 description of this operation, and * . • S* is a (5x5). matrix with each column composed' of S. Each matrix/vector in .(50) is. defined for each industry, with the exception of B which, of course, is common to all industries. Also "note that as with-the concavity tests, (50) will be computed using the predicted shares, but this time using average input prices, output, concentration level, and time period (t=11.5) to generate the shares from (43) for each industry, rather than the observed average shares. 5.5.4.2 Elasticities of Substitution The elasticities of substitution can be derived quite easily from (48) once these cross-elasticities are evaluated, and have been shown by Berndt and Wood (1975) to be: (51) a.. = e.. / S. / *j ij ij J Using matrix form once again, (51) can be generalized to: (52) Z = E r / S; ; r = 1, 2 17 where: Lr is a symmetric (5x5) matrix, with each row defined similarly to E^ , but now with the a., as each element rather than the e.. . 'J 'J The only difficulty in interpreting (52) is that the diagonal in each of the 17 matrices should be ignored, since these are the own-elasticities of substitution. As was pointed out in footnote 16, these terms are seemingly irrelevant 5.5.4.3 Returns to Concentration and Concentration Bias To determine the returns to concentration from (42), all that is needed is simple differentiation with respect to h, or: 76 ( 5 3 ) • '* • echr = 9^C(w>Q,h,t)/3/nh = ahr + .£ ^ / « w . +. Bgh InQ + Bhh Inh + Bht -t ; r = 1. 2 17 - Again, (53) will' be evaluated at the sample means -for each industry. The bias of - " concentration on each input - can be obtained by differentiating, each „ share equation in (43) with respect to h and rearranging. In fact, it is more useful to redefine bh from (39) as an elasticity, leading to the expression: ( 5 4 ) eihr = [3X.(w.QJi.t)/dh].h/xi= (B.h+ • S,. ) / S, ; / = 1, 2,.., 5 ; r = 1, 2, 17 5.5.4.4 Returns to Scale The analogue of (25) for the TL cost function is: (55) (3AC/3Q).Q/AC = i(agr- + .£ ynw ( + Bgq InQ + Bgh Inh + B -t) - 1} ; r = 1. 2, 17 What we are really concerned about is. whether this term is negative, positive, or zero; the magnitude is of less interest Note that (55) will be evaluated at the average input price, output and concentration levels for each industry. 5.5.4.5 Measuring Technical Change Both neutral technical change and technical bias are included in (42) and (43), as proposed in of Chapter 4. To determine the direction of neutral technical change, we need only determine the sign of a^ . in (42). Similarly, relative technical bias (between factors) can be assessed by inspecting the sign of 0^ for each input A final measure of interest is the 'dual rate of total cost diminution' (which applies equally to average costs), defined by Berndt and Khaled (1979 p. 122) to be: 77 (56) ear = 3/7IC(w,Q,h,t)/9t = + .£ /ynw. + Bg{ InQ + Bht In h + Expression (56) combines the neutral, input bias, and other secondr order effects for each industry,- thus measuring the total decrease in costs each year (on.average) due. to technical change. 5.5.4.6 Finding the Optimal Level of Output The optimal level of-output for each industry from (42) is: (57) Q* = exp{(l - d - t B- -Invi. - B , Inh - B , 'XVB 1 v ' r v qr /=i iq i qh qt qq ; r = 1, 2 17 As with the other measures, (57) is evaluated at the sample means for each industry, as is the average deviation of actual output from Q*. or: (58) Rgr = [ ( Q r - Q; ) / Q; MOO : r = 1, 2 17 If industry r is operating, on average, at the minimum point of its average cost curve, R will equal zero, otherwise it will be greater than or less than this. Finally, to ensure that Q* in (57) is indeed minimum point of the industry average cost curve (and not, say, a 'flat' spot elsewhere on the curve), we must check the second-order conditions, which require B to be >0. Chapter 6 - -"DATA DESCRIPTION AND SOURCES 6.1 INTRODUCTION - • The data to be used in estimation of the cost/share system include: total costs (i.e. of capital, production labour, non-production labour, energy and materials); cost shares Tor both labour inputs, energy and materials; price indices for all five inputs;, a gross output quantity index; and a concentration (Herfindahl) index. The data set is comprised of a 22 year (1961-1982) time-series for each of the 17 4-digit food manufacturing industries, giving a total sample size of 374 observations. Precise descriptions of the data and the sources of these are given below. 6.2 THE RAW DATA 6.2.1 CAPITAL COST AND PRICE The capital stock data used were adapted from a 1960-1975 4-digit and 1960-1982 3-digit series prepared by the National Wealth and Capital Stock Section of Statistics Canada's Science, Technology and Capital Stock Division. The former series was provided to Agriculture Canada in 1975 on special request and is not available from any Statistics Canada publication, to my knowledge.'1 This series was extrapolated to 1982 using a procedure described in detail in Appendix 1. The completed 1960-1981 series employed is defined as year-end net stocks (i.e. of construction, machinery, and equipment stocks aggregated to a single value) and is in nominal (current) dollars. Two other pieces of information are needed in order to calculate the cost of capital (i.e. the cost of holding capital stock in any period, which is assumed to equal the cost/value of capital 'services'). These are the appropriate rate of return to capital 78 79 (opportunity' cost of capital) and. the economic depreciation rate. Choice of an. appropriate rate of return is an important factor in the calculation of capital - costs.-In* general, there 'are two possible proxies-for this variable (which ideally should be. the ex-ante, or expected rate of return); The First approach is to use an ex-post corporate bond yield. This statistic, however, fails to take into •account the fact that investors within an industry do not expect a 'riskless' rate of return* (Le. the coeporate bond yield). Rather, they anticipate a,return on their investment which corresponds to the type of return generally experienced in industrial production of the nature they are engaged in (i.e. which accounts for an equivalent level of risk). Hence, corporate bond yields are at best an imperfect, (lower bound) substitute for rates of return of the type just described. The second approach commonly practiced, and the one which will be adopted here, is to use the ex-post corporate rate of return. This proxy is used by Berndt and Christensen (1973); specifically, they define their datum as "the after-tax corporate rate of return" (p. 106). Two excellent sources of data on rates of return to various economic activities are the studies by Jenkins (1977) and Peprah (1984), The latter is essentially an extension of the former study to cover the period 1965-1981 and so it is used here as a primary data source. The relevant data in Peprah's study are available from two possible classifications (given below) The data are defined in both cases as "private rates of return adjusted for economic depreciation", and are returns to a weighted average of debt and equity capital investment More specifically, these data are the rates of return reported by corporations ("the return net of all taxes except personal income taxes..." (Peprah 1984, p. 65)), but with depreciation rates adjusted to reflect their economic instead of accounting values." The two general classes of annual rates of return available from Peprah's study are: (a) food manufacturing rates of return, and (b) all-of-manufacturing rates of 80 return. In case (a), the data are available either for three sub-groups within the food manufacturing industry-(food industries; soft drinks; and distilleries, breweries, and-wineries) Or as a weighted average of these returns. In case (b), the data reflect an average rate of return for about 19 2-digit industries (including food manufacturing . aggregated to the 2-digit level). Although it would seem that industry-specific rates of return would be most appropriate, the drawback with these is that they probably reflect oligopoly rents and therefore do not truly reflect the cost of capital, but rather the cost of capital plus expected (received) profit This would be particularly likely in concentrated industries such as the distilleries, breweries and wineries group mentioned. Given this reservation, food then, the choice is between the weighted average/*manufacturing rate of return or (b). The latter is chosen here, since it is believed that the former is still likely to reflect rents, whereas the all-of-manufacturing rate, being an average over more industries, is more likely to represent a 'competitive' rate of return. The final choice to be made is between annual data versus an average datum. Annual data must be extrapolated from 1965 back to 1961 and from 1981 to 1982. These extrapolations are done by taking the average rate of return over the most recent 3 years and sending this backward and forward respectively (for clarification, see Table 3). An alternative to the extrapolation method is merely to take the average over 1965-1981 and assume that this also applies to 1961-1964 and 1982. This averaging method tends to 'smooth out' any purely transitory movements in the rate of return which reflect temporary abnormalities rather than sustainable changes. A final possibility (which isn't attempted here) would be to establish whether a persistent trend occurred over the period, and use that trend line to derive annual rates of return net of 'stochastic' elements. Since there was no strong preference for either annual or average data, the choice was based on whichever rate of return led to the most 'reasonable' (in a 81 Table 3. All-of-manufacturing Rate of Return Data, Canada, 1961-19821 Year 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 Estimated Rate of Return 2 9.34 9.34 9.34 9.34 10.12 9.62 8.27 8.33 9.09 6.87 8.10 9.02 11.98 13.57 11.09 10.40 10.44 12.70 14.79 14.37 12.96 14.04 average 1965-1981' 8^ 53 1 The data for 1965-1981 are taken from Peprah (1984, Table 3-2, pp. 68-69). The data for 1961-1964 are extrapolated, using the average rate of return for 1965-1967 (9.34 = (10.12 + 9.62 + 8.27V3). The datum for 1982 is similarly the average for 1979-1981. 2 Specifically, this is the private rate of return for all-of-manufacturing, net of all taxes except personal income taxes, adjusted for economic depreciation. 3 Note that this average is assumed to apply to 1961-1964 as well as 1982, and is the rate of return used to calculate cost of capital in the 17 food manufacturing industries, 1961-1982. 82 Bayesian sense) input demand elasticity estimates obtained from the share equation system (43)." The average rate of return (8.63 percent - see Table 3) yielded the least number of positive elasticities of the two methods, and so- this is the.rate of return which shall be used. A proxy for the third variable, the annual depreciation rate, is derived from the figures used" by Denny, Fuss and Waverman (1979) for food and beverages, since it appears that Peprah did riot list the rate he used, in his calculations. The data presented in their study (Table 5, p. 50) are (average) annual rates of depreciation used for the period 1961-1975. It is assumed that these also apply to the additional years covered in this study: 1976-1982 . They break their depreciation rates into construction and machinery, which for food manufacturing are 0.040 and 0.083 respectively. The authors define these rates as being "approximately equal to the average replacement rates for the sum of the compnents in the national capital stock calculation" (ibid., p. 49). Since the only 4-digit capital stock data available for this study are for all-components, the figures given above must be converted into all-components rates using the relative shares of stocks of construction versus machinery for each 3— digit industry (see Table 4). The resulting weighted average depreciation rate for all-components stock is 0.066, or 6.6 percent per annum, and is assumed to stay at this level over the period of estimation. The final data series required is the price of new investment goods (i.e. the replacement cost of capital). The only proxy available for this purpose is the "price index for capital expenditure on plant and equipment" (total components), which is a 1961-1982 time series for the whole of food manufacturing industries (i.e. at the 2-digit level of aggregation) and scaled to 1971 = 1. This was obtained from Statistics Canada catalogues 13-568 ("Fixed Capital Flows and Stocks": occasional) and 13-211 ("Fixed Capital Flows and Stocks": annual). Because these data are so aggregated (i.e. to the 2-digit level and for all components) they are somewhat suspect; they are also 83 Table 4. Estimation of Depreciation Rates for All-Components Capital Stocks: Canadian Food Manufacturing (3-digit) Industries Industry (S.I.C.) Average Construction Share (/!,.,) Average Machinery Share (/»„„•) Average All-Components Depreciation Rate1 fa) 101 0.441 0.559 0.064 102 0.435 0.565 0.064 103 0.388 0.615 0.066 104 0.316 0.684 0.069 105 0.302 0.697 0.070 106 0.449 0.551 0.064 107 0.312 0.688 0.070 108 0.363 0.637 0.067 109 0.471 0.529 0.063 average for all industries: 0.066  1 The all-components depreciation rate for each 3-digit industry is derived as: ,5, = /!,,-(0.040)^ 71,,,, (0.083) where: /},.,- = average share of construction in value of total capital stocks for industry /', and /}„„• = average share of machinery in value of total capital stocks for industry ;' (= l-/3„). The shares were calculated for each industry using disaggregated data similar to that given in Table A1.2 in Appendix 1. The years chosen to calculate the shares were 1961,1966,1971,1976 and 1982, and an average was taken of these. Since the depreciation rates were provided only at the 2-digit level, and since, as can be seen, they differ only slightly between 3-digit industries, there is little to be gained in using different rates for each industry. Averaging gives a common all-components annual depreciation rate of 0.066. 84 very..poorly documented. Even -if.it were assumed that all industries. pay the same prices -for various, types of capital (i.e. both plant.and equipment, and categories within these.groups), one would still expect each industry, to face different prices-due. to. differences in the composition of capital items utilized. Thus, this price is highly unrealistic and-"does not.seem to compensate for the very likely inter-industry differences in capital composition. A second objection to the use of such an index is that it may not be compensating for changes in the quality of capital (i.e. .the .quantity of capital services available for a given price, net of inflation). Again, documentation of the index with regards to this aspect is sparse. Nevertheless, these price data are the only figures available and so, other than to jettison the project entirely, such flaws must be accepted, and the results qualified accordingly. This is unfortunate, but points to the need for much more accurate and diverse data for capital, an input which is plagued with measurement problems at the best of times. The data described above are used to generate the two capital variables used in estimation: the cost of capital services (used with the cost of other inputs to calculate total costs of production and thereby cost shares for the other four factors), and the price of capital (which enters both the cost and share equations).43 The cost of capital services is estimated (for each industry) as follows: (59) = (r + 5) • K S r - i ; t = 1961,1962, 1982 where: is the cost of holding capital stock in period t r is the nominal rate of return described (i.e. assumed constant over the period in question) 6 is the economic depreciation rate described (also assumed constant), and K S f - i is the value of the end-year net capital stock from the previous period (in current dollars). 85 Note* that .because' end-year stocks are being used, and since investment is > assumed' to occur" at year-end,, the cost of capital in year t will -be a function of the value of capital stock at the beginning of year t (i.e.. year_ t--\'s end-year r a t e s stocks) arid interest and depreciation* in year t. ... '••-'•-The price of capital equation employed is adapted from Jorgenson. and_ .Griliches ' (1967), who point out that "the prices of capital services must be calculated beginning with the prices of new investment goods" (p. 255). The capital price series used here are derived using the relationship: (60) = qkt • (r + 5) ; t = 1961.1962.....1982 where: is the price of new investment; r and 5 are defined as above. Since, for ease in estimation, all input price variables, the output index, and the Herfindahl index will be scaled to 1971 = 1, the scaled capital price W.j^ is expressed as: (61) WJ,- q f e . ( r + 6 ) / q i k i i 7 | • (r + 5) = q^ / q ^ $ ? / = pcap? /100 ; t = 1961.1962 1982 where: pcap^  is the capital price index described above (i.e. as taken from Statistics Canada catalogues 13-568 and 13—211). As opposed to the capital cost data which differed between industries and time periods, (61) only differs between time periods (as does (60)) for reasons already discussed. Note also that the term (r + 5) drops out of (61) since this term is assumed constant over the period. 86 6.2.2 LABOUR COST AND PRICES • • * • Two labour variables are used in this study: production and non-production (salaried) labour.4 The data for these variables, as with the data -for energy, materials and output, were provided by the' Food Markets Analysis Division of* the Marketing and E^conomics Branch, Agriculture Canada. The labour variable descriptions are as follows: 1. person-hours worked by production workers ('000) 2. total wages of production workers ($ '000) 3. number of non-production (salaried) workers 4. total salaries of non-production workers ($ '000) The data are for 1961-1982 for each of the 17 4-digit industries. Wages and salaries data are in current dollars. The series were obtained from the Census of Manufacturers of Statistics Canada and most of them are published in the Statistics Canada publication "Manufacturing Industries of Canada: National and Provincial Areas" (catalogue 31-203, annual). Since the first data series (person-hours worked by production workers) is not published, the data were obtained from the public tape of the Census. Items 2 and 4 above give the cost of production labour and non-production labour Cj respectively. The average hourly (production labour) wage series for each industry is derived by the following identity: (62) Wj = Cj / ; t = 1961,1962 1982 where: Wj is the average hourly wage at time t Cj is as defined by 2 above, and Qj is as defined by 1 above. Similarly, the average salary series for non-production workers for each industry is derived by: <63> " V • %, 1 <W ; ' " ™U962,...,1982 87 where: Wy^ is the average salary at time t f- is as defined by 4 above, and is as defined by 3 above. Both prices are scaled to 1971=1. 6.2.3 ENERGY COST AND PRICE The data on fuel and electricity expenditres and prices for 1961 were obtained from industry publications of Statistics Canada. Table 5 summarizes, the relevant information on these publications and the S.I.C.'s of the industries covered. The data for the 1962-1974 period were obtained from the Statistics Canada publication "Consumption of Purchased Fuel and Electricity by the Manufacturing, Mining and Electrical Power Industries" (catalogue 57-506) For the 1975-1981 period the publication used is "Consumption of Purchased Fuel and Electricity by the Manufacturing, Logging and Electric Power Industries" (catalogue 57-208). For 1982, the data were supplied by RJ. Stavely of the Industry Division (Manufacturing and Primary Industries) of Statistics Canada, since these had not yet been published. Total cost of energy (fuel and electricity expenditure), C in period t was obtained by summing the expenditures on the 7 energy input components (coal and coke, natural gas, gasoline, fuel oils, liquified petroleum gases, electricity, and 'other fuel'). Individual energy-type price indices were then derived by dividing their cost series by their quantity series (to obtain annual prices) and then divided each by their 1971 values so that the price series for each component was scaled to 1971=1. An aggregate price index (Fisher ideal)44, W for fuel and electricity was constructed using these price components. Again, this series covers the period 1961-1982 and is available for each of the 17 industries being considered, with W again scaled to 1971=1 for each industry. 88 Tabic 5. Sources of Energy Data, Canadian Food Manufacturing Industries, 1961 Catalogue S.I.C. Statistics Canada Publication Title 1 Number (1970) Slaughtering & Meat Processors 32-221 1011 Poultry Processors 32-227 1012 Fish Products Industry 32-216 102 Fruit & Vegetable Canners & Preservers 32-218 103 Dairy Products Industries 32-209 104 Breakfast Cereal Manufacturers2 32-204 \ 105 Flour Mills 32-215 / Feed Manufacturers 32-214 106 Biscuit Manufacturers 32-202 1071 Bakeries 32-203 1072 Confectionery Manufacturers 32-213 1081 Sugar Refineries 32-222 1082 Vegetable Oil Mills 32-223 1083 Miscellaneous Food Industries 32-224 1089 Soft Drink Manufacturers 32-208 1091 Distilleries 32-206 1092 Breweries * 32-205 1093 Wineries 32-207 1094 Note that the 1961 issue was used in all cases. 2 Although Breakfast Cereals and Flour Mills were combined after 1970 they were treated as separate industries prior to then. The post 1970 convention is used throughout this study and thus the 1961 (and 1962-1969) data are combined here. 89 " 6.2.4 MATERIALS COST AND PRICE Two series were used to construct the total cost and price data for materials: a constant-dollar value series of net: material inputs. (derived; by subtracting energy^ , costs from gross materials. costs)," and a current-dollar value series with the same definition. Both sets of data were obtained from, the Industry Product Division of . Statitics Canada. Although the data actually used are not published, comparable data at the 3-digit S.I.C. level are available from the Statistics-Canada publication "Systems of National Accounts: Gross Domestic Product by Industry" (catalogue 61-213). A materials price index was obtained by dividing the current-dollar values of energy (C -^) by the constant-dollar values (CON^ ).Thus, for each industry, the price series is obtained by the identity: C64) w „ , , » c m , ' C 0 N m t : 1 = 1961,1962 ,1982 mt mt mt As with the other four prices, this is also scaled to 1971=1 for each industry. 6.2.5 OUTPUT QUANTITY The output data used, Qt, are a constant (1971) dollar series of gross output for each industry. These series were obtained from the Industry Product Division of Statistics Canada. Although these data are not published, once again comparable data at the 3-digit S.I.C. level are available from the Statistics Canada publication noted above for materials inputs. These data are also scaled to 1971= 1 for each industry. 6.2.6 CONCENTRATION (HERFINDAHL) INDEX As noted in Chapter 3, there are a number of reasons for preferring the Herfindahl (h) index over alternative indices such as the four-firm concentration ratio (CRft). Both series are available for all 17 industries being studied from the Statistics Canada publication "Industrial Organization and Concentration in the Manufacturing, 90 Mining and Logging Industries" (catalogues 31-514 (1968) and 31-402 (1980, 1982p)), with some S.I.C. concordance adjustments, for every other year from 1965-1982, ,excepting the 2-year gap between 1965 and 1968.. Observations for 1958. are also available for some industries. There are a number of significant gaps in the CRa series due to confidentiality rules, however, and so aside from the theoretical preference for the h-index, there is good practical reason for. using it instead of the CR 4. Even so, to derive a complete time-series for h, linear interpolation back to 1961 and between years of publication were required. In the first case, either the 1965-1968 'trend' was used, or else if a 1958 observation were given, the 1958-1965 'trend' was employed. In the second case, the approach was the same. In addition to the interpolation exercise, there was some conflict of concordance for S.LC's 103, 104 and 105. Consistent series were obtained for 103 by combining data for the 4-digit classifications 1031 and 1032 (years 1970-1982) using the h-index observations and total output for each industry to derive a joint h-index. More specifically, the combined index was achieved by treating each industry (1031 and 1032) as if it were a group of firms and exploiting the definition of h given in (23), i.e.: h = [h «(Q )2 + h «(Q )2] / (Q ) 2 . The data for 1 O 3 1 1 O 3 1 V V N 0 3 1 ' 1 0 3 2 v v : 1 O 3 2 ' J v v 1 0 3 y S.I.C.'s 104 and 105 (which were divided into S.I.C.'s 1050&1070 and 1240&1250 respectively for the years 1965 and 1968) were derived in the same way. Finally, note that these series are also scaled to 1971=1 for each industry. 6.2.7 THE TREND VARIABLE The trend variable, t, is set equal to 1 for 1961 and 22 for 1982, increasing by an increment of 1 each year. It sh ould be noted that an additional benefit from scaling all variables in the cost function to 1971=1 for each industry (i.e. other than econometric efficiency) is that by so doing, we retain consistency with 91 approximation theory. Thus, for complete consistency, we could have the trend variable set to 1971=0, but given the exactness assumption established, in Chapter 5,. this isn't really necessary. 6.3 ESTIMATING TOTAL COSTS OF PRODUCTION AND COST. SHARES . . In order to obtain (nominal) total costs of production, the capital, production labour, non-production labour, energy and materials costs are summed for each industry, i.e.: (65) C = C, „ + C. + C, , + C + C , ; t = 1961,1962 1982. v ' t kst Ipt Inpt et mt The cost shares are derived as follows: (66) S / f = C f t / C{ i = lp, Inp, e, m ; t = 1961,1962 1982. The set of industry time-series of total costs, 5 input prices, output, Herfindahl indexes, and 4 cost shares described in this chapter are sufficient to estimate the cost/share system (42) and (43), or, with the exclusion of total costs, the independent share system (43). A summary of the share, concentration and output data means for each industry is given in Table 7 (see Table 6 for a list of industry S.I.C's and names. The data to be used in estimation (i.e. for those variables listed above) are given in Appendix 2 (Table A2.1). 92 Table 6. Canadian Food Manufacturing Industries: Numbers, SJ.C.'s1 and Names of Industries Studied # S.I.C. INDUSTRY NAME 1 1011 Slaughtering and Meat Processors 2 1012 Poultry Processors 3 1020 Fish Products Industry 4 1030 Fruit and Vegetable Processors 5 1040 Dairy Products 6 1050 Hour and Breakfast Cereals 7 1060 Feed Mills 8 1071 Biscuits Manufacturers 9 1072 Bakeries 10 1081 Confectionary Manufacturers 11 1082 Cane and Beet Sugar Processors 12 1083 Vegetable Oil Mills 13 1089 Miscellaneous Food Processors N.E.S. 14 1091 Soft Drink Manufacturers 15 1092 Distilleries 16 1093 Breweries 17 1094 Wineries 1 Standard Industrial Code 93 Table 7. Average Cost Shares, Herfindahl Indices and Output Indices, Canadian Food Manufacturing Industries, 1961-1982 Cost Shares  non- Output production production Herfindahl 1 Index # S.I.C.2 capital labour labour energy materials Index (1971=1) 1 1011 .026 .067 .029 .006 .873 10.4 1.02 2 1012 .019 .089 .023 .009 .860 4.5 1.01 3 102 .053 .127 .036 .013 .772 6.2 1.06 4 103 .067 .101 .054 .014 .763 4.5 0.99 5 104 .039 .050 .062 .014 .834 3.6 0.99 6 105 .072 .062 .038 .008 .820 13.6 1.06 7 106 .039 .039 .033 .011 .877 2.8 0.97 8 1071 .080 .162 .089 .010 .657 17.1 1.07 9 1072 .075 .167 .129 .023 .605 3.5 0.95 10 1081 .084 .140 .074 .010 .693 8.9 0.96 11 1082 .084 .065 .031 .020 .800 22.2 0.98 12 1083 .047 .023 .014 .013 .903 20.3 1.17 13 1089 .059 .071 .065 .013 .791 5.0 1.04 14 1091 .112 .083 .144 .017 .644 8.2 0.93 15 1092 .176 .089 .086 .023 .626 25.0 0.97 16 1093 .194 .131 .112 .017 .547 30.7 1.04 17 1094 .142 .082 .083 .010 .683 15.7 0.89 average (all industries) .080 .091 .065 .014 .749 11.9 1.01 1 The actual conlentration data are multiplied by 100 for more ready comparison. Note that the Herfindahl index is normally bounded by 0 (perfect competition) and I (pure monopoly); in this table the equivalent range is 0 to 100. Also note that these data are actually scaled to 1971 = 1 (like the price, cost and output data) in estimation but are given in 'raw' form here (xlOO) to make them easily comparable with other manufacturing data averages. See Table 6 for industry names. Chapter 7 • RESULTS FROM THE FINAL MODEL AND STRUCTURAL TESTS 7.1- INTRODUCTION - , . This chapter will provide a description of the results from the prehrninary specification tests which lead to the specification and estimation of the final model, as well as a detailed discussion of the model's properties and the range and accuracy of the information generated from it The organization of this chapter (particularly the third part) will closely follow that of Chapter 5 (Section 5.5). 7.1.1 SPECIFICATION TESTS WITH THE SHARE EQUATIONS The specification test strategy outlined in Chapter 5 was first employed as much as possible with the share system alone in order to conserve computer funds. The outcomes of these tests are very useful in providing a basis for the appropriate initial specification of the cost/share system, thus reducing the number of tests required in the latter case to arrive at the final model from which inferences are drawn. In particular, they allow us to determine whether second-order concentration and technical change (bias) variables should be included. 7.1.2 MISSPECIFICATION TESTS: CONCENTRATION AND TECHNICAL CHANGE As noted in Chapter 5, the validity of the inclusion of concentration and technical change in the model should be verified formally, using the classical hypothesis test procedures outlined. Unless it can be shown that these variables are significant and therefore can be justifiably included, it is likely that the estimated variances will be biased (Harvey 1981, p. 45). Similarly, exclusion of either variable when it is significant will cause biased parameter estimates. 94 95 To perform the misspecification tests for the inclusion of concentration and technical change effects, four share system specifications were estimated, using (43) as the base. model and imposing the constraints: (i) P^rO V/. ; (ii) Pit=0 V/' ; and (iii) P-fr- P^-O'-Vi in sequential estimates.-Each system, was iterated to convergence, --using a maximum limit of -0.01 percent change in. parameter estimates from iteration, to iteration.45 All four models converged within between four and six iterations. LR and Wald tests were then employed to determine the appropriate specification of (43). The results of these tests are given in Table 8. As can be seen, (43) is preferred to the other three more restrictive versions of the model. This implies that both the concentration and trend, variables should be included in the share equations, since all the more restrictive versions are rejected (and in all cases quite soundly). The formal rejection of the alternative models indicates that the more restrictive cost functions usually estimated (i.e, the most common form which includes only input prices and quantity) could suffer from misspecification bias. Obviously, both trend and concentration effects are significant determinants in cost minimization in this case, and this result suggests that exclusion of these variables from any model of this nature (i.e. estimated with industry and time-series data) should really be done only if their effects are shown to be statistically insignificant through a formal test like that performed above. 7.1.3 PRELIMINARY SPECIFICATION TESTS WITH THE COST/SHARE SYSTEM Given the confirmation of (43) as the appropriate specification, we can be sure that the cross-price concentration and trend terms should be included in (42). It has not been possible to confirm or reject the form of the zero and first-order terms, nor the second-order terms not appearing in the share equations, however. Ideally, we would go ahead and estimate the system (42) and (43), but evidence from Denny, Fuss and Waverman (1979) seems to indicate that a wiser choice would be to 96 Table 8. Concentration and Technical Change Misspecification Tests with the T L Share System, Canadian Food Manufacturing Industries, 1961-1982 Likelihood Ratio (LR) Test Wald Test Log of Hypothesis Hypothesis Model Likelihood Tested/LR Critical Test Tested/Wald Critical Test Number Function Value xl, (95%) Outcome Statistic Xl, (95%) Outcome CO' 5606 — — — (a)2:12.8 9.49 reject H 0 (b) :18.2 9.49 reject H 0 (ii) 5582 (a)2: 49.0 9.5 reject H„ — — — (iii) 5572 (b): 67.4 9.5 reject H 0 — — — (iv) 5551 (c): 109.8 15.5 reject H 0 — — — Model (i) includes concentration and trend: specification (43); Model (ii) includes concentration only (4 restrictions):(43) with /3,, = 0 V /'; Model (iii) includes trend only (4 restrictions):(43) with fiih'= 0 V /'; and Model (iv) excludes both concentration and trend (8 restrictions):(43) with /)„, = /},-, = 0 V /. 2 Hypothesis (a) tests Model (ii) against Model (i); Hypothesis (b) tests Model (iii) against Model (i); and Hypothesis (c) tests Model (iv) against Model (i). 97 constrain B ^ arid P-^.in' (42) to zero. They found that- the, mulucollinearity problems which occurred when these. variables were included prevented convergence of their model (Denny,, Fuss and-Waverman 1979, p. 71), and so their procedure will be adopted here, with B^t • constrained to - zero as well. The loss of accuracy from this procedure-is expected to be minimal. To determine the final form of the model, cross-industry tests were conducted with • (42) modified as above .and (43). The system was only iterated once for these, first-order tests, again in order to conserve computer funds. The cross-industry tests were based on three criteria: that the coefficients for a variable were the same for high concentration industries and for low concentration industries; that the coefficients were the same for all industries; and that the coefficients were not. only equal for all industries but also equal to zero. Numerous alternative criteria are possible, of course, - for example, restrictions could be tested for 3rdigit aggregation within 4-digit industries, and so on - but considering the focus of this study, the approach used, here seems most appropriate. 7.1.3.1 First-Order Concentration Effects As can be seen from Hypothesis Tests 1(a)-1(d) in Table 9, there were four alternative' hypotheses tested to determine the appropriate specification for the first-order concentration effects. Tests 1(a) and 1(b) show that while we can reject the restriction that is the same for low-concentration industries (i.e. those with average h <10), we cannot reject a similar restriction for high-concentration (i.e. those with h £ 1 0 ) industries. Really, hypotheses 1(a) and 1(b) should have also been tested jointly, but this was not done. The more restrictive specifications 1(c) and 1(d) are easily rejected. Thus, it seems that restriction 1(b) is appropriate, and so for the final model, 1(b) will be applied to (42). Since 1(a) is rejected, a, for low-concentration industries 98 Table 9. Cross-Industry Wald Specification Test with T L Cost/Share System 1 at One Iteration, Canadian Food Manufacturing Industries, 1961-1982 Hypothesis Description of Null Number of Value of Wald Critical X2m Test Tesl Number Hypothesis (11„) Restrictions (m) Statistic (w) (at u; 95%) 2 Outcome Ka) C K h r = r'lil<> / : h , < 10 8 45.5 26.1 ; 15.5 reject H 0 (b) c ^ h r = < x h h i /•: h r > 10 7 2.8 8.8 ;14.1 cannot reject H 0 (c) o c / i r = a / , ' = 1,2,.. ,17 16 53.4 39.3 ; 26.3 reject H 0 (d) «,,,.= 0 /•= 1,2,. . ,17 17 55.5 40.8 ; 27.6 reject H 0 2(a) ^1, = ^llo r :h r < 10 8 13.9 9.5 ; 15.5 reject H 0 (b) oc,,. — oc,/|( /•: h,> 10 7 2.1 8.8 ; 14.1 cannot reject H 0 (c) <xlr=(x, r= l ,2, . . ,17 16 16.9 18.4; 26.3 cannot reject H 0 (d) <xlr= 0 /•= 1,2,. . .,17 17 17.8 19.5 ; 27.6 cannot reject H 0 3 oc(„.-oc„ / = 1,2,. . ,17 16 21.7 18.4; 26.3 reject H 0 4 /•= 1,2,. . ,17 16 16.7 18.4 ; 26.3 cannot reject H 0 1 The 'base' specification used for these tests is the system (42) with p t = fijtl = ptl = 0 and (43). Wald tests are then performed for each of the 10 more restrictive specifications outlined above. 2 Since the system is only run to one iteration, the estimated variances are probably biased. Therefore, instead of using 95% as the nominal size of the test, we should employ a more demanding probability level. Thus, where w is > x]„ (95%), in order to ensure that a Type I error is not made, the Critical \ 2 m given is x2m (99.9%). Similarily, where w is < x]n (95%), in order to reduce the probability of a Type II error, x2„ (70%) is used instead, So in the former case, u = 99.9, while in the latter, u = 70. 99 will be allowed, to vary across industries, as specified in (42). 7.1.3.2 First-Order (neutral) Technological Change The results for restrictions on a are given in Table 9 under Hypotheses 2(a)-2(d). Again,-.the. hypotheses tested are based on- the .-concentration, .level., criteria, and, once again,' there appears to be some difference between restrictions (a) and (b). Hypothesis - 2(a) is rejected and 2(b) is accepted and so, we could choose the route taken for first-order concentration effects in -the final model. A check of Hypotheses.. 2(c) and 2(d), however, shows that we cannot reject these more restrictive specifications. Given the fact that technological change is a peripheral issue here, equality of a f /. for all .industries will thus be applied to (42). Although we cannot reject the hypothesis of zero first-order (neutral) technological change, this restriction is not imposed in the final model since this coefficient could still provide interesting information, even if the effect were statistically insignificant 7.1.3.3 Other First-Order Hypothesis Tests Two additional hypothesis tests were conducted, as Table 9 shows: equality of first-order output terms and equality of (zero-order) cost function intercepts. The former hypothesis is rejected (although not at the 95% level) and so this restriction will not be imposed. As we will see in the final model, this choice is upheld by the asymptotic Wald tests. The restriction that the intercepts are the same for all industries cannot be rejected (even with 70 percent confidence) and so equality of a for all industries Of will be imposed. Other tests performed with this estimate (homogeneity, homotheticity, no biased concentration effects, etc.) were rejected; these are also performed with the final specification (see below) and their outcomes upheld. 100 7.2 RESULTS FROM THE CONVERGED COST/SHARE SYSTEM 7.2.1 THE "FINAL SPECIFICATION OF THE COST/SHARE SYSTEM: GENERAL RESULTS The final specification chosen for estimation of the cost/share. system is: (42') /«C(w,Q,h,t) = % + .£ ¥ a./ nw. * £ agr InQ * Za^ lnh * ahhi l n h + a t ' X + 1 / 2 Pijl»"t ' " V L 0. /nw. InQ + I B..lnw. lnh + t 0. ,/nw. «t + 1/20w (InQ? + / B Q /nh + 1/20^ (/nh)2 + e ^ where: Lh = r : average h <10, and ahhlm Dr'ahhi Dr = 0 * r e L h > D = 1 Vr 4Lh. r The above specification, as can be seen, incorporates the restrictions on aQr, a^r, and suggested in the previous section. The cost function (42') was estimated as a system with equations (43) and converged after 10 iterations, using a convergence limit which allowed a maximum of 0.1 percent change in the magnitude of estimated coefficients from iteration to iteration. A lower limit from that employed with the share systems noted above was chosen to conserve computer time. The comparatively low number of iterations to convergence indicates that the cost/share system, even though composed of 147 variables, is relatively stable since it converges quite rapidly. Before proceeding into a discussion of the more specific properties of the estimates, it is useful to note the general features of the results, particularly the overall significance of the parameters. As can be seen from Tables 10, 11, 12, 13, and 14, in terms of general fit, all five equations are quite successful, with exceptionally high log of likelihood function values and R2's (although the latter statistics are of 101 Tabic 10. T L Cost Function Estimated Coefficients and Summary Statistics, Final Model ' Canadian Food Manufacturing Industries, 1961-1982 Estimated Asymptotic Estimated Asymptotic Estimated Asymptotic CoelTicicnl2 Value t-ratio Coefficient Value t-ratio Coefficient Value t-ratio OC() 0.017 0.8 CQ4 0.117 34.5 « 3 8 0.098 37.5 OC 11 0.033 9.0 OC25 0.066 20.1 OC39 0.136 49.2 OC|2 0.031 8.8 « 2 A 0.083 24.1 0^310 0.084 30.2 a i.i 0.060 18.4 <*27 0.057 17.2 « 3 I I 0.041 14.6 OC|4 0.070 19.5 CX 28 0.179 56.7 OC312 0.024 8.3 ocis 0.046 13.2 « 2 9 0.182 56.9 CC313 0.075 27.4 CX |(, 0.080 21.5 « 2 I 0 0.158 45.3 OC3I-4 0.153 53.8 r ' - l7 0.050 14.2 r ' -2 l l 0.088 24.7 <*3I5 0.094 33.8 °C|8 0.087 25.6 « 2 I 2 0.041 12.8 CQ16 0.122 44.8 CC |., 0.082 23.1 OQI3 0.090 26.9 OC317 0.089 29.4 OCIKI 0.091 25.0 <*2I4 0.090 28.9 <X4| 0.003 3.6 oc 11 1 0.092 25.2 « 2 I 5 0.105 30.5 OC42 0.007 8.6 OC 112 0.058 16.1 « 2 I ( , 0.151 43.3 OC43 0.010 14.5 OC L |J 0.066 18.6 OC2I7 0.088 24.8 a 44 0.010 12.8 OC 114 0.101 27.1 CC3I 0.036 ' 13.0 OC45 0.011 14.4 OC ||5 0.160 43.8 CC32 0.028 10.0 OC46 0.006 8.0 a Uf> 0.176 48.1 a 33 0.043 17.0 CX47 0.009 12.1 0.122 31.0 « 3 4 0.062 22.8 OC48 0.008 11.1 GC2I 0.085 25.1 OC35 0.070 25.6 OC4<; 0.020 26.5 OC22 0.108 32.4 OC36 0.048 17.1 OC4I0 0.008 10.6 OC2.1 0.140 46.8 OCJ7 0.041 14.7 OC411 0.017 22.2 1 The final model specification is the system of equations (42') and (43) 2 The notation here follows that of (42) and (42') Summary Statistics: R 2 = 0.98 Log of LF = 6022 102 Table 10. T L Cost Function Estimated Coefficients and Summary Statistics, Final Model, (cont'd) Canadian Food Manufacturing Industries, 1961-1982 Coefficient Estimated Value Asymptotic t-ralio Coefficient Estimated Value Asymptotic t-ratio Coefficient Estimated Value Asymptotic t-ratio « 4 I 2 0.010 12.9 «5I(> 0.536 100.3 OC/,4 0.014 0.0 O C 4 I 3 0.010 12.8 CC517 0.695 113.2 OC/;5 -0.015 -0.2 OC414 0.014 18.2 <Xq\ 1.081 12.3 OC/17 -0.010 -0.5 OC4I5 0.019 24.3 v-tft 0.988 10.8 OC//9 -0.061 -0.4 O C 4 I 6 0.013 17.4 CQ/3 • 0.905 8.4 GC/JIO 0.119 0.4 O C 4 I 7 0.006 6.8 OQ/4 0.816 5.1 CC/;|3 -0.694 -7.0 OC5I 0.843 153.7 «</5 1.061 2.4 OC/M4 -0.155 -0.6 OC52 0.826 138.8 0.932 5.3 OC/;/;; 0.134 2.2 a 53 0.747 142.5 CQ/7 1.040 13.4 OC/ -0.001 -0.8 a 54 0.742 136.7 « < / 8 1.080 11.8 Pu 0.039 4.9 OC55 0.808 146.1 CA(fi 0.895 3.9 Pn -0.008 -1.4 OC5f, 0.783 145.9 OC</|0 0.725 5.0 / i | 3 0.022 4.2 OC57 0.843 146.4 « ( / I I 0.814 5.4 Pl4 -0.005 2.6 OC.SX 0.628 119.4 OC,/l2 0.944 19.1 P\s -0.057 -14.7 OC59 0.580 104.2 « < / l 3 0.748 8.9 hi -0.050 6.7 OC5I0 0.658 116.6 «</|4 1.319 8.9 lh) 0.013 2.6 <X.SII 0.762 135.2 r'--/15 0.932 13.9 Ih4 -0.003 -1.7 OC5I2 0.867 161.6 OC</|(, 0.822 11.1 /hs -0.053 -14.1 OC51J 0.759 137.4 <X(/|7 0.909 18.3 '•f)33 -0.006 -1.1 OC514 0.634 109.9 « / , 2 0.170 2.2 fin -0.003 -1.7 « 5 I 5 0.623 109.5 OC/;3 0.118 1.1 -0.026 -8.1 103 Table 10. T L Cost Function Estimated Coefficients and Summary Statistics, Final Model, (cont'd) Canadian Food Manufacturing Industries, 1961-1982 Coefficient Estimated Value Asymptotic t-ratio Coefficient Estimated Value Asymptotic t-ralio Coefficient Estimated Value Asymptotic t-ratio AM 0.012 18.4 Ihh 0.012 4.3 lh. 0.0001 2.2 Iks -0.012 -15.0 0.007 2.9 (is, 0.0014 4.8 Ihs 0.148 19.3 Ihh -0.010 -4.6 he, 0.361 3.1 lh<, -0.010 -2.6 Ihh -0.001 -1.8 Ih/h 0.358 2.7 lh,. -0.019 -5.6 Ihh -0.008 -1.6 lU,h -0.092 -0.7 Ihq -0.0 II -3.7 lh, -0.0002 -0.9 lhQ -0.003 -4.4 lh, -0.0009 -3.9 0.043 6.2 lh, -0.0005 -2.7 104 Table 11. Production Labour Share Equation Estimated Coefficients and Summary Statistics, Final Model, Canadian Food Manufacturing Industries, 1961-1982' Estimated Asymptotic Estimated Asymptotic Estimated Asymptotic Coefficient2 Value t-ratio Coefficient Value t-ratio Coefficient Value t-ratio OC2I 0.085 25.1 OC2IO 0.158 45.3 I'm 0.050 6.7 OC22 0.108 32.4 «2II 0.088 24.7 hi 0.013 2.6 «23 0.140 46.8 «2I2 0.041 12.8 P24 -0.003 -1.7 CX24 0.117 34.5 «2I3 0.090 26.9 hs -0.053 -14.1 GC25 0.006 20.1 0.098 28.9 h<i -0.019 -5.6 <*26 0.083 24.1 «2I5 0.105 30.5 Ihh 0.007 2.9 CX27 0.057 17.2 OC2I6 0.151 43.3 hi -0.0009 -3.9 a 28 0.179 56.7 OC2I7 0.088 24.8 OC29 0.182 56.9 Ihi -0.008 -1.4 The final model specification is the system of equations (42') and (43) 2 The notation here follows that of (43') Summary Statistics: R 2 = 0.95 Log of L F = 6022 Table 12. Non-Production Labour Share Equation Estimated Coefficients and Summary Statistics, Final Model, Canadian Food Manufacturing Industries, 1961-1982' Estimated Asymptotic Estimated Asymptotic Estimated Asymptotic Coefficient2 Value l-ratio Coefficient Value l-ratio Coefficient Value t-ratio OC.ll 0.036 13.0 «3I0 0.084 30.2 hi 0.013 2.6 OC32 0.028 10.0 OCJ1 [ 0.041 14.6 hi -0.006 -1.1 «33 0.043 17.0 OC3I2 0.024 8.3 h* -0.003 -1.7 CX34 0.062 22.8 «3I3 0.075 27.4 hs -0.026 -8.1 OC35 0.070 25.6 OC3I4 0.153 53.8 he -0.011 -3.7 « 36 0.048 17.1 «3I5 0.094 33.8 hh 0.010 -4.6 a 37 0.041 14.7 OC3K. 0.122 44.8 : hi -0.0005 -2.7 a 38 0.098 37.5 CC3I7 0.089 29.4 a 39 0.136 49.2 hi 0.022 4.2 1 The final model specification is the system of equations (42') and (43) 2 The notation here follows that of (43') Summary Statistics: R 2 = 0.96 Log of LF = 6022 105 Table 13. Energy Share Equation Estimated Coefficients and Summary Statistics, Final Model, Canadian Food Manufacturing Industries, 1961-1982' Estimated Asymptotic Estimated Asymptotic Estimated Asymptotic Coefficient* Value t-ratio Coefficient Value l-ralio Coefficient Value l-ratio <X4I 0.003 3.6 «4I(I 0.008 10.6 /^ 24 -0.003 -1.7 «42 0.007 8.6 OC4|| 0.017 • 22.2 Pu -0.003 -1.7 OC43 0.010 14.5 CX4I2 0.010 12.9 p44 0.012 18.4 a 44 0.010 12.8 GC4I3 0.010 12.8 A(5 -0.012 -15.0 CX45 0.011 14.4 OC414 0.014 18.2 P*H -0.003 -4.4 OC46 0.006 8.0 «4I5 0.019 24.3 P*h -0.001 -1.8 OC47 0.009 12.1 OC4I6 0.013 17.4 P*l 0.0001 2.2 CX48 0.008 11.1 OC417 0.006 6.8 OC49 0.020 26.5 P\4 0.005 2.6 1 The final model specification is the system of equations (42') and (43) 2 The notation here follows that of (43') Summary Statistics: R 2 = 0.89 Log of LF = 6022 Table 14. Materials Share Equation Estimated Coefficients and Summary Statistics, Final Model, Canadian Food Manufacturing Industries, 1961-1982' Estimated Asymptotic Estimated Asymptotic Estimated Asymptotic Coefficient2 Value l-ialio Coefficient Value l-ratio Coefficient Value t-ratio OC 5 | 0.843 153.7 « 5 1 ( ) 0.658 116.6 Pis -0.053 -14.1 «52 0.826 138.8 OC5I 1 0.762 135.2 Pis -0.026 -8.1 a 53 0.747 142.5 OC5I2 0.867 161.6 P*s -0.012 -15.0 OC54 0.742 136.7 OC5I3 0.759 137.9 Pss 0.148 19.3 ° c 55 0.080 146.1 «5I4 0.634 109.9 Psc, 0.043 6.2 « 5 6 0.783 145.9 « 5 I 5 0.623 109.5 Psh -0.008 -1.6 OC57 0.843 146.4 «5I6 0.536 100.3 Ps, 0.0014 4.8 GC58 0.628 119.4 « 5 1 7 0.695 113.2 a 59 0.580 104.2 P\S -0.057 -6.7 1 The final model specification is the system of equations (42') and (43) 2 The notation here follows that of (43') Summary Statistics: R 2 = 0.97 Log of L F = 6022 106 limited value)'.' In addition, most variables are highly significant on the basis of their _ t-ratios (the critical . value t (95%), assuming asymptotic properties, is .1.96 ). The . exceptions- are: cr (which, - perhaps, should have been eliminated altogether), ^ .., a, , a, , a, -, a, ' , ' a , . , a . • , a,, some of the cross-price coefficients, AI« hs hi « 9 h 1 o t v and B^. The implications- of these insignificant, terms • (other than ) will be considered below. That a o is insignificant is less troublesome, however, and this seems to-be an innocuous result,since we are more concerned with rates of change than absolute levels in this study. 7.2.2 GROSS-INDUSTRY AND PRODUCTION TECHNOLOGY HYPOTHESIS TESTS In order to determine the validity, of the final specification chosen, a number of cross-industry restrictions were tested with the converged system. In particular, Table 15 presents test results of the hypothesis that. all - industries have the same technologies. Although equality of the first-order input.price, output and concentration effects across industries could also be tested jointly, strong rejection of all 6 hypotheses outlined in Table 15 indicates that the industries studied have significantly different production technologies and suggest that rejection of a joint test would also occur. This implies that the common assumption of identical technologies within 2-digit industries -implicitly imposed in most previous industry studies employing duality - is probably wrong. Interestingly, Denny, Fuss and Waverman (1979) make the observation that "disaggregating the estimation of the production sector from aggregate manufacturing to a 2-digit industry basis indicates widely differing technological relationships among industries; aggregation of all industries into the manufacturing sector thus masks many crucial aspects of production activity" (p. vi). The results here show that their comment appears to be equally applicable to the disaggregation from 2-digit to 4-digit analysis. 107 Table 15. Cross-Industry Hypothesis Tests with Final Cost Function Specification] Canadian Food Manufacturing Industries, 1961-1982 Hypothesis Description of Nu 1 Number of Value of Wald Critical Test Test Number Hypothesis (H„) Restrictions (in) Statistic (w) A'2,,, (950/0) Outcome 1 c/. if = x i : /' = 1,2,. . ,17 16 5265.98 26.30 reject Ho 2 GC 2f ~ OC 2 ' / = 1,2,. . ,17 16 6959.33 26.30 reject H 0 3 oc3f = ocj: r— 1,2,. . ,17 16 7739.30 26.30 reject H 0 4 OC4f = OC4 '. f — 1,2, . . ,17 16 2009.17 26.30 reject Ho 5 oc5f = « 5 : /•= 1,2,. . ,17 16 9327.39 26.30 reject H 0 6 <X(/r— cc(/: /'= 1,2,. . • ,17 16 31.75 26.30 reject H 0 1 The final model is the system (42') with (43) 108 Conceivably, as noted earlier, the model defined by (42' ) and (43) is . misspecified in the sense that it assumes that all industries have the same second-order' effects. Similarly,- a completely: flexible (in second-order v^ariation) 4-digit-" analysis-'would probably misrepresent actual -activity . at the firm level., Since we .are .. unable to- empirically-investigate-either-of these two alternative, models, their . advantages are hard to quantify. Nevertheless, it seems clear that just as 2-digit analysis is an improvement from 1-digit-analysis, the*. 4-digit disaggregation employed here probably , improves upon previous 2-digit analyses of Canadian - food manufacturing. This does not rule out improvements through further disaggregation of this analysis (and through other means as well), but it does indicate that progressive industry disaggregation would seem to be a step in the right direction, particularly if such disaggregation is shown . to be formally more correct (through classical hypothesis tests). The other set of Wald tests performed with this final specification are done primarily to confirm * the validity of the system (42') and (43). Three sets of tests were conducted for: the form of concentration effects; the form of technology effects; the validity of inclusion of both variables; and the structure of the production technology (non-homotheticity versus homotheticity or homogeneity). Hypothesis Tests 1(a) to 1(g) in Table 16 provide various possibilities for the form of concentration effects, ranging from first-order restrictions (1(a)) to a concentration variable misspecification test (1(g)). All 7 hypotheses are rejected. In particular, the first and second-order effects are all correctly formed in (42') and no combination of them can be formally rejected by the alternatives 1(a) - 1(g). Thus, the preliminary specification and misspecification test results are supported, and we can be sure that concentration should not be excluded from the model. Hypotheses 2(a) and 2(b) confirm the result obtained from the share equations that technological bias does exist (the null hypothesis of no technological bias and the more general null of no technological change were both rejected). Hence, technological 109 Table 16. Cross-Industry Hypothesis Tests for Concentration and Technological Change Effects and Form of Production Technology, Final Model] Canadian Food Manufacturing Industries, 1961-1982 Hypothesis Description of Null Number of Value of Wald Critical Test Test Number Hypothesis (H„) Restrictions (w) Statistic (w) A'2,„ (95%) Outcome Ka) <x/i/ = caiiio; n Lh 8 64.7 15.5 reject H 0 (b) «/;; = Ot///i/; ;< Lh 9 71.1 16.9 reject H 0 (c) OChr— OC/;/;/ = 0 ; ;<rLh 10 71.2 18.3 reject H 0 (d) Pil, = 0V; 4 72.4 9.5 reject H 0 (c) Pnh = Phh = 0 2 8.6 6.0 reject H ( ) (0 Pil, = Pqh = Phh = V>Vi 6 80.5 12.6 reject H 0 (g) oc hr = OC/;/;/ = /)//; = fiqll 16 155.8 26.3 reject H 0 = /)/;/; = 0 V/, Vt fLh 2(a) /J/7 = 0 V/ 4 51.4 9.5 reject H 0 (b) oc, = /j,7 = 0 V/ 5 51.4 11.1 reject H 0 3 Pu, = PlH,= 0 Vi 5 57.3 11.1 reject H 0 (homotheticity) 1 The final model is the system (42') and (43). 110 change did occur over the period studied and so, the .trend variable should also be included. Since we were unable to reject equality, of neutral technological change effects -across industries.at-;ohe iteration, we can conclude that.:neutral technological change, if it did occur, was insignificantly industry-specific. The low t-ratio on a ( , however-(see Table 10), indicates' - that we cannot reject-the hypothesis that <y=0.. Thus,, there is no. evidence of significant neutral technical change at all for any of the 17 food manufacturing industries studied. The implications of this result-will be discussed in more detail in Section 7.3.9. The final hypothesis considered (number 3 in Table 16), tests for the existence of homotheticity of the production technology. Since this is rejected,- we can also reject homogeneity and linear homogeneity (see Chapter 4 (Section 4.4)).. By this,, it follows that food manufacturing production technology is non-homothetic. Rejection of homotheticity also suggests that neither the homothetic technology assumed by Gupta and Fuss (1979) nor the Cobb-Douglas or similarly homogeneous technologies are likely to be valid for the Canadian food manufacturing industries. 7.2.3 RESIDUAL ANALYSIS AND DIAGONALITY -Aside from the size of sign of the estimated coefficients of the model and the •commonly used measures of goodness of fit (such as R 2 ), a very useful source of information is the set of residuals, or the unexplained variation remaining after the model has been applied to the sample. As Chow (1983) has observed, residual analysis is probably the most important facet of model assessment since "such an analysis helps detect possible defects of the model and may suggest an improved specification" (p. 84). Three main features of residual behaviour will be discussed in this section: randomness, normality, and diagonality of the covariance matrix. Two assumptions made about the error terms e. appended to (42), (42' ) and (43) were randomness and normality. The second assumption implies that the error I l l terms must be (independently) normally distributed (e^ ~IN(0,a .^)). This assumption is a'central one, since all .our hypothesis tests are dependent on normality. Moreover, non-normality-can-lead to incorrect inferences in specification tests if the: techniques used (in this case the classical LR and Wald methods) are not 'robust' -to violations of normality. -Although Maddala (1977) has indicated that with an appropriate degrees ., of freedom adjustment the t and F tests are valid, it is. generally acknowledged that either normality should be obtained, or else-non-parametric tests or alternative . Gobust') estimation procedures be used. There are a number of means of testing for normality, and at least one test for randomness. Bickel and Doksum (1977) point out that the coefficients of skewness-( 7 1 ) and kurtosis-(72) are useful in testing for normality, although lacking "the blunderbuss properties of Kolmogovov or Shapiro-Wilk tests" (p. 388). Since for the normal distribution ( 7 x = 7 2 =0 , the sample coefficients 7 1 and 7 2 can be checked for significant deviations from zero either formally, - using probability tables, or informally (by inspection). The latter technique will be used. If either 7 x or 7 2 is different from zero, we can assume that normality is probably violated. Non-randomness is, of course, violated when heteroscedasticity or autocorrelation Occurs, but can also exist for a number of other reasons. Hence, it is useful to test for this using'the 'Runs test' (see Gujarati 1978, p.-246), since if randomness is violated, "there is some systematic aspect of behaviour which is not being picked up" (Harvey 1981, p. 6) For the cost function, the coefficients of skewness and kurtosis are valued at 7.1 and 127.8 respectively (see Appendix 3, Table A3.2). Thus, it appears that normality does not hold. Neither are the residuals random, since the normal statistic from the runs test (-9.92) is small (absolutely large) enough to significantly reject randomness. 112 Two possible sources of these violations are readily identified - both may. be responsible for the problem, but possibly other sources exist. First, the Durbin-Watson 'Statistic for the "cost" function, at 1.76 (see. also Table; A3.2), is slightly lower than; d^  = 1.78, suggesting an uncertain outcome of the test for positive autocorrelation. It is -'less "than "-^d .though, and so-the hypothesis- of no- negative autocorrelation cannot be rejected. Hence, if. autocorrelation is occurring, it is slight and positive. The value- of p (0.12) reinforces - this conclusion. -The other possible source of non-normality-is the existence of outliers in the data. The plot of residuals for the cost function (see Appendix 3, Table A3.1), indicates that most of the disturbances are close to zero, -in general, and no consistent pattern occurs for most of the sample. From observations 265-308, however, there is not only evidence of autocorrelation but also some major outliers for observations 265-286 (industry 13: miscellaneous food processors). The poor fit for this industry is not surprising considering the fact that it is comprised of numerous, relatively diverse industries which are unlikely to have common production structures, as assumed for the other industries. This group of observations, then, probably accounts for a good deal of the departure from normality and randomness for the sample. Industry 14 - soft drinks — (observations 287-308) also fits relatively poorly, with larger errors than the other industries. The remaining observations (309-374) display about the same amount of systematic tracking as do observations 1-264 and therefore are quite 'well-behaved'. So far, the discussion has been limited to the behaviour of residuals for the cost function. The details of the residual patterns for the share equations will not be given here, but it should be noted that these indicated non-randomness and some apparent outliers in all four cases. As an inspection of Table A3.2 in Appendix 3 shows, the four share equations had Durbin-Watson statistics lower than d^  =1.57 and so the hypothesis of no positive autocorrelation is rejected in each case. Thus, the 113 share equations • perform even more poorly- than the cost function on the basis of residuals". How significantly these violations contribute to the problems with the cost function is not ilear, but "they are likely xo have some impact, given the assumed cross-equation correlation of error terms built into the estimation system. As noted, the normality assumption applied to - (42') and ..(43) is important - in determining the distributions used with the LR, Wald and t-statistics (i.e. the x 2 and r t-distributions). And so; where the.-structure of. the model-and inferences made with it are based largely on'hypothesis testing with these three statistics - as is the case here - departures from normality may lead to faulty test outcomes. The chance of spurious test results when normality is violated, however, is low enough not to be troublesome. As Judge, Griffiths et al. - (1985) point out, asymptotic tests such as the Wald and LR are still valid, but may have "reduced power under certain departures from normality" (p. 824). It is also reassuring that the estimated coefficients are unbiased (see Maddala 1977, p. 305), since normality is not required for unbiasedness. Moreover, although the likely biasedness of estimated variances means that some variables (eg. concentration and trend) shown to be significant in specification tests may in fact be insignificant, the estimated coefficients will. not be biased, since inclusion of variables which have insignificant explanatory power won't bias the coefficients of the remaining (valid) variables (ibid., pp. 156-157). Thus, departures from normality and randomness through autocorrelation, outliers, heteroscedasticity or other factors, generally means that only efficiency of the estimators will be affected, not their magnitude. There are at least five methods which could be applied to the model to correct for the nonnormal, nonrandom properties observed. Three of these have been mentioned here or elsewhere: correction for autocorrelation, test/correction for heteroscedasticity and elimination of the miscellaneous food processors industry (S.I.C. 1089) from the sample. The two remaining options - robust estimation (see Maddala 1977, pp. 308-314) or transformations of data to achieve normality (ibid, pp. 314-317) 114 • - • are jrimplex alternatives which ..should only be necessary, if all else were to fail. None of the corrections/tests will be performed here and their exclusion seems justified -given thescope of this* analysis. Such refinements.-, would be an obviously useful adjunct to this study, however. - Since no attempt has been made to correct for the.problems outlined above, the significance of the results remains in question. Nevertheless, this should not prevent us-from drawing inferences, given that. the: estimated coefficients are likely to be unbiased. The above discussion simply emphasizes the fact that such inferences should be qualified on the basis of possible inefficiencies in specification and therefore the conclusions reached should be accepted with a degree of caution. The Breusch-Pagan statistic for diagonality of the covariance matrix at one iteration (where the test is applied) was 390.80. This is far greater than the critical value, x 2 (95%) =18.30, so the null hypothesis of diagonality is rejected. 1 o 7.2.4 CONCAVITY TEST RESULTS As outlined in Chapter 5 (Section 5.5.3), there are two general ways of testing for concavity: a global test and local tests (i.e. at each observation). The global test with the final model yielded 3 positive eigenvalues. This is not a surprising result, since concavity restrictions are typically rejected at some points - Diewert and Wales (1985) base their development and analysis of globally concave functional forms on this premise. Given the violation of global concavity, the eigenvalues for H were calculated at each of the 374 observations. A summary of these results, by industry, are presented in Table 17. Of the 374 sample points, 258, or 69 percent had some positive eigenvalues.46 The number of eigenvalues per violation within each industry ranged from a maximum of 1 to a maximum of 3. In the former case, the positive values were often very small, but since it is not possible to determine the 'statistical Table 17. Concavity Violations by Industry, Final Model, Canadian Food Manufacturing Industries, 1961-1982 # S.I.C. Number of Number of Number of Positive Observations Violations Eigen values per Violation 1' 1011 22 22 <3 2 1012 22 22 <2 3 102 22 22 <2 4 103 22 16 1 5 • 104 22 22 <2 6 105 22 22 < 2 7 • 106 22 22 <3 8 : 1071 22 21 1 9 1072 22 0 10 1081 22 21 1 11 1082 22 7 < 2 12 1083 22 22 < 3 13 1089 22 20 1 14 1091 22 0 15 1092 22 0 16 1093 22 0 17 1094 * 22 19 1 Total 374 258 1 See Table 6 for industry names. 116 significance' of these violations, we must assume that concavity is indeed violated where positive eigenvalues exist '." ' ' "Clearly/ there is-some room for development of a hypothesis-test rprocedure for the significance of concavity violations. This would probably entail estimation of both a constrained - concave ->TL function - (the - difficulties encountered with the constrained „ TL . ^ form are outlined in. Diewert and Wales (1985)) and an unconstrained version like that used here. Then a LR or similar inequality. test procedure, perhaps employing the techniques developed by Gourieroux, Holly- and Monfort (1982), could be applied. . However, given the absence of a fully developed methodology in this regard, we must as noted, accept positive eigenvalues as violations,- no matter' how small they are. Considering that a large number of observations (and in some cases, all observations for an industry) failed to satisfy concavity, our main concern is whether the model is thereby undermined, and particularly whether the coefficients obtained are biased. Strictly • speaking, concavity is a necessary condition for duality, but most previous studies with concavity violations tend to assume that dual inferences can still be made. Guilkey, Lovell and Sickles (1983) observe that "the current trend is clearly toward the development and use of flexible forms which, although not globally well-behaved, may nonetheless satisfy the desired regularity conditions over a range of observations that contain or intersect the set of sample observations" (p. 591). This study, then, falls into their classification, since about 31 percent of the sample points satisfy concavity. The results of Guilkey, Lovell and Sickles's investigations have already been outlined in Chapter 5 (Section 5.2); obviously the TL will not yield ideal estimates when concavity is violated (as we must suppose was the case for their model - they do not make this explicit). On the other hand, Wales (1977) has suggested that "a violation of regularity conditions (concavity) in practice does not preclude the obtaining of good price .... elasticity estimates" (p. 191). Moreover, results from Diewert and 117 Wales (1985 - Tables 1 to 5) imply a relatively high degree of consistency between those estimates obtained from their globally concave functional forms and the unconstrained TL estimates. Even, though their unconstrained TL violated concavity for 24 percent of observations as opposed to 69 percent here, it can only be assumed that the higher number of violations for this sample does not rule out accurate and unbiased coefficient estimates. 7.2.5 ESTIMATED ELASTICITIES OF FACTOR DEMANDS The own-price elasticities and some cross-price elasticities generated from the final model are given in Table 18. The own-elasticities for capital, production labour and non-production labour are generally of the right sign, with the exception of e ^ for industries 1, 2, 5 and 7, and e ip for industries 5, 7 and 12. Of these positive elasticities, three are close enough to zero to be acceptable; their positive signs are probably due to measurement error.47 Similarly, for e m , the positive elasticities observed are small enough to be assumed insignificantly different from zero. The most unstable own price elasticities are for energy; 7 of the 17 industries had positive values for ee . Although initially puzzling, the unstable energy elasticity estimates seem to result from extremely small cost share accounted for by this input (on average about 1.5 percent of total cost for all industries - see Table 7). Thus, energy share equation estimates are likely to be unstable in a statistical sense, since this input is usually overwhelmed by the others. Problems with energy elasticities have been encountered in other studies as well, notably Fuss (1975) and Hall (1986). In both cases, static models similar to that employed here were estimated. For Canadian food manufacturing, Fuss set all the energy elasticities to zero. In Hall's international comparison of energy consumption, he found that for gas, the elasticities generated for some periods were positive. 118 Table 18. Estimated Own and Selected Cross Price Elasticities of Factor Demands, Canadian Food Manufacturing Industries, 1961-1982 own-price elasticities' selected cross-price elasticities # S.I.C. 6 k C Inp €e Cm €klp 6iPk € Inpk €ek 1 1011 0.60 -0.18 -1.20 1.10 0.04 -0.26 -0.10 0.81 0.82 2 1012 1.09 -0.35 -1.26 0.37 0.03 -0.35 -0.07 0.53 -0.05 3 102 -0.20 -0.48 -1.14 -0.04 -0.04 -0.03 -0.01 0.66 0.41 4 103 -0.34 -0.40 -1.06 -0.06 -0.04 -0.02 -0.01 0.47 0.41 5 104 0.04 0.06 -1.04 -0.11 0.01 -0.16 -0.12 0.39 0.37 6 105 -0.38 -0.13 -1.13 0.50 0.00 -0.05 -0.06 0.64 0.63 7 106 0.04 0.33 -1.16 0.11 0.05 -0.17 -0.17 0.71 0.45 8 1071 -0.43 -0.53 -0.98 0.16 -0.12 0.06 0.03 0.32 0.51 9 1072 -0.40 -0.53 -0.92 -0.44 -0.15 0.06 0.02 0.24 0.28 10 1081 -0.45 -0.50 -1.01 0.20 -0.09 0.04 0.02 0.38 0.53 II 1082 -0.44 -0.17 -1.18 -0.37 -0.01 -0.03 -0.04 0.81 0.31 12 1083 -0.11 1.21 -1.44 -0.01 0.07 -0.15 -0.31 1.58 0.41 13 1089 -0.27 -0.22 -1.02 -0.02 -0.02 -0.07 -0.56 0.38 0.42 14 1091 -0.50 -0.32 -0.90 -0.28 -0.12 0.00 0.00 0.24 0.36 15 1092 -0.60 -0.36 -0.98 -0.44 -0.13 0.04 0.07 0.40 0.36 16 1093 -0.60 -0.49 -0.94 -0.26 -0.18 0.09 0.11 0.36 0.45 17 1094 -0.57 -0.31 -0.99 0.21 -0.09 0.01 0.03 0.38 0.58 for whole sample2 -0.41 -0.36 -1.03 -0.09 -0.05 -0.02 -0.01 0.41 0.42 1 A l l elasticities are estimated at industry sample means. See Table 6 for industry names. 2 Evaluated at all-industry mean cost shares. 119 •Hence/energy' appears to > be a problematic variable anyhow; given our lack of '" direct interest in this. variable and the .exceedingly small share, of total costs which it represents, these apparently bizarre results needn't,be given .too much, consideration. ° Nevertheless, we cannot rule out "the ••possibility that the model used is inflexible to very small -factor shares or that the data are- poor.4' In the first case, if small share . insensitivity is indeed a feature of the TL form, it might be useful to aggregate inputs with very" small shares with another group. ofr inputs, if separability cannot be. rejected! Since the data have been constructed as accurately as possible, there is no apparent cure for the poor data problem. The arguments used above to account for the positive energy elasticities cannot be applied as readily to those observed for capital and labour, since, on average, the shares for non-production labour were lower than for the former two inputs and yet that factor has consistently negative elasticities. The only additional possibility (beyond bad data) which might account for these divergences, then, is that a static model is inappropriate. As Norsworthy and Harper (1981) point out, "not even the most fervent apostles of the equilibrium doctrine would maintain, that, for example, quantities of factor inputs show the same variabilities as their prices... The point is that the quantities clearly adjust to price changes with a lag" (p. 178). Thus, it may be that some account should be taken of the time in which it takes to change capital (and, perhaps, other inputs) to optimal levels, given any price change.49 Although within the context of a static model we may observe changes in input levels, if the technology employed limits the ability to rapidly substitute when large price changes occur, observed changes in input levels may not reflect changes in own-input prices. Rather, they may result from the inability of the producer to moderate his consumption of the input even though the price rises, given that it is tied to the consumption of other inputs.50 On the basis of this reasoning, it would seem that adoption of a 120 partial, adjustment model would be sensible. As noted in Chapter 4 (Section 4.10), a number of limitations preclude this, and so we must make ~ do with a possibly unrealistic model in. order to obtain any useful results at all. Given the qualifications noted above, it is nevertheless of interest to determine, the general - properties of the elasticities.- Capital .demand is somewhat inelastic, as is. production labour; both sets are relatively stable between industries (other than the exceptions listed) and range between -.0.10- and -0.60. .Interestingly, non-production labour demand is relatively elastic in most cases. This is possibly due to a lower level of unionization for this group. At the very least, it indicates that aggregation of "production and non-production labour is likely to be rejected, and that - interesting information would have been lost if such aggregation had been imposed a.priori. Not surprisingly, all materials elasticities. are very low, reflecting the limited possibilities of substitution between materials and other inputs. The cross-elasticities given indicate a dominant complementarity between production labour and capital - the exceptions to this are close to zero. This result is quite different from that for capital and non-production labour where strong substitutability is evident, possibly due to an increased trend towards mechanization in management Finally, note the apparent substitution effect between capital and energy; this result will be discussed briefly' in the next section where these cross-factor relationships are supplemented by the elasticities of substitutioa It is probably useful to compare the estimates in Table 18 with those obtained by Denny, Fuss and Waverman (1979) (D.F.W.) with their static translog model. The most useful comparison is between the all-industry (i.e. food manufacturing) estimates given at the bottom of Table 18 with those in Table 1, entry (2). As can be seen, e ^ for D.F.W.'s case was -.74, slightly higher than the value (-.41) obtained here. Their elasticity for labour is not easily related to those in Table 18, since they use aggregated figures, but their energy elasticity is very similar, at -.13, to the value 121 obtained with this sample (-0.09). And their materials own-price elasticity is more elastic at -0.16 (as compared with -0.05). Given the dissimilarities between models and data, the elasticities obtained here are encouragingly in line with those of D.F.W. Thus, we can conclude that the model is quite reasonable and we can be quite confident with its results. 7.2.6 ESTIMATED ELASTICITIES OF SUBSTITUTION The generated elasticities of substitution are presented in Table 19. Unfortunately, we have less to guide us as to what is 'reasonable' for these, other than the Sato-Koizumi substitution/complementarity rule (see Chapter 4 (Section 4.6)). Since 5 factors are included -in the model, by their rule, there must be at least 4 substitutes (or positive a„). As an inspection of Table 19 will show, only industry 12 (Vegetable Oil Mills) violates this rule, and so the elasticities appear to be consistent with the theory in this regard. The cross-elasticity results observed in the previous section are more or less confirmed here, although there seems to be a weaker case for overall complementarity between capital and labour. The substitution effect between capital and non-productive labour is more robust, and there is strong evidence of a similar effect between non-production and production labour. The other elasticities are of less intuitive interest, with the possible exception of , which is positive in all cases, reflecting substitution. This is a different result from that obtained by Berndt and Wood (1975), whose finding subsequently fueled the energy-capital complementarity 'controversy'. Without entering this debate, the evidence here seems to contradict Berndt and Wood, if that is of any value at all. It should be noted that the discussion of concentration effects on both the demand and substitution elasticities has been avoided deliberately to simplify matters. Undoubtedly, some relationship may exist between these variables, but it is not obvious 122 Table 19. Estimated Elasticities of Substitution, Canadian Food Manufacturing Industries, 1961-1982 elasticities of substitution # S.I.C. Oklp (Jklnp Okc Okm Olplnp Olpe Olpm Olnpe Olnpm (Jem 1 1011 -3.95 33.07 33.34 -1.67 7.92 -5.48 0.10 -14.50 -0.06 -1.31 2 1012 -3.90 53.28 28.64 -2.57 7.44 -2.16 0.31 -11.49 -0.33 -0.52 3 102 -0.23 12.81 7.93 -0.43 3.84 -0.55 0.46 -4.49 0.07 -0.19 4 103 -0.22 7.18 6.34 -0.14 3.34 -0.88 0.32 -2.51 0.38 -0.16 5 104 -3.22 10.01 9.58 -0.77 5.13 -2.65 -0.27 -1.89 0.51 -0.01 6 105 -0.87 9.26 9.09 0.00 6.42 -3.93 -0.03 -7.07 0.18 -0.75 7 106 -4.39 18.42 11.80 -0.69 11.11 -4.82 -0.53 -5.97 0.10 -0.20 8 1071 0.36 4.17 6.63 -0.11 1.89 -0.47 0.51 -1.69 0.56 -0.69 9 1072 0.34 3.32 3.79 -0.29 1.59 0.34 0.48 0.14 0.67 0.15 10 1081 0.29 4.59 6.48 -0.01 2.25 -0.76 0.45 -2.28 0.50 -0.65 11 1082 -0.52 9.98 3.82 0.12 7.53 -0.91 0.00 -3.17 -0.07 0.27 12 1083 -6.69 34.60 9.04 -0.38 40.28 -7.72 -1.52 -13.11 -1.00 -0.04 13 1089 -0.99 6.71 7.37 -0.26 3.70 -1.79 0.07 -1.97 0.51 -0.17 14 1091 -0.01 2.57 3.79 0.08 2.04 -0.71 0.05 0.01 0.73 -0.29 15 1092 0.43 2.58 2.28 0.43 2.60 -0.21 0.10 -0.25 0.54 0.20 16 1093 0.65 2.12 2.59 0.41 1.84 -0.11 0.30 -0.31 0.60 -0.24 17 1094 0.22 3.07 4.63 0.35 2.84 -1.99 0.09 -1.95 0.56 -0.67 1 Estimated al industry sample means. Recall that positive values imply that the two factors are substitutes; negative values imply complementarity. See Table 6 for industry names. 123 from a casual inspection of Tables 18 and 19. It can now-be said with a relatively high degree of confidence that, given that the elasticities and summary statisics generated by the model so far are quite consistent with our prior notions of what would be reasonable, we can proceed into the material on concentration effects and other summary measures for which we have even scantier idea of what should be expected. The following four sections will detail these results. 7.2.7 ESTIMATED RETURNS TO CONCENTRATION AND CONCENTRATION BIAS The returns to concentration measure, (53), evaluated at the mean input price, output and concentration levels for each industry are presented in Table 20. Even though B'^ was insignificant by its t-ratio, as were the o r^'s for most of the low-concentration industries, both terms were included in the calculations since it was felt that these variables were still relevant First the results and patterns of behaviour will be assessed on this premise, arid then the impact of the exclusion of B^ and the insignificant a^'s on the outcomes will be discussed. Of central interest is whether a pattern exists between and the average concentration level of each industry. By assessing the results in this way, we can incoporate the influences of differences in levels of concentration between industries and relate these to the time-series effects of changes in concentration, thereby accounting for possible differences in effects of changes in concentration on costs between low and high-concentration industries, as postulated by both Peltzman (1977) and Gisser (1982, 1984). As an inspection of Table 20 shows, e c n is positive for all 8 high-concentration industries. In contrast 5/9 low-concentration industries have negative ech , with 3/9 positive and one with no relationship between concentration and cost Thus, it would appear that for the industries considered, increases in concentration in high-concentration industries consistently raised industry average costs, while increases in low-concentration industries generally caused average costs to fall. Interestingly, this 124 Table 20. Estimated Returns to Concentration, Canadian Food Manufacturing Industries, 1961-1982 Concentration # S.I.C. Level 2 \€ci,-phi,liih] f6c/,-/;/,/,///h -oc/,,1-' 1 1011 0.13 h 0.13 — 2 1012 0.19 1 0.17 — 3 102 0.13 1 0.13 0.01 4 103 0.00 1 0.00 -0.01 5 104 -0.01 1 -0.01 0.00 6 105 0.15 h 0.15 — 7 106 -0.12 1 -0.13 -0.03 8 1071 0.15 h 0.15 — 9 1072 -0.08 1 -0.18 -0.02 10 1081 0.10 1 0.10 -0.02 II 1082 0.13 h 0.13 — 12 1083 0.15 h 0.16 — 13 1089 -0.68 1 . -0.69 — 14 1091 -0.19 1 -0.19 -0.35 15 1092 0.11 h 0.10 — 16 1093 0.13 h 0.12 — 17 1094 0.06 h 0.07 — See (53); this is evaluated at industry sample means. Industry names can be found in table 6. 2 'High concentration1 (h) industries are those with average h(h) > 10.—see Table 7 and 21. 'Low concentration' (I) industries are therefore those with h < 10. 3 This adjustment (i.e. subtraction of rx/,r) to each £<•/, is only done for those industries where oc/,ris insignificantly different from zero (by the individual t-ralio criterion—see Table 10). These, incidentally, all happen to be 'low-concentration' industries. 125 pattern is consistent with the effect observed by Gisser (1984), and seems to imply that the concentration-cost relationship is non-monotonic (although care should obviously be - taken in making generalizations simply on the basis of these and Gisser's results). In order to investigate the relationship between levels and changes further, the results from Table 20 are rearranged from low to high average concentration levels in Table 21. In spite of a fairly large variation between the increase in average concentration levels and that of ecjj , and the presence of some inconsistent observations (i.e. industries 2 and 3), the results do suggest that increases have generally been a good thing for low-concentration industries up to an average concentration level (h) of around 8.9. Increases in concentration for industries with average concentration levels higher than this seem to have increased average costs, although not too much emphasis should be placed on this level of concentration. Rather, it would seem more sensible to specify a range (say, up to an average concentration level of h=10), beyond which we can be relatively certain that increases in concentration led to increases in average costs. As noted earlier, we should determine how robust these results are to the exclusion of the apparently insignificant influences of for all industries and for some low-concentration industries. Column 5 of Table 20 provides estimates of when Bfjfr is assumed to be zero - it can be seen that the changes are relatively insignificant On the other hand, when is also excluded (for those industries where it is insignificant), ech decreases almost to zero with only one exception. It should be kept in mind, however, that the exclusion of by industry when its t-ratio is low is somewhat arbitrary, since if this coefficient were set to zero in all the relevant cases and the model re-estimated, the remaining coefficients would probably change, thus leading to a slightly different result which we don't take account of when such 126 Tabic 21. Estimated Returns to Concentration, Canadian Food Manufacturing Industries, 1961-1982 (Ranked by Average Concentration Level) # S.I.C. Average Concentration Level (h) Returns to Concentration (€ch)[ 7 106 2.8 -0.12 9 1072 3.5 -0.08 5 104 3.6 -0.01 2 1012 4.5 0.19 4 103 4.5 0.00 13 1089 5.0 -0.68 3 102 6.2 0.13 14 1091 8.2 -0.19 10 1081 8.9 0.10 1 1011 10.4 0.13 6 105 13.6 0.15 17 1094 15.7 0.06 8 1071 17.1 0.15 12 1083 20.3 0.15 11 1082 22.2 0.13 15 1092 25.0 0.11 16 1093 30.7 0.13 1 A l l returns to concentration (see (53)) estimates made at industry sample means. Table 6 gives industry names. 127 arbitrary exclusion is done. Hence, it is probably better to accept the estimates of e c n with these variables included, and to apply only the caveat that these will be subject to measurement error but are nevertheless interesting as they stand. Aside from establishing the overall effect of concentration on average costs, a matter of additional interest is the effect which increasing concentration has had on the relative use of various factors of production. A casual indicator of the impact of concentration on factor demands is the sign of B^ for each of the five inputs in the cost function. An inspection of Table 10 indicates that increases in concentration led to increased cost shares for capital and production labour, while cost shares for non-production labour, energy and materials decreased. These coefficients are, however, not fully informative, since in referring to shares they include both the effects of concentration on total costs and factor demands (concentration is assumed to have no effect on factor prices for econometric reasons, and so countervailing power effects and oligopsony in factor markets are ruled out). To obtain a more accurate notion of concentration 'bias', (54) is evaluated at the the mean shares for each industry - the results are presented in Table 22. For most industries, there was a tendency for increases in concentration to cause increases in the use of both capital and production labour, while use of non-production labour generally decreases. The results for energy and materials demands are less consistent, with 8/17 industries with a negative concentration-energy demand elasticity and 6/17 with a negative concentration-materials demand elasticity. Whereas the (absolute) magnitude of ecjj is rather low for most industries, factor demands are more elastic to changes in concentration. For capital, a 1 percent increase in concentration led, in general, to between a .20 and .50 percent increase in demand for that factor. The concentration-production labour elasticities are of roughly the same magnitude, while the effects on non-production labour, energy and materials are somewhat smaller. 128 Table 22. Estimated Bias of Concentration by Input, Canadian Food Manufacturing Industries, 1961-1982 biases by factor (input) # S.I.C. 6 kh € i p h € itiph € mil 1 1011 0.61 0.24 -0.22 -0.03 0.12 2 1012 0.81 0.27 -0.26 0.08 0.18 3 102 0.35 0.19 -0.15 0.05 0.12 4 103 0.18 0.08 -0.18 -0.07 -0.01 5 104 0.29 0.14 -0.17 -0.08 -0.02 6 105 0.32 0.27 -0.11 0.03 0.14 7 106 0.18 0.07 -0.42 -0.20 -0.13 8 1071 0.30 0.20 0.04 0.06 0.14 9 1072 -0.08 -0.03 -0.15 -0.12 -0.09 10 1081 0.24 0.15 -0.04 0.00 0.09 11 1082 0.27 0.24 -0.21 0.08 0.12 12 1083 0.40 0.47 -0.55 0.07 0.14 13 1089 -0.48 -0.58 -0.83 -0.76 -0.69 14 1091 -0.07 -0.11 -0.26 -0.25 -0.21 15 1092 0.19 0.19 0.00 0.07 0.10 16 1093 0.20 0.18 0.04 0.07 0.11 17 1094 0.15 0.14 -0.06 -0.04 0.04 1 Estimated at industry sample means. See (54) for derivation of this term, Table 6 for industry names. 129 One criterion often used in judging the desirability of structural change in the manufacturing sector is the effect- which such change has on unemployment. Already, __we have seen that for all of the industries studied there has been, a substitution effect between capital and non-production labour,.. while for production labour this effect has -often- been reversed. Of, additional interest here, then,-is the effect concentration increases or decreases have.had on overall employment (i.e. number of employees). On the surface, the results of Table 22 seem to indicate a general increase ..in the employment of production workers (measured in hours); while non-production worker numbers have decreased as concentration increased. To pursue- this result further, average effects on total employment are calculated, using a 2000-hour year for each production worker and evaluating the elasticities at the. average production and non-production worker employment levels for each industry. Thus, a total employment effect is calculated (for. each industry) as: AE = e. , -(Q. / 2000) + e. , •Q. ; r = 1,2 17 r Iphr ^Ipr ' Inphr Inpr where: AE .^ is the total employment effect of a 1 percent increase in the average concentration level in industry r, and all other variables are as defined previously. The results of these calculations are presented in Table 23, with overall employment results given in the last column. O f the 17 industries, the majority (12) show increases in employment due to increases in concentration, ceteris paribus; the converse is also true. The five overall decreases observed were experienced in low-concentration industries, indicating that there may be a conflict between the social benefits due to increasing concentration in these industries: lower average costs have been attained at the expense of overall employment Obviously, the optimality criterion being used will govern the way in which we judge how beneficial increases in concentration have been in the low-concentration sectors. Two caveats apply to the above analysis, though. 130 Table 23. Simulated Average Employment Effects of Increases in Concentration, Canadian Food Manufacturing Industries, 1961-1982 # S.I.C. average number employed average change in employment from a 1% increase in h Net Change 2 (AE) Production (CJ/,,) Non-Production (Qinn) AQlnp 1 1011 22591 8249 54 -18 +36 2 1012 6499 1087 18 -3 + 15 3 102 16888 3016 32 -5 +27 4 103 13797 4446 11 -8 +3 5 104 4083 15500 6 -26 -20 6 105 3330 1871 9 -2 +7 7 106 5447 3695 4 -16 -12 8 1071 4857 1868 10 1 + 11 9 1072 17494 11419 -5 -\? -22 10 1081 7154 2585 11 -1 + 10 11 1082 2137 738 5 -2 +3 12 1083 591 276 3 -2 + 1 13 1089 10566 7281 -61 -60 -121 14 1091 5851 8056 -6 -20 -26 15 1092 2932 2460 6 0 +6 16 1093 5732 4444 5 2 +7 17 1094 549 441 1 0 + 1 Note: AQ//> for industry r= (€iPh • Qip) I IOO;AQ/„„ = (€i„Ph ' Qhw) I 100, /•= 1, 2 17. See Table 6 for industry names. Net change in employment for each industry /; = (AQ//« + AQlnpr). 131 First, it should be recalled that out-of-sample-use of the elasticities obtained . may lead to faulty inferences, even if the model accurately reflects behaviour over the period studied!. The above calculations come dangerously close to violating this rule, since they are evaluated in terms of artificial- and not--actual changes. Thus, they are -probably best accepted as a very rough guide to-what- actually occurred,-.and only serve to illustrate the possible trade-offs between cost minimization and employment Second, note that the result indicated for industry 13 (miscellaneous industries), should be viewed with scepticism. Given the heterogeneity of this industry, and the inability of the model to accurately explain its behaviour, not too much faith should be placed in this very large employment change, since it is subject to a much larger error than the other figures. Finally, it is interesting, to note that these results appear to be inconsistent those of Cowling and Molho (1982) who postulated and observed a decrease in labour's share of value-added as concentration increased for cross-sectional British manufacturing data. Although they didn't investigate the issue, they also proposed that if salaries were competitively determined, the share of salaries (non-production labour) would be constant as concentration increased. On the other hand, "in a world of managerial capitalism .... we would expect to observe a positive association with concentration" (p.101). The experience in Canadian food manufacturing industries has, by the results in Table 23, been quite the opposite in the majority of cases, since increases in concentration have generally resulted in decreases in the employment of salaried workers and thereby, presumably, this group's share of value-added. Nevertheless, from the standpoint of income distribution, it would seem that the whole subject of employment and concentration would warrant further study and analysis. 132 7.2.8 ESTIMATED RETURNS TO SCALE It is difficult, as suggested in Chapter 5, to determine how concentration and returns to scale might be related. Even so, scale effects are worth looking into, if only to better characterize the industries being studied. Expression (55) was evaluated at sample means for all components' and for each industry (with (0 • t) deleted, of course). The results are given in Table 24. Evidently... there is no clear relationship between returns to scale and levels of concentration: As Table 24 shows, 6/8 high-concentration industries and 8/9 low-concentration industries had increasing or approximately constant returns to scale, while 2/8 and 1/9 respectively had decreasing returns to scale. This is consistent with Denny Fuss and Waverman's (1979) two-digit analysis which indicated increasing returns to scale; a result which proved to be insignificantly different from zero, however (see p. 30). Significance tests were not constructed for these results. The outcomes obtained here, then, support the view that the industries being studied are not competitive, since in most cases, industry output is less than the average cost-minimizing point Probably this is also true of most firms in these industries, since if most are experiencing increasing returns to scale, it is likely that the industry curve will reflect this behaviour as well. More detail on this issue is provided in section 7.8,10. 7.2.9 ESTIMATED TECHNICAL CHANGE AND BIAS There was very little, if any, significant technological change leading to overall cost reductions in the Canadian food manufacturing industries over the period 1961-1982. In particular, we cannot reject the hypothesis that no neutral technical change occurred in any industry, evident by the low t-ratio for at (see Table 10). 133 Table 24. Estimated Dual Returns to Scale, Canadian Food Manufacturing Industries, 1961-1982 # S.I.C.1 Estimated Dual Returns to Scale2 (£«,-!) average concentration level 3 1 Kill 0.064 h 2 1012 -0.139 1 3 102 -0.083 I 4 103 -0.188 1 5 104 0.008 1 6 105 -0.034 h 7 106 -0.005 1 8 1071 0.094 h 9 1072 -0.128 1 10 1081 -0.282 1 11 1082 -0.196 h 12 1083 -0.002 h 13 1089 -0.289 1 14 1091 0.271 1 15 1092 -0.133 h 16 1093 -0.152 h 17 1094 -0.172 h For industry names, see Table 6 2 Estimated at industry sample means. Note that 6cq is defined by (24)—the term estimated here is (25). Recall: if (£«/-!) is <0 then increasing returns to scale existed (on average). 3 Only rankings (high (h) vs. low (1)) are given here, using the criterion described in fn. 2, Table 20. 134 The dual rate of total1 cost diminution (56) was evaluated for each industry, with results - ranging from between -.0010 to -.0013, showing an almost insignificant., amount of reduction in costs attributable to overall technical change. Obviously, with-numbers this small, it would be'difficult to detect a pattern with regards to :-concentration levels,- and since-the results were so-similar for,, all .industries, there didn't seem much point in tabling them. Moreover, when a{ was set to zero, ec t became positive, now ranging between 0.0001 and 0.0004, but again probably insignificantly different from zero. This result confirms that of Denny Fuss and Waverman (1979, p. 90), who found that for their Canadian food manufacturing sample, only a very minor amount of technical change occurred (ect =0.002), indicating-a deterioration in costs over time. Their result was insignificantly different from zero, however, as was their coefficient for neutral technical change. The conclusion reached' here that no significant change in productivity occurred over the period is nevertheless in conflict with Johannsen (1981) who,, as noted in Chapter 5 (Section 5:3), found that TFP increased in general for most industries, but that the growth rates differed between time periods. Similarly,. Lopez (1984b) noted that "productivity growth has been steady throughout the period and ... has led to an almost 0.5% average annual decline of the unit cost of production ... " (p. 229). How he arrived at this figure is not clear, since the cost function was not estimated, but both his and Johannsen's results indicate that there may be some difference in opinion to whether cost-reducing technical change has occurred in Canadian food manufacturing. Given a lack of evidence of the significance of Johannsen's results and the unclear source of Lopez's figures, it is probably safe to conclude that technical change has been a negligible factor in cost reductions. The insignificant amount of cost-reducing technical change observed here is not too surprising - very good reasons could be found to explain it In particular, Carter (1985) found that although the food, beverage and tobacco industry accounted for 15 135 • percent of total Canadian manufacturing sales in 1982, it only accounted for about 3 -percent of the total R & D . expenditures for manufacturing. An. extension of his 'figures back to 1976 shows that this' industry's share of total-manufacturing current R -& D expenditures has been cohsistendy falling, from a high, of 4.4 percent in that •year. And when it is taken into-account that tobacco-manufacturing is-excluded from this study, the relative proportions of R & D for food (and beverage) manufacturing alone is likely even lower. Whereas no overall reduction in costs occurred due to the adoption of improved technology, there was a significant bias towards or away from various inputs over the period. Table 25 summarizes the degree and direction of technological bias which occurred-in the 17 industries considered here, and provides a comparison with the outcomes of two previous studies. . For this sample, technological bias was capital-saving (but insignificantly so) and labour-saving in both cases. There was an energy-using and materials-using bias. These results are consistent with those of Denny, Fuss and Waverman (1979) and Lopez (1984b). Both studies obtained capital-using bias (in the DFW case this was insignificantly different from zero - the result here) and labour-saving bias, which is observed in this sample for both types of labour. Although they both found an energy-saving bias, Denny, Fuss and Waverman observed materials-using bias,, as in this study, and Lopez found no evidence of bias towards or from materials use. 7.2.10 TESTING FOR OPTIMAL OUTPUT LEVELS The final summary measure to be discussed is the level of industry output in relation to the optimal level (i.e. that where average total costs are minimized); expressions (57) and (58) were evaluated at the sample means and these results are presented in Table 26. Although these represent only the average relative levels, they do provide a useful means of determining how 'competitive' the industries were (and. 136 Table 25. Estimated Bias of Technical Change, Canadian Food Manufacturing Industries, 1961-1982 sign comparison with previous studies2 Input Estimated Bias1 DFW (1979) Lopez (1984b) capital -0.0002 + + (-0.9) (insignificant) production labour -0.0009 ^ (-3.9) 1 I _ non-production labour -0.0005 J J (-2.7) J energy 0.0001 — — (2.2) materials 0.0014 + 0 (4.8) 1 Note that the relevant values for /j,-, were taken from Tables 11-14, since bias as defined by (37) means that we can measure it just by the coefficient on I in each share equation. The capital bias coefficient is taken from Table 10. The /-ratio values are given in parentheses below each estimate above. 2 Only a sign comparison is made here since both those studies considered food manufacturing at the 2-digit instead of the 4-digit level. Nevertheless, given our assumptions on second-order terms, the biases estimated here are, in theory, the same for all industries. DFW (1979) refers to Denny, Fuss and Waverman (1979, Table 1, pp. 93-95). Lopez's results are given in his Table 1, p. 224. 137 Table 26. Estimated Optimal and Actual Output, Canadian Food Manufacturing Industries, 1961-1982 Optimal Output 1 Average Output 2 Average Estimated Actual Modal Average % Deviation # S.I.C. (0*) (0) Condition 3 from Q* (Rqry 1 1011 0.85 1.02 Q > Q* (22/22) Q < Q* (13/22) Q < Q* (15/22) Q < Q* (22/22) 19.4 2 1012 1.56 1.01 -18.6 3 102 1.33 1.06 -15.3 4 103 1.65 0.99 -40.3 5 104 l . l l 0.99 Q > Q* (13/22) 20.4 6 105 1.17 1.06 Q < Q* (18/22) -8.2 7 106 0.95 0.97 Q > Q* (14/22) 1.7 8 1071 0.81 1.07 Q > Q* (16/22) Q < Q* (22/22) 33.5 9 1072 1.37 0.95 -29.3 10 1081 2.08 0.96 Q < Q* (22/22) -54.0 11 1082 1.68 0.98 Q < Q* (22/22) -41.7 12 1083 1.08 1.17 Q < Q* (14/22) 4.1 13 1089 2.27 1.04 Q < Q* (22/22) Q > Q* (22/22) Q < Q* (22/22) Q < Q* (21/22) Q < Q* (15/22) -51.7 14 1091 0.43 0.93 132.9 15 1092 1.33 0.97 -29.0 16 1093 1.11 1.04 -20.7 17 1094 2.46 0.89 11.4 The average value for each industry was calculated using industry mean values for the arguments of (57).— see Table 6 for industry names. Also note that since = 0.361 > 0 —see Table 10), Q* is the output level which minimizes average cost (i.e. the second-order condition is fulfilled). 2 The variable is scaled such that 1971 = 1.00. 3 The ratio in parentheses gives the proportion of observations for which the modal condition held. Thus, Q < Q* (13/22) means that Q was <= Q* for 13 of the 22 years studied. 4 Sec (58) for a description of this term. 138 probably, are). As can be seen, most industries produced at outputs significantly lower 'or higher than Q*, on average. There does not seem to be any pattern between the size or sign of the average divergence with regards to" concentration levels, but a comparison of these results with those of Table 24 shows that those industries-with •increasing returns' to scale usually-produced at a point-lower than- Q* and vice versa. It is not clear whether the the suboptimal or superoptimal production behaviour was p^lanned or not, but the modal-condition does, indicate that some industries (about half) were absolutely consistent in producing above or below Q*. Interestingly, only four industries produced above Q* at outputs which exceeded this optimal level by 19 percent or greater, indicating "a preference in behaviour towards optimal or suboptimal production. Furthermore, • only two of these industries produced at output levels which were consistently greater than Q*. Overall, this result supports the original assumption of non-competitive behaviour for these industries (as established in Chapter 3), and confirms the observations made with regards to the returns to scale results presented earlier. Chapter 8 CONCLUSIONS, CAVEATS, AND RECOMMMENDATIONS 1, -:' " The premise.Tfpm which this study evolved was. that changes in industrial concentration have had an effect on costs of' production, in the Canadian food i manufacturing industries. In part, the investigation was... an-.attempt to extend, the analysis of Gisser (1982), but in fact, it has both accomplished that objective and • provided a-useful-methodology and ,evidence which may assist in resolving a long-standing controversy in the industrial organization literature: namely whether the • generally accepted positive relationship between concentration and profits is due to efficiency or non-competitive output pricing. By focussing on the efficiency claim, it has been possible to generate some rather interesting results from this perspective, which suggest that changes in concentration have indeed affected costs within the industries studied. The approach taken was to compare changes in concentration and costs between industries using a dual cost function with a concentration variable integrated in its structure. The justification for this approach was first established on general grounds in Chapter 3. In particular, it was argued that since there is good reason to believe that market share will affect firm-level average costs, and since the distribution of market shares within an industry and industrial concentration for that industry are intimately related, it follows that concentration levels and changes in these should affect industry average costs. The absence of an adequate model within the established concentration-efficiency literature, and'•the useful properties of dual cost functions, was established an integration of concentration and duality'in Chapter 4. Since there was no strong prior notion of how concentration might affect costs, a number of relevant summary statistics were derived in Chapter 4, which it was believed would assist in explaining the nature of the relationship (if there were, indeed, any at all). The Translog (TL) cost function was the flexible form chosen, and 139 140 a number' of possible hypothesis, tests established in Chapter 5. A possibility allowed for was that concentration might not affect costs at all. or that it may affect both average costs and input levels chosen. Technical, change-and bias were similarly allowed for. • '-•;-•.-. - • , , • • • T h e - sample used included 17 4-digit-Canadian food manufacturing industries, and covered-the period 1961-1982. A 'pooling' . technique proposed by Fuss (1977) " was used, which allowed for. some -differences in production., technologies between these industries, and some similarities (i.e. the second-order TL parameters were assumed to be the same for all industries). Zellner's method of seemingly unrelated regressions was employed to estimate the parameters of the model. The ' final model chosen indicated non-homothetic production technologies. for the industries studied and established that changes in concentration did indeed affect average costs of production. Specifically, it was found that decreases in concentration , led, in general, to a decrease in average costs within low-concentration industries (i.e. . those with Herfidahl indices <10, on average). On the other hand, increasing concentration resulted in increases in average costs for high-concentration industries (i.e. those with Herfindahl indices £10, on average). Although, as noted, it was not known, a priori, how this relationship might . come about, a number of possible causes were investigated which helped at least in characterizing the industries and suggested some possible sources of the effects. Most directly, it was found that concentration changes had a strong effect on the choice of inputs employed on production. For most industries, the elasticity of capital demand with respect to concentration was positive and employment of production workers was similarly affected. The results for energy and materials were more mixed, with positive and negative elasticities in roughly equal proportions for both across industries, while, interestingly, for salaried employees, it was found that increases in concentration generally led to decreases in employment for this group. 141 The overall employment effects of increases in concentration for each of the 17 , industries" were also calculated, and the results, revealed an interesting tradeoff between the impacts of concentration on e^fficiency and -employment Although: increases in employment occurred in the- majority of cases, the negative effects which were --generated were 'only in the-low-concentration industries. Thus, while increases, in concentration led. to efficiency gains . for this group, this was achieved at the cost of -"lower employment Similarly, while,.;for high-concentration..industries,, increases in concentration were bad in an efficiency sense, they did increase employment It follows that the apparent social. benefits of concentration increases in the former group and costs in the latter must be weighed against the (opposite) employment effects. Depending on the welfare • criterion-being used, the overall benefits/costs could be good or bad; concentration changes do not lead to unequivocal outcomes in this regard. : There was less, evidence of structural differences between the two,groups of industries, however. Almost all of the industries (14/17) had increasing or constant returns to scale (in costs), on average, with no apparent relationship between these effects and levels of concentration. The optimal level of output was, on average, higher than the actual output of most industries, indicating that the original conjecture of ... non-competitive behaviour in output markets within these industries is probably correct Overall productivity changed very little in all industries due to the adoption of new technology over the period considered, but there was a slight bias of technical change towards energy and materials use, and away from capital and both production and salaried labour employment Factor demand and substitution elasticities were also calculated; of these, probably the most interesting was a consistent substitution effect between capital and salaried labour, with capital-production labour complementarity in the majority of industries. Both the technical change and elasticity results were similar in many regards to those of previous studies at the 2-digit level of aggregation for Canadian food manufacturing. 142 • A number- of caveats are worth mentioning, since the observations made above should- be qualified. First, it should be kept in mind that the results are conditional on a-number of econometric and data flaws. With regards to data, the capital series employed in • estimation was imputed from 1975-1981 and so, the accuracy of these data are unknown;'-In -addition, the energy costs were very low in relation, to• other inputs for most industries, and so energy's cost share was usually so small that it probably created econometric difficulties. There ..were a number of positive elasticities of demand generated for both these inputs and it is believed that the data characteristics of each may have caused these problems. . Concavity was often violated; in fact the majority of observations generated positive eigenvalues. It is- hard to determine what effect these violations had on the results, but it certainly would have been more encouraging had the violations not occurred at all. Other violations encountered were: a minor amount of autocorrelation in the cost function and strong autocorrelation in the share equations; non-normality of the residuals; and non-randomness of the residuals" (both of the latter violations were probably caused by the presence of some major outliers in the sample). No corrections were made for any of these problems,- but it is believed that the concavity violations did not cause biased parameter estimates; certainly the econometric violations (autocorrelation, non-randomness and non-normality) did not cause biases. Therefore, we can be confident that the estimates are accurate and the inferences correct Only the outcomes of the hypothesis test procedures must be qualified by the fact that the variance estimates may have been biased. Aside from these difficulties, it is still possible, as noted, to use the results of this study with confidence. Nevertheless, care should be taken in using the results to make out-of-sample forecasts, since the model is not meant to do this type of analysis. The results illustrate how concentration changes have affected costs in Canadian food manufacturing, not how concentration will affect costs in the future. 143 Thus,- as. a policy ..tool, the model is limited - this • does not mean, however, that the . behaviour it has identified will not continue to occur in the future, nor that it might net help in7 directing policy analysts' in assessing future -changes by suggesting where. they . might direct their interest -A final caveat to note is that the ..results outlined here (and discussed .in more detail in Chapter 7) have been assessed using average levels of costs, concentration, input prices and output,-.in general, in order, to-conserve space and keep computational costs to a reasonable level. Thus; the analysis could be extended greatly, and much additional interesting information produced, if one were to evaluate the summary statistics at each sample point instead of at the sample means, as has been done here. In this way, the patterns of change could be understood much better, for any particular topic, if that additional information were desired. . Aside from the difficulties noted above, the model and results do suggest that the avenue of analysis chosen in this study is a useful way of approaching the problem and, in many regards, a significant improvement on previous attempts to determine how changes in concentration and costs are related at the industry level. The focus chosen does, however, limit our understanding to costs and exposes the possible tradeoff between concentration, efficiency and employment Thus, an obviously useful extension would be to study the effects of concentration changes on prices for these industries, in this way allowing us not only to assess the efficiency effects, but also the welfare implications of increased or decreased output prices. Some work has been done in this regard already; along with his cost analysis Peltzman (1977) also looked at concentration-price effects, while Appelbaum (1982) and Slade (1982) have developed dual models which simultaneously measure cost and output price behaviour. Appelbaum's paper is more directly concerned with the impact of concentration on prices and so is more relevant to the concerns of this study. In fact Lopez (1984b) applied Appelbaum's model to Canadian food manufacturing at the 2-digit level, and 144 rejected the hypothesis. of prices taking (competitive behaviour) in output markets. Although his results cannot be used to directly supplement • those obtained here (due to conflicts between samples), his application does suggest that - it would be worthwhile to pursue this issue at the 4-digit level (which would be possible with the 'rich' database available). In this way, a more'complete welfare analysis could be obtained, since we would be able to calculate the effects of concentration on producer's surplus, consumer's surplus (i.e. the 'transfers' involved), and the costs (deadweight loss) of divergences from the competitive solution. These relative transfers could be weighed against any employment gains/losses due to concentration changes, and tell us alot • more not only about how concentration affects profits and efficiency, but who gains and who loses. Thus, the framework" developed in this study could be fruitfully extended much further. Other possibilities for extensions exist For example, although the research strategy chosen for this study closely' followed (inadvertently) the five criteria prescribed by McAleer, Pagan and Volker (1985, p. 299) to remove the 'con' from econometrics, one approach which would increase our confidence in the results obtained would be to adapt their fourth criterion, and instead of applying the model used here to new data, try an alternative flexible functional form in place of the TL, and see whether the results obtained from this alternative are consistent with those obtained in this study. Thus, the data uncertainty would be held constant but the adequacy of the TL and the robustness of the inferences presented here would be tested. To conclude, having discussed both caveats and possible constructive extensions, it should be said that from the results obtained here, it is not possible to establish whether high versus low concentration has been good or bad in the Canadian food manufacturing industries. Rather, we have been able to see how the effects of changes in concentration have differed between high and low-concentration industries. Whether the results can be generalized beyond food manufacturing is really an empirical issue; 145 inferences of this nature should be made with caution.. And if a policy • prescription is possible from the evidence observed here, it is probably that increases in - concentration in high-concentration "industries in this sector should be: viewed with concern, and . perhaps discouraged',- while increases in low-concentration industries should be much less worrisome. This conclusion, - of' course,. depends upon the criterion being used to, judge changes (cost-minimization is the assumed policy objective above). If the policy objective is increased employment; for .^example, the, policy prescription might be quite different FOOTNOTES. 1. There is considerable disagreement in the literature as to the appropriate methods of measuring TFP, output and the inputs themselves (see, for example, Yotopoulos and Nugent (1976, p. 156)). No doubt Gisser's results would be significantly different even if the same model were used with respecified variables. This option was beyond the scope of the deliberately cursory analysis employed here. 2. Both of these models.will be described in more detail later. 3. Green (1980) also notes the possibility that high performance (efficiency, profitability) may lead to higher concentration, "thereby reversing the lines of causation" (p. 139). Nevertheless, he also sidesteps the matter, commenting that "we do not intend to resolve these issues here" (ibid). Waterson (1984) provides more insight, however, and discusses the results from some simultaneous models (see pp. 207-209). 4. Note that a distinction between C here and c in (1), (2) and (3) is done through the use of upper- and lowercase, respectively. The dot over C, M, and L are the derivatives of these variables with respect to time. 5. This argument assumes 6 =0 for simplicity. Of course, if m is >1 (5 >0), then this effect could be reversed. If m is <1, however, this argument is strengthened. 6. This assumption results from the observation that market growth is more advantageous to small, rather than large firms. If based purely on simple correlation coefficients this holds for both Petzman's and Gisser's data (i.e. the relationship between changes in concentration and market growth is a negative one). 146 147 •7. Peltzman- assumes, that ...-the industries .can be represented by a linearly homogeneous Cobb-Douglas technology. Both assumptions are unlikely to be satisfied in reality. 8. Note that as previously mentioned, with a minor adjustment to (20), the change in TFP can just'as validly 'be used- as the dependent variable. Recall that if C - I /3.W. y=1 •/ J is >0, where the B. are. the (constant) factor shares, this means that costs have increased (assuming costs are always defined as being >0) over the period, over and above the change due to changes in input prices. This or course,, indicates a decrease in TFP. Similarly, if C - I 0.W. is <0, this indicates an increase in TFP. Since cost changes and TFP changes are inversely related, one would set the dependent variable to be the negative of the change in TFP. If TFP is defined as A, it is clear then how Lustgarten derives (21). 9. Gisser does give a plausible explanation for these different effects, but once again, his model lacks enough structure to support his views. Rather than basing his model on a theory and testing for it, he appears to do the opposite. 10. Like most topics in the field of industrial organization, that of limit pricing, or pricing decisions made by leading firms to prevent entry or expansion by fringe/secondary firms, is a well-documented one. It falls under the general heading of barriers to entry; Waterson (1984, pp. 58-60) provides a useful introduction to the oi theory a limit prices. Also, recall that allusions to this issue have already been made with reference to Carter's (1978) study, in Chapter 2, (Section 2.2.1). 148 11. The problems involved in aggregating from the firm to industry level are legion, and the relationship between 'industry' and 'firm' behaviour is usually conveniently ignored as it: is -here. Diewert (1982,. p. 5.78)_ provides, a brief outline of two aggregation techniques; both necessarily assume that all firms have the same technology. The-most familiar practical model-which, explicily allows for consistent cross-firm, aggregation . is the Gorman. polar form (see Gorman (1968, pp. 145-146); Appelbaum (1982, p. -294)) which ,is, not surprisingly; .highly restrictive. 12. As we will see, it is easier to use a total cost function and adapt it to represent average costs than to define an explicit average cost function. 13. This proposition is commonly referred to as the Samuelson-Shephard duality theorem. For a proof, see Silberberg (1978, pp. 304-306). 14. For a proof, again consult Silberberg (pp. 307-308). 15. As Gupta and Fuss (1979) demonstrate, homotheticity can allow for any shape of average cost function: U-shaped L-shaped or in the homogeneity case, linear. 16. There is a tendency in the applied duality literature to specify and estimate o.. (often called the 'own elasticity of substitution' : see, for example, Berndt and Wood (1975) or Binswanger (1974a)). The term appears to have no useful interpretation, and is never referred to in either Uzawa (1962) or Sato and Koizumi (1973), arguably two classic references on this subject. 17. It is generally believed that the higher a., is, the less flexible the technology is. 149 Yotopoloiis and Nugent (1976) have stated that o.. "secularly declines as modern technology replaces traditional technology" (p. 151), with reference to agriculture. Similarly, Russell and • Wilkinson (1979) suggest that a low o^ . is preferable, since the less convex the isoquant is (the lower is a.j), "one input can be substituted for -another without a rapid increase required in one input to hold the output level constant when the amount of the other input is diminished" (p. 144). Consequently, the lower a .j is, 'the fewer, costly disruptions are necessary in the changeover, to a different set of input levels. Where we are dealing with similarly advanced technologies, however, we would expect consistent differences in substitution possibilities to be hard to identify; spurious conclusions are highly probable. 18. Other interpretations of technical neutrality/bias exist: two examples are Harrod-neutral and Solow-neutral technical change. Since the Hicksian definition is most commonly referred to in the literature, only this form is considered here. 19. See Yotopoulos and Nugent (1976, p. 137). 20. In the case of the translog functional form, factor shares are used. For other forms, optimal factor demands or input/output ratios are used. t 21. Berndt and Khaled (1979) have used a non-homothetic function to estimate technical biases. Their analysis of bias, however, differs from (45) in that it is integrated with a more general term, which they call the 'dual rate of total factor cost diminution' (ibid., pp. 1224-1225). Moreover, Diewert and Wales (1985) allow for technical bias in their non-homothetic forms (see p. 32). Greene (1983) also uses a non-homothetic form to measure non-neutral technical change. So homotheticity doesn't 150 seem to be. necessary. 22. Although this expression is defined for factor demands, it is equally valid if X^ . is the factor share or input/output ratio. 23. A common alternative to this is to assume that a subset of inputs is completely fixed in the short-run, which could be equally unrealistic. 24. The results of this study, which along with the conventional but concavity-constrained TL and GL presented two new cost functions (the Symmetric Generalized McFadden (SGM) and the Symmetric Generalized Barnett (SGB)), will not be reviewed here. This is because the globally constrained TL and GL versions, the SGM and the SGB all require nonlinear estimation techniques which are more difficult to apply than conventional systems estimation. They also require specialized programs which are not readily available nor maintained. 25. With the GL, it is not possible to impose homotheticity without also imposing linear homogeneity (Woodland 1976, p. 26). 26. For example, two marginally relevant papers will be left out of this study, namely Kotwitz (1968) and Tsurumi (1970). These studies yielded elasticities of substitution between capital and labour which ranged between 0.48 and 1.0; a not too useful result for our purposes given the level of aggregation used by them. 27. Gupta and Fuss define MES as "that plant size at which average cost is one percent higher than the estimated average cost at LES [Largest Efficient Scale]" (pp. 151 9-ll).* LES, is. the output at which average costs are minimized for a U-shaped AC curve; if the AC 'curve' is L-shaped or linearly declining;, LES is taken to -equal the average!plant size (output) in the largest size^ group (ibid.-, p. 9). ~28. A strong positive relationship between'concentration and MEPS seems to exist (compare results in Table 2 with mean concentration levels in Table 7, Chapter 6). However, MEPS for 1960 S.I.C.'s 124 and-125 in Table 2 cannot -really be related to concentration in 1970 S.I.C. 105 which combines, (illogically) these two industries. Similarly, Gupta and Fuss do not consider industries 10-12 (S.LC.'s 1081-1083) nor the nebulous industry 13 (S.I.C. 1089). Nevertheless, the results are interesting and lend credence to the arguments of Chapter 3, since as MEPS increases, so typically does concentration. 29. The whole issue of exactness is a complex one and cannot be done justice here; Lau (1974) is a useful reference in this regard. If the translog function is assumed to approximate the true cost function in the economic analysis, "then the error terms appended to each equation must account for errors in approximation as well as random errors in profit-maximizing [cost-minimizing] behaviour" (Gordon 1984, p. 112). Hence, unless exactness is assumed, the expected error will be non-zero and the econometric complications arising from this are severe. Nevertheless, Fuss (1977) seems to get around the problem and maintains the assumption of approximation, but his techniques are not obvious to me. The econometric problem encountered if the approximation notion is maintained is that given that the TL is only a second-order Taylor's-series approximation, a 'remainder' exists. So, if this 'remainder' is to be acknowledged (as it should be), the expected remainder error will be non-zero, thus violating the necessary econometric assumption that E(e) = 0. 152 * Neglect of me. 'remainder' term,'however, does not remove the problem.. This • "implied" exactness assumption (i.e. that a-second-order approximation is exact) has been, criticized by White (1980),. who' suggests that this leads to biased estimates. Byron and Bera (1983) show that White's conclusions may be a bit extreme, noting that higher-order Taylor's-series expansions - can reduce the biases, to a manageable level. Nevertheless, the practical difficulties of estimating multivariate higher-order approximations (i.e. multicollinearity and data scarcity) leave such .solutions in the realm of theoretical musings, and so, such arguments don't really extricate us. The conclusion to make from all this is that White's criticisms should not be avoided; either we deal with the econometric problem of including approximation errors,' or else other forms need to be considered (such as,, for example, those based instead on Fourier approximations - see Gallant (1984)). Thus, although the exactness assumption is expedient in this case, the use of it doesn't imply' acceptability; the objections noted above suggest a need for more practical research of this topic. 30. In order to conserve parameters, symmetry is imposed here and will be imposed in estimation. It should also be noted that although these homogeneity restrictions are not intuitively obvious, their correctness can be established if it is recalled that /n(Xw) = ln\ + In w. From this rule, derivation of these restrictions is a tedious, but simple task. 31. Since the translog is in logarithms, differentiation with respect to Inw. yields the factor shares instead of factor demands. This leads to an econometric complication (which will be noted later) since, of course, the shares must sum to 1. 32. Notice that t is not logged. This distinction is typically made in the duality literature (see for example, Diewert and Wales (1985, p. 5)). 153 33. Only'duality applications for Canadian food manufacturing are being referred to here. All previous studies have been at the twor digit level of aggregation; Denjy, Fuss and Waverman (1979,-.1981) allow regional differences, however, as does-Fuss (1975)? . 34. Fuss's choice of the covariance method over error-components also probably arose because at the time no, useful theory or algorithm had been developed to allow estimation of SUR's (see definition later in-this section ) with. error-components. Since then, a small body of literature on the subject has developed, most notably the seminal article by Avery. (1977) and a more recent paper by Prucha (1985). However, the method developed by Avery, aside from employing the stochastic assumption, imposes some rather strong additional assumptions and is only useful with very large samples (pers. comm., Robert Avery, December 11, 1985). 35. w^  is capital price, w^ is production labour price, w ^ is non-production labour price, wg is energy price and is materials price. 36. Ideally, the parameters, when estimated, would satisfy these restrictions without their imposition. However, since such results seldom occur in practice, these restrictions are imposed to maintain consistency with the theory. 37. This useful feature of the econometric model being employed here was pointed out by Robert Avery (pers. comm., December 11, 1985). 38. Denny, Fuss and Waverman (1979) exploit this cost-saving in a rather unique way, noting that the "parameters of the cost function which do not appear in the share equations were estimated conditional on the estimated share equations parameters in 154 order to reduce computational 'costs" (p. 71). Presumably they subtract the variation accounted for by the share equations from total. costs and then estimate the remaining parameters by regressing the residual on the variables not entered in the share ~ • equations using OLS. Their technique is not adopted - here, however. 39. Concavity can be imposed, as Diewert and Wales (1985) show. But the cost of doing this is prohibitive for this study. Besides, the TL loses its flexibility when their procedure is followed (pp. 11-12). . 40. Predicted shares are used in order to remove the stochastic element from evaluation of these terms. Actual shares should not be used since we can only explain that proportion of their change accounted for by the model; inclusion of the remaining stochastic element would tend to yield false results. 41. Landry, RJ. (pers. comm.): correspondence between Ms. Pamela Cooper (Food Markets Analysis Division, Agriculture Canada) and Mr. RJ. Landry (Chief of National Wealth and Capital Stock Division), August 30, 1985. 42. Peprah (1984) found that the use of depreciation rates used by corporations (in manufacturing) in their financial statements created a bias which decreased "the reported rate of return by approximately 6.92 [nominal] percentage points on average ..." (p. 58) for 1965-1981. 43. Note that since the TL form is being used, the actual 'quantity' of capital services, x^  , is not required. If it were, an index of this could be obtained by dividing the total cost of capital services by the price of capital, w, . 155 44. Diewert (1979) has shown that the Fisher ideal price index is superlative (i.e. "it is exact for a unit cost function c which can provide a second-order differential approximation to an arbitrary twice, continuously differentiable unit cost function" .(p. 44% Thus, it is consistent with the flexible TL cost function. Since this index was provided as part of .the data-series obtained from Agriculture Canada there was no good reason for re-estimating it or trying other indices (eg. the Divisia) given the focus of this study. . . . 45. The package used was SHAZAM (version 5.0). The DN option was used in all cases with the SYSTEMS command. This option exploits asymptotic properties in estimating the covariance matrix (see Theil 1971, pp. 321-322). 46. The existence of violations of concavity when technological bias is allowed for has been Observed elsewhere. Moroney and Trapani (1981) found that their TL model, when only neutral technical change was included, usually satisfied concavity, while their biased model violated concavity at almost all sample points. Such a relationship was not checked for in this study. 47. There are methods by which confidence intervals can be derived for the elasticities (see, for example, Moroney arid Trapani (1981 fn.5, p. 69)), but these were not computed for this study. 48. Positive signs for some elasticities were also observed when the share system was estimated separately for each industry in some preliminary analysis not discussed here, industry. Thus, the problem is more related to the TL function or the data than to the pooling technique used, since theory predicts that the elasticities generated from the 156 share equations are usually very • close to those obtained with a full system. This, in fact, was the experience with this model; the elasticities generated from the share system were' almost identical' to those obtained, from the full system.., 1 . 49. This is. probably the case for this sample, since Denny^Fuss and Waverman (1979, p. 77) found that, for Canadian food manufacturing over a similar period, only 21 percent of the adjustment of capital to its 'optimal-level' took .place in one year. 50. Although the elasticities are generated by partial differentiation, when own factor prices rise, ceteris paribus,. relative factor prices will also change and so substitution will occur. Thus, although we hold all other prices constant, the elasticity also implicitly accounts for the amount of substitution that occurs at the same time. BIBLIOGRAPHY Allen, R.F.," "Efficiency, Market Power, and Profitability in American Manufacturing", Southern Economic Journal , 29 (1983),-933- 940. 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Hall, V.B., "Industrial Sector Fuel Price Elasticities Following the First and Second Major Oil Price Shocks,", Economics Letters , 20 (1986), 79-82. Harvey, A.C., The Econometric Analysis of Time Series , Oxford: Philip Allan, 1981. Hazledine, T. and S. Cahill, "Welfare Implications of Oligopoly in U.S. Food Manufacturing: Comment", American Journal of Agricultural Economics , 68 (1986), 165-167. Horn, R.A. and CR. Johnson, Matrix Analysis , Cambridge: Cambridge University Press, 1985. Jenkins, G.P. "Capital in Canada: Its Social and Private Performance 1965-1974", Discussion Paper 98, Economic Council of Canada, 1977. Jorgenson, D.W. and Z. Griliches, "The Explanation of Productivity Change", Review of Economic Studies , 34 (1967), 249-283. 160 Judge, G.G., W.E. Griffiths, et al., The Theory and Practice of Econometrics (2nd Edition), New York: John Wiley, 1985. Kmenta, J. and R.G. 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Lopez, R., "Measuring Oligopoly Power and Production Responses of the Canadian Food Processing Industry", Journal of Agricultural Economics , 35 (1984b), 219-230. Lustgarten, S., "Gains and Losses from Concentration: A Comment", Journal of Law and Economics , 22 (1979), 183-190. ttjke McAleer, M., A.R. Pagan and P. Volker, "What Will*the Con Out of Econometrics?", American Economic Review , 75 (1985), 293-307. Maddala, G.S., Econometrics , New York: McGraw-Hill, 1977. Martin, S. and D. Ravenscraft, "Aggregation and Studies of Industrial Profitability", Economics Letters , 10 (1982), 161-165. Moroney, J. and J.M. Trapani, "Alternative Models of Substitution and Technical Change in Natural Respurce Intensive Industries", in Berndt, ER. and B.C. Field (eds.), Modelling and Measuring Natural Resource Substitution , Cambridge: MIT Press, 1981. Nerlove, M., "On Lags in Economic Behaviour",. Econometrica , 40 (1972), pp.221-251. Norsworthy, J.R. and MJ. Harper, "Dynamic Models of Energy Substitution in U.S. Manufacturing", in Berndt, ER. and B.C. Field (eds.), Modelling and Measuring Natural Resource Substitution , Cambridge: MIT Press, 1981. Peltzman, S., "The Gains and Losses from Industrial Concentration", Journal of Law and Economics , 20 (1977), 229-263. Peprah, I., "Capital in Canada: Its Social and Private Performance 1965-1982", unpublished report, Tax Policy and Legislation Branch, Canada Department of Finance, November, 1984. 161 Porter, M.,. "The Structure within Industries and Companies'' Performance", Review of Economics and Statistics , 61 (1979), 214-227. Prucha^  I.R., "Maximum Likelihood and Instrumental Variable Estimation in Simultaneous Equation Systems with Error Components", International Economic Review , 26 (1985), 491-506. Round, D.K., "Industry Structure, Market Rivalry and Public Policy: Some Australian Evidence", Journal of Law. and Economics , 18 (1975), 273-281. Russell, R.R. and M. Wilkinson, Microeconomics: A Synthesis of Modern and Neoclassical Theory , New York: John Wiley, 1979. Sato, R. and T." Koizumi, "On the Elasticities of Substitution •and Complementarity", Oxford Economic Papers , 25 (1973), 44-56. Scherer, F.M. Industrial Market Structure and Economic Performance , Chicago, Rand McNally, 1980. Silberberg, E., The Structure of Economics: A Mathematical Analysis , New York: McGraw-Hill, 1978. Slade, M.E., "Empirical Tests of Economic Rent in the U.S. Copper Industry", in Moroney, J.R, (ed.), Advances in the Economics of Energy and Resources , Greenwich: Jai Press, 1982. Smiley, R., "Learning and the Concentration - Profitability Relationship", Quarterly Review of Economics and Business , 22 (1982), 27-40. Solow, R.M., "Technical Change and the Aggregate Production Function", Review of Economics and Statistics , 39 (1957), 212-230. Theil, H., Principles of Econometrics , New York: John Wiley, 1971. Tsurumi, H., "Nonlinear Two-stage Least Squares Estimation of CES Production Functions ...", Review of Economics and Statistics , 52 (1970), 200-207. Uzawa, H., "Production Functions with Constant Elasticity of Substitution", Review of Economic Studies , 29 (1962), 291-299. Varian, H., Microeconomic Analysis , New York: Norton, 1978. Wales, T.J., "On the Flexibility of Flexible Functional Forms", Journal of Econometrics, 5 (1977), 183-193. Waterson, M., Economic Theory of the Industry , Cambridge: Cambridge University Press, 1984. White, H., "Using Least Squares to Approximate Unknown Regression Functions", International Economic Review , 21 (1980), 149-170. Woodland, A.D., "Modelling the Production Sector of an Economy: A Selective Survey and Analysis", Disc. Paper 76-71, Dept. of Economics, U.B.C., 1976. Yotopoulos, P.A. and J.B. Nugent, Economics of Development: Empirical Investigations , 162 New York: Harper and Row, 1976. Zellner, A., " A n Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias", Journal of the American Statistical Association, 57 (1962), 348-368. Addendum Gujarati, D., Basic Econometrics, New York: McGraw-Hill, 1978. Johannsen, E., "Productivity Trends in the Food and Beverage Industries", unpublished mimeo, Marketing and Economics Branch, Agriculture Canada, 1981. APPENDIX 1: CAPITAL STOCK DATA DERIVATIONS > Introduction Due to the fact, that capital stock data at the 4-digit level are only available for the period 1960-1975, it has been necessary to make imputations for the period 1976-1981. The purpose of this Appendix is to provide a summary of the techniques used to: 1. revise existing 4-digit data to correspond with published 3-digit data, 1960-1975; 2. impute 4-digit data using published 3-digit data, 1976-1981; and 3. deflate the revised and imputed current-dollar capital stocks to give both a current and constant (1971) dollar capital stock series, 1960-1981.1 The following section provides a description of the data used in the calculations and the sources of these data. In the third section, both the revision procedure and the imputation methodology are outlined. The final section offers some details on the completed data series, some comments on reliability of the data and alternative techniques, and to conclude, some suggestions for improvements are made. Data Description and Sources The primary data source used in these calculations is the 4-digit capital stock database shown in Appendix TableAl.l. As can be seen, they are aggregate figures for all components of the capital stock, and therefore, a disaggregation into machinery and equipment versus structures is not possible. Given this restriction, the matter of choice is between the eight versions of capital stocks listed (end-year gross, mid-year gross, end-year net, mid-year net: current versus constant dollars) arises. First, end-year stocks are the obvious choice, since all other input data being used in the cost function are year-long averages. Current- dollar values are also more 1 Note that, in keeping with the assumption made about investment-timing in Chapter 6, the year-end stocks from the previous year apply to the year for which the cost of capital is being calculated (see expression (59)). Thus, the capital series required is for the period 1960-1981, not 1961-1982 as with all other data. 163 164 appropriate, due to the fact that capital costs and other inputs are typically defined in nominal "terms in applied duality studies. The final choice is between net and gross stocks. The former is equal to the difference between the cumulative value of past gross investment and cumulative depreciation^  and therefore represents a value of the depreciated capital stock.2 In calculating costs of capital, depreciation costs need to be 'netted out' anyhow, so the net stock is the appropriate choice to make. Hence, completion of the current-dollar end-year net stock series -will-be the objective of the imputations. Along with the 4-digit data for 1961-1975, 3-digit data (which are available up to 1981) must be used as a guide for imputing the 4-digit data. These are shown in Table Al.2. Once again, the appropriate choice of capital stock for our calculations is end-year net stock in current dollars. It should be noted, though, that the sum of 4-digit data in TableAl-1 (within each 3- digit group) doeshot equal the 3-digit data in Table^ 3.2 (for the years 1960-1975). It is not clear why this difference exists, but it could be due to the fact that the 3- digit data are more recent, adjusted figures which are more representative of the 'true' capital stocks. Since, for our imputing purposes it is essential that the 3-digit and 4—digit data correspond, it will be necessary to revise the data in TableAl.l to make them compatible with those in . TableA1.2. This procedure is outlined in the next section. , The third set of data required are the investment statistics for the 4-digit industries. These are taken from the Statistics Canada publications "Investment Statistics - Manufacturing Sub-industries, Canada 1960-1977" and "Investment Statistics -Manufacturing Sub-industries and Selected Energy Related Industries" (catalogues 61-518 2 This definition was obtained from the introduction in Statistics Canada catalogue 13-568, "Fixed Capital Flows and Stocks, 1926-1978". Note that gross stocks are, in a sense, depreciated values, but the form of depreciation is 'one-hoss shay' (i.e. the value of an asset is assumed constant until the end of its lifetime, when it is dropped from the value of the stock). This is considered less appropriate than straight-line depreciation, as used for the net stocks. 165 (occasional) and 61-214 (annual), respectively). The data used (1975-1981) are defined as "actual capital expenditures, subrtotal" (i.e. the sum of construction .and machinery and equipment expenditures, in current dollars (see TableA1.3. " In order to obtain net investment 'figures (i.e. net of direct replacement), it "would be ideal to have-data-on capital discards at the. 4-digit level. Since it appears that these data don't exist, or, are not available, an alternative (but inferior) procedure is to use -1975 capital cost allowances as an estimate of „ the. cost of replacement of existing stocks (through physical or economic obsolescence). Thus, the net increase in capital stock3 is seen to be the gross investment minus the capital cost allowance. The 1975 capital cost allowances at the 4-digit level are found in TableAl.l, column 3. Finally, we need an implicit price index (pcap) to deflate the capital stocks ipto real terms (in order to relate stocks between years, net of inflation). The only published index is" the "price index for capital expenditure on plant and equipment" (total components) available for the whole of food and beverage industries, in Statistics Canada catalogues 13-568 and 13-211 (for titles, see Chapter 6, where these data are discussed in more detail). They are shown in TableA1.4 for 1960-1981 and are scaled to 1971 = 100. This index was chosen to deflate the 'revised' and 'imputed' 4-digit capital stock data, the 3-digit capital stock data, the investment series, and the observed and imputed capital cost allowances. Note that the index used to convert the 3-digit data from current to constant dollars in TableAl.2 (pcap2) is not the same as pcap. The former differs somewhat between industries; the average (absolute) percentage difference between pcap and pcap2 was calculated for each of the nine 3-digit industries, and this ranged between 0.09 percent for industry (S.I.C.) 103 and 0.68 percent for industry (S.I.C.) 109.4 Although 3 This is often referred to as net fixed capital formation (see, for example, The Statistics Canada publications, "Fixed Capital Flows and Stocks (catalogue 13-568 (occasional), p. 12). 4 Note that these figures apply irrespective of whether pcap or pcap2 is used as the 166 there is sound justification for using industry-specific price indices, there doesn't-appear to be any documentation to support these data, and therefore, pcap will be the deflator used here which, of course, will be the same for all seventeen 4-digit industries being considered. Revision Procedure and Imputing Methodology As noted in the previous section, before the 4-digit, imputations are made, the existing' 4-digit data must be revised to correspond to the 3-digit "data. For industries (S.I.C.'s) 1011, 1012, 1081, 1081, 1083, 1089, 1091, 1092, 1093 and 1094, the period of revision is 1960-1975; for industries (S.I.C's) 1071 and 1972, the period is 1960-1971 (data for 1071, although they run to 1975, cannot be revised without data for 1072, therefore, we are limited to this period for industry 1071 as well).5 The revision procedure is as follows. First, the 4-digit capital stock data (from • TableAl.l, column 6) (eynsc4) within each 3-digit group are summed to give an estimate of the 'old' 3-digit capital stock (eynsce3), i.e.: ni (1) eynsce3., = I eynsc4. ; / = 1, 2, 3, 4 ; It y=1 jt t = 1960, 1961 1975 (or 1971 if / = 2) where: / = 1 is for S.I.C. 101 . / = 2 is for S.I.C. 107 / = 3 is for S.I.C. 108 / = 4 is for S.I.C. 109, and ni is the number of 4-digit industries within 3-digit industry / . From (1), the relative shares of the 4-digit stocks of estimated 'old' 3-digit stocks '(cont'd) denominator in these calculations. Even though the differences are small, it seems wise to use pcap, given the lack of documentation. 5 As can be seen from an inspection of TableAl.l, data for 1072 are only available for end-year gross stock, and mid-year gross and net stocks. To arrive at end-year net stocks, the depreciation factor used to reduce mid-year gross to midyear net stocks was calculated (MYNS/MYGS) and applied to the end-year gross stocks for 1961-1971, thus yielding an estimate of 'old' data for this industry. 167 are calculated: (2) S. = eynsc4. / evnsce3. ; / = 1, 2, 3,-4 ; /= 1, 2 ' ni ; . jt jt it • t = 1960, 1961, 1975 (or 1971 if i = 2) Then - the' revised 4-digit digit data are derived by applying the- shares from (2) to the 3-digit (eynsc3) data from TableAl.2: (3) eynscn4^  = eynsc3/t ; / = 1, 2, 3, 4 ; 1, 2, .... ni ; t = 1960, 1961 1975 (or 1971 if / =2) From this procedure, a 'revised' data set for 1960-1975 (1961-1971 for 1071 and 1072) is generated. These data (particularly the years 1974 and 1975) provide the base for the imputing procedure described below. : Rather than make a distinction between industries 1071 and 1072 and the other 4-digit industries, the procedure outlined below is generalized for all cases; it should be clear whether revised or imputed data are being used (for instance, capital stocks for any year beyond 1975 which are imputed are re-entered into the algorithm below to provide estimates for the following year, etc.) and which years are relevant Note that throughout variables are deflated using pcap. First it is necessary to calculate net investment using the capital cost allowance, capital stock, and investment data. This is done in two steps. Replacement rates for period t and 4-digit industry j within 3-digit industry /.are calculated as follows: (4) aJt = (CCA^ / pcapf )/(eynscn4^  _ 1 /pcap? _ 1 ) where: a. f is the estimated replacement rate6 6 The procedure used here is to estimate on annual replacement rate. A valid alternative would be to assume ott is constant (ie. constant economic rate Of depreciation). This was not tried but it would appear to be an obvious possibility for sensitivity analysis, which was not done here due to the time limitations and focus of 168 CCA. is the' observed or estimated capital cost allowance, and J' eynscn4^  _ ^  is the 'revised' or imputed capital stock from the previous period in current dollars; • . ' - . : Given a , we can estimate the capital cost allowance for the next period: (5) CCA: f + i = eynscn4^  • o-t ; j= 1~, 2 ni From (5) it is. possible to estimate net investment, using the (observed) data from Table Al.3 (inv) and pcap: (6) invrn. =; {[(inv; • 1000) - CCA. ]/ pcap. }• 100 ; v ' jt+1 jt+1 jt + i ' rt j= 1, 2, .... ni Having the net investment figures for each 4- digit industry within industry / , we can now calculate the share of each industry j in the total net investment of / , using the data generated from (6), i.e.: ni (7) iprop. = invrn. / L invrn. ; /= 1, 2, .... ni ' v yjt+y jt+1 y=i jt+y J These proportions are then applied to the change in 3-digit capital stocks (from TableAli) from t to t + 1 to give an estimate of the relative increase in each 4- digit industry's real stocks, or: (8) cheynsr4^  = iprop ; 7 + 1 «(eynsr3rt + i - eynsr3/f ) ; /= 1, 2, .... ni where: eynsr3^  = (eynsr3^  / pcap^  ) ; similarly for eynsr3^  1 . Finally, the imputed capital stock for t + l for 3-digit industry j in 3-digit industry i is calculated, using (8): (9) eynscn4. = eynscn4 + [(cheynsr4. • pcap )/100] ; y'= 1, 2, .... ni jt +1 jt ji i Steps (4)-(9) are done for each 4-digit industry within each 3-digit industry, then '(cont'd) this study. 169 data generated in step (9) are substituted in step (5) to generate data-for the following period and so-on until t + l = 1981 for all 4-digit industries. The imputed data (in current dollars) are described in the following, section. ' ' • The Imputed Data and Comments . -The-final data set, including the revised data and imputed data is given in. . TableAl.5. These are end-year current-dollar net stock data (eynsc3 and eynsen4). For industries (S.I.C.'s) 102, 103, • 104, 105. and 106, current dollar data are . taken directly from x TableAl.2. Data for industries (S.I.C.'s) 1011, 1012, 1081-1089 and 1091-1094 for 1960-1975 are the revised data generated using the procedure (equations (1) - (3)) outlined earlier; similarly the data for 1071 and 1072 for 1960-1971 are obtained using this procedure as well. Finally, the 1976-1981 data . for the first group of 4-digit industries and the 1972-1981 data for 1071 and 1072 are derived using equations (4) to (9) above. Although, by the use of the procedures outlined above, we now have a 4-digit capital stock data set for the period of this study, it is far from clear that the imputed data are good estimates of the actual capital stocks employed at the 4-digit level. In particular, we can't be sure that the method used to allocate changes in 3-digit stocks between 4-digit industries (see equation (7)) is appropriate. On the other hand, it is quite possible that within each 3-digit industry containing 4-digit industries, the capital data has in fact been distributed in the manner assumed and yet there is no means of verifying the imputed data and assuaging our doubts. For this reason, we cannot be entirely confident that the imputed data are correct, or insignificantly incorrect There are at least two means by which we might improve our level of confidence in the imputed data (assuming that the revised data are as correct as possible). One approach would be to test the accuracy of the imputing procedure on the existing 4-digit data set (i.e. for the period 1961-1975 or some subperiod thereof), 170 and see whether large errors in distribution occur. If consistently large errors (and the matter of what is large would have to be addressed) were observed, clearly- the procedure would need to be altered or else discarded altogether. For example, one possible improvement might be to use the economic rate of depreciation rather than the CCA to estimate' the rate of replacement of capital. Another would.be to estimate the value of discards for each year, in order to arrive at an alternative to the present net investment derivation. * - -A second avenue of analysis which might improve our confidence in the capital data would be to use the 'perpetual inventory' method employed by Statistics Canada to arrive. at the data in . TablesA2.1 andA2.2. This, however, would require a good deal of additional information; for example, relative service, lives and quantities of the various components of the capital stocks, and the composition of investment would have to be known. Such information may or may not be available. Neither of these alternative procedures have been attempted, given the time constraints which exist for this study. Since we cannot be certain whether the imputed stocks are reliable or not, there is no reason to be too pessimistic about the accuracy of these figures. Nevertheless, some care should be taken in their use, and any results should be qualified with the origins of these data kept in mind. Finally, it is clear that if detailed and reliable research, using disaggregated figures is to be done, it is necessary that the data can be used with confidence. As suggested in Chapter 4 (Section 4.10), many useful 'separability' tests can be performed with disaggregated data in order to establish the validity of aggregation within and across input classes. Implementation of these tests, however, cannot be done without the support of a large and accurate body of (disaggregated) statistics. Imputed or interpolated data as aggregated as the capital series developed here thus suffer both from an untestable and unproven assumption of separability, as well as possible (unquantifiable) imputation errors. Dependence on such 171 second-rate substitutes in place of accurate-data can only hinder endeavours to, verify theoretical - hypotheses, and leave the outcome of otherwise sound empirical analysis open. to question. . . . Table A l . l . Capital Stock and Related Data, Canadian 4-digit Food Manufacturing Industries: Slaughtering and Meat Processors (S.I.C. 1011), 1947-1975  gross fixed capital year lormnlion capital C O I L S . allowance cnd-yr mid-yr gross gross slock slock cnd-yr ncl stock inid-yr ncl stock gross fixed capital formation capilal cnd-yr niid-yr cnd-yr cons. gross gross ncl allowance slock slock slock mid-yr net slock thousands ol'current dollars thousands of constant (1961) dollars 1 9 4 7 5 9 0 1 . 0 teoe.o 1 9 1 1 4 9 . 3 ia:-9on. , 5 1 1 3 0 4 7 . 2 1 0 5 7 I B . 5 9 6 6 1 . 8 1 1 6 5 2 . 0 3 0 8 2 4 0 . 0 2 9 6 4 0 6 . 0 1 7 9 7 9 9 . 0 I S ' . B 6 6 7 3 . 0 7 6 3 3 . 3 2 1 J B 0 B . 7 2 l 3 S ? f . R 1 2 5 6 7 9 . 2 1 2 5 3 5 8 . 9 1 2 P 9 6 . 0 1 1 7 3 B . 1 3 0 9 3 1 5 . S 2 0 8 7 7 7 . 8 1 8 1 0 5 7 . 1 1 "49 1 1 7 3 0 . 0 7 9 3 9 .7 2 / - . 9 1 0 . 6 2 3 T 3 P 1 . 2 136336 . 2 1 3 " 5 ^ 1 . 2 1 5 9 1 5 . 7 1 1 4 6 0 . 4 3 1 3 5 2 8 . 0 3 1 1 5 2 5 . 1 1 8 5 C - 4 7 . 0 1 9 5 0 R 4 : n . 0 8 1 4 7 . 1 3 3 7 0 7 0 . 4 2 2 7 9 7 n . , 9 1 4 1 8(11 . 1 1 4 1 7 3 9 . 2 i V > 0 2 . 9 11177.1 3 1 3 9 0 7 . 4 3 1 3 2 5 7 . 5 I 8 5 0 7 3 . 1 1 9 5 1 9 0 5 4 . 0 8 5 2 7 . 9 3 5 7 7 7 2 . 1 2 S 7 9 G 7 . 6 1 5 4 5 7 0 . 7 1 5 4 3 3 2 . 7 1 1 2 3 5 . 7 1 0 7 5 4 . 6 3 1 3 3 7 9 . 5 3 I 2 6 B 3 . 3 1 8 C 4 5 4 . 1 1 9 5 2 1 • ' ~> t*i . 0 B 6 S 3 . 4 3 7 C 4 4 S . S . 2 6 P 3 7 3 . 4 . . . 1 6 3 1 6 9 . 5 . 161307 . 5 " . . 1 5 1 7 C . 9 _ 1 0 5 & 7 . 1 . . . 3 1 8 2 1 9 . 9 _ . ' 3 1 5 2 2 9 . 6 . _ 1 - J 0 D G 4 . 3 .. 1 9 5 3 1 1 1 ' 0 . 0 9 0 6 3 . 6 2 7 C 9 7 9 . 6 3 7 3 - J 3 6 . , 1 1 0 9 0 7 8 . u 16C1010.3 1 3 5 8 3 , 5 1 0 3 0 6 . 3 3 2 3 1 9 8 . 0 3 2 : 2 0 " ' . 0 1 9 3 6 4 1.2 1 9 5 4 1 3 2 3 1 . 0 9 3 6 2 . 2 3 8 4 9 9 3 . 0 2 6 3 5 9 5 . , 6 1 7 3 0 6 0 . 1 1 7 1 1 0 0 . -3 1 5 6 5 1 . 0 1 1 0 8 9 . 1 3 3 7 7 B B . B 2 3 - 9 9 1 . 9 1 9 S 3 0 3 . 1 1 9 5 S 1 0 5 4 1 . 0 9 5 9 8 . 7 2 1 2 8 0 1 . 0 2 9 1 6 7 9 . . 1 1 7 7 2 3 3 . B 1 7 6 3 2 8 . 8 1 2 2 3 3 . 5 1 1 2 1 0 . 1 3 3 0 3 7 9 . 1 3 3 . - 0 8 3 . 5 1 9 9 2 7 6 . 4 i3r»A 3 0 9 0 0 . 0 1 0 3 3 9 . 9 3 1 6 1 5 0 . 2 3 0 9 ? 6 4 . . 0 1 « j 4 3 7 6 .5 1 C 9 C 9 1 . 5 2 3 2 f 3 . 3 1 1 5 0 0 . 9 3 4 4 1 5 0 . 7 3 3 7 2 < i - : . 8 2 1 0 9 3 7 . 7 1 9 5 7 • 1 B 3 3 0 . 0 1 1 1 7 3 . 1 3 3 4 1 1 4 . 4 3 2 9 5 1 3 . , 3 2 0 6 7 2 7 . 0 3 C 3 1 i B . 7 1 9 6 5 3 . 0 1 3 0 C C . 4 3 5.* 97 6 . 5 3 4 9 0 * 3 . 4 2 1 8 5 1 4 . 3 i 9 5 n 1 B P 6 2 . 0 1 1 7 C 5 . 5 . . 3 4 9 3 9 6 . 0 _ . 3 4 . 4 5 $ ; , 2.... 2 1 7 3 5 6 . 2 _ 2 1 3 3 3 8 . 0 . .... 1 9 E 2 B . 4 . _ 1 2 4 3 3 . 2 _ 3 6 3 7 0 u . 0 _ . 3 5 8 f l 4 : . 0 _ . 2 7 5 9 1 0 . 3 1 9 5 9 1 5 1 4 3 .0 1 2 1 * 1 . 6 - 3 5 7 4 3 7 . 2 3 5 4 6 4 3 . , 1 2 2 1 8 1 6 .3 2 2 0 3 2 5 . 7 1 5 8 1 1 . 9 1 2 7 0 3 . 6 3 6 P 5 S 4 . 5 : - i t ' - 1 3 0 . 1 2 2 9 0 1 8 . 4 1 9.">0 2 2 C 4 3 . 0 1 2 7 3 0 . 2 3 7 6 6 6 0 . 2 3 7 0 : 0 8 . . 3 2 3 5 4 0 6 .5 2 3 C 4 5 0 . 4 3 3 0 1 B . 0 1 3 0 3 4 . 6 3 8 2 6 : 5 . 7 3 7 6 1 9 0 . 0 3 3 ? 0 1 1 , 8 1 9 6 1 1 9 0 5 8 . 0 1 3 5 3 3 . 9 3 C I 2 5 5 . 3 3 B 7 C 4 3 . , 4 2 4 4 7 3 5 .9 2 4 I B 7 3 . 3 1 9 0 5 8 ' . 0 1 1 3 3 3 . 9 3 9 1 2 5 5 . 3 3 8 7 0 4 0 . 4 3 4 4 7 2 5 . 9 1 9 4 2 1 7 1 6 9 . 0 1 3 8 6 9 . 7 4 0 6 1 7 0 . 1 4 0 3 0 0 3 . 6 2 5 3 0 i ) 0 .5 2 5 1 4 4 0 . 9 16716.2 1 3 4 B B . 8 3 9 7 4 4 0 . 8 3 9 4 3 J R . 0 2 4 7 9 G 3 . 3 1 4 5 4 0 .0 1 4 3 5 4 . 2 4 2 0 2 6 0 . 6 418476. , 4 2 5 9 6 0 0 . 7 3 5 9 5 D B . 0 1 3 B 4 3 . 7 1 3 5 2 9 . 7 4 0 C 9 3 6 . 8 399189.9 3 4 8 3 7 6 . 5 1 9 6 4 1 or-67 . 0 1 5 0 0 3 . 4 4 4 1 1 1 5 . 2 4 4 ' 3 0 9 . , Q 2 6 8 1 2 1 • 9 . _ 2 7 0 1 3 0 . 4 . 9 7 2 4 . 3 . _ . 1 3 4 1 B . 6 _ 4 0 0 5 3 9 . 4 _ 4 0 0 7 3 B . 1 . . . 2 4 4 5 B 2 . 2 . 1 9 6 S 3 0 3 3 0 . 0 1 5 9 2 8 . 5 4 7 2 6 3 9 . 2 4 6 S 5 6 B . 3 2 P 6 4 G e . 6 2P-1317 . 3 1 7 0 8 1 . 8 1 3 4 2 4 . 7 4 0 7 4 1 7 . 6 4 C 3 9 : B . 4 2 4 6 7 3 9 . 1 1966 3 3 6 2 0 .0 1 5 8 1 6 . 1 5 0 3 1 3 5 . 0 49915B. . 0 3 0 5 1 7 3 . 5 3 C 3 2 7 1 . 8 1 B 3 6 2 . S 1 3 6 6 7 . 2 4 1 5 4 7 4 .9 4 I 1 4 4 5 . J 2 5 3 9 3 4 . 7 1 ? 6 7 2 1 9 H 7 .0 1 6 8 8 0 . 7 5 1 0 4 0 1 . 5 . 5 C 5 5 6 5 . . 3 3 0 9 6 5 2 .2 2 0 7 0 3 9 . 4 1 8 1 7 6 . 9 1 3 P 5 0 . 7 4 2 3 4 7 4 . 5 4 1 9 4 " 4 . 5 3 5 7 1 6 0 . 7 I 9 f f l 2 4 5 7 5 . 0 1 7 2 0 9 . 8 5 2 2 3 0 2 . 8 515635. 3 3 1 6 3 9 5 .2 3 1 2 7 5 3 .0 2 0 2 7 3 . 0 1 4 . 1 1 ? . 6 4 3 4 1 9 3 . 7 4 3 E 8 3 3 . S 2 6 3 2 0 3 . B 1969 3 3 0 3 7 . 0 1 6 5 5 2 . 6 5 5 4 8 2 8 . 8 5 4 ? ; 8 3 . . 0 3 3 3 2 8 3 . 3 3 3 1 5 4 5 . 1 1 7 5 7 0 . 2 1 4 7 D 6 . 0 4 4 2 7 2 . 1 .0 4 3 9 4 5 6 . 6 2 6 5 9 7 8 . 0 1 9 7 0 3 0 8 2 3 . 0 2 0 0 G 6 . S C01537 .9 5 9 : 7 8 9 . 3 3 6 1 9 8 0 • 7 . . . 3 5 5 6 3 2 .5 . _ . 2 3 4 1 3 . 9 . 1 5 7 0 8 . 4 . . . . 4 5 5 9 P 8 . 0 .449359.3 . . 2 7 4 1 2 3 . 6 . 1 9 7 1 3 4 3 1 1 .0 " 2 1 3 3 7 . 3 6 4 3 0 0 3 . 0 " 6 3 3 ? 7 B . 9 3 B K 3 7 7 .8 3 6 1 7 9 1 . 1 2 5 2 4 1 . 1 1 5 7 4 8 . 8 ' . 7 0 7 2 2 . 4 4 6 3 3 5 1 . 9 3 8 3 6 1 5 .7 1 9 7 2 3 6 7 5 9 . 0 22566.0 6 0 1 4 7 0 . 5 6 7 0 3 9 0 . 8 4 1 3 4 6 B . 1 4 0 5 3 7 1 .5 3 6 4 5 6 . 7 1 6 2 9 3 . 4 4 8 6 0 0 4 . 2 4 7 8 7 6 3 . 1 2 9 3 7 8 0 . 2 1973 3 3 ' B 4 . 0 25026.6 7 5 0 2 3 7 . 2 7 4 1 5 1 3 , .2 4 5 1 6 1 1 .6 4 4 7 7 S 3 . 3 2 2 3 3 7 . 3 1 6 B 2 8 . 9 49e500.2 4 9 3 6 3 3 . 3 2 9 9 2 8 8 . 6 1 9 7 4 4 7 7 3 1 . 0 3 0 1 5 3 . 1 6 9 9 6 1 4 . B 6 8 4 6 2 7 , .4 5 4 0 6 1 1 . 7 5 3 1 8 2 2 .e 2 7 5 1 9 . 6 1 7 4 0 8 . 7 515858 .7 5 0 7 2 1 9 . 5 3 0 9 3 9 9 . 0 1 9 7 5 4 9 3 4 6 . 0 3 3 7 4 6 . 0 1 0 P 4 2 6 1 . 8 9 B 9 t l 7 . ,0 6 0 2 1 4 3 . 5 5 9 4 3 1 6 . 6 2 6 4 3 1 . 8 1 6 0 4 7 . 6 5 3 1 5 5 4 . 5 5 3 3 7 0 6 . 5 3 1 7 7 8 4 . 0 1 6 9 5 3 3 . 0 1 6 0 4 7 7 . 9 1 6 3 4 14.1 1 6 5 7 6 0 . I 1 8 G I 6 3 . S 1 0 B 7 0 9 . 1 1 9 2 3 0 2 . 6 1 9 5 9 3 1 . 9 1 9 3 7 1 4 . 7 2 0 5 0 7 7 . 1 7 1 4 7 3 1 . 2 222212.3 7 3 7 4 6 4 . 3 7 J i . 0 1 5 . 0 _ ' " 3 4 i e ~73 .B 2 4 G 3 4 9 . 8 3 4 B I 1 9 . B 2 4 5 4 2 9 . 2 3 4 6 4 1 0 . 8 2 5 0 5 8 6 . 8 2 5 S 0 4 7 . f i 2 6 0 1 B 3 . 3 3 6 4 5 9 1 . 0 . 2 7 0 0 5 0 . 7 3 7 B C - 6 9 . 7 2 8 8 6 9 8 . 0 2 9 6 5 3 4 . 3 3 0 4 3 4 3 . 9 3 1 3 5 9 1 . 8 1 Source of these data is: Statistics Canada, Science, Technology and Capital Stock Division. See Chapter 6, Section 6.2.1 for more information about these data. Table A 1.1. Capital Slock and Related Data, Canadian 4-digit Food Manufacturing Industries: (cont'd) Poultry Processors, (S.I.C. 1012), 1947-1975 yciir gross fixed c;ipilal fornialion capilal cons, allowance end-yr gross slock mid-yr gross slock end-yr net slock thousands of current dollars inid-yr net slock gross fixed capital formation capital end-yr mid-yr end-yr niid-yr cons. gross gross net nci allowance slock slock slock slock thousands of constant (1961) dollars 1 Source of these data is: Statistics Canada, Science, Technology and Capital Stock Division. See Chapter 6, Section 6.2.1 for more information about these data. Table A 1.1. Capital Stock and Related Data, Canadian 4-digit Food Manufacturing Industries: (cont 'd) Biscuits Manufacturers, (S.I.C. 1071), 1947-1975 year gross fixed capital fornialion capilal cons, allowance end-yr gross stock mid-yr gross slock end-yr net slock mid-yr net slock thousands of current dollars gross fixed capilal formation capilal cons, allowace end-yr gross slock mid-yr gross slock end-yr net slock thousands of constant (l%l) dollars mid-yr net slock 1 9 * 7 " 1 9 2 4 , . 0 " ( 3 8 2 . 3 ' • 1 0 7 3 3 . 7 ~ " 1 C 3 ? I . 3 " ~ - "• 6 2 9 1 . . 6 F . 9 . H . 4 " 3 1 2 K B " 6 5 4 . 3 1 7 3 6 9 . 0 1 6 6 " . 0 1 0 0 9 6 . 0 9 5 2 0 . 0 1 9 4 8 4 7 4 5 . , 0 5 0 3 . 4 1 6 2 6 4 . 0 1 4 ) 0 8 . 6 1 1 2 5 1 . . 2 9 1 3 0 . 6 6 8 c 6 . 9 7 7 4 . 1 2 3 5 0 6 . 4 2 0 4 0 7 . 7 1 6 1 8 9 . 0 1 3 1 4 7 .3 1 9 4 9 1 7 5 - 5 , , 0 6 7 8 . 3 1 8 9 1 7 . 5 1 8 2 6 4 . 8 1 3 2 6 9 . 4 T 2 7 0 2 . 6 2 5 3 0 . 4 9 8 9 . 3 2 6 0 5 4 . 6 2 5 1 1 5 . 2 1 8 2 1 8 . 4 1 7 4 0 3 . 1 1 9 5 0 4 3 3 6 , . 0 B C 6 . 4 2 3 4 9 1 . 4 2 1 5 9 1 . 3 1 7 3 3 1 . 9 1 5 5 6 7 _ Q 5 B 2 7 . 7 1 1 1 9 . 6 3 1 . 1 3 8 . 3 2 B 5 9 6 . 3 2 2 9 2 6 . 3 2 0 5 7 2 . 3 1 9 0 1 3 0 7 3 , . 0 9 9 9 . 4 2 7 9 4 B . S 2 6 7 0 4 . 4 2 0 8 5 2 , . 5 1 9 8 1 5 . 7 3 ' 9 B 6 . 5 1 2 7 6 . 4 3 4 3 8 0 . 3 3 2 7 5 9 . 2 2 5 6 3 6 . 5 2 4 7 0 1 . 2 1 9 5 2 1 9 1 8 . . 0 1 0 6 0 . 2 3 0 0 3 9 . 8 2 9 3 9 2 . 0 2 2 7 B 6 . 3 2 1 8 7 0 . 7 . • 2 3 7 8 . 2 1 3 6 4 . 8 3 5 9 7 7 . 1 3 5 1 7 B . 9 7 6 6 5 0 . 2 2 6 1 4 3 . 2 1 9 5 3 3 9 2 S , . 0 1 1 7 2 . 2 3 * 9 2 0 . 0 • ' 3 2:-59. 1 - 2 5 5 5 9 . . 1 ' — 2 4 2 2 3 . 4 " ~ 4 & 4 2 . 0 U 3 3 . 4 3 9 6 4 1 . B 3 7 8 0 4 . i 2 9 8 5 8 . 7 2 B 2 5 4 . 4 1 9 5 4 4 3 3 9 . 0 1 2 B 3 . 3 3 7 7 3 4 . 2 3 5 E C 5 . 2 2 8 7 3 4 , .9 2 7 2 0 7 . 5 5 1 3 3 : 4 1 5 5 6 . 4 4 3 9 9 3 . B 4 1 8 1 7 . 3 3 3 4 3 5 . 7 3 1 6 4 7 . 2 1 9 5 5 5 3 2 6 , . 0 1 4 3 2 . 0 4 3 0 C 0 . 4 4 0 7 9 2 . 4 3 3 2 2 1 . 1 3 1 2 7 3 . 8 ' 5 9 0 0 . 3 1 6 8 7 . 3 4 8 9 5 0 . 6 4 6 4 7 2 . 0 3 7 6 4 R . B 3 5 5 4 3 . 2 1 ? 5 6 4 2 9 1 , . 0 1 6 0 6 . 3 4 8 2 3 3 . 6 4 5 - . B 2 . 2 3 7 1 7 2 . 8 3 5 8 3 1 . 8 4 6 6 5 . 2 1 8 1 0 . 6 5 2 9 1 9 . 1 5 0 9 3 4 . B 4 0 7 0 3 . 3 3 9 1 7 6 . 0 1 9 5 7 . 2 8 0 6 , . 0 1 7 7 4 . 0 5 1 8 1 3 . 6 5 0 7 6 2 . 8 3 9 3 1 9 . 6 3 B 8 0 3 . 3 . 3 0 5 1 . 9 1 9 2 2 . 9 5 5 3 0 5 . 0 5 4 0 6 2 . 1 4 1 B 3 2 . 5 4 1 2 6 7 .7 1 9 5 0 2 9 4 3 . . 0 1 6 6 2 . 2 5 4 B S 9 . 7 5 3 E 4 T . 7 4 1 1 0 9 . 9 4 0 5 * 6 . 9 3 1 2 6 . 3 1 9 9 5 . 1 5 7 4 4 3 . 2 5 6 3 2 4 . 2 4 2 9 6 3 . 6 4 7 3 9 7 . 9 1 9 5 9 3 4 1 8 , . 0 ' 1 9 5 4 . 2 . 5 7 9 3 4 . 4 S R f . 7 2 . 4 • 4 2 9 3 0 . « ' 4 2 2 0 3 . 5 - T 3 S 2 1 . 9 2 0 4 3 . B 6 0 0 3 5 . 5 5 B 7 3 > . 4 4 4 4 4 1 . B 4 3 7 0 3 . 7 1 9 * 0 2 B 9 7 . 0 2 0 3 6 . 3 6 1 0 4 4 . 1 6 0 0 0 2 . 9 4 4 5 3 7 . 7 4 4 1 0 7 . 4 '• 2 9 S 1 . 5 2 0 8 4 . 8 6 2 1 5 0 . 4 6 1 0 9 3 . B 4 5 3 0 8 . 3 4 4 B 7 5 . 0 1 9 6 1 3 4 4 2 . 0 2 1 3 4 . 5 6 4 6 2 6 . 8 6 3 3 8 8 . 7 4 6 6 1 6 . 0 4 5 9 5 2 . 0 3 4 4 2 . 0 2 1 3 4 . 5 6 4 6 2 6 . 8 6 3 3 1 8 . 7 4 6 6 1 6 . 0 4 5 9 6 2 . 0 1 9 6 2 4 8 3 2 . 0 2 2 9 7 . 3 7 0 2 2 1 . 3 6 3 2 3 3 . 9 v 5 0 2 6 8 . 3 4 9 0 0 1 . 0 4 6 9 0 . 2 2 2 2 7 . 0 6 8 4 B 5 . B 6 6 5 5 6 . 3 4 9 0 7 9 . 3 4 7 B 4 7 . 5 1 9 6 3 51 1 4 . 0 2 5 1 3 . 9 7 6 3 4 3 . 3 7 4 J 2 2 . 6 5 4 1 9 3 . 4 5 2 8 9 3 . 4 4 6 0 4 . 6 2 3 6 4 . 3 7 2 4 - 2 . 2 7 0 4 : 9 . 0 5 1 5 1 9 . 7 5 0 7 9 9 . 6 1 9 6 4 4 2 9 1 . 0 2 B 1 5 . 2 8 4 0 6 5 . 8 8 2 3 4 3 . 4 5 8 6 2 8 . 7 5 7 B 9 0 .7 3 6 4 3 . 9 2 4 B B . 6 7 5 5 6 7 . 4 7 4 0 1 9 . 6 5 2 B 7 5 . 0 5 3 1 9 7 .3 1 9 5 5 - • • 3 1 6 5 . 0 " 3 0 7 4 . 1 — ~ 9 0 9 0 2 . 9 - 8 9 7 5 1 . 3 - 6 1 B 8 2 . « " ' 6 1 B 2 6 . 4 ' 2 6 6 2 . 7 ' 7 5 7 3 . 3 7 1 4 9 1 7 2 7 6 5 3 3 . M 5 2 9 6 4 . 6 5 2 9 1 9 . 8 1 9 G 6 4 7 3 9 . 0 3 2 7 9 . 1 9 8 2 5 6 . 6 9 6 4 0 9 . 1 6 5 8 9 8 . 8 6 5 1 6 9 . 5 3 8 4 8 . 7 2 6 5 2 . 2 8 0 5 1 3 . \ 7 9 0 0 2 . 1 5 4 1 6 1 . 3 5 3 5 6 2 . 9 1 9 6 7 3 5 2 9 . 0 3 2 9 6 . 0 9 9 6 0 5 . 6 9 9 3 8 7 . 5 6 5 5 5 8 . 0 6 5 4 4 1 . 5 2 9 1 1 . 7 2 7 2 2 . 4 B 2 5 2 5 . 0 B 1 5 I B . 9 5 4 3 5 0 . 6 5 4 2 5 5 . 9 1 9 6 8 3 2 8 5 . 0 3 3 4 1 . 4 1 0 1 6 1 9 . 5 1 0 0 5 4 0 . 6 6 5 3 9 9 . 3 6 5 4 7 7 . 6 2 7 1 0 . 2 2 7 6 5 . 2 8 4 3 0 1 . 0 8 3 4 1 3 . 0 5 4 2 9 5 . 2 5 4 3 2 2 . 9 1 9 6 9 6 3 9 9 . 0 3 5 7 3 . 9 1 1 1 0 2 5 . 2 1 0 6 3 4 2 . 7 7 0 8 7 2 . 5 6 9 4 6 0 . 0 5 1 0 5 . 2 2 8 5 0 . 6 8 8 5 8 2 . 1 6 6 4 4 1 . 6 5 6 5 5 0 . 1 5 5 4 2 2 . 6 1 9 7 0 B 1 8 4 . 0 3 9 8 1 . 1 1 2 3 9 1 9 . 2 1 2 0 3 3 0 . 1 7 B 7 7 1 . 9 7 6 G 7 0 . 3 6 2 7 8 . 9 3 0 2 9 . 3 9 4 0 4 4 . 1 9 1 3 1 3 . 0 5 9 7 4 9 . 5 5 B 1 4 9 . 6 1 9 7 1 • — 4 4 1 5 . 0 - " 2 9 7 . ? : — - 1 3 1 2 0 4 . 5 - I 7 ? T 5 5 . T 8 1 5 2 6 . 7 T 3 U 6 7 . 9 3 2 6 2 . r 3 1 7 9 . 6 9 6 4 7 9 . " 5 5 2 6 1 . 6 ~ 5 9 8 3 1 . 8 5 9 7 9 0 . 6 1 9 7 2 3 3 9 2 . 0 4 4 B 1 . 0 1 3 6 5 2 0 . 2 1 3 5 3 7 3 . 1 8 2 3 8 3 . 6 8 2 9 2 8 . 1 ' 2 4 B 2 . 6 3 2 4 8 . 6 9 8 1 6 8 . 3 9 7 3 2 3 . 8 5 9 0 6 6 . 1 S 9 4 4 B . a 1 9 7 3 4 6 2 8 . 0 4 9 2 3 . 1 1 5 0 4 4 4 . 9 1 4 B 6 2 1 . 2 8 0 4 9 6 . B B B 5 4 4 . 3 ' 3 2 6 0 . 2 3 3 2 2 . 9 1 0 0 6 3 2 . 3 9 9 4 0 0 . 3 5 9 0 0 3 . 4 5 9 0 3 4 . 7 1 9 7 4 7 4 1 2 . 0 5 9 1 9 . 5 1 8 0 9 0 3 . 8 1 7 7 9 S 7 . 9 1 0 4 2 6 6 . 2 1 0 3 S 2 0 ; o • 4 2 7 7 . 9 3 4 2 1 . 2 1 0 4 0 2 8 . 9 1 0 2 3 3 0 . 7 5 9 8 6 0 . 1 5 9 4 3 1 . 7 1 9 7 5 6 G 4 2 . 0 6 5 2 0 . B . 2 0 0 3 5 1 . 6 1 9 B 0 1 9 . 8 1 1 3 0 2 4 . 7 1 1 2 9 6 4 . 2 3 5 3 9 . 2 3 4 9 3 . 3 1 0 6 5 0 2 . 0 1 0 S 2 6 S . 6 5 9 9 0 6 . 2 5 9 B B 3 . 1 1 Source o f these data is: Statistics Canada, Science, Technology and Capital Stock Div is ion. See Chapter 6, Section 6.2.1 for more information about these data. Tabic A 1.1. Capi la l Stock and Related Data 1 , Canadian 4-digil Food Manufacturing Industries: (cont'd) Bakeries, (S.I.C. 1072), 1947-1971 gross fixed capital yciir fornialion capilal cons, allowance end-yr gross stock mid-yr gross stock mid-yr net slock' thousands of current dollars gross fixed capilal formation capital cons, allowance end-yr gross slock mid-yr gross stock mid-yr ncl slock thousands nf constant (I%1) dollars 1 9 0 7 1 0 9 3 6 . 0 1 0 3 2 . 2 2 9 0 2 2 . 5 2 7 9 0 8 . 1 1 6 0 5 2 . 2 1 8 4 4 5 .4 1 7 6 8 . 5 4 6 7 7 6 . 0 4 4 9 8 1 . 0 2 5 7 2 7 . 0 1 9 4 8 1 1 4 9 4 .0 1 3 9 2 . 2 4 2 6 2 4 . 4 3 7 4 6 3 . 9 2 3 9 9 5 . 0 1 7 4 6 8 .0 2 1 5 5 . 1 6 2 4 3 5 . 4 5 4 6 0 5 . a 3 4 9 4 0 . 7 1 9 4 9 9 1 6 5 . 0 1 9 4 8 . 3 5 3 6 1 1 . 5 4 9 6 3 9 . 2 3 4 7 2 2 . , 1 1 3 2 5 4 . 2 2 8 6 3 . 5 7 4 8 3 9 . 1 6 9 0 9 7 . 3 4 8 4 0 8 . 9 1 9 5 0 1 2 1 6 3 .0 2 4 6 4 . 6 C 6 6 3 3 . 1 6 1 2 4 3 . 1 4 4 8 1 S . , 7 1 6 6 7 2 . 2 3 4 4 2 . 8 8 9 6 0 0 . 0 8 2 2 1 9 . 4 6 0 2 8 7 . 1 1 9 5 1 1 1 9 8 7 .0 3 1 3 2 . ,5 8 2 3 2 4 . 5 7 7 0 8 3 . 1 5 7 B 7 6 .  1 1 5 3 8 7 . 1 4 0 4 5 . 2 1 0 3 0 7 5 . 3 9 6 3 3 7 , .4 7 2 5 7 2 . 4 1 9 5 ? 1 4 ^ R d . n T«;KR n O f M k R T f% fi«ti <\ 1 B 1 7 9 . . 5 4 5 4 0 . 4 1 1 R 0 4 R 7 1 i n ^ f i n q ., P . M f i J , n 1 9 5 3 1 6 0 5 1 . 0 4 0 6 9 . 3 1 1 2 6 5 6 . 1 1 0 5 8 7 5 . 6 8 2 9 5 2 . , 8 1 9 7 6 6 . 1 5 0 4 4 . 2 1 3 4 7 0 2 . 0 1 2 6 3 7 4 . , 7 9 9 2 4 3 . 2 1 9 5 4 1 2 9 0 2 . 0 4 5 3 0 , 0 1 2 4 1 8 5 . 9 1 1 8 8 5 0 . .1 9 3 8 5 5 . , 7 1 5 5 6 8 . 7 5 5 5 7 . , 9 1 4 7 5 1 7 . 9 1 4 1 1 0 9 , . 9 1 1 1 6 0 9 . 3 1 9 5 5 1 3 1 8 9 .0 5 0 1 9 . 0 1 3 7 8 4 8 . , 4 1 3 2 4 7 3 . 9 1 0 4 4 3 0 . 9 1 5 7 0 6 . 9 5 9 8 7 , , 9 1 6 0 3 0 0 . 3 1 5 3 9 0 8 . . 8 1 2 1 4 7 4 . ,3 1 9 5 6 1 3 3 3 1 .0 5 6 3 3 . ,7 1 5 4 7 1 3 . , 4 1 4 9 2 7 3 . . 9 1 1 7 0 9 9 . . 6 1 5 1 1 3 . 0 6 4 1 0 , , 7 1 7 2 6 1 9 . 4 1 6 6 4 5 9 , . 5 1 3 0 6 8 4 . ,7 1 9 5 7 1 3 2 7 4 .<5 6 2 1 4 . .4 1 7 0 9 6 3 . 4 . 1 6 5 6 5 9 , . 6 1 2 8 9 2 4 , , 0 1 4 3 5 5 . 0 6 7 8 5 , . 3 1 8 4 0 4 8 . 6 1 7 8 3 3 4 , . 3 1 3 8 8 2 1 . , 1 1 9 5 8 i i r m n 7 1 Rfi lf l-J n 1 nn<374 4 1 6 0 0 4 R 7 11fi R I R f i E f l S 7 1 o,-> 7 7 7 n 1 ain^.rt 1 1 9 5 9 1 3 0 5 1 .0 7 0 8 6 . . 4 1 9 9 0 5 9 . 0 1 9 3 9 3 6 . . 4 1 4 B 4 C 2 . , 4 1 3 6 2 4 . 6 7 4 3 3 . . 6 2 0 7 2 6 7 . 7 2 0 1 9 3 6 , .3 1 5 4 5 8 9 . ,3 1 9 6 0 1 S 1 7 6 .0 7 5 8 5 . . 3 2 1 4 9 Q 6 . 9 2 0 8 8 4 0 , . 6 1 5 8 0 0 6 . , 8 1 5 5 8 1 . 6 7 7 9 2 , . 2 2 1 9 8 7 8 . 1 2 1 3 5 7 2 . .9 1 6 1 5 7 9 . 3 1 9 6 1 1 1 6 9 1 .0 8 1 2 0 . .9 2 2 8 6 3 2 , . 6 2 2 4 2 5 5 , . 6 1 6 7 2 5 9 , . 4 1 1 6 9 1 . 0 8 1 2 0 , . 9 2 2 0 6 3 2 . 6 2 2 4 2 5 5 . 6 1 6 7 2 5 9 , , 4 1 9 6 2 1 2 B 5 8 . 0 . 8 6 7 9 . .5 2 4 5 8 3 9 . 8 2 4 0 8 3 9 . . 7 1 7 6 4 1 5 , . 9 1 2 4 5 2 . 8 8 3 7 5 , . 3 2 3 8 3 2 3 . 2 2 3 3 4 7 7 . 8 1 7 1 0 8 3 , .3 1 9 6 3 1 5 7 8 5 . 0 " 9 2 6 4 . .0 2 6 5 3 4 5 . . 3 2 5 9 0 6 3 . , 8 1 8 6 7 9 1 , . 3 1 4 8 9 5 . 8 8 6 7 5 , . 3 2 5 0 2 0 5 . 1 2 4 4 2 6 3 . 9 1 7 6 2 3 2 . . 4 1 9 6 4 ft • " m m a O d l f i i 7 7 R 7 Q ^ 7 O *Jftdl 11 7 . 1 2 . 7 6 . 5 . n n q f i o ? 5R07DU 1 3 ^ 7 r n s •S i n i 5 - , a q 1 9 6 5 1 4 8 5 8 .0 1 1 1 2 9 . . 8 3 2 0 7 8 2 . . 6 3 1 5 1 7 2 . 6 2 1 9 2 6 7 . . 4 1 2 4 2 9 .2 9 2 3 3 . 2 2 6 9 6 1 1 . 3 2 6 4 9 0 8 . 0 1 8 4 7 2 5 . 3 1 9 6 6 2 3 3 S 9 .0 1 1 9 7 3 . 5 3 5 2 5 7 7 , .4 3 4 2 5 2 7 . 4 2 3 5 0 7 4 , . 8 1 9 0 5 8 . 6 9 6 1 7 . 0 2 6 6 0 1 6 . 3 2 7 7 8 1 3 . 6 1 9 1 0 4 3 . 6 1 9 6 7 1 5 1 0 7 .0 1 2 1 6 2 .4 3 5 7 7 9 0 . . 8 3 5 1 8 0 1 . 8 2 3 8 0 8 9 . . 9 1 2 4 8 3 . 9 - 1 0 0 3 5 . 8 2 9 5 9 2 2 . 9 - 2 9 0 9 6 9 . 7 1 9 6 9 8 0 . 6 1 9 6 8 1 6 4 3 9 .0 1 2 5 2 2 . . 8 3 7 0 6 8 4 . 9 3 6 4 1 6 8 . 9 2 4 1 3 3 2 . . 6 1 3 S 9 4 . 1 1 0 3 4 1 . 0 3 0 6 6 9 5 . 3 3 0 1 3 0 9 . 1 1 9 9 8 3 9 . 3 1 9 6 9 1 3 2 1 4 .0 1 3 3 0 4 .5 3 9 4 4 6 0 .0 3 8 9 4 6 6 . 1 2 5 2 5 1 3 . . 9 1 0 5 3 7 . 2 1 0 6 0 8 . 1 3 1 4 6 6 3 . 4 3 1 0 6 7 9 . 0 2 0 1 4 2 9 . 9 1 9 7 0 n l d l 7 A 1 1 K i c / i 1 y. R 9 3 1 R . 5 , 1 0 7 9 5 n .19I37B n 1 1 R o i n q 1 1 9 7 1 1 2 4 5 7 .0 1 4 7 0 9 . 3 4 4 3 6 5 9 .2 4 3 9 4 2 0 . 1 2 7 0 1 0 8 . 8 9 2 2 2 . 1 1 0 9 1 5 .2 3 2 7 6 4 8 . 9 3 2 4 5 1 3 . 3 1 9 9 0 7 1 . 6 1 Source o f these data is: Statistics Canada, Science, Technology and Capital Stock Div is ion. See Chapter 6, Section 6.2.1 for more information about these data. 2 Note the absence o f data on end-year net stocks. Tabic A 1.1. Capi la l Slock and Related Data ' , Canadian 4-digil Food Manufacturing Industries: (cont'd) Confectionery Manufacturers, (S.I.C. 1081), 1947-1975 year gross fixed capital formation capital cons, allowance cnd-yr gross stock mid-yr gross slock cnd-yr ncl slock mid-yr net stock thousands of current dollars 1 9 4 7 3 0 7 1 . 0 "\ 6 5 1 .6 1 8 2 5 8 .3 " " l - £ 9 4 . 2 — i ? 4 8 4 3 7 3 . 0 8 1 7 . 2 2 4 0 1 5 . 8 2 3 ^ 9 6 . 8 i 9-19 3 7 7 7 . 0 1 0 0 9 . 7 7 8 3 7 3 . 6 2 5 6 7 9 . 7 1 9 5 0 3 9 0 0 . 0 1 1 8 7 . 2 3 2 6 1 4 .2 3 1 : 7 7 . 7 < 9 5 1 4 3 9 8 . 0 1 4 1 1 . 4 3 8 6 9 9 . 2 3 £ r 5 0 . 6 19 5 2 7 6 5 7 . 0 1 5 2 2 . 5 4 1 3 0 3 .4 4 C 5 0 B . 5 I P 5 3 3 1 9 9 . 0 1 6 0 3 . 4 4 4 4 4 4 . 7 ~ 4 3 - 5 7 . 9 I S 5 4 4 2 3 9 . C 1 6 7 6 . 5 4 7 B 3 3 . 1 4 6 2 6 8 . 3 . 1 9 1 5 4 5 7 6 . 0 1 P 2 3 . 5 5 2 3 3 2 . 9 5 0 5 1 0 . 3 . 1 9 5 6 4 7 6 5 . 0 2 0 7 6 . 0 5 0 1 7 3 . 9 5 6 2 5 2 . 7 , r . 4 3 3 8 . 0 2 2 3 6 . 8 6 2 4 7 7 . 1 6 1 E 6 9 . 5 1 9 5 8 3 4 6 2 . 0 2 3 8 7 . 4 6 7 0 7 9 . 9 6 5 9 2 6 . 3 1 9 5 9 5 6 4 3 . 0 2 5 2 1 . 0 7 2 2 8 5 . 9 " " " " 7 0 C 9 1 . B 1 9 6 0 7 0 4 3 . o 2 7 3 2 . 3 7 9 4 3 1 . 9 7 6 5 4 5 . 2 1 9 6 1 1 3 3 3 6 . 0 ' 3 0 7 6 . 9 9 3 1 2 1 . 5 8 7 1 2 5 . 4 1 9 6 7 1 7 1 7 5 . 0 3 6 3 4 . 4 1 1 1 5 1 0 . 1 1 0 3 6 1 9 . 4 1 9 G 2 8 3 9 6 . 0 4 1 7 4 . 8 1 2 1 6 7 2 .4 1 1 8 1 1 9 . 7 1 9 6 4 6 4 7 7 . 0 4 7 0 5 . 8 I 3 . 1 B 6 6 . 7 1 3 1 3 4 0 . 3 1 9 6 5 ' 7 5 5 3 . 0 " ' 5 1 8 5 . 2 1 4 7 0 4 1 .4 ~ 1 4 4 1 0 5 . 3 ~ 1 9 6 6 7 7 7 1 . 0 5 5 3 3 . 7 1 5 7 9 2 4 . 7 1 5 5 2 6 7 . 3 1 9 6 7 1 0 1 2 1 . 0 5 5 7 4 . 0 1 6 3 3 1 6 . 7 1 5 9 3 8 7 . 7 1 9 6 8 9 J 5 4 . 0 5 7 9 2 . 6 1 7 0 7 3 6 . 7 1 6 6 = 3 4 . 5 1 9 6 9 5 5 2 1 . 0 6 1 6 7 . 3 1 8 1 0 3 4 .5 1 7 9 1 7 0 . 3 1 9 7 0 0 4 4 3 . 0 6 5 9 3 . 0 1 9 4 6 8 4 .0 1 9 7 4 1 8 . 0 1 9 7 1 " 6 * 3 3 . 0 ~ ~ " 6 9 3 1 . 5 — 2 0 7 5 7 3 . 3 3 0 4 1 4 3 . 2 1 9 7 2 8 0 5 1 . 0 7 2 3 5 . 6 2 1 7 8 B B .4 2 1 4 9 B B . 1 1 9 7 3 1 0 1 5 0 . 0 7 9 6 9 . 2 2 4 2 1 1 2 . 1 2 3 8 1 9 7 . 1 1 9 7 4 2 5 5 7 8 . 0 9 8 7 9 . 1 3 0 5 5 7 8 . 7 7 9 3 5 2 5 . 8 1 9 7 5 1 3 5 0 0 . 0 1 1 3 3 2 . 4 . 3 4 1 3 1 4 . 3 3 3 S 7 7 6 . 0 1 0 7 2 8 1 5 5 1 4 1 9 1 6 4 3 2 6 5 9 2 7 3 9 5 2 9 2 . 8 1 ' 3 1 6 6 2 . 4 3 4 4 4 I . 9 3 7 9 S B . 4 4 3 3 1 6 . 3 4 5 9 6 0 . 7 4 7 9 9 1 . 8 " 5 1 7 1 3 5 7 0 0 3 6 B 4 7 4 B 3 B 3 1 9 0 3 0 9 9 7 3 3 6 . f l 1 0 4 8 7 9 . 2 1 1 0 6 4 3 1 1 3 6 9 3 1 1 7 2 1 1 1 2 1 1 2 8 1 2 7 1 3 7 1 3 3 1 0 0 . i 1 3 6 9 1 7 . 6 1 4 9 4 0 3 . 7 1 8 9 6 0 9 . 5 2 0 7 2 8 6 . 8 1 0 1 1 9 . 1 3 7 3 3 1 7 7 8 1 2 1 3 0 3 2 5 9 0 2 2 B 7 1 1 3 0 8 5 4 3 3 1 6 1 . .8 3 6 5 9 1 . 6 4 0 9 4 6 . 6 4 4 9 1 8 . 4 4 7 4 5 4 . 5 " 5 0 1 5 1 . 3 5 4 8 4 7 . 8 6 3 3 4 4 . 2 7 7 0 7 5 . 9 B 8 1 9 7 . 9 9 6 3 5 2 . 5 1 0 . - 6 9 5 . 3 1 3 9 7 ? 8 . S 1 1 1 4 7 0 . 4 1 1 5 3 e 0 . 4 1 2 1 4 6 1 . 8 1 7 7 3 1 3 . 9 " 1 3 2 0 9 9 . 2 1 3 6 5 1 0 . 1 1 4 B 3 1 3 . 4 1 B 1 7 G 0 . 4 2 0 6 2 3 2 . 9 gross fixed capilal formation capilal cons, allowance cnd-yr gross slock mid-yr gross , stock cnd-yr net stock mid-yr net slock ! thousands bl*constant (1961) dollars 5 1 3 6 . 3 " 6 7 3 9 . B 5 4 7 6 . 1 £ 3 8 4 . 1 5 5 6 2 . 9 3 4 8 2 . 5 3 9 5 < \ . 3 " 5 1 7 6 . 4 5 3 7 3 . 5 • 5 4 0 B . 6 4 7 2 1 . 4 3 6 9 7 . 3 5 8 6 3 . B " 7 1 9 7 . 8 1 3 3 3 6 . 0 1 6 7 3 7 . 6 7 B 5 B . 2 _ 5 6 1 9 . 8 6 2 2 5 . 2 " 5 8 2 7 . 2 8 3 5 0 . 1 7 6 1 B . 0 4 4 0 2 . 3 4 P 0 6 . 5 " " 6 5 9 3 . 7 " 5 S 3 7 . 6 6 8 9 3 . 2 1 4 6 8 5 . 0 7 3 0 4 . 5 1 1 1 4 . 9 1 2 6 3 . 0 1 4 7 7 . 5 1 6 5 3 . 2 1 8 1 5 . 9 1 9 3 7 . 0 " 1 9 7 7 . 0 2 0 5 0 . 3 2 1 6 7 . 0 3 3 0 0 . 5 3 4 3 7 . 1 _ 3 5 4 1 . 2 3 6 4 3 . 5 3 8 0 3 . 2 3 0 7 6 . 9 3 5 1 7 . 2 3 9 1 7 . 9 4 1 4 7 . 4 " 4 3 1 6 . 7 4 4 5 7 . 7 4 5 9 9 . 9 4 7 8 9 . 5 4 9 3 4 . 2 5 0 2 0 " 5 i 3 9 5 3 5 9 5 3 9 2 5 7 1 5 6 0 8 1 . 9 2 9 5 0 7 . 0 . 3 5 1 0 5 . 7 3 S 4 5 2 . 6 4 3 6 3 4 . 4 4 B 1 1 4 . 8 _ 5 0 3 0 7 . 4 5 2 7 3 4 . t" 5 6 5 5 0 . 0 6 C 5 3 3 . 1 6 4 7 2 4 . 4 6 B 2 1 5 . 4 7 0 6 8 7 . 5 7 5 2 3 4 . 1 8 1 1 2 9 . 5 9312TT5" 1 0 8 5 5 6 . 0 1 1 5 2 0 2 . 4 1 1 9 5 6 5 . 2 "124386.6 1 2 8 6 7 G . X ) 1 3 5 1 6 4 . 8 1 4 1 4 4 9 . 7 1 4 4 4 2 2 . 8 1 4 7 B 7 0 . 8 " " ' 5 3 0 7 8 . 7 " 1 5 7 2 8 6 . 6 1 6 2 6 1 2 . 5 1 7 5 9 8 2 . 1 1 8 1 9 8 6 . 5 " 2 8 3 7 ' 2 . 0 3 7 3 0 6 . 2 3 7 2 8 5 . 2 4 1 5 7 3 . 5 4 5 9 0 4 . 7 4 9 7 0 8 5 1 5 2 6 5 4 6 5 7 5 8 5 6 6 6 3 6 5 3 6 6 4 * 9 . 5 6 9 4 5 1 . 3 7 7 9 6 0 . 7 7 8 1 8 1 . 7 " " 8 7135". 4 1 0 0 8 3 a 1 1 1 8 7 9 1 1 7 3 3 3 " 1 2 1 9 7 5 1 2 G 5 3 1 1 3 1 9 2 0 1 3 B 3 0 7 . 2 1 4 2 9 3 6 . 2 1 4 6 1 4 6 . 8 " " 1 5 0 4 7 4 . 7 1 5 5 1 8 2 . 7 1 5 9 9 4 0 . 5 1 6 9 2 9 7 . 3 1 7 8 9 8 4 . 2 1 7 2 1 5 . 0 2 2 6 9 1 . 5 2 6 0 9 9 . 3 3 0 4 2 9 . 2 3 4 1 7 6 . 2 _ 3 5 7 3 1 . 6 3 7 7 m . 9 ' 4 0 8 4 5 . 1 4 4 0 5 7 . 0 4 7 1 6 0 . 1 4 9 4 4 4 . 3 5 0 6 0 0 . 3 ~ 5 3 8 2 0 . 2 " 5 8 7 1 4 . 9 6~84 7 4T0 8 1 6 9 4 . 6 8 5 6 3 5 . 1 _ 8 7 1 1 3 . 8 9 0 7 0 . 9 0 3 9 0 . 9 4 1 4 0 . 9 7 1 6 8 . 9 6 6 3 6 . 8 _ 9 6 5 7 3 . 2 9 7 9 7 7 . 8 " 9 8 5 5 5 . 7 1 0 0 0 5 6 . 6 1 0 9 0 2 6 . 6 1 1 0 2 4 9 . 4 1 6 2 7 0 . 0 1 9 9 5 3 . I 2 4 6 9 7 . 3 • 2 B 5 6 3 . 7 3 7 3 0 7 . 4 3 4 9 5 3 . 9 3 0 7 2 5 . 4 3 9 7 B 2 . I 4 2 4 4 R . S 4 5 6 0 G . 0 4 B 3 0 3 . I 5 C P J 3 . 0 5 7 : 1 0 . 0 5 6 0 1 7 . 6 — E 3 T 4 V T J -7 5 0 8 4 . 3 8 3 0 6 4 . 8 8 G 3 7 3 . 7 8 8 0 6 6 . 4 8 9 7 0 5 . 4 9 7 7 6 S . 2 9 5 5 5 4 . 8 9 A 9 0 3 . S 9 6 5 7 9 . 9 9 7 2 5 0 . 5 9 6 7 6 6 . 6 9 9 3 0 6 . 0 1 0 4 5 4 1 . 5 1 0 9 6 3 7 . 9 1 Source of these data is: Statistics Canada, Science, Technology and Capital Stock Divis ion. See Chapter 6, Section 6.2.1 for more information about these data. Table A 1.1. Capital Stock and Related Data 1 , Canadian 4-digit Food Manufacturing Industries: (cont'd) Cane and Beet Sugar Processors, (S.I.C. 1082), 1947-1975 year gross fixed capilal fornialion capilal cons, allowance end-yr gross slock mid-yr gross slock end-yr net slock mid-yr net slock gross fixed capilal formation capital end-yr mid-yr end-yr mid-yr cons. gross gross nei net allowance slock stock slock stock thousands of current dollars thousands of constant (I%1) dollars 1 9 4 7 1 9 4 0 1 9 4 9 1 9 5 0 1 9 5 1 1 9 5 2 1 9 5 3 1 9 5 4 1 9 5 5 1 9 5 6 1 9 5 7 1 «.i;.ri 1 9 5 9 1 9 6 0 1 9 6 1 1 9 6 2 1 9 0 3 1 9 6 4 1 9 6 5 " 1 9 6 6 1 9 6 7 1 9 5 0 1 9 6 9 1 9 7 0 1 9 7 1 -1 9 7 2 1 9 7 3 1 9 7 4 1 9 7 5 1 3 3 1 3 . 0 E 6 S 5 B . 0 6 9 0 " 5 . I 6 B 6 0 3 . 9 7 0 7 7 1 . B 7 4 1 2 1 . 4 7 6 1 5 4 . 3 • 7 7 6 - J . B 7 B 7 3 B . 5 7 9 7 9 2 . 3 B 2 1 B 5 . 7 B R 2 S 7 . 9 1 0 C 3 3 ? . 0 1 1 1 2 ' 7 . 9 1 1 5 8 3 2 . 5 1 2 G 5 f - > 5 . 9 1 2 4 8 0 9 . 7 1 2 7 9 5 1 . 3 1 3 1 3 3 } . 5 ' 1 3 3 2 1 0 . 8 1 3 3 - 1 7 3 . 2 1 3 3 6 1 5 . 3 1 3 4 0 6 1 . 1 . 1 3 4 7 9 4 . 7 T - T 5 2 5 E ' . T > -1 3 6 5 3 0 . B 1 4 0 5 * 6 . 9 1 4 4 4 8 7 . $ 1 4 7 5 3 9 . 4 4 0 3 9 8 . 0 4 0 0 5 2 . 4 3 9 6 3 4 . 8 4 4 6 . 2 8 . 2 4 6 5 1 2 . 3 4 8 4 7 3 . 5 4 B 7 4 4 . 0 4 9 4 8 3 . 1 4 9 9 4 3 . B 5 3 4 9 6 . 7 G 1 0 4 6 . 7 71 l ^ r . . ! 7 4 I U I . 6 JLB4 .6iu.3_ B 0 6 9 6 . 2 8 4 5 4 3 . 1 8 6 1 6 7 . 0 8 7 7 1 2 . 9 • 6 9 3 7 6 . 2 B 7 5 2 2 . 5 B 6 7 0 7 . 9 8 4 1 7 3 . 5 8 3 7 5 8 . 9 B 1 6 7 7 . 8 " 8 0 0 3 0 : 9 " 7 9 B S 2 . 1 8 3 5 5 3 . 5 6 2 8 3 9 . 3 6 4 5 5 8 . 5 3 8 0 9 2 . 4 0 7 2 5 . 3 9 8 4 3 . 4 2 1 3 1 . 4 5 5 7 0 . 4 7 4 6 7 . 9 4 B 5 8 3 . 7 4 9 1 1 6 . 4 4 9 7 1 6 . 0 5 1 7 1 9 . 7 5 7 J 7 1 . 7 r .C.JOl . 5 7 J 1 H 9 . 0 J7__>A.-5 7 9 5 7 5 . 8 8 2 6 1 4 . 6 8 5 3 5 5 . 0 8 6 9 3 9 . 9 8 H 5 - U . S ' 8 6 4 4 9 . 2 8 6 8 6 5 . 3 B 5 I 9 0 . 8 8 3 7 1 6 . 4 8 2 4 4 3 . 3 " B 0 B 2 9 . 4 7 9 9 4 1 . 7 8 1 7 0 2 . B 8 3 1 9 6 . 5 8 3 6 9 8 . 8 Source o f these data is: Statistics Canada, Science, Technology and Capital Stock Divis ion. Sec Chapter 6, Section 6.2.1 for more information about these data. Table A 1.1. Capital Stock and Related Data 1 , Canadian 4-digit Food Manufacturing Industries: (cont 'd) Vegetable O i l M i l l s , (S.I.C. 1083), 1947-1975 year gross Fixed capital formation capital cons, allowance cnd-yr gross slock mid-yr gross slock cnd-yr net slock mid-yr ncl stock gross fixed capital formation capital cons, allowance cnd-yr gross stock mid-yr gross stock cnd-yr ncl stock mid-yr ncl . stock thousands of current dollars thousands of constant (1961) dollars 1 9*7 1 6 0 4 . 0 1948 3 7 9 2.0 1949 1 4 3 6.0 1950 5 9 7.0 1951 1 2 4 0.0 1952 1 291.0 1953 6 0 9 . 0 1954 1 7 0.0 1955 3 0 8.0 1956 1 1 3 8.0 1957 • 3 5 7.0 1958 1 2 1 1 . 0 1959 1744 .0 1960 1 774.0 . 1961 1 052.0 1962 1 5 0 9.0 1 9 6 3 5 3 2 . 0 1964 5 5 2.0 1905 1599.0 1906 1 8 7 4 . 0 1907 1 0 0 4.0 1908 2 6 0 0.0 1909 7 2 2.0 1970 3 4 0 3 . 0 1971 " 4 6 1 5.0 1972 4 2 4 5.0 1973 1 4 2 2.0 1974 9 6 2 4.0 1975 3 0 4 3 7.0 1*333.6 1 4 1 0 . 7 1 4 7 5 . 4 1 4 7 0 . 2 1 5 0 0 . 7 1 4 9 1 . 7 1 5 0 2 . 5 1 4 5 7 . 4 1 4 4 4 . 3 1 4 7 9 . 7 1 4 9 9 . 8 1 5 0 4 . 2 1 5 3 5 . 6 1 5 9 1 . 0 1 6 2 3 . 3 1663 .1 1 6 9 8 . 6 1 7 4 7 . 3 1 8 1 3 . 9 " 1 8 9 3 . 5 1 8 6 3 . 4 1 8 6 9 . 7 1 9 5 8 . 0 2 0 8 0 . 9 2 2 4 2 . 1 " 2 3 9 0 . 3 2 5 9 0 . 2 3 1 2 8 . 2 3 8 9 4 . 5 3 4 6 4 0 . 5 4 0 9 6 7 . 4 4 3 1 9 4 . 4 4 3 9 4 6 . 6 4 7 2 5 5 . 4 4 8 6 6 3 . 1 ' 4 8 9 5 4 . 3 4 7 7 5 8 . 1 4 7 6 2 1.2 4 9 0 4 7 . 1 4 9 1 7 6 . 5 _ 4 9 7 4 8 . 0 5 0 3 9 4 . 2 5 1 4 8 2 . 6 5 1 7 4 4 . 9 5 2 8 3 6 . 0 5 3 0 5 7 . 9 5 4 4 1 3 . 8 5 7 0 3 2 . 2 " 5 9 5 2 4 . 4 5 8 4 6 5 . 8 5 9 1 2 6 . 9 6 0 4 9 5 . 1 6 5 0 3 9 . 0 6 9 8 3 7 . 3 " 7 3 6 7 2 . 1 7 e 2 l 0 . 6 9 7 5 2 1 . 0 • 1 2 2 9 7 8 . 5 " ' 3 3 3 0 8 , 3 9 7 7 2 . 4 3 2 1 & . 4 4 4 3 0 , 4 7 4 8 6 . 4 6 6 9 8 , 4 5 3 B 2 , 4 8 3 6 1 , 4 8 1 4 1 , 4 9 2 0 5 . 4 9 7 5 1 , 4 9 8 7 6 . " 5 0 7 2 9 . 5 1 3 5 4 . 5 2 0 0 6 . 5 2 8 1 6 . 5 3 6 1 4 , 5 5 0 3 0 , " 5 7 1 5 3 . 5 9 5 5 0 . 5 8 9 1 3 . 5 8 7 3 5 . 6 1 0 6 6 . _ 6 4 3 7 B . 6 8 6 2 4 . 7 2 6 4 0 . 7 8 7 1 6 . 9 4 0 5 2 . 1 1 4 3 6 4 . 3 2 5 8 2 . 0 3 5 8 4 6 . 1 3 5 7 4 9 . 3 3 4 5 7 2 . 5 3 4 2 6 1 . 9 3 4 0 7 1 . 7 , 3 3 0 5 1 . 3 3 1 5 3 4 . 8 3 0 3 2 7 . 2 2 9 8 6 9 . 6 2 8 6 4 9 . 2 3 8 3 5 3 . 3 . 2 8 5 7 6 . 1 2 8 7 0 7 . 1_ " 2 8 1 3 6 . 7 2 8 0 5 8 . 7 2 6 9 4 8 . 7 2 5 8 7 5 . 1., 2 5 6 5 0 . 2 2 5 5 7 1 . 0 2 4 8 5 6 . 8 2 5 4 6 5 . 6 2 4 4 7 9 . 4 . 2 5 4 8 7 . 2 _ 2 7 3 4 6 . 3 3 8 5 6 0 . 6 2 7 7 8 7 . 9 3 1 5 0 4 . 3 4 0 3 7 2 . 1 3 0 7 2 2 . 0 3 4 7 1 3 . 9 3 5 7 9 7 . 7 3 5 1 6 0 . 8 3 4 4 1 7 . 1 3 4 1 6 6 . 6 3 3 5 6 1 . 4 3 7 7 9 3 . 0 3 0 8 8 1 . 0 3 0 0 4 8 . 4 3 9 3 5 9 . 4 2 8 5 0 1 . 2 . 3 R 4 6 4 . B 2 8 6 4 1 . 5 2 8 4 3 1 . 7 " 2 0 0 9 7 . 7 2 7 5 0 3 . 7 2 6 4 1 1 . 9 2 5 7 6 2 . 5 2 5 6 1 0 . 5 3 5 7 1 3 . 9 2 5 1 6 1 . 2 2 4 9 7 2 . 4 . 2 4 9 8 3 . 3 3 6 3 6 6 . 7 2 7 9 0 3 . 5 3 B 1 7 4 . 2 2 9 6 4 6 . 0 3 5 9 3 B . 1 1 Source o f these data is: Statistics Canada, Science, Technology and Capital Stock Divis ion. See Chapter 6, Section 6.2.1 for more information about these data. Table A 1.1. Capital Stock and Related Data 1 , Canadian 4-digit Food Manufacturing Industries: (cont'd) Miscel laneous Food Processors N.E.S., (S.I.C. 1089), 1947-1975 year gross fixed capital formation capilal cons, allowance end-yr gross slock mid-yr gross slock end-yr net slock mid-yr nel slock gross fixed capital formation capilal cons, allowance end-yr gross slock mid-yr gross slock end-yr nel slock mid-yr net slock thousands of current dollars thousands of constant (1961) dollars t 9 " 7 8 7 4 7 . 0 2 3 6 0 . 7 6 6 5 1 1 . 1 6 395 7 .0 3 8 9 8 5 .7 3 6 7 8 6 . 0 194-1 7 4 6 7 . 0 2 7 4 4 . 7 7 8 8 4 4 . B 7 6 4 5 7 . 1 4 8 1 5 9 . 6 4 S 7 9 B . 6 1949 5 0 3 S . 0 3 1 6 9 . 2 8 7 4 0 7 . 2 6 6 2 8 7 . 1 5 4 0 9 0 . 5 5 3 0 3 1 . 4 1900 4 3 9 7 . 0 3 3 1 2 . 7 9 2 1 3 3 . 3 9 1 5 4 5 . 6 5 7 3 3 9 . 0 5 6 7 9 6 . B 1951 7 C 1 7.0 3 5 5 4 . 7 1 0 3 3 6 7 . 1 1 0 1 6 1 5 . 1 6 5 5 9 8 .5 6 3 8 6 7 . 5 . 1952 5 6 0 0 . 0 3 6 1 0 . 6 1 0 9 6 7 5.2 1 0 7 5 6 1 . 2 6 9 5 7 8 . 6 _ 6 8 5 9 4 . 1 , 1953 7 2 6 3 . 0 3 7 4 2 . 0 1 1 5 1 6 3 . 9 1 1 3 2 3 9 . 5 74781 . 0 7 3 0 2 2 . 1 1 -»54 7 l >53 .0 3 9 1 2 . 0 1 2 0 3 2 3.2 1 1 T E 6 6 . 6 7 8 9 8 5 . 2 7 6 9 6 4 . 7 1555 8 4 4 3 . 0 4 2 1 9 . 3 1 2 8 1 4 4 . 6 1 2 5 4 5 6 . 6 84801 . 6 8 2 6 9 1 . 3 1955 8 1 9 6 . 0 4 6 3 4 . 0 1 3 8 1 1 8 . 7 1 3 5 C 3 7 . 5 9 1 6 7 7 .9 6 9 B 9 6 . 9 1 5 . . 1 1 4 1 7.0 5 0 9 0.0 1 5 0 5 3 3 . 4 1 4 6 4 7 2 . 1 1 0 0 8 7 9 . 5 9 7 7 1 5 . B 1900 1 6 2 5 8.0 5 5 9 4 . 5 . 1 6 5 9 5 9 . 4 1 5 3 6 6 3 . 8 1 1 3 4 3 6 . 0 . 1 0 8 1 0 4 . 2 . 1950 1 1 4 3 1.0 6 0 2 1.3 1 7 5 2 0 7 . 4 1 7 1 3 6 5 . 4 1 1 9 9 3 8 . 0 1 1 7 2 2 3 . 2 I 9 6 0 1 1 7 6 0.0 6 3 9 9 . 9 1 8 6 3 0 3 . 7 1 8 3 3 3 1 . 2 1 2 7 4 2 6 • ( 1 2 4 7 4 6 . 7 1961 1 3 2 4 4 . 0 6 8 0 8 . 9 199070.8 1 9 4 4 3 3 . 0 1 3 6 3 1 5 .1 1 3 2 9 9 7 . 5 1962 13 . - . 59.0 7 2 8 3 . 8 2 1 3 3 3 1 . 9 2 3 5 7 2 4 . 3 1 4 5 6 7 5 .3 1 4 2 6 3 7 . 5 1963 1 9 0 1 3.0 7 8 4 1 . 1 2 3 3 4 6 4 . 2 2 2 3 2 5 9 . 1 1 6 0 6 8 6 .1 1 5 5 1 0 0 . 6 1964 1 3 9 9 4 . 0 8 7 2 2 . 7 2 5 5 7 7 5 . 1 2 5 1 0 4 2 . 0 . 1 7 4 6 1 5 . 6 _ 1 7 1 9 7 9 . 9 . 1965 1 9 6 2 0 . 0 9 5 8 8 . 3 2 8 4 4 2 8 . 5 2 T e 9 8 9 . 0 1 93897 .1 1 8 8 9 3 1 . 5 196S 3 7 9 7 2 . 0 1 0 9 7 9.5 3 2 8 9 9 0 . 9 3 1 2 4 3 3 . 6 2 2 8 8 4 9 . 4 2 1 5 3 5 3 . 2 1967 3 9 7 6 7 . 0 1 2 0 9 7 . 6 3 6 0 2 3 8 . 5 3 4 3 7 7 1 . 7 2 5 4 2 8 2 . 2 2 4 0 4 4 7 . 5 I 9 6 0 1 9 7 2 5.0 1 3 0 1 4.3 3 7 4 2 5 6 . 1 3 6 6 9 6 6 . 1 2 8 0 6 1 4 . 7 2 5 7 2 5 9 . 5 1969 2 3 4 6 9 . 0 1 4 0 4 1 . 6 407306.8 3 9 3 3 3 3 . 9 2 8 0 5 1 9 . 6 2 7 5 8 0 5 . 9 : 1970 2 2 0 9 2 . 0 1 S 2 6 4 . S 4 4 4 3 5 9 . 4 . 4 3 6 2 7 7 . 3 3 0 1 9 1 2 . 1 2 9 P 4 9 8 . 6 1971 " 3 5 8 3 3 . 0 16331 .7 " 4 8 7 3 7 9 . 1 4 7 3 0 6 9 . 2 " 3 3 1 4 7 3 . 2 3 2 1 7 2 2 . 6 1972 3 5 8 5 1 . 0 1 7 4 5 6 . 3 5 2 6 7 7 3 . 6 5 1 2 7 5 4 . 7 3 S 7 7 9 9 .5 3 4 8 6 0 2 . 2 1973 5 2 1 3 9 . 0 3 0 0 7 9 . 1 6 1 1 9 5 5 . 6 5 8 9 1 8 4 . 7 4 1 6 8 3 2 . 5 4 0 0 B 0 2 . 7 1974 6 1 7 0 7 . 0 2 5 5 2 4 . 0 7 6 5 7 4 8 . 2 7 3 8 7 4 4 . 0 5 2 0 4 6 3 . 6 5 0 2 3 7 2 . 0 1S7S 6 5 4 2 4 . 0 2 9 7 B 0 . 6 * 885206.8 6 5 6 7 7 4.3 5 9 9 0 3 6 . 0 5 8 1 2 1 4 . 5 1 4 3 8 7 . 6 1 1 1 4 9 . 4 7 1 8 5 . 4 6*067.4 8 6 8 8 . 0 _ 6 B 3 6 . 9 8981 ' . 8 9 6 4 0 . 7 9 9 5 1 . 6 9 3 7 0 . 6 1 2 2 9 3 . 8 - . 1 7 1 4 3 . 6 1 1 9 1 1 . 6 1 1 9 9 6 . 3 4 0 5 4 . 2 4 2 2 4 . 1 4 6 1 5 . 7 4 5 7 4 . 1 4 5 1 2 . 9 4 4 8 2 . 7 . 4 5 2 5 . 5 4 7 0 5 . 4 4 9 5 6 . 2 5 2 1 5 . 3 5 5 1 7 . 5 . 5 9 3 0 . 6 6 3 0 1 . 2 6 5 5 6 . 7 1 0 7 2 S 3 . 0 1 1 4 2 5 5 . 0 1 2 0 2 7 5 . 5 1 2 1 8 7 2 . 3 1 2 6 0 8 9 . 9 . 1 2 8 7 2 5 . 7 1 3 3 5 6 5 . 7 1 3 9 5 6 3 . 7 1 4 5 9 4 3 . 0 1 5 1 6 9 9 . 2 1 6 0 4 4 2 . 2 . 1 7 3 7 0 9 . 2 1 8 1 7 3 3 . 6 1 8 9 7 Q S . 6 1 0 3 1 3 6 . 0 1 1 0 7 5 4 . 0 1 1 8 7 1 1 . 6 1 2 1 0 7 3 . 6 , 2 3 3 8 1 . 1 . 1 2 7 4 0 7 . 7 1 3 1 1 4 5 . 6 1 3 6 5 6 4 . 5 1 4 2 7 5 2 . 9 1 4 8 8 3 0 . 5 1 5 6 0 7 3 . 4 1 6 7 0 7 5 . 6 1 7 7 7 0 6 . 3 1 8 5 7 4 9 . 4 1 3 7 4 4 . 0 1 3 0 4 7 . 8 1 8 0 4 9 . 4 . 1 2 3 4 7 . B . 1 6 3 9 4 . 3 3 0 9 1 5 . 2 3 2 8 7 2 . 4 1 6 3 4 5 . 6 1 6 7 2 2 . 6 . 1 6 7 9 9 . 7 _ 2 6 2 9 6 . 4 2 6 0 6 5 . 2 3 5 0 5 3 . 5 3 5 5 8 9 . 0 3 5 0 6 6 . 5 6 8 0 9 . 9 7 0 5 8 . 8 7 3 7 3 . 1 _ . 7 7 1 5 . 6 _ . 8 1 0 B . S B B 7 4 . B 9 9 8 6 . 0 1 0 7 7 0 . 7 1 1 1 9 7.7 _ J . 1 6 2 2 . 6 _ 1 2 0 8 6 . 5 1 2 6 5 2 . 2 1 3 0 5 3.7 1 4 7 5 8 . 9 1 5 9 7 1 . 4 1 9 9 0 7 0 . 8 2 0 8 0 9 4 . 6 7 3 1 8 1 8 . 1 2 3 0 1 4 4 . 3 3 4 3 5 5 0 . 8 3 6 9 5 2 2 . 7 2 9 8 4 0 4 . 4 3 1 0 4 8 4 . 3 2 4 9 3 2 . . 3 3 7 2 4 3 . 3 5 8 2 0 3 . 3 7 8 6 1 2 . 4 0 9 2 2 3 . 8 4 4 0 3 5 9 . 8 4 7 0 6 3 6 . 9 1 9 4 4 3 3 . 0 2 9 3 5 8 2 . 6 2 1 4 9 5 6 . 2 _ 2 2 5 9 9 l . 0 2 3 6 3 4 7 . 5 2 5 6 0 3 6.7 2 8 3 9 * 3 . 4 3 0 4 4 4 4 . 0 3 1 7 7 2 3.5 _ 3 3 H 0 3 . 2 3 4 7 7 2 3 3 6 8 4 0 7 3 9 3 9 1 8 424791 4 5 5 5 9 8 6 7 5 6 1 . 0 6 9 4 8 6 . 4 7 4 1 7 5 . 7 7 5 0 6 9 . 0 7 9 8 4 4 . 3 6 2 1 9 8 . 3 8 6 6 5 4 . 5 9 1 5 8 9 . 7 9 6 5 8 4 . 9 1 0 0 7 4 0 . 3 1 0 7 5 1 6 . 5 . 1 1 8 7 2 9 . 7 . 1 2 4 3 4 0 . 4 _1_39779..7_ ' 1 3 6 7 1 5 . 1 1 4 3 3 0 4 . 0 1 5 2 8 0 0 . 2 1 5 7 5 1 2 . 2 . 1 6 5 7 9 7 . 9 1 8 7 R 3 8.3 2 1 0 7 2 4 . 6 2 1 6 2 9 9 . 4 2 2 3 8 2 4 . 3 2 3 9 0 0 1 . 6 . 2 4 3 2 1 3 . 5 2 5 5 6 2 6 . 6 2 7 8 1 2 6 . 3 2 9 8 9 5 6 . 8 3 1 8 0 5 1 . 6 5 B 9 9 I . 0 6 6 0 2 3 . 5 7 7 6 9 3 . 0 7 4 9 2 2.3 7 7 7 5 6 . 5 8 1 0 2 1 . 4 8 4 4 7 6 . 5 8 9 1 2 2 . 0 9 4 0 6 7 . 2 9 8 6 6 2 . 5 1 0 4 1 2 B . 4 1 1 3 1 2 3 . 1 1 2 1 5 3 4 . S J 2 7 0 5 9 . 7 1 3 7 9 9 7 . J 1 3 9 2 0 9 . 4 1 47542 . 1 1 5 5 1 9 6.3 1 6 1 6 5 4 . 9 I 7 6 B 1 8 . 2 1 9 9 2 B 1.3 2 1 3 5 1 1 . 6 2 2 0 0 6 1 . 7 2 2 6 4 1 3 . 0 2 3 6 1 0 7 . 4 2 4 9 9 2 0 . 1 2 6 7 3 7 6.3 2 8 8 5 4 1 . 5 3 0 8 5 0 4 . 1 1 Source o f these data is: Statistics Canada, Science, Technology and Capital Stock Divis ion. See Chapter 6, Section 6.2.1 for more information about these data. Table A 1.1. Capital Stock and Related Data 1 , Canadian 4-digit Food Manufacturing Industries: (cont'd) Soft Drink Manufacturers, (S.I.C. 1091), 1947-1975 gross fixed capital end-yr mid-yr end-yr mid-yr capilal cons. gross gross nel nel year formation ' allowance slock slock . slock slock thousands of current dollars 1947 - ' 2499 .0 — 15657.7 15055.9 9176 . 9 " 1948 4577 .0 7 1 3 . 4 213BO.0 19403.3 14067 .9 1949 6043 .0 956.1 28246.2 25562.0 20172 .9 1950 5154 . 0 1 1 6 6 . 4 33814.7 31607.5 24974 .9 1951 4031 .0 1387.7 39832 . 9 38220.2 29667 .0 1952 7C0O.O 1487.S 43708.2 41647.5 3 1 6 6 1 ' : 1 19S3 7357 .0 1620 . 8 50021.6 " ' 4 6 8 0 S . 9 " 3 8 1 8 4 .8 ' 1954 6017 .0 1776.0 55249.8 52701.7 43595 .5 1955 3968 .0 •.-•27.6 59355.5 57EG4 .4 45486.7 1956 6791 .0 2165.5 67523.7 64593.0 51858 .9 •957 7437 .0 2489 . 8 76115 . 3 72863.2 583B1 .3 1958 8956 .0 2791 . 9 , HS31B.0 61431 .1 65635 .8 1959. 9638 . 0 3109 . 8 ' 94625.3 *"* " 90364.3 "73734 .4 " I 9 6 0 11726.0 3525.6 107025.2 101673.8 62221 .5 1961 11233 . 0 3977.5 118876.0 113939.0 90942 .4 1962 15113 . 0 4531.5 135653.7 12B7B2.1 103765.1 1963 12361 . 0 5130.2 150219 . 9 144765.0 1 13769 .9 1964 20258 .0 5968 .0 177138.4 167983*3 134273 .2 1 9 6 5 ' 20291 .0 6 9 4 4 . 5 " - " 2 0 5 1 4 5 . 9 — " i&5j08.9 '154797 .8"' 1966 19457 .0 7839.1 230909.5 222200.7 172892 .4 1967 19206 . 0 8299.3 245455.0 236979.2 182375 .5 1 9 6 8 21867 .0 8937.5 264792.6 2 5 * 9 3 ) . 4 195009 .4 1969 19435 . 0 9 9 1 6 . 1 292407.3 263692.6 212438 .7 1970 16414 . 0 10897 . 8 321188.9 . 314304.3 22B984 .3 1971 ~ 13999 .0 f 1 6 0 3 . 8 341843 . 8 "337J23.9" *3390SS.'-r' 1972 14521 . 0 12183.5 362159.7 356455.8 247066 .3 1973 28219 . 0 13684 . 8 414261.2 401834.5 2e0211 .0 1974 26566 . 0 16890.5 S04B69.6 493444.7 335339 .3 197S 26095.0 19036.9 563389.0 557307 . 9 36996S . 5 gross fixed capilal end-yr mid-yr end-yr mid-yr capilal cons. gross gross net nel jormalion allowance slock slock slock slock thousands of constant (1961) dollars "25249.0 31289.7 49060,7 44903.1 4BB63.0 51009.6 5B204.8 64066 67506 74125 81110 89244 98119 24279.0 262*9.2 3-.368.6 41961.B . 4 6 8 8 3 . 1 49936 5«607 61M5 65796 7081S 77617.8 85177.1 9 3 6 8 1 . 9 109001.7 103560.5 14726.0 20640.5 27B64 33115 36329 37733 1 4 3 1 4 49779 51606 56839.4 67138.1 6B573.7 75368.1 B3G06.8 118876.0 133380.6 143586.0 159476.5 "175197.8* 189353.6 203347.2 219708.1 233293.9 243756.9 252108:7" 260460.3 277218.0 290450.9 302414.3 13886.0 17663.2 24379.1 30490.0 34722.6 37026 . 4 41018.7 46797.0 50443.0 54722.7 59488.S 65355 . 9 71970 . 9 79527.5 87314.8 9 6 1 1 2 . 7 104713.7 1 14721 .2 127007.0 137443 .9 146669.8 156537.7 165705.0 171597 .4 "174598.1 176392.7 182IB3.0 1B9B92.6 194667.0 1 Source o f these data is: Statistics Canada, Science, Technology and Capi lal Stock Divis ion. See Chapter 6, Section 6.2.1 for more information about these data. Tabic A 1.1. Capital Slock and Related Data 1 , Canadian 4-digit Food Manufacturing Industries: (cont 'd) Disti l leries, (S.I.C. 1092), 1947-1975 your gross fixed capital formation capilal cons, allowance cnd-yr gross slock mid-yr gross slock cnd-yr net slock mid-yr ncl stock gross fixed capilal formation capital cons, allowance cnd-yr gross stock mid-yr gross slock cnd-yr net stock mid-yr ncl slock thousands of current dollars thousands of constant (1961) dollars 1 9 4 7 1 9 4 9 1 9 1 9 1 9 5 9 1 9 5 1 1 9 5 2 1 9 5 3 1 9 5 4 1 9 5 5 1 9 5 6 1 S 5 7 1 9 5 8 1 9 5 9 1 9 6 0 1 9 6 1 I 9 G 2 1 9 6 3 1 9 6 4 1 9 6 5 1 9 C 6 1 9 6 7 1 9 6 8 1 9 6 9 1 9 7 0 1 9 7 1 1 9 7 2 1 9 7 3 1 9 7 4 I S 7 5 5 6 8 5 . 0 7 6 3 5 . 0 3 9 1 8 . 0 2 7 2 7 . 0 5 3 1 4 . 0 5 4 6 7 . 0 4 4 8 5 . 0 4 2 9 4 . 0 8 0 5 6 . 0 8 1 6 7 . 0 * 8 3 2 1 . 0 6 2 5 4 . 0 " 1 0 8 2 6 . 0 • 9 3 8 5 . 0 7 4 6 6 . 0 7 2 8 6 . 0 6 1 6 2 . 0 1 2 6 0 3 . 0 1 5 5 7 7 . 0 2 0 0 0 3 . 0 1 8 0 1 4 . 0 2 8 6 6 7 . 0 4 6 0 6 6 . 0 5 7 4 5 0 . 0 3 3 5 7 4 . 0 1 9 1 1 9 . 0 3 3 6 1 6 . 0 2 2 6 1 5 . 0 2 5 6 9 0 . 0 " ' 8 8 7 . 9 1 0 8 5 . 2 1 2 G 3 . 1 1 3 6 4 . 6 1 5 3 5 . 9 1 6 7 1 . 8 1 8 0 5 . 2 1 8 8 4 . 4 2 1 0 3 . 7 2 4 4 3 . 0 2 7 3 3 . 7 2 9 4 9 . 8 3 1 6 9 . 7 ' 3 4 6 4 . 3 3 7 2 4 . S 3 9 9 8 . 7 4 2 6 9 . 3 4 7 3 4 . 7 ' " 5 3 3 9 . 8 6 0 2 2 . 5 6 5 0 5 . 1 7 2 3 5 . 8 B 7 6 7 . 6 1 0 9 5 2 . 6 1 2 8 2 9 . 8 1 3 8 2 9 . 2 1 5 2 4 9 . 2 1 8 0 4 7 . 4 1 9 6 5 4 . 6 2 4 9 2 7 . 5 3 4 3 7 6 . 3 3 9 1 1 2 . 7 4 7 2 6 2 . 7 5 0 1 1 7 . 7 5 6 0 1 3 . 1 6 0 4 8 0 . 8 6 3 4 3 4 . 0 7 1 4 8 9 . 0 8 0 8 9 4 . 9 8 9 7 5 9 . 6 9 6 0 7 0 . 1 1 0 5 9 5 6 . 6 ' 1 1 5 0 9 9 . 5 1 2 2 4 3 9 . 9 1 3 C 2 4 2 . 4 1 3 8 0 6 2 . 4 1 5 5 1 0 4 . 9 " 1 7 6 5 4 4 . 2 " 2 0 2 7 5 7 . 9 2 1 9 3 4 8 . 5 2 4 5 6 1 8 . 7 3 0 0 2 6 3 . 8 3 7 1 5 0 5 . 4 1 6 5 5 0 . 4 4 3 8 2 9 . 4 9 7 1 3 7 . 5 9 1 8 0 9 . . 0 . 7 . 4 . 3 . 6 6 6 1 4 6 6 . 8 8 8 , 7 7 . 3 1 0 6 7 0 . 2 5 3 6 2 . 4 3 5 5 6 . 7 6 3 7 3 . 9 6 3 8 2 . 8 " 5 l 5 7 i 5 4 8 9 0 . 6 9 1 7 5 . 6 8 8 5 4 . 7 8 7 4 6 . 3 6 4 5 2 . 3 i 1 1 2 9 . 8 ^ . . 9 5 6 5 . 5 . . 7 4 6 6 . 0 7 1 1 7 . 4 5 8 8 4 . 4 J 1 5 9 B . 9 1 3 5 0 4 . 0 " 1 6 6 2 9 . 2 1 4 0 < i . 2 2 3 8 3 7 . 7 3 6 7 6 0 . 2 4 3 5 6 8 . 9 2 4 6 2 6 . 6 1 3 5 4 9 . 1 1 5 G 4 4 . 5 1 7 9 7 3 . 0 1 3 6 5 0 . 4 3 8 6 5 5 . 0 4 4 7 2 9 . 9 S i 1 6 6 . 6 5 4 0 7 1 . 4 5 7 4 8 3 . 2 6 3 3 4 3 . 3 " 6 6 6 0 1 . 1 7 0 1 3 1 7 5 7 5 6 8 3 3 9 3 9 0 7 3 1 9 6 8 4 7 1 0 4 1 8 4 1 1 2 8 3 J .9 1 1 9 5 3 7 . B 1 3 5 1 9 3 . 5 1 3 0 1 6 3 . 4 1 3 7 3 7 4 . 0 ' 1 4 8 3 4 3 . 3 1 6 1 5 6 7 . 1 1 7 5 6 * 0 . 8 1 9 3 4 5 6 . 7 3 2 3 1 1 9 . 4 2 6 0 4 7 1 . 3 3 9 3 5 8 9 . 9 3 0 9 5 8 8 . 5 3 3 1 8 4 9 . 9 3 3 3 3 4 6 . 7 3 4 3 3 8 1 . 0 3 3 4 4 8 . 0 3 3 4 0 6 . 8 3 5 9 5 8 . 4 3 7 6 5 6 . 7 4 2 1 1 3 . 6 . 4 6 4 6 1 . 6 " 4 9 4 7 8 . 5 5 2 1 4 5 . 4 S B B 9 2 . 2 6 5 0 3 7 . 1 7 . 0 8 5 0 . 4 7 4 2 0 4 . 0 ~~ 8 2 0 3 5 . 9 BB0_6_7. B_ 9 1 B 0 9 . 2 9 5 0 2 9 . 7 9 6 B 7 0 . 0 1 0 4 2 1 6 . 4 1 1 3 2 5 4 . 1 2 4 9 4 9 . 1 3 4 5 0 5 . 1 5 2 3 3 5 . 1 6 2 1 0 1 . 2 1 7 3 4 6 . 1 2 3 2 5 3 0 . 2 2 3 6 1 3 6 . 8 3 4 1 5 7 8 . 5 2 4 4 1 6 3 . P 2 4 7 3 G 2 . 3 2 7 1 0 B . 0 3 7 9 7 7 . 4 3 4 1 8 3 . 6 3 6 8 0 7 . 5 3 9 B B S . 1 4 4 2 8 7 . 8 4 7 9 7 0 . 0 S O B ! 1 . 9 5 5 5 1 8 . 8 6 1 9 6 4 . 7 6 7 9 4 3 . B 7 3 5 7 7 . 2 7 8 1 1 9 . 9 B 5 0 5 2 . 0 8 9 9 3 0 . 5 9 3 4 1 9 . 5 9 5 9 4 9 . a 1 0 0 5 4 4 . 4 1 0 8 7 3 6 . 3 11 9 1 0 1 . 6 1 2 9 7 2 6 . 9 1 4 3 4 2 0 . 2 1 6 7 7 1 8 . 6 1 9 P 7 2 3 . 9 3 3 - 1 9 3 8 . 1 3 3 4 3 3 3 . 4 3 3 R R 5 7 . 6 3 4 2 8 7 1 . 3 3 4 5 7 6 3 . 1 1 Source o f these data is: Statistics Canada, Science, Technology and Capital Stock Divis ion. See Chapter 6, Section 6.2.1 for more information about these data. Tabic A 1.1. Capita l Stock and Related Data, Canadian 4-digit Food Manufactur ing Industries: (cont 'd) Breweries, (S.I.C. 1093), 1947-1975 year gross fixed capital formal ion capilal cons, allowance cnd-yr gross slock niid-yr gross slock cnd-yr ncl slock mid-yr ncl slock gross fixed capilal formation capital cnd-yr mid-yr cnd-yr mid-yr cons. gross gross ncl net allowance slock . slock slock slock thousands of current dollars thousands of constant (1961) dollars » 9 4 7 14103 . 0 \ 2 7 9 . 2 35918 .7 34541.0 21054 .8 19854.9 • 22935.1 3 1 8 9 .7 . 9 4 3 17410 . 0 1743.B 55956.8 4 7 0 7 8 . 5 39134 .7 31391.4 25676.8 3689.4 1949 13303 . 0 3 4 1 3.4 7 1 3 3 8 . S 65516.7 53489 .3 47P93.0 1B372.6 3 5 1 5 . 8 1 9 5 0 1 3 2 1 1 . 0 3 9 3 4 . 8 8 5 7 5 1 .6 79991.8 64873 .9 59735.B 1 7 ^ 4 4 . 3 4057 .9 1 V 5 . 13099 . 0 3 5 5 5 . 9 102308 .5 98080.3 78049 .9 74570.3 1 4 9 4 9 . 2 4524% 5 1953 12025 . 0 3 8 7 4 . 0 1 1 5 6 9 8 . 4 - 1 1 0 ? 6 B . B 8937.3 .8 85398.3 14370.4 482-7.6 1953 1 4 5 0 1 . 0 4 1 9 4 . 3 130177.6 1 3 4 3 4 5 . 7 1 0 1 9 3 3 .9 " 96735.9 " 1 7 5 4 4 .,6 5 0 e 3 . U 1 V 5 4 2 1 2 5 5 . 0 4619 .3 1 4 9 3 5 5 .1 1 3 9 9 1 7 . e 1 1 8 7 8 3 .8 1 1 0 4 5 4 . 9 2 4 4£6 . ' 2 5S50.7 1 9 5 5 1 B B 6 4 . 0 5337 .0 10*1810.4 160575.8 134753 .3 137939.9 21362.7 6126 .5 1956 1 3 3 2 3 . 0 5877.4 185352.2 13C249.3 146377 .3 143055 .1 13792 .9 65B2.7 I S J6338 . 0 6 5 2 6 . B 304594 .8 19761B.1 160234 .3 155333.6 17612 .3 7050 .8 1 9 5 6 10510 . 0 7009.4 2 1 5 9 9 9 .6 312158.2 1 6 6 5 9 6 .1 164845.8 11 0 2 7 . 5 7409.4 1959 16769 . 0 7359 .8 3 3 1 6 3 1 . 1 234713.1 "*" 177398.2 177598.5 i 7423.2 7694 .0 1960 2 1 0 S 3 . O 7991 .9 2 5 J B 1 4 . 5 244735.3 193400 .4 106870.5 21437.2 6175 .2 1961 21763 . 0 8746.7 3 7 7 1 4 4 . 9 3 6 7 5 8 1 . 2 209G51 .0 303143 .0 21763.0 8746 .7 " ' 1963 1 6 0 7 5 . 0 9 4 9 7 . 6 29B475.4 3 9 1 0 6 4 . 5 333916 . 1 . 218627 .5 , 17 6 8 4 . 2 9218 .8 1963 17663 . 0 i 0 3 1 4 . 2 3 3 1 1 7 6 . 0 313735.1 3 3 6 1 1 1 .4 3 3 7 3 3 7 . 6 16749.2 9629 .2 1964 15095 . 0 11 2 4 6 . 6 3 4 9 7 9 3 . 5 3 4 3e.63.4 251057 . 1 750033 .0 13561 .1 9 9 9 1 . 1 1965 15970 . 0 1 2 1 8 0 . 9 3H06S5.4 3 7 J 5 5 I . 3 " " ' 769391 .4 ' 367197 .0 """ 1 3 4 7 2 . r " 1 0 2 5 2 . 9 " " 1966 12543 . 0 1 3 8 4 9 . 3 405336.4 401016.3 7B05D3 . 5 200G56.7 iorr.7.0 10436.5 1967 1BP97 . 0 17905 .3 417870 .1 410168.7 7U535B. 1 282363 .2 15658.8 10670.7 I960 3 5 0 5 9 . 0 13C5C.1 4 4 0 6 0 2 . 5 433377.8 307081 .7 295925.8 " 29P69 .2 1 1 3 1 3 . 7 1969 2466.1 . 0 15100 .5 4n934S.1 478740.7 379614 . 5 324833.4 1 P 6 7 6 . 9 12044.7 1970 3 7 2 0 2 . 0 1 6 8 0 5 . 5 5 4 8 5 0 1 . 3 5 3 1 7 7 5 . 8 367530 . 9 357333.6 26758.0 12777.2 1971 4 3 7 4 7 . 0 1 8 7 1 6 . 5 6 0 6 8 3 0 . 8 : ' ' 5 B 7 1 G B . 9 404943 . 9 397H37.7 31511.3 1 3 R 1 6 . 3 1972 34391 . 0 2 0 4 9 3 . 9 0 5 7 0 0 3 . 3 635314.0 429134 . 1 433175.1 24P13.4 14808.8 1973 4 7 3 4 4 . 0 23273 .9 742910 .2 733031.2 4BS52S .7 473490.6 31614.4 15656.8 1974 65793 . 0 3BB90 .8 9 3 3 4 4 3 .1 893343.B 599354 .0 580807 .8 3773G.2 16671.6 1975 3 4 4 4 3 . 0 33640 .7 .1036683.8 1013018.7 651711 . 0 C50B10.1 18395.2 17442 .3 57921.0 B1357 .9 98219.9 113527.4 126129.9 137240.7 151137.3 177683 .1 191196.3 702368.3 217396.3 325412.5 239751 .6 358217.2 27714-1.9 391678.1 305839.1 31 0 3 7 3 . 7 336710.8 3 3 3 B 1 I . V 3 4 6 5 9 1 373544 390467 .415863 444838 466738 494584 529191 543749 55700.0 59639.4 90344.2 105871.1 119826.1 •131685 .2 . 1 4 4 1 8 8 . 9 161910.1 1 8 1 9 3 9 . 7 196782.1 309BS2.1 221404.3 233583. 1' 243984.5 ' 257681 .2" 784411.4 298758.4 311105.7 "321541 .6 330760.9 340701.2 3600*7.6 3B7005.7 4 03164.7 " ' 4 3 0 3 4 5 . 1 4 557.97. 9 480661.1 5 1 1 8 B 7 . 9 536470.2 33766.0 5 6 7 7 3 .6 77087.2 85673.7 96098.5 . 105641.5 1 I R I 0 7 . 4 1 3 7 0 1 7 . 7 1522S3.6 159464.0 170075.7 . 1 73643.8 183372.8 _ 1 9 6 0 3 4 . 9 209651 .0 218116.6 225236.5 2 7 8 * 0 6 . 5 . 337025.7 23IHS1 .2 23GR39.5 2 5 5 3 9 5 . 1 263037 .2 2 7 B 5 0 7 . 9 . 2 9 6 3 0 3 .9 306307.5 3 3 3 1 6 5 . I 3 4 3 3 3 9 . 7 344162 .7 31056.0 45779.8 64701.7 7B880.3 90BB6.0 100BG9.8 111871.9 177560.1 144635.7 155858. 164744. 171834. 17R50B. 190003.^ 703143.0 213883.8 271676.3 2 7 7 0 7 1 . I 230416.0 231938.5 2 3 4 3 4 5 . I 246117.2 250711 .2 770767.8 287355.4 301705.3 314)88 .3 337697.4 343706.1 1 Source o f these data is: Statistics Canada, Science, Technology and Capital Stock D iv i s ion. See Chapter 6, Section 6.2.1 for more informat ion about these data. Table A l . 1. Capita l Stock and Related Data, Canadian 4-digit F ood Manufactur ing Industries: (cont 'd) Winer ies, (S.I.C. 1094), 1947-1975 ycjir gross fixed capital formation capital cons, allowance end-yr gross slock mid-yr gross slock end-yr net slock mid-yr nel slock gross fixed capital formation capital cons, allowance end-yr gross slock mid-yr gross stock end-yr net stock mid-yr net stock thousands of current dollars thousands of constant (1961) dollars 1 9 4 7 9 0 S . 0 *• • • ' < 1 7 8 . 6 " ' 5 0 1 6 . 2 J ( J j 3 . 9 " " " " 5 7 7 8 ; 9 1 9 4 8 5 8 0 . 0 2 0 8 . 7 5 9 7 1 . 4 1 9 4 9 3 1 6 0 2 2 6 . 9 6 4 0 8 . 2 6 3 5 7 . 6 • 9 5 0 2 8 0 0 2 3 6 . 0 6 7 2 0 . 6 6 6 9 3 . 9 1 9 5 1 3 5 0 0 2 5 1 . 7 7 3 7 5 . 5 7 3 2 3 . 8 1 9 5 2 2 6 3 0 2 4 8 . 9 7 5 8 0 . 3 ° 7 5 8 5 . 2 1 9 5 3 3 1 5 . 0 ' " 2 4 7 . 3 "" 7 8 3 6 . 1 7 6 0 3 . 2 -1 9 5 4 1 0 2 2 . 0 2 5 5 . 9 8 6 6 3 . 6 8 2 6 3 . 1 ,. 1 9 5 5 1 5 0 5 0 • 2 9 0 . 2 1 0 1 2 0 . 3 9 4 7 8 . 3 • 1 9 5 6 5 6 2 . 0 3 2 8 . 0 1 0 8 3 3 . 2 1 0 6 6 6 . 4 : 1 9 5 7 • 6 7 2 . 0 3 5 6 . 3 1 1 5 3 7 . 3 1 1 3 3 8 . 5 1 9 5 8 6 2 6 0 3 8 0 . 3 1 2 1 2 9 . 1 1 1 9 3 6 . 2 1 P 5 9 1 l 5 S . 0 4 0 5 . 5 * — 1 3 1 3 3 . 6 1 3 £ 8 0 . 2 " ~ 1 9 6 0 0 7 9 . 0 4 3 7 . 4 1 3 9 6 1 . 2 1 3 6 5 9 . 8 1 9 6 1 1 7 8 3 . 0 4 7 3 . 7 1 5 2 0 7 . 0 1 4 7 0 3 . 5 . 1 9 6 2 1 1 8 0 . 0 5 2 1 . 7 1 6 4 5 9 . 9 1 6 0 1 0 . 1 1 9 6 3 1 6 7 6 . 0 5 8 1 . 1 1 8 2 8 4 . 4 1 7 5 8 8 . 8 1 9 6 4 1 2 8 0 . 0 6 6 4 . 0 2 0 2 3 4 . 4 1 9 7 5 3 . 0 1 9 6 5 7 3 - 3 . 0 7 6 0 . 1 - ~ 2 3 3 2 2 . 3 — s ; 3 2 i . 7 — 1 9 6 6 3 5 4 C . 0 8 8 7 . 3 2 / 4 4 8 . 2 2 5 E 5 9 . 1 1 9 6 7 2 6 7 2 . 0 9 7 3 . 1 2 9 4 6 4 . 3 2 S 3 1 3 . 8 1 9 6 8 2 6 1 3 . 0 1 0 4 6 . 1 3 1 6 4 0 . 6 3 C 5 2 9 . 5 1 9 6 9 1 8 3 6 . 0 1 1 4 3 . 4 3 4 3 5 9 . 4 3 3 6 3 7 . 9 1 9 7 0 2 5 6 3 . 0 1 2 5 9 . 5 3 6 2 2 3 . 5 3 7 1 7 8 . 2 1 9 7 1 " 3 6 7 2 . 0 1369.-4- 4 2 5 9 1 . 7 i 1 S J 4 . 5 1 9 7 2 1 2 6 7 2 . 0 1 6 7 4 . 4 5 5 7 3 1 . 5 4 9 6 6 4 . 6 1 9 7 3 1 0 4 7 5 . 0 2 2 3 9 . 4 6 9 9 0 5 . 4 6 4 9 1 4 . 8 1 9 7 4 4 4 4 5 . 0 2 9 1 2 . 9 8 5 1 0 1 . 8 6 3 1 7 5 . 8 1 9 7 5 6 7 3 6 . 0 3 3 2 7 . 4 • 9 8 1 2 0 . 1 9 5 0 9 8 . 8 8 0 8 9 . 0 • B 6 B 0 . 7 8 8 3 3 . 1 8 9 1 7 . 5 9 0 S 9 . 5 9 0 4 9 . 7 9 1 4 0 . 9 " 1 0 0 2 1 . 9 1 1 4 2 1 . 0 1 1 B 0 7 . 2 1 2 2 4 1 . 4 1 2 6 4 9 . 3 1 3 5 8 t . 8 " 1 4 2 Q 0 . 0 " 7 7 7 9 . 0 4 7 2 1 . 0 4 4 5 0 0 8 3 8 4 . 8 5 3 0 3 . B 5 0 1 2 4 8 7 5 6 . 9 5 4 3 9 . 4 5 3 7 1 6 8 8 7 5 . 3 5 5 1 0 . 9 5 4 7 5 . 1 8 9 8 B . 4 5 0 4 5 . 0 5 5 7 8 0 9 0 S 4 . 6 5 G G 7 . 1 5 6 5 6 . 0 " 9 0 9 5 . l " 5 7 6 1 . 2 5 7 1 4 2 9 5 8 1 . 4 6 5 9 8 . 6 6 1 7 9 . 8 1 0 7 2 1 . 3 7 9 1 6 . 6 7 7 5 7 5 1 1 6 1 4 . 0 B 1 9 1 . 3 B C 5 3 .9 1 2 0 2 4 . 2 8 4 8 2 . 7 B 3 D 7 . 0 1 2 4 4 5 . 3 £ 7 4 2 . 3 8 6 1 2 5 1 3 1 1 5 . 4 ' 9 5 1 4 . 1 9 1 2 8 2 1 3 8 9 0 . 8 9 9 6 7 . 4 9 7 4 0 8 1 4 7 0 3 . 5 1 0 7 7 6 . 8 1 0 3 7 2 2 1 5 6 4 1 . 3 1 1 4 1 1 . 5 1 1 0 9 4 1 1 6 7 3 4 . 1 1 2 4 4 9 . 9 1 1 9 3 0 . 7 1 7 8 1 3 . 2 1 2 9 9 2 . 7 1 2 7 1 6 .3 1 4 3 1 3 . 8 I 3 C-4B .3 2 1 2 1 2 . 4 1 6 4 8 5 . 6 1 5 3 9 9 a 2 3 4 6 1 . 1 1 7 B B 9 . 9 1 7 1 6 7 . 4 2 5 3 3 7 . 7 1 9 1 9 9 . 5 I B 5 ' 4 6 2 * 8 3 8 . 7 1 9 7 5 7 . 0 1 9 4 7 5 . 7 7 3 2 0 . 7 2 0 7 4 7 . 6 2 0 2 4 7 .2 "30f4O°:'3 " ' 2 2 4 1 6 . 8 2 1 5 7 9 .8 3 5 6 5 3 . 2 3 0 3 4 5 . 0 2 6 3 B 0 . 9 4 3 3 5 0 . 2 3 5 E 2 9 . 4 3 3 0 8 7 .3 4 7 8 0 8 . 3 3 6 7 2 1 . 3 3 6 7 7 5 .4 5 0 5 2 4 . 3 3 B 5 0 9 . 4 3 7 6 1 5 .2 Source o f these data is: Statistics Canada, Science, Technology and Capital Stock Div i s ion. See Chapter 6, Section 6.2.1 for more informat ion about these data. Table A 1.2. Cap i ta l Stock and Related Data 1 , Canad ian 3-digit F ood Manufac tu r i ng Industries: Meat and Poul t ry Products Industries (S.I.C. 101), 1955-1982  end-yr m id - y r end-yr mid-y r end-yr mid-y r end-yr mid-y r gross gross net net gross gross net net v c a r stock stock stock stock stock stock stock stock thousands o f current dol lars thousands o f constant (1971) dol lars 1955 213224 209870 134300 132275 • 329196 323940 207474 204304 1956 238977 230172 153019 1466 34 355714 342455 229093 21fi2e6 1957 259423 252397 160433 163250 376156 365935 244325 236712 1956 277275 270421 101677 176431 395740 3C5943 259313 251819 1959 291048 285225 190526 1S66S0 412199 403970 269392 264602 1960 313794 304318 £05069 199316 437222 424710 2C6S02 276347 1961 ! 335449 327246 219502 214411 459565 443393 300710 293756 1962 350112 350411 232601 22C434 479962 469763 311060 306205 1963 330432 373953 244191 241416 496960 433461 319436 315648 1964 410767 405411 259204 257926 510069 503514 322673 321054 1965 451896 442028 283117 277370 533176 521623 335122 32£S?3 1966 •: 491040 431277 306756 301179 554365 544021 347492 341307 1967 507279 497925 315673 3106 34 575930 565423. 35JE63 353177 1966 527622 517174 326517 320265 600035 502003 371679 365271 1969 576272 562990 354457 347313 629CU 614523 367343 3795U 1970 636948 621622 3925G4 332C'i4 660734 644372 407602 397473 1971 ' 693777 677255 4 20405 41CC03 693777 677255 4234C5 410003 1972 752335 734513 462970 452930 720390 711C33 447374 438139 1973 824307 806003 504016 495000 753702 743546 463121 455497 1974 9C5679 966374 599164 539401 790001 774351 475937 471029 1975 1140258 1122137 6eC596 679545 816157 803073 492099 465518 1976 1266241 1242996 761505 749310 * 8474 96 831627 5CC73S 500417 1977 1431172 1403900 061711 044514 031218 664357 530C43 519391 1976 1612027 1589150 971403 956595 906902 894100 546729 538333 1979 1859913 1829941 1119050 1101926 937350 922166 564046 555387 1950 i 2151963 2109141 1292630 1267746 976265 956503 536647 57534 7 1931 > 2448105 2424591 1456495 1449401 995524 9e5S95 5924C3 589564 1932 2681910 2663090 1572295 1573109 1009939 1002732 592010 592247 1 Sou rce o f these data is: Statistics Canada, Sc ience, Technology and Capita l Stock D i v i s i on , Na t i ona l Wea l th and Cap i ta l Stock Sect ion. See Chapter 6, Sect ion 6.2.1 for more in format ion about these data. Tab ic A1.2. Cap i l a l S lock and Related Data 1 , Canad ian 3-digit Food Manufactu r ing Industries: (cont 'd ) F i s h Products Industry (S.I.C. 102), 1955-1982 end-yr m id - y r end-yr mid-y r end-yr mid-y r end-yr mid-yr gross gross net net gross gross net net year stock stock stock stock stock stock stock stock thousands o f current dol lars thousands o f constant (1971) dol lars 1955 73762 71381 46370 44430 1140e2 110309 71843 66848 1956 78743 77677 49640 48910 117262 115672 74029 72936 1957 83551 82213 52746 51890 121136 119193 76515 75272 1953 85*20 85331 53793 53599 122550 121C'i3 76793 76656 1959 89125 87839 55790 5501O 126193 124379 78979 77C39 1960 92510 91543 57330 57019 1233 91 127545 79253 79416 1961 97303 95677 59327 59065 133333 131114 81946 80399 1962 103087 103745 67767 64451 144371 139104 90303 86374 1963 117742 114320 74C65 71793 153594 1492*33 96595 93693 1964 134591 129259 35953 81960 166311 159953 106094 101345 1965 156603 149123 101911 96135 134293 175302 120066 112030 1966 186337 174353 125748 116026 210755 197524 142521 131293 1967 212336 198926 14S073 136696 241117 225915* 163316 155419 1963 224135 21C093 155249 151549 254741 247929 176577 172447 1969 244821 239137 168021 164364 267074 260907 133424 leccco 1970 276926 267231 190621 103707 237046 277060 197667 190545 1971 297033 292039 201835 199751 297033 292039 201835 199751 1972 323C95 315277 219405 213976 313733 305403 212523 207132 1973 363355 354731 251657 241233 340004 326094 231753 222140 1974 452813 433124 30S695 293374 353661 351833 247493 239525 1975 513389 513116 3'i01S5 346923 371035 367773 249171 243334 1976 566046 560466 372354 372432 379299 375592 249023 249100 1977 630274 626337 415094 409268 393253 306276 255339 252133 1973 736679 717635 479504 466526 414789 404021 269258 262604 1979 830042 351246 577033 556249 442237 429333 290790 20032.9 1930 1023689 1000631 673929 657432 464603 454233 305746 293268 1931 1167397 1155027 755370 753670 475141 469915 307133 306439 -1982 1304313 1202064 832317 C24307 491301 463221 313140 310137 1 Source o f these data is: Statistics Canada, Sc ience, Technology and Capi ta l Stock D i v i s i on , Na t i ona l Wealth* and Cap i ta l Stock Sect ion. See Chapter 6, Sect ion 6.2.1 for more in format ion about these data. Table A 1.2. Cap i ta l Stock and Related Data 1 , Canadian 3-digit F o o d Manufac tu r ing Industries: (cont 'd) F ru i t and Vegetable Process ing Industries (S.I.C. 103), 1955-1982 end-yr m id - y r end-yr mid-yr end-yr mid-yr end-yr mid -y r gross gross net net gross gross net net year stock stock stock stock stock stock stock stock thousands o f current dol lars thousands o f constant (1971) dol lars 1955 114416 111981 69583 67774 i;77554 173705 108167 105305 1956 124189 121559 76366 74362 105502 181528 ' 114234 111200 1957 135146 131471 84553 81600 196283 190892 122912 116573 1958 144183 140798 91561 C3784 205925 201104 130816 126864 1959 154162 149320 99432 95956 218219 212072 14C2C0 1358C8 1960 169711 163229 111436 106304 236212 227215 155051 147925 1961 109217 181002 126252 119802 2526S5 24 74 ".3 172534 163792 1962 210112 201C97 1415C0 135390 2CC512 269593 1E2393 160716 1963 228701 222211 153402 149354 297429 203971 199*20 194259 1964 255926 248537 171192 166423 315269 306399 211113 2C5269 1965 237101 278273 191933 186060 325319 325594 224313 217966 1966 310475 304757 205904 202933 343404 342112 231303 22eC53 1967 318052 312916 209041 206633 359921 354163. 226664 2339C4 1963 328603 323133 213492 211130 372277 366099 242043 239353 1969 351683 346784 2255C4 223333 3023-iS 377571 2s5616 242829 1970 378306 247966 242533 4C0594 391729 2E6911 251264 1971 419285 409939 26S054 262432 4192C5 409939 26S054 262432 1972 452334 442704 287547 232105 439112 429193 27C643 273349 1973 505965 490901 322392 312354 466963 453040 297119 207851 1974 616551 59S4S9 394101 332117 496261 481664 216622 306370 1975 ' 714284 703024 452690 447685 512472 504916 325332 320977 1976 782450 773201 493348 491694 525906 519639 334434 329903 1977 879622 665603 557922 5S0075 543261 534534 244219 339351 1973 996155 9S0371 626326 618917 561152 552206 352606 34S412 1979 1137355 11245S8 706533 702862 574253 567702 356323 354497 19C0 1316405 1290142 814770 799953 593166 586210 269330 363109 1931 15061C0 1437358 920244 914639 613--51 605653 374393 372111 19S2 1681399 1653454 1017764 10C5666 634767 624159 333529 370960 1 Source o f these data is: Statistics Canada, Sc ience, Technology and Capi ta l Stock D i v i s i on , Na t i ona l Wea l th and Cap i ta l Stock Sect ion. See Chapter 6, Sect ion 6.2.1 for more in format ion about these data. Table A 1.2. Cap i ta l Stock and Related Data 1 , Canad ian 3-digit F ood Manufac tu r i ng Industries: (cont 'd) Da i ry Products (S.I.C. 104), 1955-1982 end-yr m id -y r end-yr mid-yr end-yr mid-yr end-yr mid-y r gross gross net net gross gross net net year stock stock stock stock stock stock stock stock thousands o f current dol lars thousands o f constant (1971) dol lars 1955 227999 224324 149367 147764 357834 352900 234751 232315 1956 242212 239926 156C39 156312 364S25 361329 236547 225649 1957 254913 252701 163539 162948 371293 363059 233267 237417 1953 267979 263761 172690 169613 333368 377320 247109 242593 1959 278344 274938 179470 177133 394257 332SI2 253727 25C418 1960 293507 238669 167017 164249 407316 401033 259756 256742 1961 3o::-7i 3C4242 193413 192172 420293 414053 263105 261430 1962 323463 203203 201016 435925 423111 252577 265991 1963 365214 351919 227046 216260 469916 452920 293266 201072 1964 413576 400419 252611 250079 501429 425672 313316 303541 1965 461055 448337 206725 279506 520125 515777 330062 321949 1966 513127 495348 321317 209503 560503 549316 356568 343325 1967 544604 524976 244451 320556 612711 590610 337797 372102 1968 571268 sseoso 360606 352379 643760 62C235 406361 397079 1969 626558 610224 39'»521 324567 679055 661403 427904 417133 1970 669149 673525 431031 423117 711175 695115 445945 425925 1971 ,736370 723773 455322 45C234 736370 723773 455222 45022* 1972 .'787716 772700 432173 475731 765655 751013 463355 462059 1973 660532 04 3043 522479 514066 796318 701937 483924 476139 1974 1018506 1001439 612244 605206 C26026 812171 495165 489554 1975 1178091 1160766 703957 695433 650900 833503 507367 501276 1976 1275613 1266261 764393 757973 663252 857116 515967 511667 1977 1412614 1401637 646639 039794 876624 669963 524676 520222 1978 . 1579337 1566565 946361 923349 891176 833930 533719 529193 1979 16277C0 1794741 1107612 1061720 924519 907047 559215 546767 1980 2100715 2070183 1281105 1256032 959569 942C44 522621 571218 1931 2419456 2335820 1467699 1446449 92-6945 973257 590279 590450 1932 2642143 2625668 15S2S56 1526153 999322 993134 600296 595287 1 Source o f these data is: Statistics Canada, Sc ience, Technology and Capita l Stock D i v i s i on , Nat i ona l Wea l th and Cap i ta l Stock Sect ion. See Chapter 6, Sect ion 6.2.1 for more in format ion about these data. Table A 1.2. Cap i ta l Stock and Related Data 1 , Canad ian 3-digit F o o d Manufac tu r ing Industries: (cont 'd) F l o u r and Breakfast Cerea l s (S.l.C. 105), 1955-1982 end-yr mid -y r end-yr mid-yr end-yr mid-yr end-yr mid-y r gross gross net net gross gross net net year stock s lock stock stock stock stock stock stock thousands o f current dol lars thousands o f constant (1971) dol lars 1955 90791 82812 61731 60505 143112 139935 97307 95413 1956 99509 97120 67678 66051 150467 146790 102427 99907 1957 103400 105763 73639 71909 153216 154341 107520 104974 1953 116302 113391 79064 77064 166577 162397 113264 110392 1959 121072 119453 81320 80735 171147 162262 114940 114102 1960 135155 129216 91C64 87353 187591 179369 127426 121213 1961 160553 149355 112736 103323 213140 202865 153206 140346 1962 173739 169525 120079 11C046 229234 223712 153549 155377 1963 182075 160413 122322 122904 233496 231390 157095 157822 1964 199911 196623 131126 130479 241243 237370 152i51 157374 1965 220308 215746 143034 14C605 252525 246914 164071 161361 1966 236618 232790 151729 150063 261203 256e95 167957 166014 1967 246155 239352 157793 153563 2764*5 26 82-44- 177423 172722 1968 257651 251320 163130 160402 289517 233002 123601 160545 1969 270231 26S862 165656 167630 292602 291060 179201 181701 1970 280270 235993 172750 173462 297262 294932 1783:3 179064 1971 302169 299715 176317 177322 302169 299715 176317 177322 1972 310602 310661 174242 177A"53 202076 302122 169274 172795 1973 327500 326397 173021 1003!]5 304192 303133 164943 167108 1974 382733 378541 204447 204110 310946 307569 165355 165149 1975 432958 431337 225499 2274C3 313333 312142 162614 1639Q4 1976 464674 463194 239490 240111 315203 314271 161667 162140 1977 513320 510045 265575 263217 319102 317153 164522 162094 1978 579946 572451 307755 297637 327524 323313 173643 169032 1979 661205 653975 352936 345129 33'.246 3311S5 170523 176025 1980 737133 736076 390526 391400 335793 335320 177772 178150 1981 825296 623739 420937 433306 337074 336424 175916 176S44 1932 924517 907073 437003 475902 350253 343663 124295 180106 1 Source o f these data is: Statistics Canada, Sc ience, Technology and Capi ta l Stock D i v i s i on , Nat i ona l W c a l l h ajid Cap i l a l Stock Sect ion. Sec Chapter 6, Sect ion 6.2.1 for more in format ion about these data. Table A 1.2. Cap i ta l Stock and Related Da ta 1 , Canad ian 3-digit F o o d Manu fac tu r i ng Industries: (cont 'd) Feed Industry (S.I.C. 106), 1955-1982 end-yr mid -y r end-yr mid-yr end-yr mid-yr end-yr mid-y r gross gross net net gross gross net net year stock stock stock stock stock stock stock stock thousands o f current dol lars thousands o f constant (1971) dol lars 1955 97722 96224 59974 59006 i50289 147919 92362 90021 1956 105302 103330 65020 63626 156207 153243 96573 94467 1957 111031 109502 63509 67651 16C220 152513 99231 97976 1959 115691 114232 71604 70637 164995 162907 102153 100767 1959 122156 119319 764 20 74277 173025 169010 103214 105183 1960 131513 1270C8 83019 80335 133325 173175 115669 111941 1961 140261 136939 03495 05444 192263 187344 121263 112466 1962 147130 145143 91503 90951 197519 194941 122639 121976 1963 156473 153697 96523 95193 204722 201120 126210 124450 1964 170337 1672C6 104233 102.? 56 211942 205332 129634 127922 1965 1C6574 102876 113559 111604 220696 216319 134368 132001 1966 205376 200076 125904 122231 232776 226736 142824 132596 1967 217325 210993 134545 130033 247126 239951' 153067 147945 1968 232075 224536 14 5347 139e',3 264296 255711 165655 159261 1969 257433 249624 162109 156334 231253 272778 177235 171470 1970 285492 278211 130359 175530 296354 232306 187313 162293 1971 303eas 302620 194333 190343 300237 302620 194333 190243 1972 329464 324334 204779 202871 313357 313871 193073 196228 1973 366321 356573 228745 222217 336901 327878 210112 2C4092 1974 451445 436256 206159 274637 261413 349157 223670 219391 1975 532942 519173 339424 329319 331139 371276 242443 235557 1976 591090 5S1036 377372 370360 395550 323344 251849 247146 1977 667132 655126 422161 416006 410235 402913 259237 255613 1978 751122 740196 473645 ,= 467345 422635 416460 266519 262953 1979 833077 860927 562651 545315 445C63 433352 233515 275017 1980 103254? 1006740 660402 642652 46C534 4562C1 299637 291576 1981 1195731 1173910 760619 743751 406350 477442 3093^30 3044S4 1982 1331339 1311507 033390 830139 501356 492353 315617 312474 1 Source o f these data is: Statistics Canada, Sc ience, Technology and Cap i ta l Stock D i v i s i on , Na t i ona l Wea l t h and Cap i t a l Stock Sect ion. See Chapter 6, Sect ion 6.2.1 for more in format ion about these data. 190 Tabic A 1.2. Capital Stock and Related Data 1, Canadian 3-digit Food Manufacturing Industries: (cont'd) Bakery Products (S.I.C. 107), 1955-1982 end-yr mid-yr end-yr mid-yr end-yr mid-yr end-yr mid-yr gross gross net net gross gross net net year slock slock stock stock stock stock stock stock thousands of current dollars thousands of constant (1971) dollars 1955 210603 202377 150560 144635 331905 319733 237225 227916 1956 233938 226362 167042 162062 353647 342776 252423 244824 1957 254117 248203 179961 176521 370692 362169 262458 257441 1956 271527 265224 191903 107623 333767 379729 274745 263602 1959 20C099 201559 202233 193332 407252 39G009 225921 280333 1960 307414 300383 213343 209653 426710 416931 2S6157 291039 1961 325332 319996 221937 219967 442445 434578 301461 292209 1962 350953 343251 234S91 231692 462656 452551 309965 305713 1963 377373 369176 243901 245224 433605 473170 319559 314762 1964 416031 403496 269203 266719 501822 492739 325733 322646 1965 < 451134 444785 205361 2e't502 516291 509061 327S33 326735 1966 439315 476573 306765 301453 540189 528240 339S92 332265 1967 493166 437031 303545 302301 553966 547078" 341621 340756 1960 506123 499500 305551 304442 568737 561377 344131 342876 1969 541067 533203 320996 319174 EC--373 577330 348193 346162 1970 533239 575645 339710 33S442 601510 592691 35C339 349516 1971 612406 606953 340272 349556 6124C6 606953 342272 349556 1972 645022 637433 357963 358297 627200 619304 347605 347933 1973 686135 680886 370312 372901 637C22 632111 342751 345177 1974 797709 791092 420303 422215 647333 642427 339578 341164 1975 913634 904533 474032 472631 6 6 0 94 7 654390 341520 340548 1976 977604 976014 500556 507370 662£63 661905 343192 342356 1977 1061193 1063651 549324 551863 659615 661239 340686 341939 1973 1161577 1164746 591551 5<>77oi 656012 657813 333765 337225 1979 1285115 1290263 652471 6S6219 650737 653374 3:9973 331871 I960 1434997 1431709 729237 727144 652677 652207 331348 320913 1931 1592768 1596679 e04 0 7 7 303772 650480 652078 3C8030 329939 1932 1703184 1710291 85'5C43 663277 644913 647697 3247e5 326408 1 Source of these data is: Statistics Canada, Science, Technology and Capital Stock Division, National Wealth and Capilal Slock Section. Sec Chapter 6, Section 6.2.1 for more information about these data. Table A 1.2. Cap i ta l Stock and Related Da ta 1 , Canad ian 3-digit F o o d Manufac tu r i ng Industries: (cont 'd) M i s ce l l aneous F o o d Industries (S.I.C. 108), 1955-1982 end-yr mid -y r end-yr mid-yr end-yr mid-yr end-yr mid-yr gross gross n c l net gross gross net net year stock stock stock stock stock stock stock stock thousands o f current dol lars thousands o f constant (1971) dol lars 1955 303371 298341 189121 105313 471729 463727 294453 289174 1956 327709 321600 205004 200911 490403 431066 307237 300373 1957 355763 3466G0 225301 210373 516044 502624 327446 317367 1950 207065 374421 250518 239326 553054 534949 353046 342746 1959 409666 400233 266503 259790 579712 566233 377021 367533 1960 437121 426391 203620 277353 603116 593914 394449 2S5735 1961 472759 459044 306315 297930 645614 626555 416e02 405565 1962 52CS56 502625 339764 327107 69*002 669309 452753 435318 1963 560795 54704? 363767 356331 727239 710620 472013 462383 1964 613100 602651 392233 3CS122 752619 739923 432034 477C23 1955 672455 659000 425034 416966 733173 767093 493797 48S915 1966 732491 719146 46 7365 454911 825999 804533 523457 509527 1967 773164 751934 491670 477246 873446 649722 555740 539599 1968 795737 784038 499256 49S2C3 899722 666514 564925 560333 1969 854424 840933 529074 524153 929117 914449 575713 570324 1970 922041 910047 563756 559939 953734 941451 533473 579593 1971 996299 975041 603168 595320 996299 975041 603168 595620 1972 1069969 1046521 649133 630225 1033154 1017226 629443 612203 1973 1186337 1154337 721019 701474 1096263 1067508 665S05 647627 1974 1439566 1399562 872447 852667 1161690 1129277 707416 6e6611 1975 1693104 1653764 1035432 101C00O 1216530 1190110 744126 725776 1976 1056113 1837276 1123229 1122221 1257650 1235090 765996 755066 1977 2092645 2065444 12S0159 1259552 1292610 1273129 791509 773753 1978 2376691 2340295 1445168' 1424643 13397C0 1319195 814672 602090 1979 2 750330 2701429 1679352 1646073 1339930 1364355 £43335 831529 1980 3254547 3155319 2012553 1939277 1479331 1434630 915037 681711 1931 3765193 3707e02 2333190 2267167 1542025 1511423 951026 933032 1902 4246610 4215023 2700474 2609097 1642711 1592668 10202O1 935654 1 Source o f these data is: Statistics Canada, Sc ience, Technology and Cap i ta l Stock D i v i s i on , Na t i ona l Wea l th and Cap i ta l Stock Sect ion. See Chapter 6, Sect ion 6.2.1 for more in format ion about these data. Tab ic A 1.2. Cap i l a l Stock and Related Data 1 , Canad ian 3-digit Food Manufac tu r i ng Industries: (cont 'd ) Beverage Industr ies (S.I.C. 109), 1955-1982  end-yr m id -y r end-yr mid-yr end-yr mid-y r end-yr mid-yr gross gross net net gross gross net net year s lock stock stock stock stock stock stock stock thousands o f current dol lars thousands o f constant (1971) dol lars 1955 499591 486331 326401 316674 766967 747251 . 5CCS59 425856 1956 530653 523307 352072 345219 790102 732534 521552 5112C6 1957 575344 563765 376953 368759 833257 815679 545414 533483 1953 599717 592192 391613 327093 055261 844259 552274 551344 1959 635150 619414 417471 4C5777 899317 877539 5 f'1379 574227 1960 678694 661033 446610 435201 946579 923193 622837 607133 1961 723164 706060 473375 463619 993151 969265 65CS64 636376 1962 773103 755166 503667 493356 1C40909 1017030 67S520 664722 1963 821327 697003 52S' t16 522379 1077312 1059360 694205 686442 1964 904691 033204 579331 566697 1131675 1104743 1156332 7265-6 710450 1965 993505 972420 631C09 620043 1181039 752521 739563 1966 1077309 1057013 600257 670052 1225205 1203147 775659 764095 1967 1118705 1097161 704C49 692043 1274041 1249623 002715 769137 1968 1187960 1152477 752326 727606 1354522 1314261 652895 630205 1969 1320568 1279401 841500 012974 1444406 1399464 921279 890037 1970 1492002 1441148 961770 923931 1549601 1497003 999516 960397 1971 1630011 1589206 1048991 1024254 1630011 1539SC6 1048991 1C24254 1972 1755536 1720352 1118207 1101627 1690425 1664218 1C31192 1C65091 1973 1940793 1094744 1232956 1205590 1782655 1741040 1131670 11C6431 1974 2316344 2274047 1459642 1439234 1651761 1817703 1164348 1148008 1975 2640671 2616500 1640690 1626631 1836522 1869141 .1170201 1167224 1976 2877725 2852199 1771493 1764321 1920775 1903643 1180324 1175312 1977 3203440 3164435 1969293 1946095 1966575 1944675 1203992 1194653 1978 3565743 3532262 2174479 2161706 2006617 1937596 1223553 1216273 1979 4055371 4010304 2453176 2440961 2C43394 2025255 1236039 1229796 1930 4628351 4566428 2772403 2743320 2102637 2072291 1257993 1247016 1931 5259126 5211975 3097317 3095417 2139366 2120026 1259703 1258250 1932 5770187 5726231 3348393 3343144 2172375 2156123 1262571 1260139 1 Source o f these data is: Statistics Canada, Sc ience, Technology and Capita l Stock D i v i s i on , Na t i ona l Wea l th and Cap i ta l Stock Sect ion. See Chapter 6, Sect ion 6.2.1 for more in format ion about these data. 193 Table A 1.3. All-Components Capital Expenditures (Investment), Canadian 4-digit Food Manufacturing Industries, 1972-1981 Industry Investment by S.I.C. (millions of current $) Year1 10112 1012 1071 1072 1081 1082 1083 1089 1091 1092 1093 1094 1972 2.9 20.4 1973 4.2 14.7 1974 6.2 17.3 1975 7.6 27.0 1976 47.9 9.4 7.6 29.5 13.1 9.9 11.1 47.9 34.6 13.9 33.8 4.7 1977 59.2 12.3 7.9 25.3 13.2 8.3 19.7 57.3 49.8 11.4 60.3 6.3 1978 60.8 11.7 6.5 20.5 16.3 13.8 29.5 48.7 55.8 12.6 44.6 7.6 1979 70.8 13.9 10.5 22.8 25.6 6.7 20.6 93.2 48.7 23.2 53.3 6.1 1980 95.3 17.4 14.4 40.0 31.9 21.0 10.4 157.3 57.9 18.8 75.4 10.5 1981 61.2 24.2 14.0 27.3 23.2 30.1 35.2 107.3 34.4 18.9 80.3 12.4 1 Note that since capilal stock data for S.I.C. 1072 only run to 1971 (see Table A l . l ) , imputations for S.I.Cs 1071 and 1072 must be made for 1972-1981. The data for all other industries are only reported for 1976-1981 since 'observed* (updated) data exist up to 1975 for these industries. 2 See Table 6 for industry names. Source of these data is: Statistics Canada (catalogues 61-518 and 61-214). Data are defined as "capital expenditures sub-total" in both publications. 194 Table A1.4. Implicit Price Index (pcap) for Capital Expenditure on Total Components, Canadian Food Manufacturing Industries, 1960-1982 Year all-components implicit price index (1971 = 100)2 I960 71.84 1961 73.15 1962 74.91 1963 76.95 1964 81.20 1965 85.52 1966 89.09 1967 88.34 1968 88.26 1969 91.84 1970 96.54 1971 100.00 1972 • 103.15 1973 108.35 1974 124.26 1975 139.25 1976 148.82 1977 161.95 1978 177.50 1979 198.10 1980 220.09 1981 245.52 1982 265.01 Total components is comprised of construction, machinery and equipment. 2 Source of these data is Agriculture Canada, Policy Branch, (Food Markets Analysis Division) database RAW85. See Statistics Canada (catalogues 13-568 and 13-211) for rounded figures. 195 Table A1.5. Observed, Revised and Imported End-Year Capital Stock Series, Canadian Food Manufacturing Industries, 1961-1982 S.I.C. KS 1 S.I.C. KS S.I.C. KS S.I.C. KS S.I.C. KS S.I.C. KS S.I.C. KS 1 0 1 1 . 2 0 4 0 1 6 . 1 0 2 0 . 3 7 2 3 8 4 . 1 0 5 0 . 1 7 2 7 5 0 . 1 0 7 2 . 2 1 0 0 4 6 . 1 0 8 2 . 2 8 5 7 0 0 . 1 0 9 1 . 3 4 3 2 4 4 . 1 0 9 4 . 2 4 5 6 6 . i o n . 2 1 5 8 2 0 . 1 0 2 0 . 4 1 5 0 9 4 . 1 0 5 0 . 1 7 6 3 1 7 . 1 0 7 2 . 2 2 3 4 3 2 . 1 0 8 2 . 3 8 1 9 7 5 . 1 0 9 1 . 3 8 7 8 3 4 . 1 0 9 4 . 2 6 2 0 4 . 1 0 1 1 . 2 2 7 1 2 8 . 1 0 2 0 . 4 7 9 5 0 4 . 1 0 5 0 . 1 7 4 2 4 2 . 1 0 7 2 . 2 4 1 0 6 5 . 1 0 8 3 . 2 7 7 1 0 . 1 0 9 1 . 4 4 0 5 0 0 . 1 0 9 4 . 2 B 8 6 9 . 1 0 1 1 . 2 3 5 2 3 0 . 1 0 2 0 . 5 7 7 0 3 8 . 1 0 5 0 . 1 7 8 0 2 1 . 1 0 7 2 . 2 3 8 9 6 5 . 1 0 8 3 . 2 7 5 3 6 . 1 0 9 1 . 5 0 3 2 6 7 . 1 0 9 4 . 3 2 2 G 6 . 1 0 1 1 . 2 4 6 3 0 1 . 1 0 2 0 . 6 7 3 9 2 9 . 1 0 5 0 . 2 0 4 4 4 7 . 1 0 7 2 . 2 4 1 3 3 1 . 1 0 8 3 . 2 8 1 7 5 . 1 0 9 1 . 5 6 4 8 2 0 . 1 0 9 4 . 4 4 9 8 3 . 1 0 1 1 . 2 G 4 7 6 4 . 1 0 2 0 . 7 5 5 3 7 0 . 1 0 5 0 . 2 2 5 4 9 9 . 1 0 7 2 . 2 5 1 3 1 5 . 1 0 8 3 . 2 7 6 5 4 . 1 0 9 1 . 6 4 5 3 9 4 . 1 0 9 4 . 5 5 8 4 4 . 1 0 1 1 . 2 8 3 4 5 6 . 1 0 3 0 . 1 1 1 4 3 6 . 1 0 5 0 . 2 3 9 4 9 0 . 1 0 7 2 . 2 6 2 2 9 6 . 1 0 8 3 . 2 7 8 6 8 . 1 0 9 1 . 7 3 5 6 9 9 . 1 0 9 4 . 6 5 4 1 9 . 1 0 1 1 . 2 8 9 0 1 2 . 1 0 3 0 . 1 2 6 2 5 2 . 1 0 5 0 . 2 6 5 5 7 5 . 1 0 7 2 . 2 6 8 1 5 0 . 1 0 8 3 . 2 8 9 5 9 . 1 0 9 1 . 8 2 1 4 8 3 . 1 0 9 4 . 7 G 1 1 1 . 1 0 1 1 . 2 9 7 2 6 7 . 1 0 3 0 . 1 4 1 5 2 0 . 1 0 5 0 . 3 0 7 7 5 5 . 1 0 7 2 . 2 7 4 9 2 6 . 1 0 8 3 . 3 0 1 6 9 . 1 0 9 2 . 1 0 4 5 0 9 . 1 0 9 4 . 8 3 3 6 9 . 1 0 1 1 . 3 1 7 8 7 7 . 1 0 3 0 . 1 5 3 4 0 2 . 1 0 5 0 . 3 5 2 9 3 6 . 1 0 7 2 . 2 7 8 5 1 7 . 1 0 8 3 . 2 9 3 0 1 . 1 0 9 2 . 1 0 7 9 0 6 . 1 0 9 4 . 9 2 9 3 7 . 1 0 1 1 . 3 4 9 2 1 8 . 1 0 3 0 . 1 7 1 1 9 2 . 1 0 5 0 . 3 9 0 5 3 6 . 1 0 7 2 . 3 1 6 4 7 2 . 1 0 8 3 . 2 9 9 6 2 . 1 0 9 2 . 1 1 1 8 6 5 . 1 0 9 4 . 1 0 3 3 7 9 . 1 0 1 1 . 3 7 8 8 4 1 . 1 0 3 0 . 1 9 1 9 3 8 . 1 0 5 0 . 4 3 0 9 8 7 . 1 0 7 2 . 3 5 7 1 1 8 . 1 0 8 3 . 3 0 2 3 6 . 1 0 9 2 . 1 1 4 8 6 9 . 1 0 9 4 . 1 1 6 7 1 3 . 1 0 1 1 . 4 0 8 1 1 3 . 1 0 3 0 . 2 0 5 9 0 4 . 1 0 6 0 . B 3 0 1 9 . 1 0 7 2 . 3 8 1 9 8 5 . 1 0 8 3 . 3 3 2 8 5 . 1 0 9 2 . 1 2 7 5 0 1 . 1 0 9 4 . 1 3 3 2 4 3 . 1 0 1 1 . 4 3 8 0 4 6 . 1 0 3 0 . 2 0 9 0 4 1 . 1 0 6 0 . 8 8 4 9 5 . 1 0 7 2 . 4 1 4 6 5 1 . 1 0 8 3 . 3 7 1 2 4 . 1 0 9 2 . 1 4 2 9 8 4 . 1 0 9 4 . 1 4 9 2 4 8 . 1 0 1 1 . 5 1 6 1 8 4 . 1 0 3 0 . 2 1 3 4 9 2 . 1 0 6 0 . 9 1 5 0 3 . 1 0 7 2 . 4 4 5 6 7 6 . 1 0 8 3 . 4 0 2 7 5 . 1 0 9 2 . 1 6 3 1 5 6 . 1 0 1 1 . 5 9 2 1 3 3 . 1 0 3 0 . 2 2 5 5 0 4 . 1 0 6 0 . 9 6 5 2 3 . 1 0 7 2 . 4 9 3 0 7 8 . 1 0 8 3 . 4 1 2 5 8 . 1 0 9 2 . 1 7 4 8 9 6 . 1 0 1 1 . 6 5 1 7 7 6 . 1 0 3 0 . 2 4 7 9 6 6 . 1 0 6 0 . 1 0 4 2 3 8 . 1 0 7 2 . 5 5 0 9 5 8 . 1 0 8 3 . 5 3 2 0 6 . 1 0 9 2 . 1 9 4 1 7 1 . l O I 1 . 7 3 4 3 4 7 . 1 0 3 0 . 2 6 8 0 5 4 . 1 0 6 0 . 1 1 3 5 5 9 . 1 0 7 2 . 6 0 9 0 5 4 . 1 0 8 3 . 7 5 8 1 9 . 1 0 9 2 . 2 4 1 5 2 1 . 1 0 1 1 . 8 2 6 0 0 9 . 1 0 3 0 . 2 8 7 5 4 7 . 1 0 6 0 . 1 2 5 9 0 4 . 1 0 8 1 . 5 5 7 7 0 . 1 0 8 3 . 8 8 4 2 9 . 1 0 9 2 . 3 0 3 1 4 9 . 1 0 1 1 . 9 4 9 5 6 9 . 1 0 3 0 . 3 2 2 3 9 2 . 1 0 6 0 . 1 3 4 5 4 5 . 1 0 8 1 . 6 7 0 1 1 . 1 0 8 3 . 1 1 0 5 7 5 . 1 0 9 2: 3 3 6 9 1 8 . 1 0 1 1 . 1 0 9 5 7 0 1 . 1 0 3 0 . 3 9 4 1 0 1 . 1 0 6 0 . 1 4 5 3 4 7 . 1 0 8 1 . 8 2 6 3 2 . 1 0 8 3 . 1 4 1 0 8 4 . 1 0 9 2 . 3 5 4 2 0 2 . 1 0 1 1 . 1 2 3 0 2 0 4 . 1 0 3 0 . 4 5 3 6 9 0 . 1 0 6 0 . 1 6 2 1 8 9 . 1 0 8 1 . 8 8 8 7 0 . 1 0 8 3 . 1 6 8 0 2 8 . 1 0 9 2 . 3 8 1 1 2 3 . 1 0 1 2 . 1 8 5 3 . 1 0 3 0 . 4 9 8 3 4 8 . 1 0 6 0 . 1 8 0 3 5 9 . 1 0 8 1 . 9 6 0 5 8 . 1 0 8 3 . 1 9 4 1 8 9 . 1 0 9 2 . 4 3 7 7 0 8 . 1 0 1 2 . 3 6 8 2 . 1 0 3 O . 5 5 7 9 2 2 . 1 0 6 0 . 1 9 4 3 8 3 . 1 0 8 1 . 1 0 3 1 1 6 . 1 0 8 3 . 3 0 3 3 5 4 . 1 0 9 2 . 4 9 3 5 6 4 . 1 0 1 2 . 5 4 7 3 . 1 0 3 0 . 6 2 6 3 2 6 . 1 0 6 0 . 2 0 4 7 7 9 . 1 0 8 1 . 1 0 8 5 3 4 . 1 0 8 9 . 1 2 4 6 8 2 . 1 0 9 2 . 5 1 6 4 5 9 . 1 0 1 2 . 8 9 6 1 . 1 0 3 0 . 7 0 6 5 8 3 . 1 0 6 0 . 2 2 8 7 4 5 . 1 0 8 1 . 1 1 1 4 0 1 . 1 0 8 9 . 1 3 3 3 0 5 . 1 0 9 2 . 5 5 5 0 6 9 . 1 0 1 2 . 1 2 9 0 3 . 1 0 3 0 . 8 1 4 7 7 0 . 1 0 6 0 . 2 8 6 1 5 9 . 1 0 8 1 . 1 1 4 8 0 4 . 1 0 8 9 . 1 4 3 6 0 8 . 1 0 9 2 . 6 0 5 6 4 3 . 1 0 1 2 . 1 8 3 5 3 . 1 0 3 0 . 9 2 0 2 4 4 . 1 0 6 0 . 3 3 9 4 2 4 . 1 0 8 1 . 1 1 9 4 1 7 . 1 0 8 9 . 1 5 8 1 2 6 . 1 0 9 2 . 6 7 8 0 6 0 . 1 0 1 2 . 2 3 3 O 0 . 1 0 4 0 . 1 8 7 0 1 7 . 1 0 6 0 . 3 7 7 3 7 2 . 1 0 8 1 . 1 2 5 6 5 0 . 1 0 8 9 . 1 7 2 4 9 8 . 1 0 9 2 . 7 5 2 9 2 9 . 1 0 1 2 . 2 6 6 6 1 . 1 0 4 0 . 1 9 3 4 1 3 . 1 0 6 0 . 4 2 2 1 6 1 . 1 0 8 1 . 1 3 2 4 4 7 . 1 0 8 9 . 1 9 0 6 3 7 . 1 0 9 2 . B 3 9 B 7 B . 1 0 1 2 . 2 9 2 5 0 . 1 0 4 0 . 2 0 3 2 0 3 . 1 0 6 0 . 4 7 3 6 4 5 . 1 0 8 1 . 1 3 7 4 5 9 . 1 0 8 9 . 2 2 4 4 8 9 . 1 0 9 3 . 2 3 1 7 9 5 . 1 0 1 2 . 3 6 5 8 0 . 1 0 4 0 . 2 2 7 B 4 6 . 1 0 6 0 . 5 6 2 6 5 1 . 1 0 8 1 . 1 4 6 7 8 1 . 1 0 8 9 . 2 4 9 1 5 4 . 1 0 9 3 . 2 4 6 4 0 9 . 1 0 1 2 . 4 3 3 8 6 . 1 0 4 0 . 2 5 8 6 1 1 . 1 0 6 0 . 6 6 0 4 0 2 . 1 0 8 1 . 1 8 3 0 9 7 . 1 0 8 9 . 2 5 5 2 6 2 . 1 0 9 3 . 2 5 8 1 2 6 . 1 0 1 2 . 4 9 5 6 4 . 1 0 4 0 . 2 8 6 7 2 5 . 1 0 6 0 . 7 6 0 6 1 9 . 1 0 8 1 . 2 0 5 8 6 3 . 1 0 8 9 . 2 7 6 5 5 6 . 1 0 9 3 . 2 6 9 0 2 0 . 1 0 1 2 . 5 4 8 6 5 . 1 0 4 0 . 3 2 1 3 1 7 . 1 0 7 1 . 4 5 8 7 0 . 1 0 8 1 . 2 2 2 4 9 S . 1 0 8 9 . 2 9 8 3 7 9 . 1 0 9 3 . 2 8 4 1 G 7 . 1 0 1 2 . 6 5 9 7 0 . 1 0 4 O . 3 4 4 4 5 1 . 1 0 7 1 . 4 7 6 3 8 . 1 0 8 1 . 2 4 4 2 0 2 . 1 0 8 9 . 3 2 9 8 4 7 . 1 0 9 3 . 2 9 8 0 3 7 . 1 0 1 2 . 8 2 9 8 0 . 1 0 4 0 . 3 6 0 6 0 6 . 1 0 7 1 . 5 1 2 3 3 . 1 0 8 1 . 2 7 1 9 6 8 . 1 0 8 9 . 3 5 9 2 1 5 . 1 0 9 3 . 3 0 6 3 4 9 . 1 0 1 2 . 9 6 4 6 3 . 1 0 4 0 . 3 9 4 5 2 1 . 1 0 7 1 . 5 4 9 4 3 . 1 0 8 1 . 3 1 4 5 7 0 . 1 0 8 9 . 4 0 9 5 1 4 . 1 0 9 3 . 3 0 8 S 8 7 . 1 0 1 2 . 1 0 9 8 0 9 . 1 0 4 0 . 4 3 1 8 8 1 . 1 0 7 1 . 5 9 1 5 7 . 1 0 8 1 . 4 0 0 6 8 6 . 1 0 8 9 . 5 0 2 5 8 6 . 1 0 9 3 . 3 2 6 2 9 1 . 1 0 1 2 . 1 2 7 3 6 5 . 1 0 4 0 . 4 5 5 8 2 2 . 1 0 7 1 . 6 1 9 2 9 . 1 0 8 1 . 4 7 7 5 5 8 . 1 0 8 9 . 5 9 4 9 2 1 . 1 0 9 3 . 3 4 8 9 0 9 . 1 0 1 2 . 1 4 5 3 9 5 . 1 0 4 0 . 4 8 2 1 7 3 . 1 0 7 1 . 6 5 6 8 0 . 1 0 8 2 . 7 5 4 7 3 . 1 0 8 9 . 6 5 6 3 3 2 . 1 0 9 3 . 3 8 8 0 0 9 . 1 0 1 2 . 1 6 9 4 8 2 . 1 O 4 0 . 5 2 2 4 7 9 . 1 0 7 1 . 6 4 5 8 0 . 1 0 8 2 . 7 8 9 6 3 . 1 0 8 9 . 7 3 9 9 3 5 . 1 0 9 3 . 4 2 7 4 6 0 . 1 0 1 2 . 1 9 6 9 2 9 . 1 0 4 0 . 6 1 2 2 4 4 . 1 0 7 1 . G 4 2 2 0 . 1 0 8 2 . 8 5 3 4 9 . 1 0 B 9 . 8 2 4 7 0 5 . 1 0 9 3 . 4 5 6 3 0 6 . 1 0 1 2 . 2 2 6 2 9 2 . 1 0 4 0 . 7 0 3 9 5 7 . 1 0 7 1 . 6 9 6 8 1 . 1 0 8 2 . 8 9 1 1 7 . 1 0 B 9 . 9 6 7 1 1 2 . 1 0 9 3 . 5 0 4 7 0 8 . 1 0 2 0 . 5 7 3 3 0 . 1 0 4 0 . 7 6 4 3 9 3 . 1 0 7 1 . 7 7 4 1 4 . 1 0 8 2 . 9 5 8 1 4 . 1 0 8 9 . 1 1 3 1 9 8 3 . 1 0 9 3 . 6 1 3 2 7 0 . 1 0 2 0 . 5 9 8 2 7 . 1 0 4 0 . 8 4 6 8 3 9 . 1 0 7 1 . 8 0 1 2 2 . 1 0 8 2 . 1 0 2 3 2 2 . 1 0 8 9 . 1 1 7 0 3 0 9 . 1 0 9 3 . 6 8 3 1 8 1 . 1 0 2 0 . 6 7 7 6 7 . 1 0 4 0 . 9 4 6 3 6 1 . 1 0 7 1 . 8 3 0 4 2 . 1 0 8 2 . 1 0 4 1 7 3 . 1 0 9 1 . 9 8 7 0 3 . 1 0 9 3 . 7 3 1 1 6 6 . 1 0 2 0 . 7 4 0 6 5 . 1 0 4 0 . 1 1 0 7 6 1 2 . 1 0 7 1 . 9 1 7 9 7 . 1 0 8 2 . 1 0 1 8 2 2 . 1 0 9 1 . 1 0 6 8 9 3 . 1 0 9 3 . 8 1 8 0 2 6 . 1 0 2 0 . 8 5 9 5 3 . 1 0 4 0 . 1 2 8 1 1 8 5 . 1 0 7 1 . 1 0 3 8 3 4 . 1 0 8 2 . 9 9 2 2 8 . 1 0 9 1 . 1 2 0 1 5 5 . 1 0 9 3 . 9 O 0 6 3 6 . 1 0 2 0 . 1 0 1 9 1 1 . 1 0 4 0 . 1 4 6 7 6 9 9 . 1 0 7 1 . 1 1 6 9 4 6 . 1 0 8 2 . 1 0 2 8 6 4 . 1 0 9 1 . 1 2 9 6 2 7 . 1 0 9 3 . 1 0 1 6 0 1 0 . 1 0 2 0 . 1 2 5 7 4 8 1 0 5 0 . 9 1 8 6 4 . 1 0 7 1 . 1 2 4 7 8 4 . 1 0 3 2 . 1 0 6 4 4 3 . 1 0 9 1 . 1 5 1 4 3 8 . 1 0 9 3 . 1 1 5 0 5 3 5 . 1 0 2 0 . 1 4 8 0 7 8 1 0 5 0 . 1 1 2 7 3 6 . 1 0 7 1 . 1 3 5 5 3 4 . 1 0 8 2 . 1 0 8 7 4 8 . 1 0 9 1 . 1 7 1 4 4 9 . 1 0 9 3 . 1 2 8 6 7 0 4 . 1 0 2 0 . 1 5 5 2 4 9 1 0 5 0 . 1 2 0 0 7 9 . 1 0 7 1 . 1 4 5 9 7 2 . 1 0 8 2 . 1 1 2 1 8 4 . 1 0 9 1 . 1 8 8 8 2 3 . 1 0 9 4 . 1 1 6 1 2 . 1 0 2 0 . 1 6 8 0 2 1 1 0 5 0 . 1 2 2 3 2 2 . 1 0 7 1 . 1 5 9 8 3 3 . 1 0 8 2 . 1 2 3 4 6 7 . 1 0 9 1 . 1 9 7 2 2 1 . 1 0 9 4 . 1 2 6 6 6 . 1 0 2 0 . 1 9 0 6 2 1 1 0 5 0 . 1 3 1 1 3 6 . 1 0 7 1 . 1 7 8 7 6 9 . 1 0 8 2 . 1 3 9 5 5 8 . 1 0 9 1 . 2 0 7 2 0 8 . 1 0 9 4 . 1 3 5 2 1 . 1 0 2 0 . 2 0 1 8 3 5 1 0 5 0 . 1 4 3 0 3 4 . 1 0 7 1 . 1 9 5 5 6 9 . 1 0 8 2 . 1 5 8 8 2 9 . 1 0 9 1 . 2 2 4 B 7 4 . 1 0 9 4 . 1 4 9 0 0 . 1 0 2 0 . 2 1 9 4 8 5 1 0 5 0 . 1 5 1 7 2 9 . 1 0 7 2 . 1 6 7 4 7 8 . 1 0 8 2 . 1 7 0 9 7 1 . 1 0 9 1 . 2 4 1 7 4 3 . 1 0 9 4 . 1 6 2 2 4 . 1 0 2 0 . 2 5 1 6 5 7 1 0 5 0 . 1 5 7 7 9 3 . 1 0 7 2 . 1 7 4 2 9 9 . 1 0 8 2 . 1 8 5 4 4 7 . 1 0 9 1 . 2 5 2 3 4 B . 1 0 9 4 . 1 8 5 3 9 . 1 0 2 0 . 3 0 8 6 9 5 1 0 5 0 . 1 6 3 1 3 0 . 1 0 7 2 . 1 8 3 6 5 0 . 1 0 8 2 . 2 0 7 4 1 2 . 1 0 9 1 . 2 6 2 7 1 6 . 1 0 9 4 . 2 1 9 2 8 . 1 0 2 0 . 3 4 S 1 5 5 1 0 5 0 . 1 6 5 B 5 6 . 1 0 7 2 . 1 9 3 9 5 8 . 1 0 8 2 . 2 2 9 6 4 5 . 1 0 9 1 . 2 9 1 2 8 1 . 1 0 9 4 . 2 3 3 4 5 . 1 KS is net capital stock, measured in current dollars. These are given for industry (S.I.C.) 1011 starting with the 1961 capital stock and running down the column to 1982. The format is the same for all industries. For a further description of these data, see text. APPENDIX 2: DATA USED IN ESEMATION OF COST AND SHARE EQUATIONS This Appendix provides a listing of the data used to estimate the share system (43) and the cost/share system (42' ) and (43). Table A2.1 covers all 374 observations. The first column gives the S.IG. of the industry; within each industry the observations run from 1961-1982. The second column gives total costs, scaled to 1971 = 1 for each industry. Columns 3-6 give the cost shares of production labour, non-production labour, energy and materials; these data are not scaled. Columns 7-11 give the prices of capital, production labour, non-production labour, energy and materials; all are scaled to 1971 = 1. The last three columns give the output quantity indices, the Herfindahl indices, and the trend variable for each industry. As can be seen, only the output and HerfiSahl data are scaled. These data, as well as the larger Agriculture Canada database from which most of them are drawn, will be available from the data library in the UBC Computing Building later in 1986. 196 w Table A2.1. Data Used in Estimation of Final Model] Canadian Food Manufacturing Industries, 1961-1982 S.I.C.2 C Sip Ship s, S»( WA- w,„ Q h t 1011. 0 .532 .072 .033 .006 .860 0 .731 0 .552 0 .576 0 .852 0 .823 0 .641 1 .235 1 . 1011. 0 .553 .070 .031 .006 .864 0 .749 0 .575 0 .579 0 .884 0 .868 0 .635 1 .236 2. 1011. 0 .565 .07 1 .031 .006 .862 0 .769 0 .584 0 .596 0 .894 0 .845 0 .671 1 .238 3. 1011. 0 .594 .072 .032 .006 .860 0 .812 0 .610 0 .614 0 .909 0 .810 0 .735 1 .239 4. 1011. 0 .664 .069 .031 .006 .867 0 .855 0 .635 0 .641 0 .908 0 .868 0 .770 1 .241 5. 1011. 0 .750 .065 .030 .006 .873 0 .891 0 . 683 0 .679 0 .911 0 .967 0 .784 1 . 199 6. 1011. 0 .80 1 .069 .030 .006 .869 0 .883 0 .744 0 .739 0 .919 0 . 944 0 .861 1 . 158 7. 1011. 0 .821 .070 .031 .006 .867 0 .883 0 .799 0 .788 0 .931 0 .940 0 .883 1 .115 8. 1011. 0 .898 .066 .028 .005 .875 0 .918 0 .856 0 .830 0 .936 1 .051 0 .869 1 .065 9. 1011. 0 .965 .069 .034 .005 .868 0 .966 0 .918 0 .934 0 .944 1 .042 0 .934 1 .014 10. 1011. 1 .000 .075 .033 .005 .861 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 1 . 1011. 1 .211 .066 .029 .005 .877 1 .031 1 .082 1 .084 1 .052 1 .189 1 .039 0 .986 12. 1011. 1 .547 .054 .025 .004 .897 1 .003 1 . 159 1 .178 1 .141 1 .539 1 .044 0 .907 13. 1011. 1 .674 .060 .027 .005 .888 1 .243 1 .302 1 .334 1 .387 1 .534 1 . 126 0 .842 14. 1011. 1 .803 .067 .027 .006 .878 1 .392 1 . 558 1 .491 1 .668 1 .584 1 . 1 56 0.840 15. 1011. 1 .884 .073 .028 .007 .868 1 .488 1 .734 1 .614 2 .021 1 .517 1 .260 0 .836 16. 1011. 2 .010 .074 .029 .007 .865 1 .619 1 .869 1 .803 2 .346 1 .554 1 .302 0 .776 17. 1011. 2 .576 .062 .026 .006 .885 1 .775 2 .000 1 .847 2 .626 2 .069 1 .264 0 .716 18. 1011. 2 .999 .058 .022 .006 .893 1 .981 2. 198 2 .050 2 .921 2 .404 1 .277 0 .736 19. 1011. 3 .158 .063 .024 .007 .883 2 .201 2 .405 2 .287 3 .492 2 .384 1 .336 0 .756 20. 1011. 3 .512 .064 .023 .008 .881 2 .455 2 .697 2 .454 4 .385 2 .493 1 .416 0 .687 21. 1011. 3 .700 .065 .024 .009 .877 2 .650 3 .034 2 .740 5 .204- 2 .586 1 .432 0 .616 22. 1012. 0 .449 .068 .023 .009 .898 0 .731 0 .478 0 .540 0 .878 0 .953 0 .502 0 .215 1 . 1012. 0 .503 .064 .019 .008 .904 0 .749 0 .509 0 .561 0 .899 1 .000 0 .537 0 .297 2. 1012. 0 .532 .064 .020 .008 .902 0 .769 0 .512 0 .586 0 .908 1 .006 0 .566 0 .378 3. 1012. 0 .589 .067 .020 .008 .896 0 .812 0 .544 0 .634 0 .923 0 .951 0 .648 0 .458 4. 1012. 0 .634 .070 .019 .008 .892 0 .855 0 .577 0 .651 0 .918 0 .984 0 .674 0 .539 5. 1012. 0 .776 .069 .020 .008 .891 0 .891 0 .621 0 .737 0 .920 1 .024 0 .790 0 .620 6. 1012. 0 .789 .076 .020 .008 .880 0 .883 0 .683 0 .807 0 .928 0 .984 0 .831 0 .700 7. 1012. 0 .834 .077 .022 .008 .876 0 .883 0 .733 0 .823 0 .942 1 .008 0 .856 0 .781 8. 1012. 0 .941 .082 .024 .007 .870 0 .918 0 .825 0 .959 0 .943 0 .987 0 .974 0 .881 9. 1012. 0 .948 .092 .025 .008 .855 0 .966 0 .904 1 .011 0 .951 0 .968 0 .988 0 .980 10. 1012. 1 .000 .096 .024 .009 .848 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 1. 1012. 1 .198 .094 .024 .008 .852 1 .031 1 . 120 1 .118 1 .046 1 .089 1 .106 1 .020 12. 1012. 1 .659 .085 .020 .007 .870 1 .083 1 .247 1 .219 1 . 1 34 1 .474 1 .149 0 .936 13. 10,12. 1 .782 .090 .021 .008 .862 1 .243 1 .467 1 .359 1 .354 1 .636 1 .096 0 .849 14. 1012. 1 .820 .096 .024 .009 .847 1 .392 1 .699 1 .563 1 .590 1 .757 1 .038 0 .919 15. 1012. 2 .075 .108 .024 .010 .833 1 .488 2 .043 1 .780 ,1 .899 1 .754 1 . 1 66 0 .988 16. 1012. 2 .265 .114 .025 .010 .825 1 .619 2 .235 1 .861 2 .189 1 .771 1 .257 0 .973 17. 1012. 2 .591 .108 .024 .011 .830 1 .775 2 .418 2 .071 2 .412 1 .924 1 .329 0 .956 18. 1012. 3 .098 . 106 .026 .010 .832 1 .981 2 .704 2 . 157 2 .670 2 .080 1 .460 0 .905 19. 1012. 3 .212 .113 .025 .012 .822 2 .201 3 .018 2 .380 3 . 168 2 .181 1 .427 0 .853 20. 1012. 3 .651 .111 .025 .013 .823 2 .455 3 .362 2 .757 4 .084 2 .549 1 .388 0 .856 21 . 1012. 3 .928 .110 .026 .015 .818 2 .650 3 .772 3 .183 4.797 2 .524 1 .498 0 .858 22. 1020. 0 .454 .108 .041 .013 .796 0 .731 0 .553 0 .486 0 .866 0 .656 0 .737 0 .582 1 . 1020. 0 .527 . 106 .042 .013 .800 0 .749 0 .569 0 .543 0 .880 0 .664 0 .838 0 .647 2. 1020. 0.521 .116 .042 .016 .783 0 .769 0 .586 0 .538 0 .879 0 .685. 0 .782 0 .713 3. 1020. 0 .590 .110 .041 .013 .793 0 .812 0 .615 0 .577 0 .893 0 .705 0 .876 0 .779 4. 1020. 0 .643 .116 .040 .013 .785 0 .855 0 .646 0 .656 0 .884 0 .748 0 .890 0 .845 5. 1020. 0 .742 .118 .039 .012 .785 0 .891 0 .686 0 .751 0 .894 0 .758 0 .992 0 .911 6. 1020. 0 .730 .120 .043 .012 .767 0 .883 0 .703 0 .789 0 .903 0 .780 0 .916 0 .977 7. 1020. 0 .838 .122 .038 .012 .768 0.883 0 .762 0 .794 0 .911 0 .798 1 .033 1 .043 8. 1020. 0.884 .120 .037 .013 .770 0 .918 0 .804 0 .857 0 .905 0 .880 1 .024 1 .021 9. 1020. 0 .984 . 120 .033 .01 1 .778 0 .966 0 .897 0 .963 0 .918 0 .955 1 .040 0.998 10. 1020. 1 .000 .124 .032 .011 .768 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 1. 1020. 1 .098 . 133 .036 .012 .757 1 .031 1 .141 1 .086 1 .069 1 . 1 42 0 .959 1 .002 12. 1020. 1 .486 . 124 .028 .010 .788 1 .083 1 .305 1 .225 1 . 196 1 .435 1 .073 1 .114 13. 1020. 1 .483 .134 .032 .014 .762 1 .243 1 .593 1 .358 1 .585 1 .685 0 .889 1 .226 14. 1020. 1 .535 . 140 .039 .016 .737 1 .392 1 .874 1 .584 1 .849 1 .680 0 .881 1 .262 15. 1020. 2 .026 .144 .035 .013 .749 1 .488 2 . 195 1 .806 2 .112 1 .990 1 .005 1 .297 16. 1 The final model is the cost/share system (42') and (43). Descriptions of each data type are given in Chapter 6. 2 See Table 6 for industry names. 198 Table A2.1. Data Used in Estimation of Final Model, (cont'd) Canadian Food Manufacturing Industries, 1961-1982 s:i.c. C S/p Sinp s, Sin WA W/„ W/„p w,„ Q h t 1 0 2 0 . 2 . 4 8 1 . 1 4 8 . 0 3 3 . 0 1 3 . 7 5 5 1 . 6 1 9 2 . 4 28 1 . 9 0 0 2 . 4 4 5 2 . 2 1 9 1 . 1 1 9 1 . 2 1 9 1 7 . 1 0 2 0 . 3 . 1 9 5 . 1 4 4 . 0 3 0 . 0 1 2 . 7 6 9 1 . 7 7 5 2 . 6 59 2 . 0 6 2 2 . 7 2 6 2 . 5 3 2 1 . 2 8 4 1 . 1 4 2 1 8 . 1 0 2 0 . 3 . 7 7 9 . 149 . 0 3 2 . 0 1 5 .761 1 .981 2 .981 2 . 2 3 3 3 . 1 19 2 . 9 7 3 1 . 2 8 5 1 . 1 7 3 19 . 1 0 2 0 . 4 . 4 3 6 . 132 . 0 3 0 . 0 1 5 . 7 78 2 .201 3 . 2 04 2 . 4 3 3 3 . 768 2 .991 1 .451 1 . 204 2 0 . 1 0 2 0 . 5 . 123 . 1 3 3 . 0 2 8 . 0 1 3 .781 2 . 4 5 5 3 . 6 4 6 2 . 6 9 9 4 . 658 3 . 1 1 2 1 . 5 9 0 1 . 1 29 21 . 1 0 2 0 . 5 . 109 . 1 2 6 .031 . 0 1 5 . 7 78 2 . 6 5 0 3 . 8 04 2 . 8 7 4 5 .404 3 . 2 0 5 1 . 5 5 3 1 .051 2 2 . 1 0 3 0 . 0 . 5 3 2 . 1 0 0 . 0 5 9 . 0 1 2 . 7 7 3 0 .731 0 . 5 0 5 0 . 5 9 2 0 . 808 0 . 8 0 6 0 . 6 5 5 1 . 118 1 . 1 0 3 0 . 0 . 5 8 4 . 100 . 0 5 8 . 0 1 2 . 7 7 3 0 . 7 4 9 0 . 5 29 0 . 6 0 9 0 . 8 4 5 0 . 8 1 5 0 . 7 24 1 . 112 2 . 1 0 3 0 . 0 . 6 2 0 . 0 9 5 . 0 5 5 . 0 1 2 . 7 7 7 0 . 7 6 9 0 . 554 0 . 6 2 2 0 . 8 58 0 . 8 54 0 . 7 3 7 1 . 1 0 5 3 . 1 0 3 0 . 0 . 6 7 6 . 0 9 7 . 0 5 5 . 0 1 2 . 7 7 6 0 . 8 1 2 0 . 5 7 3 0 . 6 5 2 0 . 8 8 0 0 . 8 6 2 0 . 7 8 5 1 . 0 9 6 4 . 1 0 3 0 . 0 . 7 3 1 . 1 0 0 . 0 5 6 . 0 1 2 . 7 7 0 0 . 8 5 5 0 . 6 2 5 0 . 6 7 4 0 . 8 8 2 0 . 8 5 6 0 . 8 4 3 1 . 0 89 5 . 1 0 3 0 . 0 . 7 9 0 . 103 . 0 5 6 . 0 1 2 . 7 6 5 0 .091 0 . 667 0 . 7 0 7 0 . 8 88 0 . 8 8 3 0 . 8 8 5 1 . 083 6 . 1 0 3 0 . 0 . 8 2 2 . 104 . 0 5 7 . 0 1 2 .761 0 . 8 8 3 0 . 7 1 2 0 . 7 5 8 0 . 8 9 7 0 . 9 04 0 . 8 9 8 1 . 074 7 . 1 0 3 0 . 0 . 8 5 0 . 105 . 0 5 8 .011 . 7 6 0 0 . 8 8 3 0 . 7 8 0 0 . 8 3 5 0 . 9 0 5 0 . 9 2 0 0 . 9 1 6 1 . 0 67 8 . 1 0 3 0 . 0 . 9 1 4 . 103 . 0 5 9 .011 . 764 0 . 9 1 8 0 . 8 3 7 0 . 8 9 6 0 . 908 0 . 9 4 9 0 . 9 64 1 . 0 6 5 9 . 1 0 3 0 . 0 . 9 5 4 . 103 . 0 5 9 . 0 1 0 . 7 6 5 0 . 9 6 6 0 .901 0 . 9 7 0 0 .921 0 . 9 6 6 0 . 9 8 8 1 . 0 6 3 1 0 . 1 0 3 0 . 1 . 0 0 0 . 105 . 0 5 8 . 0 1 0 . 7 6 0 1 .000 1 .000 1 .000 1 .000 1 . 0 0 0 1 .000 1 .000 1 1 . 1 0 3 0 . 1 . 0 9 4 . 1 0 6 . 0 5 7 .011 .761 1 .031 1 . 094 1 . 0 84 1 . 0 69 1 . 0 5 3 1 . 0 5 3 0 . 938 1 2 . 1 0 3 0 . 1 . 2 3 5 . 1 0 6 . 0 5 4 .011 . 7 6 7 1 . 0 8 3 1 . 2 0 7 1 . 1 9 0 1 . 1 7 3 1 . 1 5 0 1 . 0 9 6 0 .891 1 3 . 1 0 3 0 . 1 . 5 0 7 .101 . 0 4 8 . 0 1 2 . 7 8 2 1 . 2 4 3 1 . 3 5 9 1 . 2 7 4 1 . 494 1 . 4 1 3 1 . 1 1 7 0 . 8 4 2 14 . 1 0 3 0 . 1 . 6 9 6 . 105 . 0 4 8 . 0 1 3 . 7 7 2 1 . 3 9 2 1 . 5 4 2 1 . 4 1 3 1 . 8 08 1 . 5 8 3 1 . 1 0 7 0 . 877 1 5 . 1 0 3 0 . 1 . 7 5 7 . 1 0 8 . 0 5 3 . 0 1 5 . 7 5 6 1 . 4 8 8 1 . 7 2 2 1 . 6 28 2 . 160 1 . 6 0 6 1 . 1 24 0 . 9 1 3 16 . 1 0 3 0 . 1 . 8 2 0 . 1 0 5 . 0 5 3 . 0 1 6 . 7 5 3 1 . 6 1 9 1 . 9 3 5 1 . 7 9 3 2 . 5 3 3 1 . 7 04 1 . 0 8 0 0 . 9 2 9 17 . 1 0 3 0 . 2 . 1 1 6 . 100 . 0 5 0 . 0 1 6 . 7 6 3 1 . 7 7 5 2 .131 2 .001 2 . 834 1 . 9 1 2 1 . 1 1 9 0 . 9 4 2 18 . 1 0 3 0 . 2 . 3 8 6 . 0 9 7 . 0 4 9 . 0 1 7 . 7 6 7 1 .981 2 . 3 1 5 2 . 1 1 0 3 . 1 7 3 2 . 0 7 6 1 . 176 0 . 9 98 19 . 1 0 3 0 . 2 . 6 2 3 . 0 9 8 . 0 5 0 . 0 1 9 .761 2 .201 2 . 6 0 7 2 . 3 1 9 3 . 8 56 2 . 2 54 1 . 177 1 .051 2 0 . 1 0 3 0 . 2 . 9 1 9 . 0 9 7 . 0 5 0 . 0 1 9 . 7 6 0 2 . 4 5 5 3 . 0 24 2 . 5 84 4 . 8 4 3 2 . 6 0 6 1 .131 1 . 0 16 21 . 1 0 3 0 . 3 . 1 0 9 . 0 9 9 . 0 5 4 . 0 2 2 . 7 4 6 2 . 6 5 0 3 . 2 9 3 2 . 9 9 6 5 . 727 2 . 7 9 5 1 . 107 0 . 978 2 2 . 1 0 4 0 . 0 . 5 8 5 . 0 4 9 . 0 7 6 . 0 1 7 . 8 2 5 0 .731 0 . 5 0 2 0 . 5 4 0 0 . 8 4 7 0 . 7 4 2 0 . 7 8 2 0 . 3 3 5 1 . 1 0 4 0 . 0 . 6 0 2 . 0 5 0 . 0 7 6 . 0 1 6 . 8 2 6 0 . 7 4 9 0 . 5 1 6 0 . 5 64 0 . 8 7 2 0 .741 0 . 8 0 9 0 . 3 73 2 . 1 0 4 0 . 0 . 6 3 2 . 0 4 8 . 0 7 6 . 0 1 6 . 8 2 7 0 . 7 6 9 0 . 5 4 2 0 .581 0 .881 0 . 7 4 7 0 . 8 48 0 . 408 3 . 1 0 4 0 . 0 . 6 7 0 . 0 4 8 . 0 7 4 . 0 1 6 . 8 2 6 0 . 8 1 2 0 . 5 6 6 0 . 6 0 7 0 . 897 0 . 7 6 7 0 . 8 8 3 0 . 4 46 4 . 1 0 4 0 . 0 . 7 1 0 . 0 4 8 . 0 7 4 . 0 1 6 . 8 2 5 0 . 8 5 5 0 . 6 0 9 0 . 6 34 0 . 898 0 . 7 8 5 0 .911 0 .481 5 . 1 0 4 0 . 0 . 7 6 9 . 0 4 8 . 0 7 3 . 0 1 5 . 8 2 6 0 .891 0 . 6 5 3 0 . 6 7 8 0 . 9 0 0 0 . 8 28 0 . 9 3 7 0 . 5 16 6. 1 0 4 0 . 0 . B 2 9 . 0 4 8 .071 . 0 1 5 . 8 2 7 0 . 8 8 3 0 .701 0 .731 0 . 9 09 0 . 8 78 0 . 9 5 2 0 .554 7 . 1 0 4 0 . 0 . 8 5 0 . 0 5 0 .071 . 0 1 5 . 8 2 3 0 . 8 8 3 0 . 7 6 0 0 .801 0 . 9 2 7 0 . 9 08 0 . 9 4 3 0 . 5 8 9 8 . 1 0 4 0 . 0 . 9 1 0 . 0 5 0 . 0 6 9 . 0 1 5 . 8 2 6 0 . 9 1 8 0 . 8 3 7 0 . 8 6 2 0 . 9 3 2 0 . 9 4 0 0 . 9 7 5 0 . 7 43 9 . 1 0 4 0 . 0 . 9 2 7 . 0 5 2 . 0 7 3 . 0 1 4 . 8 18 0 . 9 6 6 0 . 8 9 9 0 . 9 3 6 0 . 9 4 5 0 . 9 54 0 . 9 6 9 0 . 8 95 10 . 1 0 4 0 . 1 . 0 0 0 . 0 5 2 . 0 7 0 . 0 1 3 .821 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 1 . 1 0 4 0 . 1 . 0 6 9 . 0 5 2 . 0 6 8 . 0 1 3 . 8 24 1 .031 1 . 0 9 8 1 . 0 9 9 1 . 0 5 3 1 . 0 58 1 .011 1 . 105 12 . 1 0 4 0 . 1 . 1 6 8 . 0 5 0 . 0 6 6 . 0 1 2 . 8 3 0 1 . 0 8 3 1 . 2 2 2 1 . 1 9 7 1 . 1 5 3 1 . 168 1 . 0 04 1 .251 1 3 . 1 0 4 0 . 1 . 417 . 0 4 7 . 0 6 0 . 0 1 3 . B 43 1 . 2 4 3 1 . 4 0 2 1 . 3 4 8 1 . 437 1 . 4 2 5 1 . 0 2 0 1 . 397 14 . 1 0 4 0 . 1 . 7 4 7 . 0 4 7 . 0 5 5 . 0 1 2 . 8 5 0 1 . 3 9 2 1 . 6 5 0 1 . 5 4 8 1 . 7 2 2 1 . 7 2 8 1 .04 1 1 . 427 1 5 . 1 0 4 0 . 1 . 8 9 5 . 0 4 9 .051 . 0 1 2 . 8 5 0 1 . 4 8 8 1 . 8 78 1 . 7 5 6 2 . 0 2 3 1 . 8 3 5 1 . 0 5 9 1 . 457 16 . 1 0 4 0 . 2 . 0 5 5 .051 . 0 5 0 . 0 1 3 . 8 4 9 1 . 6 1 9 2 . 0 98 1 . 8 94 2 . 3 2 0 1 . 9 7 0 1 . 0 7 0 1 . 430 17 . 1 0 4 0 . 2 . 2 0 5 . 0 5 3 . 0 4 8 . 0 1 3 . 8 4 6 1 . 7 7 5 2 . 2 3 3 1 . 9 8 7 2 . 5 7 2 2 . 0 7 3 1 . 0 8 3 1 . 403 18 . 1 0 4 0 . 2 . 4 7 4 .051 . 0 4 8 . 0 1 3 . 8 4 9 1 .981 2 . 4 1 2 2 . 2 5 2 2 .861 2 . 2 6 0 1 . 1 18 1 . 4 1 9 19 . 1 0 4 0 . 2 . 8 8 3 . 0 5 0 . 0 4 4 . 0 1 3 . 8 54 2 .201 2 . 9 1 3 2 . 4 3 7 3 . 4 38 2 . 5 9 3 1 . 1 4 0 1 . 432 2 0 . 1 0 4 0 . 3 . 2 5 2 . 0 5 0 . 0 4 3 . 0 14 . 8 5 3 2 . 4 5 5 3 . 2 2 5 2 . 7 3 7 4 . 4 5 9 2 .921 1 . 1 38 1 . 443 21 . 1 0 4 0 . 3 . 6 4 2 . 0 4 9 . 0 4 2 . 0 1 5 . 8 5 3 2 . 6 5 0 3 . 5 6 9 3 . 0 3 3 5 . 2 8 9 3 . 2 3 6 1 . 1 4 9 1 .454 2 2 . 1 0 5 0 . 0 . 8 1 6 . 0 5 6 . 0 3 2 . 0 0 8 . 8 4 7 0 .731 0 . 5 0 9 0 . 5 3 3 0 . 884 0 .851 1 .011 1 . 263 1 . 1 0 5 0 . 0 . 8 9 5 . 0 5 2 . 0 3 3 . 0 08 . 8 44 0 . 7 4 9 0 . 5 4 9 0 . 5 5 7 0 . 9 0 2 0 . 9 3 5 1 .011 1 . 232 2 . 1 0 5 0 . 0 . 8 8 9 .051 . 0 3 5 . 0 0 7 . 8 3 8 0 . 7 6 9 0 . 5 5 9 0 . 5 5 3 0 . 9 08 0 . 9 6 9 0 . 9 6 6 1 . 200 3 . 1 0 5 0 . 1 . 112 . 0 4 5 . 0 3 0 . 0 0 6 . 8 6 3 0 . 8 1 2 0 . 5 8 6 0 . 5 8 9 0 . 9 3 0 0 . 9 7 0 1 . 2 2 6 1 . 169 4 . 1 0 5 0 . 0 . 9 1 6 . 0 5 2 . 0 3 6 . 0 0 7 . 8 3 2 0 . 8 5 5 0 . 6 08 0 . 5 9 6 0 . 9 24 0 . 9 5 9 0 . 9 9 7 1 . 1 38 5 . 1 0 5 0 . 0 . 9 7 8 . 0 5 2 . 0 3 7 . 0 0 7 . 8 3 0 0 .891 0 . 644 0 . 6 58 0 .931 0 . 9 8 2 1 . 0 44 1 . 106 6 . 1 0 5 0 . 0 . 9 9 7 . 0 5 5 . 0 3 6 . 0 0 7 . 8 2 6 0 . 8 8 3 0 . 6 8 7 0 . 6 94 0 . 938 1 . 0 1 9 1 .001 1 . 0 7 5 7 . 1 0 5 0 . 0 . 9 2 3 .061 . 0 3 8 . 0 0 8 . 8 0 7 0 . 8 8 3 0 . 7 7 0 0 . 8 0 0 0 . 9 48 0 . 9 8 7 0 . 9 4 3 1 . 044 8 . 1 0 5 0 . 0 . 9 4 3 . 0 6 5 . 0 3 8 . 0 0 8 .801 0 . 9 1 8 0 . 8 6 3 0 . 8 5 0 0 . 9 54 0 . 9 9 2 0 . 9 64 1 .048 9 . 1 0 5 0 . 0 . 9 8 6 . 0 6 9 . 0 4 5 . 0 08 . 7 9 3 0 . 9 6 6 0 . 9 3 5 0 . 9 3 5 0 . 9 54 0 . 9 9 8 0 . 9 9 5 1 . 053 10 . 199 Table A2.1. Data Used in Estimation of Final Model, (cont'd) Canadian Food Manufacturing Industries, 1961-1982 S.I.C. C Si up S, Sin W A W/„ W/„„ w,„ Q h t 1050. 1 .000 .071 .045 .008 .788 1 .000 1 .000 1 .000 1 . 000 1 .000 1 .000 1 . 000 1 1 . 1050. 1 .029 .076 .048 .009 .781 1 .031 1 . 1 07 1 .084 1 . 041 1 .006 1 .004 0. 947 12. 1050. 1 . 157 .073 .037 .008 .807 1 .083 1 .21 1 1 .135 1 . 103 1 .171 0 .983 0. 947 13. 1050. 1 .532 .062 .031 .006 .842 1 .243 1 .345 1 .196 1 . 238 1 .576 1 .010 0. 937 14. 1050. 1 .734 .062 .036 .007 .835 1 .392 1 .522 1 .395 1 . 437 1 .719 1 .043 0. 946 15. 1050. 1 .831 .069 .041 .009 .820 1 .488 1 .755 1 .629 1 . 794 1 .696 1 .096 0. 954 16. 1050. 1.915 .073 .040 .010 .814 1 .619 1 .869 1 .635 2. 070 1 .655 1 . 1 64 0. 932 17. 1050. 2.063 .072 .042 .011 .810 1 .775 2 .032 1 .744 2. 307 1 .734 1 .202 0. 910 18. 1050. 2.550 .065 .038 .010 .826 1 .981 2 .179 2 .066 2. 523 2 .210 1 .192 0. 930 19. 1050. 2.927 .061 .038 .010 .831 2 .201 2 .396 2 .326 2. 909 2 .597 1 .174 0. 949 20. 1050. 3.385 .060 .038 .010 .834 2 .455 2 .755 2 .691 3. 457 3 .016 1 . 173 0. 917 21 . 1050. 3.203 .070 .046 .012 .804 2 .650 3 .059 2 .903 4. 044 2 .700 1 .195 0. 886 22. 1060. 0.494 .044 .040 .013 .863 0 .731 0 .526 0 .553 0. 879 0 .894 0 .539 0. 891 1 . 1060. 0.541 .040 .039 .012 .870 0 .749 0 .551 0 .578 0. 894 0 .959 0 .552 0. 901 2. 1060. 0.584 .038 .038 .012 .874 0 .769 0 .608 0 .603 0. 903 0 .973 0 .590 0. 911 3. 1060. 0.626 .037 .038 .012 .876 0 .812 0 .625 0 .628 0. 918 0 .959 0 .654 0. 917 4 . 1060. 0.683 .037 .036 .012 .878 0 .855 0 .650 0 .648 0. 916 0 .972 0 .705 0. 927 5. 1060. 0.800 .036 .034 .011 .885 0 .891 0 .687 0 .700 0. 920 1 .034 0 .787 0. 937 6. 1060. 0.876 .037 .034 .011 .883 0 .883 0 .727 0 .755 0. 929 1 .027 0 .866 0. 944 7. 1060. 0.882 .040 .036 .012 .876 0 .883 0 .801 0 .795 0. 946 0 .985 0 .899 0. 954 8. 1060. 0.922 .042 .039 .012 .870 0 .918 0 .877 0 .868 0. 948 0 .969 0 .957 0. 977 9. 1060. 0.969 .042 .041 .010 .867 0 .966 0 .920 0 .957 0. 955 0 .995 0 .973 1 . 000 10. 1060. 1 .000 .043 .036 .011 .867 1 .000 1 .000 1 .000 1 . 000 1 .000 1 .000 1 . 000 1 1 . 1060. 1 .090 .043 .033 .010 .870 1 .031 1 .081 1 .081 1 . 044 1 .057 1 .036 0. 997 12. 1060. 1 .540 .034 .028 .009 .898 1 .083 1 . 1 93 1 .199 1 . 1 29 1 .616 0 .982 0. 950 13. 1060. 1 .904 .034 .026 .009 .903 1 .243 1 .482 1 .361 1 . 334 1 .841 1 .059 0. 904 14. 1060. 1 .969 .039 .025 .008 .892 1 .392 1 .651 1 .515 1 . 569 1 .854 1 .074 0. 917 15. 1060. 2.044 .040 .028 .010 .882 1 .488 1 .956 1 .673 1 . 892 1 .888 1 .072 0. 927 16. 1060. 2. 175 .040 .030 .011 .877 1 .619 2 .141 1 .812 2. 181 1 .928 1 .112 0. 937 17. 1060. 2.366 .043 .030 .012 .873 1 .775 2 .339 1 .977 2. 416 1 .971 1 .172 0. 947 18. 1060. 2.879 .039 .027 .011 .883 1 .981 2 .562 2 .259 2. 684 2 .280 1 .248 0. 914 19. 1060. 3.442 .037 .026 .012 .086 2 .201 2 .808 2 .454 3. 208 2 .571 1 .334 0. 877 20. 1060. 3.901 .036 .026 .012 .885 2 .455 3 . 1 48 2 .723 4. 039 2 .821 1 .369 0. 838 21 . 1060. 3.719 .039 .030 .017 .865 2 .650 3 .411 2 .993 4. 795 2 .561 1 .406 0. 798 22. 1071 . 0.594 . 170 .099 .013 .624 0 .731 0 .537 0 .633 0. 850 0 .802 0 .765 0. 891 1 . 1071 . 0.626 .171 .098 .012 .626 0 .749 0 .551 0 .650 0. 888 0 .801 0 .819 0. 897 2. 1071 . 0.672 . 162 . 100 .011 .635 0 .769 0 .594 0 .672 0. 897 0 .871 0 .819 0. 902 3. 1071 . 0.665 .161 . 100 .011 .627 0 .812 0 .625 0 .689 0. 915 0 .898 0 .775 0. 908 4. 1071 . 0.689 .164 .102 .012 .619 0 .855 0 .652 0 .701 0. 915 0 .858 0 .825 0. 913 5. 1071 . 0.724 .171 .099 .012 .614 0 .891 0 .690 0 .737 0. 914 0 .869 0 .841 0. 930 6. 1071 . 0.807 .178 .101 .011 .612 0 .883 0 .735 0 .783 0. 925 0 .892 0 .904 0. 947 7. 1071 . 0.842 .181 .100 .011 .615 0 .883 0 .790 0 .819 0. 931 0 .907 0 .929 0. 964 8. 1071 . 0.902 . 186 .092 .010 .625 0 .918 0 .837 0 .891 0. 943 0 .950 0 .965 0. 969 9. 1071 . 0.947 .188 .093 .010 .620 0 .966 0 .899 0 .938 0. 949 0 .979 0 .971 0. 974 10. 1071 . 1 .000 .191 .088 .010 .617 1 .000 1 .000 1 .000 1 . 000 1 .000 1 .000 1. 000 1 1 . 1071 . 1 .177 . 197 .099 .010 .61 1 1 .031 1 .093 1 .034 1 . 050 1 .031 1 .151 1. 025 12. 1071 . 1 .332 .195 .097 .010 .623 1 .083 1 .246 1 .106 1 . 125 1 .159 1 .172 0. 980 13. 1071 . 2.064 . 137 .079 .008 .723 1 .243 1 .374 1 .204 1 . 341 1 .630 1 .328 0. 935 14. 1071 . 2.552 . 134 .072 .007 .738 1 .392 1 .702 1 .417 1 . 644 1 .841 1 .384 0. 959 15. 1071 . 2.542 .150 .072 .010 .712 1 .488 1 .943 1 .529 2. 071 1 .723 1 .465 0. 982 16. 1071 . 2.569 .159 .076 .011 .695 1 .619 2 .197 1 .646 2. 410 1 .864 1 .327 0. 982 17. 1071 . 2.792 .149 .079 .012 .700 1 .775 2 .289 1 .869 2. 765 2 .015 1 .325 0. 982 18. 1071 . 2.983 . 140 .080 .011 .710 1 .981 2 .532 2 .065 3. 069 2 .316 1 .221 1. 050 19. 1071 . 3.378 .135 .077 .011 .720 2 .201 2 .655 2 .311 3. 666 2 .629 1 .248 1. 1 17 20. 1071 . 3.796 . 125 .079 .012 .727 2 .455 3 . 1 63 2 .551 4. 496 3 .092 1 . 1 97 1. 124 21 . 1071 . 3.869 . 136 .089 .014 .700 2 .650 3 .478 2 .982 5. 415 3 .112 1 .174 1. 131 22. 1072. 0.661 .144 .141 .029 .608 0 .731 0 .536 0 .502 0. 852 0 .840 0 .844 0. 791 1 . 1072. 0.698 .142 .145 .027 .609 0 .749 0 .578 0 .537 0. 973 0 .861 0 .875 0. 819 2. 1072. 0.733 . 139 .139 .026 .619 0 .769 0 .615 0 .554 0. 878 0 .903 0 .874 0. 847 3. 1072. 0.790 . 140 . 137 .026 .622 0 .812 0 .643 0 .576 0. 897 0 .926 0 .921 0. 872 4. 200 Table A2.1. Data Used in Estimation of Final Model, (cont'd) Canadian Food Manufacturing Industries, 1961-1982 S.I.C. C Sip Ship s. Sni W * W/, W/„ p W m Q h t 1 0 7 2 . 0 . 8 3 2 .141 . 142 . 0 2 6 . 6 14 0 . 8 5 5 0 . 673 0 .611 0 . 900 0 . 9 05 0 . 9 68 0 . 9 0 0 5 . 1 0 7 2 . 0 . 8 7 4 . 146 . 140 . 0 2 5 .611 0 .891 0 . 708 0 . 634 0 . 906 0 . 912 0 . 9 8 2 0 .891 6 . 1 0 7 2 . 0 . 9 1 5 . 1 4 7 . 139 . 0 2 4 . 6 1 0 0 . 0 8 3 0 . 747 0 . 6 6 5 0 . 913 0 . 931 1 . 0 1 9 0 . 8 8 3 7 . 1 0 7 2 . 0 . 9 2 9 .151 . 1 4 2 . 0 2 4 . 6 0 5 0 . 8 8 3 0 . 808 0 . 7 24 0 . 934 0 . 930 1 . 034 0 . 8 7 5 8 . 1 0 7 2 . 0 . 9 4 9 . 1 5 8 . 142 . 0 2 4 . 5 9 7 0 . 9 1 8 0 . 884 0 . 7 7 3 0 . 942 0 . 9 55 1 . 0 0 3 0 . 9 08 9 . 1 0 7 2 . 0 . 991 . 170 . 130 . 0 2 0 . 6 0 2 0 . 9 6 6 0 . 921 0 . 9 3 3 0 . 953 0 . 976 1 .021 0 . 9 4 2 10 . 1 0 7 2 . 1 . 0 0 0 . 177 . 129 . 0 2 0 . 5 94 1 . 0 0 0 1. 000 1 . 0 0 0 1. 000 1. 000 1 . 0 0 0 1 . 0 0 0 1 1 . 1 0 7 2 . 1 . 0 5 9 . 182 . 125 . 0 1 9 . 596 1 .031 1. 108 1 . 0 5 3 1. 048 1. 029 1 . 0 3 2 1 . 0 58 12 . 1 0 7 2 . 1 . 124 . 1 8 0 .131 . 0 1 9 . 5 9 6 1 . 0 8 3 1. 250 1 . 1 4 3 1. 142 1. 126 1 . 0 0 6 1 . 142 13 . 1 0 7 2 . 1 . 3 3 8 . 166 .121 . 0 1 8 .631 1 . 2 4 3 1. 480 1 . 2 7 0 1. 384 1. 477 0 . 9 7 0 1 . 223 14 . 1 0 7 2 . 1 . 5 2 0 . 1 7 5 . 1 1 7 . 0 1 9 . 6 2 6 1 . 3 9 2 1. 666 1 . 4 8 5 1. 660 1. 708 0 . 9 38 1 . 1 34 1 5 . 1 0 7 2 . 1 .631 . 185 . 124 . 0 2 0 . 6 0 5 1 . 4 8 8 2 . 028 1 . 6 7 6 1. 978 1. 708 0 . 9 6 9 1 . 0 4 2 16 . 1 0 7 2 . 1 . 719 . 187 . 123 . 0 2 0 . 6 0 2 1 . 6 1 9 2 . 210 1 . 8 0 6 2 . 258 1. 769 0 . 9 7 4 1 . 0 3 6 17 . 1 0 7 2 . 1 . 8 5 2 . 1 9 5 . 122 . 0 2 2 . 5 94 1 . 7 7 5 2 . 336 1 . 9 3 7 2 . 501 1. 884 0 . 9 7 5 1 .031 18 . 1 0 7 2 . 2 . 0 8 3 . 1 9 5 . 1 1 6 .021 . 6 0 3 1 .981 2 . 533 2 . 2 6 2 2 . 772 2 . 296 0 . 9 1 9 1 . 047 19 . 1 0 7 2 . 2 . 2 9 2 . 1 9 0 . 1 1 3 . 0 2 2 . 6 0 9 2 .201 2 . 8 15 2 . 5 4 6 3 . 320 2 . 590 0 . 8 98 1 . 064 2 0 . 1 0 7 2 . 2 . 5 7 5 . 188 . 1 1 3 . 0 2 5 . 6 0 8 2 . 4 5 5 3 . 206 2 . 8 1 6 4 . 329 2 . 9 73 0 .881 1 . 1 0 0 21 . 1 0 7 2 . 2 . 6 3 7 . 194 . 122 . 0 34 . 5 8 0 2 . 6 5 0 3 . 423 3 . 0 9 0 5 . 174 3 . 009 0 .861 0 . 9 94 2 2 . 1081 . 0 . 5 6 3 . 155 . 0 7 9 .011 . 6 8 6 0 .731 0 . 531 0 . 5 6 6 0 . 852 0 . B05 0 . 708 1 . 0 3 2 1 . 1081 . 0 . 6 0 0 . 1 5 2 . 0 7 8 .011 .681 0 . 7 4 9 0 . 548 0 . 6 0 3 0 . 886 0 . 791 0 . 7 5 7 1 . 0 24 2 . 1081 . 0 . 6 6 5 . 1 4 2 . 0 7 4 . 0 1 0 . 6 8 8 0 . 7 6 9 0 . 575 0 . 6 3 9 0 . 898 0 . 8 5 9 0 . 7 8 0 1 . 0 1 6 3 . 1081 . 0 . 7 0 5 . 138 . 0 7 3 . 0 1 0 .691 0 . 8 1 2 0 . 600 0 . 6 44 0 . 912 0 . 892 0 . 7 98 1 . 0 0 8 4 . 1081 . 0 . 7 4 8 . 1 4 7 . 0 7 3 . 0 1 0 .681 0 . 8 5 5 0 . 629 0 . 7 14 0 . 907 0 . 8 46 0 . 884 1 . 0 0 0 5 . 1081 . 0 . 7 9 1 . 1 5 3 . 0 7 4 . 0 1 0 . 6 7 2 0 .891 0 . 678 0 . 7 2 2 0 . 91 1 0 . 844 0 . 9 38 1 . 0 5 5 6 . 1081 . 0 . 8 3 5 . 156 . 0 7 7 . 0 1 0 . 6 6 6 0 . 8 8 3 0 . 734 0 . 7 6 0 0 . 926 0 . 861 0 . 9 6 6 1 . 108 7 . 1081 . 0 . 8 9 2 . 151 . 0 7 7 . 0 1 0 . 6 7 5 0 . 8 8 3 0 . 771 0 . 8 0 8 0 . 936 0 . 8 9 2 1 .011 1 . 162 8 . 1081 . 0 . 9 4 1 . 151 . 0 8 0 . 0 1 0 . 6 74 0 . 9 1 8 0 . 847 0 . 877 0 . 936 0 . 937 1 . 0 1 9 1 . 1 1 6 9 . 1081 . 0 . 9 7 5 . 152 . 0 7 4 . 0 0 9 . 6 7 9 0 . 9 6 6 0 . 905 0 . 9 4 5 0 . 943 1 . 002 0 . 9 94 1 . 0 68 10 . 1 0 8 1 . 1 . 0 0 0 . 157 . 0 7 8 . 0 1 0 . 6 6 8 1 . 0 0 0 1. 000 1 . 000 1 . 000 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 1 . 1081 . 1 . 0 6 0 . 1 5 0 . 0 8 0 . 0 1 0 . 6 7 2 1 .031 1. 069 1 . 0 6 7 1 . 050 0 . 996 1 . 067 0 .931 12. 1081 . 1 . 184 . 146 . 0 9 7 . 0 0 9 . 6 6 7 1 . 0 8 3 1. 168 1 . 1 2 4 1 . 136 1. 042 1 .131 0 . 9 99 13 . 1081 . 1 . 5 9 6 . 1 1 9 . 0 6 7 . 0 0 9 .741 1 . 2 4 3 1. 315 1 .271 1 . 359 1. 802 0 . 9 7 6 1 . 0 66 14. 1081 . 1 . 812 . 1 1 9 . 0 6 8 . 0 0 9 . 7 3 4 1 . 3 9 2 1. 527 1 . 5 38 1 . 613 2 . 1 52 0 . 914 1 . 0 33 15 . 1081 . 1 . 8 44 . 1 3 2 . 0 7 3 .01 1 . 7 0 6 1 . 4 8 8 1. 783 1 . 7 0 6 1 . 944 1 . 938 1 . 0 0 5 0 . 9 99 1 6 . 1081 . 2 . 0 4 9 . 1 2 5 . 0 7 5 . 0 1 2 . 7 1 3 1 . 6 1 9 1. 964 1 . 8 5 6 2 . 251 2 . 303 0 . 9 4 9 0 .961 17. 1081 . 2 . 3 0 5 . 120 . 0 7 3 .011 . 7 2 3 1 . 7 7 5 2 . 107 2 . 0 2 6 2 . 531 2 . 486 1 . 0 0 6 0 . 924 18 . 1081 . 2 . 4 7 2 . 1 2 6 . 0 6 7 .01 1 . 7 1 9 1 .981 2 . 291 2 . 2 6 6 2 . 806 2 . 626 1 . 0 1 5 0 . 9 35 19 . 1081 . 2 . 9 9 9 . 122 . 0 6 6 .011 . 7 2 7 2 .201 2 . 444 2 . 422 3 . 324 3 . 127 1 .04 1 0 . 9 4 5 2 0 . 1081 . 3 . 4 0 6 . 1 1 7 . 0 6 4 . 0 1 2 . 7 2 5 2 . 4 5 5 2 . 901 2 . 674 4 . 081 3 . 554 1 . 0 36 0 . 964 21 . 1 0 8 1 . 3 .341 . 1 2 6 . 0 7 5 . 0 1 5 . 6 8 4 2 . 6 5 0 3 . 187 3 . 1 3 2 4 . 804 3 . 308 1 . 0 3 3 0 .981 2 2 . 1 0 8 2 . 0 . 5 6 8 . 0 7 9 . 0 3 6 . 0 2 2 . 7 5 9 6 .731 0 . 496 0 . 6 3 5 0 . 801 0 . 7 35 0 .741 1 . 1 2 0 1 . 1 0 8 2 . 0 . 6 0 3 . 0 8 0 . 0 3 6 . 0 2 2 . 7 6 0 0 . 7 4 9 0 . 532 0 . 6 6 3 0 . 834 0 . 708 0 . 818 1 . 106 2 . 1 0 8 2 . 1 . 0 4 6 . 0 4 8 , 0 2 2 . 0 1 3 . 8 5 2 0 . 7 6 9 0 . 549 0 . 7 3 3 0 . 841 1 . 368 0 . 8 3 0 1 . 092 3 . 1 0 8 2 . 1 . 0 3 2 . 0 5 0 . 0 2 4 . 0 1 3 . 8 44 0 . 8 1 2 0 . 565 0 . 7 34 0 . 850 1 . 3 46 0 .821 1 . 079 4 . 1 0 8 2 . 0 . 6 3 6 .081 . 0 4 3 . 0 2 3 . 7 3 5 0 . 8 5 5 0 . 573 0 . 7 3 8 0 . 846 0 . 690 0 .861 1 . 064 5. 1 0 8 2 . 0 . 6 3 0 . 0 8 5 . 0 3 9 . 0 2 3 . 7 2 5 0 .891 0 . 642 0 . 7 4 0 0 . 854 0 . 653 0 . 8 8 7 1 .041 6. 1 0 8 2 . 0 . 6 0 8 . 0 9 5 . 0 4 4 . 0 24 . 7 0 3 0 . 8 8 3 0 . 6 85 0 . 7 5 7 0 . 863 0 . 597 0 . 9 0 0 1 . 017 7 . 1 0 8 2 . 0 . 6 5 9 .101 .041 . 0 2 4 . 7 1 3 0 . 8 8 3 0 . 7 76 0 . 8 08 0 . 869 0 . 616 0 . 9 44 0 . 994 8 . 1 0 8 2 . 0 . 7 9 4 . 0 8 5 . 0 3 6 . 0 1 7 . 7 64 0 . 9 1 8 0 . 8 66 0 . 8 5 7 0 . 8 93 0 . 761 0 . 9 9 3 0 . 994 9 . 1 0 8 2 . 0 . 8 7 8 . 0 8 3 . 0 3 4 . 0 1 6 . 7 7 5 0 . 9 6 6 0 . 9 25 0 . 9 3 3 0 . 907 0 . 8 7 2 0 . 9 84 0 . 994 10 . 1 0 8 2 . 1 . 000 . 0 7 5 . 0 3 5 . 0 1 6 .791 1 . 0 0 0 1 . 000 1 . 0 0 0 1 . 000 1. 000 1 . 0 0 0 1 . 000 1 1 . 1 0 8 2 . 1 . 2 7 8 .061 . 0 2 7 . 0 1 3 . 8 3 2 1 .031 1 . 085 1 . 0 08 1. 087 1. 298 1 . 0 5 7 1 . 0 0 5 12 . 1 0 8 2 . 1 .414 . 0 5 7 . 0 2 8 . 0 1 3 . 8 4 0 1 . 0 8 3 1 . 188 1 . 1 3 3 1 . 207 1. 420 1 . 0 9 7 0 . 983 1 3 . 1 0 8 2 . 2 . 9 2 5 . 0 3 3 . 0 1 5 . 0 0 9 . 9 1 0 1 . 2 4 3 1 . 347 1 . 3 1 0 1 . 644 3 . 3 2 2 1 . 0 3 0 0 . 960 14. 1 0 8 2 . 2 . 9 8 4 . 0 3 7 . 0 1 7 . 0 1 2 . 8 9 8 1 . 3 9 2 1 . 544 1 . 4 9 9 2 . 079 3 . 321 0 .961 0 . 9 1 8 15 . 1 0 8 2 . 2 . 1 6 0 . 0 5 6 . 0 2 6 . 0 2 0 . 8 3 9 1 . 4 88 1 . 775 1 . 5 9 5 2 . 520 2 . 220 1 .031 0 . 8 7 5 16 . 1 0 8 2 . 2 . 148 . 0 6 5 . 0 2 9 . 0 2 5 . 8 1 7 1 . 6 1 9 2 . 005 1 . 7 7 3 3 . 017 1 . 976 1 . 1 46 0 . 878 17 . 1 0 8 2 . 2 . 071 .071 .031 . 0 3 2 . 7 9 5 1 . 7 7 5 2 . 040 1 . 8 8 0 3 . 472 1 . 81 1 1 . 1 9 7 0 . 880 18 . 1 0 8 2 . 2 . 421 . 0 6 2 . 0 2 8 . 0 3 0 . 8 1 2 1 .981 2 . 258 1 . 9 0 7 3 . 936 2 . 208 1 . 163 0 . 867 19 . 1 0 8 2 . 4 . 0 4 8 . 0 3 7 . 0 1 9 . 0 1 8 . 8 8 2 2 .201 2 . 421 2 . 2 9 0 4 . 837 4 . 620 0 . 9 84 0 . 854 2 0 . •I 201 Tabic A2.I. Dala Used in Estimation of Final Model,' (cont'd) Canadian Food Manufacturing Industries, 1961-1982 S.I.C. C Sip Ship Sin WA- W/p w P w„, I Q h t 1082. 4. 051 .040 .020 .024 .860 2 .455 2 .644 2 .408 6 .143 3. 971 1 .116 0 .899 21 . 1082. 2. 618 .065 .035 .043 .742 2 .650 3 .099 2 .700 7 .388 2. 333 1 .061 0 .944 22. 1083. 0. 463 .023 .018 .014 .872 0 .731 0 .576 0 . 549 0 .829 0. 864 0 .517 1 .332 1 . 1083. 0. 502 .023 .016 .013 .881 0 .749 0 .615 0 .552 0 .897 0. 866 0 .563 1 .330 2. 1083. 0. 578 .022 .015 .013 .891 0 .769 0 .627 0 .549 0 .903 0. 883 0 .643 1 .329 3. 1083. 0. 598 .021 .014 .011 .897 0 .812 0 .645 0 .588 0 .918 0. 898 0 .658 1 .327 4. 1083. 0. 687 .020 .012 .01 1 .907 0 .855 0 . 663 0 .583 0 .912 0. 960 0 .715 1 .325 5. 1083. 0. 718 .020 .014 .012 .905 0 .891 0 .678 0 .602 0 .910 1 . 019 0 .705 1 .291 6. 1083. 0. 744 .022 .016 .012 .901 0 .883 0 .744 0 .691 0 .918 0. 925 0 .799 1 .258 7. 1083. 0. 687 .025 .015 .013 .895 0 .883 0 .771 0 .703 0 .920 0. 883 0 .768 1 .224 8. 1083. 0. 731 .025 .016 .013 .896 0 .918 0 .826 0 .800 0 .931 0. 870 0 .830 1 . 127 9. 1083. 0. 864 .025 .014 .012 .906 0 .966 0 .886 0 .890 0 .934 0. 936 0 .922 1 .030 10. 1083. 1. 000 .027 .014 .012 .907 1 .000 1 .000 1 .000 1 .000 1 . 000 1 .000 1 .000 1 1 . 1083. 1. 182 .028 .015 .011 .907 1 .031 1 . 1 50 1 .028 1 .057 1 . 055 1 . 1 2 0 0 . 970 12. 1083. 1. 644 .020 .010 .009 .931 1 .083 1 .181 1 .069 1 .141 1 . 708 0 .989 0 .986 13. 1083. 2. 214 .017 .008 .008 .944 1 .243 1 .400 1 . 1 97 1 .373 2. 107 1 .095 1 .002 14. 1083. 2. 059 .019 .011 .011 .927 1 .392 1 .739 1 . 267 1 .679 1 . 967 1 .071 1 .066 15. 1083. 2. 262 .025 .013 .015 .906 1 .488 1 .968 1 .492 2 .160 1 . 785 1 .267 1 .131 16. 1083. 3. 287 .023 .012 .013 .919 1 .619 2 .112 1 .504 2 .556 2. 060 1 .616 1 .046 17. 1083. 3. 809 .023 .011 .014 .916 1 .775 2 .246 1 .51 1 2 .917 2. 279 1 .686 0 .961 18. 1083. 4. 664 .021 .014 .013 .915 1 .981 2 .567 1 .718 3 .221 2. 475 1 .899 0 .884 19. 1083. 5. 375 .023 .017 .014 .907 2 .201 2 .955 2 .114 3 .853 2. 362 2 .269 0 .808 20. 1083. 6. 084 .025 .016 .016 .903 2 .455 3 .430 2 . 323 4 .735 2. 427 2 .487 0 .820 21 . 1083. 5. 747 .029 .019 .021 .866 2 .650 3 .900 2 .563 5 .716 2. 347 2 .333 0 .831 22. 1089. 2. 985 .065 .059 .01 1 .815 0 .731 0 .506 0 .589 0 .842 0. 831 0 .625 0 .590 1 . 1089. 0. 536 .065 .058 .011 .815 0 .749 0 .530 0 .620 0 .873 0. 843 0 .655 0 .638 2. 1089. 0. 571 .063 .060 .011 .814 0 .769 0 .558 0 .645 0 .887 0. 857 0 .692 0 .685 3. 1089. 0. 632 .063 .058 .011 .816 0 .812 0 .589 0 .668 0 .909 0. 895 0 .733 0 .732 4. 1089. 0. 658 .064 .059 .011 .812 0 .855 0 .624 0 .690 0 .907 0. 906 0 .753 0 .780 5. 1089. 0. 693 .067 .059 .011 .806 0 .891 0 .663 0 .725 0 .906 0. 921 0 .778 0 .827 6. 1089. 0. 733 .073 .061 .011 .792 0 .883 0 .716 0 .752 0 .917 0. 907 0 .836 0 .743 7. 1089. 0. 779 .076 .064 .011 .783 0 .883 0 .773 0 .806 0 .926 0. 891 0 .893 0 . 922 8. 1089. 0. 829 .080 .065 .011 .780 0 .918 0 .860 0 .880 0 .934 0. 916 0 .916 0 .953 9. 1089. 0. 944 .078 .079 .011 .772 0 .966 0 .927 0 .940 0 .941 0. 983 0 .964 0 .982 10. 1089. 1 . 000 .082 .080 .012 .765 1 .000 1 .000 1 .000 1 .000 1 . 000 1 .000 1 .000 1 1 . 1089. 1 . 078 .083 .082 .012 .760 1 .031 1 .099 1 . 052 1 .053 1 . 013 1 .058 1 .016 12. 1089. 1 . 243 .081 .076 .011 .772 1 .083 1 .239 1 . 123 1 . 138 1 . 1 40 1 . 102 1 .086 13. 1089. 1 . 739 .065 .063 .010 .814 1 .243 1 .392 1 .268 1 .372 1 . 707 1 .086 1 . 155 14. 1089. 1 . 876 .069 .068 .012 .796 1 .392 1 .578 1 .456 1 .681 1 . 760 1 . 103 1 . 140 15. 1089. 2. 062 .074 .070 .014 .782 1 .488 1 .852 1 .626 2 .086 1 . 722 1 .214 1 . 126 16. 1089. 2. 555 .068 .065 .014 .800 1 .619 1 .959 1 .753 2 .437 2. 150 1 .218 1 .035 17. 1089. 2. 840 .070 .065 .015 .797 1 .775 2 .097 1 .908 2 .779 2. 200 1 .316 0 .936 18. 1089. 3. 165 .070 .064 .016 .796 1 .981 2 .305 2 .048 3.096 2. 324 1 .399 0 .907 19. 1089. 3. 619 .068 .065 .016 .796 2 .201 2 .513 2 . 182 3 .696 2. 452 1 .498 0 .878 20. 1089. 3. 892 .071 .068 .018 .783 2 .455 2 .809 2 .530 4 .548 2. 503 1 .561 0 .862 21 . 1089. 3. 885 .072 .076 .022 .768 2 .650 3 .151 2 .899 5 .455 2. 526 1 .509 0 .845 22. 1091 . 0. 365 .098 .196 .027 .575 0 .731 0 .482 0 .528 0 .849 0. 772 0 .510 0 .848 1 . 1091 . 0. 387 .097 . 194 .027 .576 0 .749 0 .500 0 .538 0 .858 0. 776 0 .531 0 .813 2. 1091 . 0. 437 .092 .180 .024 .598 0 .769 0 .546 0 .561 0 .873 0. 873 0 .546 0 .778 3. 1091 . 0. 462 .092 .183 .024 .594 0 .812 0 .569 0 .597 0 .893 0. 931' 0 .536 0 .743 4. 1091 . 0. 491 .091 .186 .024 .581 0 .855 0 .610 0 .631 0 .898 0. 846 0 .593 0 .708 5. 1091 . 0. 568 .090 .181 .022 .592 0 .891 0 .653 0 .683 0 .902 0. 842 0 .680 0 .768 6. 1091 . 0. 640 .088 .179 .020 .599 0 .883 0 .703 0 .721 0 .911 0. 855 0 .756 0 .827 7. 1091 . 0. 700 .089 .170 .020 .613 0 .883 0 .763 0 .771 0 .937 0. 881 0 .793 0 .886 8. 1091 . 0. 794 .083 .162 .018 .636 0 .918 0 .838 0 .824 0 .945 0. 918 0 .862 0 .942 9. 1091 . 0. 885 .084 . 152 .016 .651 0 .966 0 .890 0 .926 0 .958 0. 943 0 .929 0 .998 10. 1091 . 1 . 000 .081 .144 .015 .668 1 .000 1 .000 1 .000 1 .000 1. 000 1 .000 1 .000 11 . 1091 . 1 . 068 .079 .140 .014 .676 1 .031 1 .082 1 .099 1 .045 1 . 053 1 .029 1 .002 12. 1091 . 1 . 216 .077 . 1 32 .014 .694 1 .083 1 .238 1 .209 1 .141 1 . 1 29 1 . 132 1 .089 13. 1091 . 1 . 491 .071 .121 .013 .721 1 .243 1 .412 1 .305 1 .373 1.. 472 1 .086 1 . 174 14. 202 Table A2.1. Data Used in Estimation of Final Model, (cont'd) Canadian Food Manufacturing Industries, 1961-1982 S.I.C. c , Sip Ship s. Sni W/p W/„, W W m < 3 h t 1091. 1 .765 .077 . 106 .011 .731 1 .392 1 . 629 1 .476 1 . 627 1 .775 1 .086 1 .160 15. 1091. 1 .901 .092 .118 .013 .699 1 .488 1 . 897 1 .771 1 . 905 1 .699 1 . 158 1 .145 16. 1091. 2.074 .085 .13 1 .013 .690 1 .619 2. 135 1 . 937 2. 160 1 . 796 1 . 185 1 .113 17. 1091 . 2.255 .084 . 129 .014 .687 1 .775 2. 287 2 .031 2. 373 1 .892 1 .209 1 .080 18. 1091 . 2.603 .080 .117 .014 .706 1 .981 2. 547 2 . 187 2. 645 2 . 126 1 .265 1 .100 19. 1091 . 2.861 .078 . 104 .014 .718 2 .201 2. 806 2 .425 3. 171 2 .616 1 .178 1 .119 20. 1091 . 3.241 .077 .099 .015 .723 2 .455 3. 1 1 7 2 .682 4. 157 2 .916 1 .207 1 .175 21 . 1091 . 3.396 .075 .101 .018 .714 2 .650 3. 514 2 .969 4. 991 2 .814 1 .282 1 .230 22. 1092. 0.418 .112 .088 .019 .631 0 .731 0. 521 0 .599 0. 778 0 .893 0 .448 0 .873 1 . 1092. 0.434 .106 .090 .018 .636 0 .749 0. 563 0 .610 0. 813 0 .902 0 .469 0 .879 2. 1092. 0.463 .099 .088 .018 .649 0 .769 0. 581 0 .632 0. 821 0 .91 1 0 .515 0 .885 3. 1092. 0.500 .098 .087 .018 .659 0 .812 0. 606 0 .664 0. 835 0 .944 0 .548 0 .891 4. 1092. 0.556 . 100 .089 .020 .652 0 .855 0. 640 0 .714 0. 835 0 .945 0 .597 0 .897 5. 1092. 0.645 .097 .086 .021 .662 0 .891 0. 672 0 .739 0. 841 0 .955 0 .704 0 .973 6. 1092. 0.71 1 .096 .086 .021 .659 0 .883 0. 697 0 .760 0. 857 0 .970 0 .760 1 .049 7. 1092. 0.758 .096 .091 .020 .654 0 .883 0. 767 0 .788 0. 870 0 .988 0 .799 1 . 126 8. 1092. 0.847 .098 .090 .019 .655 0 .918 0. 834 0 .843 0. 883 0 .994 0 .892 1 .098 9. 1092. 0.926 .097 .091 .019 .636 0 .966 0. 937 0 .934 0. 904 1 .003 0 .927 1 .071 10. 1092. 1 .000 .093 .088 .021 .615 1 .000 1 . 000 1 .000 1 . 000 1 .000 1 .000 1 .000 1 1 . 1092. 1 . 139 .091 .085 .019 .626 1 .031 1 . 076 1 .058 1 . 082 1 .009 1 .143 0 .929 12. 1092. 1 .345 .086 .083 .018 .654 1 .083 1 . 172 1 .170 1 . 174 1 .091 1 .299 0 .932 13. 1092. 1 .463 .091 .086 .022 .644 1 .243 1 . 320 1 .332 1 . 509 1 .270 1 .199 0 .934 1 4 . 1092. 1 .759 .080 .082 .021 .667 1 .392 1 . 502 1 .509 1 . 908 1 .422 1 .327 0 .880 15. 1092. 1 .694 .085 .090 .024 .625 1 .488 1 . 696 1 .668 2. 381 1 .373 1 .238 0 .825 16. 1092. 1 .872 .079 .087 .027 .640 1 .619 1 . 827 1 .868 2. 861 1 .461 1 .316 0 .842 17. 1092. 1 .925 .077 .089 .025 .635 1 .775 1 . 971 1 .972 3. 262 1 .598 1 .224 0 .858 18. 1092. 2.254 .079 .083 .031 .646 1 .981 2. 198 2 .082 3. 673 1 .770 1 .321 0 .810 19. 1092. 2.514 .081 .087 .034 .635 2 .201 2. 528 2 .458 4. 469 1 .957 1 .311 0 .762 20. 1092. 2.795 .079 .086 .038 .635 2 .455 2. 778 2 .617 5. 365 2 .251 1 .269 0 .775 21 . 1092. 2.821 .086 .099 .039 .596 2 .650 3. 250 3 . 139 6. 449 2 .405 1 .125 0 .788 22. 1093. 0.563 .131 .114 .016 .549 0 .731 0. 533 0 .563 0. 855 0 .892 0 .637 1 .115 1 . 1093. 0.593 .120 .111 .015 .561 0 .749 0. 546 0 .591 0. 878 0 .906 0 .670 1 .104 2. 1093. 0.618 .117 .115 .015 .560 0 .769 0. 561 0 .620 0. 885 0 .900 0 .699 1 .093 3. 1093. 0.648 .113 .117 .015 .562 0 .812 0. 579 0 .627 0. 901 0 .919 0 .720 1 .082 4. 1093. 0.686 .114 . 120 .015 .559 0 .855 0. 605 0 .654 0. 897 0 .931 0 .737 1 .071 5. 1093. 0.732 .114 . 122 .014 .561 0 .891 0. 658 0 .716 0. 902 0 .942 0 .791 1 .045 6. 1093. 0.762 .114 .123 .014 .564 0 .883 0. 687 0 .769 0. 913 0 .955 0 .811 1 .018 7. 1093. 0.829 .115 .121 .014 .578 0 .883 0. 753 0 .797 0. 923 0 .969 0 .856 0 .992 8. 1093. 0.873 .123 .116 .013 .575 0 .918 0. 848 0 .852 0. 923 0 .973 0 .895 0 .982 9. 1093. 0.928 .129 .117 .014 .566 0 .966 0. 888 0 .963 0. 933 0 .971 0 .953 0 .972 10. 1093. 1 .000 . 135 .120 .015 .550 1 .000 1 . 000 1 .000 1 . 000 1 .000 1 .000 1 .000 1 1 . 1093. 1 .082 .136 .121 .015 .545 1 .031 1 . 071 1 .071 1 . 055 1 .017 1 .066 1 .028 12. 1093. 1 .233 .142 .114 .015 .558 1 .083 1 . 129 1 .124 1 . 148 1 .099 1 . 146 1 .065 13. 1093. 1.513 . 143 .111 .016 .576 1 .243 1 . 327 1 .248 1 . 409 1 .359 1 .170 1 .102 14. 1093. 1 .784 .151 .108 .018 .564 1 .392 1 . 503 1 .462 1 . 722 1 .522 1 .213 1 .111 15. 1093. 1 .94 1 .155 .113 .021 .548 1 .488 1 . 697 1 .683 2. 099 1 . 585 1 .231 1 .120 16. 1093. 2.095 .160 .117 .022 .540 1 .619 1 . 854 1 .783 2. 449 1 .628 1 .245 1 .110 17. 1093. 2.280 .155 .114 .022 .543 1 .775 r. 981 1 .908 2. 773 1 .689 1 .301 1 .101 18. 1093. 2.599 .157 .114 .021 .548 1 .981 2. 222 2 .130 3. 098 1 .846 1 .355 1 .102 19. 1093. 3.095 .150 .110 .022 .566 2 .201 2. 497 2 .431 3. 747 2 .077 1 .399 1 .102 20. 1093. 3.679 .145 .098 .023 .589 2 .455 2. 759 2 .663 4. 653 2 .446 1 .472 1 .084 21 . 1093. 4.065 .144 .103 .024 .583 2.650 2. 947 2.984 5. 515 2 .647 1 .485 1 .065 22. 1094. 0.327 .079 .096 .011 .697 0 .731 0. 540 0 .665 0. 834 0 .796 0 .351 1 .391 1 . 1094. 0.360 .078 .095 .010 .700 0 .749 0. 559 0 .666 0. 856 0 .809 0 .390 1 .344 2. 1094. 0.388 .078 .091 .009 .707 0 .769 0. 580 0 ,665 0. 868 0 .814 0 .416 1 .297 3. 1094. 0.401 .080 .093 .010 .694 0 .812 0. 590 0 .679 0. 893 0 .844 0 .420 1 .250 4. 1094. 0.441 .083 .092 .010 .693 0 .855 0. 646 0 .704 0. 908 0 .828 0 .476 1 .204 5. 1094. 0.486 .082 .092 .01 1 .689 0 .891 0. 686 0 .780 0. 913 0 .830 0 .520 1 .149 6. 1094. 0.545 .081 .092 .01.1 .683 0 1883 0. 733 0 .801 0. 923 0 .845 0 .565 1 .094 7. 1094. 0.575 .082 .101 .011 .672 0 .883 0. 758 0 .854 0. 936 0 .882 0 .572 1 .040 8. 203 Table A2.1. Dala Used in Estimation of Final Model, (cont'd) Canadian Food Manufacturing Industries, 1961-1982 S.I.C. C Si,, Ship Sc S/H W* W/, W e w, 71 Q h t 1094. 0 .679 .001 .094 .010 .696 0.918 0 .835 0 .899 0. 943 0 . 920 0.669 1 .037 9. 1094. 0 .787 .081 .085 .009 .715 0 .966 0 .922 0.932 0. 949 0. 956 0.792 1 .033 10. 1094. 1 .000 .079 .073 .008 .745 1 .000 1 .000 1 .000 1 . 000 1 . 000 1 .000 1 .000 1 1 . 1094. 1 . 129 .084 .076 .008 .737 1 .031 1 .053 1 .007 1 . 051 1 . 053 1 .060 0 .966 12. 1094. 1 .279 .084 .087 .009 .704 1 .083 1 .224 1 .073 1 . 126 1 . 122 1 .079 1 .071 13. 1094. 1 .508 .084 .082 .009 .702 1 .243 1 .431 1.136 1 . 336 1 . 213 1.171 1 . 175 14. 1 094 . 1 .561 .080 .082 .010 .689 1 .392 1 .606 1 .205 1 . 593 1 . 297 1 .114 1 .237 15. 1094. 1 .691 .086 .080 .011 . 675 1 .488 1 .770 1 .483 1 . 967 1 . 545 0.993 1 .299 16. 1094. 1 .653 .093 .088 .012 .640 1.619 2 .038 1 .654 2. 290 1 . 459 0.975 1 .291 17. 1094. 2 .249 .086 .072 .011 .694 1 .775 2 . 158 1 .848 2. 581 1 . 656 1 .266 1 . 283 18. 1094. 2 .595 .089 .080 .010 .689 1 .981 2 .318 2.142 2 . 845 1 . 844 1 .299 1 .217 19. 1094. 2 .969 .081 .073 .012 .704 2.201 2 .596 2.143 3. 362 1 . 909 1 .471 1 .151 20. 1094. 3 .430 .088 .074 .012 .697 2 .455 3 .034 2 .449 4 . 130 2. 176 1 .476 1 . 150 21 . 1094. 3 .648 .094 .070 .015 .685 2 .650 3 .489 2.827 5. 078 2 . 304 1 .455 1 . 148 22. APPENDIX 3: RESIDUAL PLOT FOR THE COST FUNCTION AND RESIDUAL STATISTICS FOR THE COST/SHARE SYSTEM This Appendix provides the residual (42') and (43). Table A3.1 gives observations. Table A3.2 gives the equations in the system. diagnostics for the final cost/share system a plot of the residuals for all 374 residual summary statistics for all 5 204 205 Table A3.1. Estimated Residuals from Total Cost Function Equation, Final Model] Canadian Food Manufacturing Industries, 1961-1982 Observed Predicted Observation Value Value • Calculated Plot of Calculated Number 2 (/»C) (/i/C) Residual Residuals around zero 3 1 - 0 . 6 3 0 9 8 - 0 68066 0 4 9 6 7 7 E - 0 1 i a - 0 . 5 9 1 6 2 - 0 64 105 0 4 9 4 3 3 E - 0 1 i * 3 - 0 . 5 7 1 2 5 - 0 60604 0 3 4 7 9 3 E - 0 1 i ' 4 - 0 . 5 2 1 1 5 - 0 54267 0 2 1 S 2 8 E - 0 1 i .» 5 - 0 . 4 0 8 9 2 - 0 43O04 0 2 1 1 2 6 E - 0 1 i * e - 0 . 2 8 7 0 8 - 0 3 1069 0 2 3 6 0 9 E - 0 1 i + 7 - 0 . 2 2 2 3 8 - 0 22505 0 2 6 6 5 5 E - 0 2 8 - 0 . 1 9 7 4 8 - 0 19874 0 12625E-02 9 - 0 . 1 0 8 1 2 - 0 1 1523 0 7 1 1 0 1 E - 0 2 i • 10 - 0 . 3 5 2 0 2 E -01 - 0 41915E -01 0 6 7 1 3 0 E - 0 2 i» 11 0 . 0 0 20O09E - 0 2 - 0 2 0 0 0 9 E - 0 2 12 0 . 19147 0 19895 - 0 7 4 7 5 7 E - 0 2 * i 13 0 . 4 3 6 0 3 0 42899 0 7 0 3 2 4 E - 0 2 i * 14 0 . 5 1 5 0 8 0 50543 0 9 6 5 6 1 E - 0 2 i * 15 0 . 5 8 9 5 2 0 57828 0 1 1236E-01 i * 16 0 . 6 3 3 4 2 0 64356 - 0 10137E-01 • i 17 0 . 6 9 8 2 3 0 69229 0 5 9 4 8 7 E - 0 2 i • 18 0 . 9 4 6 3 4 0 89858 0 4 7 7 G 2 E - 0 1 i « 19 1.0984 .0597 0 3 0 6 6 8 E - 0 1 i * 20 1 . 1500 . 1 168 0 3 3 1 9 0 E - 0 1 i » 2 1 1 . 2 5 6 2 . 2049 0 5 1 2 9 8 E - 0 1 i * 22 1.3084 .228 1 0 8 0 2 7 8 E - 0 1 i * 23 - 0 . 8 0 0 3 5 - 0 70984 - 0 9 0 5 1 0 E - 0 1 * i 24 - 0 . 6 B 8 0 6 - 0 62392 - 0 6 4 1 3 7 E - 0 1 * i 2 5 - 0 . 6 3 1 7 3 - 0 58253 - 0 4 9 2 0 6 E - 0 I » 2 26 - 0 . 5 2 9 0 6 - 0 54145 0 I 2 3 8 9 E - 0 1 I » 27 - 0 . 4 5 5 4 4 - 0 46947 0 14028E-01 I • 28 - 0 . 2 5 3 2 4 - 0 30046 0 4 7 2 2 0 E - 0 1 I * 29 - O . 2 3 7 4 5 - 0 27063 0 3 3 1 8 3 E - 0 1 I * 30 - O . 1 8 1 4 0 - 0 20457 0 2 3 I 6 6 E - 0 1 I • 31 - 0 . 6 0 7 9 1 E -01 - 0 76083E -01 0 15292E-01 I • 32 - 0 . 5 3 2 B 5 E -01 - 0 49773E -01 - 0 3 5 1 2 I E - 0 2 3 3 0 . 0 0 . 2O009E - 0 2 - 0 2 0 0 0 9 E - 0 2 34 0 . 1 8 0 3 4 0 . 19353 - 0 13190E-01 * I 35 0 . 5 0 6 1 0 0 . 48710 0 18997E-01 I * 36 0 . 5 7 7 4 8 0 . 52794 0 4 9 5 4 2 E - 0 1 I -37 0 . 5 9 8 9 0 0 . 57054 0 2 8 3 5 7 E - 0 1 I * 38 0 . 7 2 9 9 2 0 7224 1 0 7 5 0 5 2 E - 0 2 I * 39 0 . 8 1 7 6 7 0 8 1 6 9 0 0 7 6 5 0 4 E - 0 3 40 0 . 9 5 2 2 1 0 95307 - 0 B 6 0 2 8 E - O 3 41 1 . 1309 1 . 1 182 0 12745E-OI I * 42 1 . 1 6 6 9 1 . 1299 0 3 6 9 7 1 E - 0 1 I » 4 3 1 .2951 1 . 2 5 2 2 0 4 2 9 1 5 E - 0 1 I * 44 1 .3680 1 . 3 4 1 5 0 2 6 4 7 2 E - 0 1 I • 45 - 0 . 7 8 8 8 9 - 0 . 71239 - 0 7 6 4 9 8 E - 0 1 * I 46 - 0 . 6 4 0 7 3 - 0 . 60082 - 0 3991OE-01 • I 47 - 0 . 6 5 1 4 1 - 0 61543 - 0 3 5 9 8 3 E - 0 1 * I 48 - 0 . 5 2 7 0 9 - 0 49 121 - 0 3 5 B 8 4 E - 0 1 t j 49 - 0 . 4 4 2 0 0 - 0 . 4 1228 - 0 2 9 7 2 4 E - 0 1 • I SO - 0 . 2 9 7 B O - 0 28733 - 0 10472E-01 • I 51 - 0 . 3 1 4 8 1 - 0 . 3252 1 0 10398E-01 I * 52 - 0 . 1 7 7 1 4 - 0 . 18285 0 5 7 0 5 1 E - 0 2 1 • 53 - 0 . 1 2 2 8 1 - 0 . 10828 - 0 14534E-01 * I 54 - 0 . 1 6 0 3 8 E -01 - 0 14121E -01 - 0 19165E-02 55 0 . 0 0 20009E - 0 2 - 0 2 0 0 0 9 E - 0 2 56 0 . 9 3 9 1 8 E -01 0 . 87690E -01 0 6 2 2 B 0 E - 0 2 j * 57 0 . 3 9 5 9 4 0 . 40726 - 0 11317E-01 » I 58 0 . 3 9 3 8 4 0 . 39784 - 0 3 9 9 1 6 E - 0 2 * 1 The final model is comprised of the system of equations (42') and (43). To conserve space, only the estimated residuals from (42') are given here. 2 The data here are ordered as for the data used in estimation (see Table A2.1). Thus, observation 1 is for S.I.C. 1011 0= 1, or 1961); observation 22 for S.I.C 1011 (7 = 22, or 1982); observation 23 is for S.I.C. 1012 (/ = 1, or 1961), etc. 3 The intercept is T ; this represents the point where e,,, = 0. An V indicates those points which exceed the scale of the plot-these may be viewed as 'problem' observations. 206 Table A3.1. Estimated Residuals from Total Cost Function Equation, Final Model, (cont'd) Canadian Food Manufacturing Industries, 1961-1982  Observed Predicted Observation Value Value Calculated Plot of Calculated Number 0»C) OnC) Residual Residuals around zero 5 9 0 . 4 2 8 8 1 0 4 2 0 9 9 0 7 8 2 3 3 E - 0 2 I * S O 0 . 7 0 6 0 5 0 7 1 1 4 9 - 0 S 4 4 5 5 E - 0 2 * I 6 1 0 . 9 0 8 4 8 0 9 1 6 6 6 - 0 8 1 B 4 2 E - 0 2 ••I 6 2 t . 1 6 1 5 1 . 1 7 0 3 - 0 8 7 2 2 3 E - 0 2 * I 6 3 1 . 3 2 9 5 . 3 2 6 3 0 3 2 1 8 0 E - 0 2 * 6 4 1 . 4 8 9 8 1 . 4 8 4 0 0 5 8 2 8 1 E - 0 2 I * 6 5 1 . 6 3 3 7 . 6 2 5 1 O 8 6 7 0 2 E - 0 2 I « 6 6 1 . 6 3 0 9 . 6 1 4 1 0 1 6 8 6 0 E - 0 1 I 6 7 - 0 . 6 3 0 2 3 - O 6 0 6 3 7 - 0 2 3 8 6 0 E - 0 1 » I 6 8 - 0 . 5 3 7 3 7 - 0 5 1 7 0 5 - 0 2 0 3 2 9 E - 0 1 • I 6 9 - 0 . 4 7 7 5 2 - 0 4 5 9 5 9 - 0 1 7 9 3 1 E - 0 1 * I 7 0 - 0 . 3 9 1 2 2 - 0 3 9 4 8 2 0 3 6 0 1 0 E - 0 2 * 7 1 - 0 . 3 1 3 6 2 - 0 3 3 0 8 5 0 1 7 2 3 0 E - 0 1 I 7 2 - 0 . 2 3 5 6 5 - 0 2 5 7 2 8 0 2 1 6 3 3 E - 0 1 I 7 3 - O . 1 9 5 9 2 - o 2 1 8 3 0 O 2 2 3 7 B E - O I I 7 4 - 0 . 1 6 2 0 0 - 0 1 7 5 1 2 0 1 3 I 2 3 E - 0 1 I 7 5 - O . 9 O 0 5 6 E - 0 I - o 9 7 0 0 9 E - 0 1 0 6 9 5 2 9 E - 0 2 I * 7 6 - 0 . 4 7 3 1 2 E - 0 1 - 0 4 7 8 9 3 E - 0 1 0 5 8 1 S 9 E - 0 3 * 7 7 0 . 0 o 2 0 0 O 9 E - 0 2 - O 2 0 0 O 9 E - 0 2 * 7 8 0 . 9 O 2 4 3 E - 0 1 0 9 6 9 4 2 E - 0 1 - 0 G 6 9 9 2 E - 0 2 •I 7 9 0 . 2 1 1 1 0 o 2 1 2 7 3 - O 1 6 2 4 0 E - 0 2 * 8 0 0 . 4 1 0 1 1 0 4 0 9 0 2 0 1 0 9 8 8 E - 0 2 * 8 1 0 . 5 2 B 1 7 0 5 1 8 2 3 0 9 9 3 3 2 E - 0 2 I -8 2 0 . 5 6 3 6 2 0 5 6 8 3 6 - 0 4 7 3 9 6 E - 0 2 •I 8 3 0 . 5 9 8 9 4 0 6 0 5 3 7 - 0 6 4 3 1 1 E - 0 2 * I 8 4 0 . 7 4 9 3 7 0 7 4 5 0 7 0 4 2 9 9 2 E - 0 2 I * 8 5 0 . 8 6 9 7 1 0 8 7 3 2 6 - 0 3 5 4 9 3 E - 0 2 * 8 6 0 . 9 6 4 2 9 0 9 6 6 2 9 - 0 1 9 9 3 2 E - 0 2 * 8 7 1 . 0 7 1 2 . 0 7 0 2 0 9 7 5 6 5 E - 0 3 • 8 8 1 . 1 3 4 3 . 1 2 6 5 0 7 7 7 1 1 E - 0 2 I * 8 9 - 0 . 5 3 5 8 9 - 0 5 1 9 1 7 - 0 1 6 7 1 6 E - 0 1 • I 9 0 - 0 . 5 0 6 8 2 - 0 4 9 3 5 8 - 0 1 3 2 3 7 E - 0 1 * I 9 1 - 0 . 4 5 8 9 8 - 0 4 5 0 4 6 - 0 B 5 1 4 4 E - 0 2 * I 9 2 - 0 . 4 0 0 5 7 - 0 3 9 2 9 0 - 0 7 6 7 0 3 E - 0 2 •I 9 3 - 0 . 3 4 1 9 0 - 0 3 4 1 7 7 - 0 1 3 2 1 9 E - 0 3 * 9 4 - 0 . 2 6 3 2 2 - 0 2 6 5 2 5 0 2 0 3 0 6 E - 0 2 * 9 5 - 0 . 1 8 8 1 1 - 0 1 9 4 0 8 0 5 9 6 8 3 E - 0 2 I * 9 6 - 0 . 1 6 2 2 2 - 0 1 6 4 1 0 0 1 8 7 9 1 E - 0 2 * 9 7 - 0 . 9 4 2 8 9 E - 0 1 - 0 9 3 6 7 6 E - 0 1 - 0 6 1 2 7 6 E - 0 3 * 9 8 - 0 . 7 6 2 3 3 E - 0 1 - 0 7 7 9 B 5 E - 0 1 0 1 7 5 1 2 E - 0 2 * 9 9 0 . 0 0 2 0 O 0 9 E - 0 2 - 0 2 0 0 0 9 E - 0 2 * i o o 0 . 6 6 6 9 6 E - 0 1 0 7 0 0 1 B E - 0 1 - 0 3 3 2 2 B E - 0 2 * 1 0 1 0 . 1 5 5 0 4 0 1 5 3 5 0 0 I 5 4 0 I E - 0 2 * 1 0 2 0 . 3 4 8 2 3 0 3 5 5 2 5 - 0 7 0 1 6 3 E - 0 2 * I 1 0 3 0 . 5 5 7 9 1 0 5 6 2 7 2 - 0 4 8 1 S 0 E - 0 2 * I 1 0 4 0 . 6 3 9 1 9 0 6 5 0 5 9 - 0 1 1 4 0 3 E - 0 1 * I 1 0 5 0 . 7 2 O 1 4 0 7 3 7 6 1 - o 1 7 4 6 3 E - 0 1 * I 1 0 6 0 . 7 9 0 7 5 0 B 0 4 9 7 - 0 1 4 2 2 2 E - 0 1 * I 1 0 7 0 . 9 0 5 9 2 0 9 3 1 0 5 - 0 2 5 1 3 1 E - O I • I 1 0 8 1 . 0 5 8 8 . 0 8 9 5 - 0 3 0 7 0 9 E - 0 1 • I 1 0 9 1 . 1 7 9 3 . 2 0 6 4 - 0 2 7 0 8 8 E - 0 1 + I 1 1 0 1 . 2 9 2 5 . 3 1 9 9 - 0 2 7 3 4 8 E - 0 1 * I 1 1 1 - 0 . 2 0 2 9 4 - 0 1 7 1 6 1 - 0 3 1 3 3 I E - 0 1 * J 1 1 2 - 0 . 1 1 0 4 5 - 0 B 9 5 2 1 E - 0 1 - 0 2 0 9 3 I E - 0 1 * I 1 1 3 - 0 . 1 1 7 8 4 - 0 1 0 5 9 7 - 0 1 1 8 6 4 E - 0 1 * I 1 1 4 0 . 1 0 6 5 9 0 1 4 5 3 1 - 0 3 8 7 1 5 l £ - 0 1 * I 1 1 5 - 0 . 8 7 6 6 2 E - 0 1 - 0 7 6 5 3 5 E - O I - 0 1 1 I 2 7 E - 0 I * I 1 1 6 - 0 . 2 2 3 5 8 E - 0 1 - 0 5 6 1 6 1 E - 0 2 - 0 1 6 7 4 2 E - 0 1 * I 1 1 7 - 0 . 2 7 3 3 7 E - 0 2 - o 1 6 7 6 1 E - 0 1 0 1 4 0 2 7 E - 0 1 I 1 1 8 - 0 . 8 0 1 1 5 E - 0 1 - 0 9 1 6 0 7 E - 0 1 0 1 1 4 9 2 E - 0 1 t * 207 Table A3.1. Estimated Residuals from Total Cost Function Equation, Final Model, (cont'd) Canadian Food Manufacturing Industries, 1961-1982  Observed Predicted Observation Value Value Calculated Plot of Calculated Number UllC) (/«C) Residual Residuals around zero 1 1 9 -0 S 8 2 8 6 E - 0 1 , - 0 . 5 5 0 0 5 E - 0 1 - 0 3 2 8 0 8 E - 0 2 1 2 0 - 0 1 4 3 3 2 E - 0 1 - O . G 4 7 7 8 E - 0 2 - 0 7 8 5 4 5 E - 0 2 • i 1 2 1 0 0 0 . 2 0 0 O 9 E - 0 2 - 0 2 0 O 0 9 E - O 2 * 1 2 2 0 2 8 6 0 7 E - 0 1 0 . 1 5 8 2 3 E - 0 1 0 1 2 7 8 4 E - 0 1 i * 1 2 3 0 1 4 5 6 5 0 . 1 2 9 0 1 0 1 6 6 4 2 E - 0 1 i * 1 2 4 0 4 2 6 3 7 0 . 4 1 3 8 4 0 1 2 5 3 4 E - 0 1 i * 1 2 5 0 5 5 0 2 9 0 . 5 3 7 6 1 0 1 2 6 8 3 E - 0 1 i * 1 2 6 o 6 0 4 6 1 0 . 5 9 4 3 9 0 1 0 2 2 2 E - 0 1 i * 1 2 7 0 6 4 9 5 8 0 . 6 3 8 3 2 0 1 1 2 5 9 E - 0 1 i * 1 2 8 0 7 2 4 3 5 0 . 7 1 6 5 2 0 7 8 2 9 0 E - 0 2 i * 1 2 9 0 9 3 6 1 2 0 . 9 2 8 8 0 0 7 3 2 4 4 E - 0 2 i * 1 3 0 . 0 7 4 0 1 . 0 6 9 2 0 4 7 8 2 6 E - 0 2 i * 1 3 1 . 2 1 9 4 1 . 2 0 7 1 0 1 2 3 3 9 E - 0 1 i * 1 3 2 . 1 6 4 1 1 . 1 4 1 3 0 2 2 8 4 3 E - 0 1 i * 1 3 3 - 0 7 0 4 3 1 - 0 . 6 9 3 0 3 - 0 1 1 2 7 5 E - 0 1 • i 1 3 4 - 0 6 1 4 6 7 - 0 . 6 1 1 4 3 - 0 3 2 3 4 1 E - 0 2 * 1 3 5 - 0 5 3 7 0 5 - 0 . 5 4 2 0 9 0 5 0 4 0 6 E - 0 2 i * 1 3 6 - 0 4 6 7 9 6 - 0 . 4 6 4 2 1 - 0 3 7 4 5 4 E - 0 2 * 1 3 7 - 0 3 8 1 1 6 - 0 . 3 8 4 1 9 0 3 0 3 5 8 E - 0 2 1 3 8 - 0 2 2 3 5 3 - 0 . 2 2 5 6 0 0 2 0 G 4 5 E . - 0 2 * 1 3 9 - o 1 3 2 3 3 - 0 . 1 3 7 0 9 0 4 7 5 8 3 E - 0 2 i * 1 4 0 - 0 1 2 5 0 2 - 0 . 1 3 4 1 0 0 9 0 7 6 I E - 0 2 i • 1 4 1 - 0 8 0 9 S 0 E - 0 1 - 0 . 8 0 9 6 4 E - 0 1 0 1 4 3 0 I E - 0 4 1 4 2 - 0 3 1 1 0 9 E - 0 1 - 0 . 3 6 9 5 5 E - 0 1 0 5 8 4 6 6 E - 0 2 i » 1 4 3 0 0 0 . 2 0 0 0 9 E - 0 2 - o 2 0 0 0 9 E - 0 2 1 4 4 0 8 6 2 4 2 E - 0 1 0 . 9 3 4 8 7 E - 0 1 - o 7 2 4 5 2 E - 0 2 * i 1 4 5 0 4 3 1 9 5 0 . 4 2 6 8 7 0 5 0 8 0 8 E - 0 2 i * 1 4 6 o 6 4 3 9 8 0 . 6 4 2 4 2 0 1 5 6 0 2 E - 0 2 1 4 7 0 6 7 7 5 0 0 . 6 7 1 5 3 0 5 9 6 5 2 E - 0 2 i * 1 4 8 0 7 1 5 0 2 0 . 6 9 8 1 1 0 1 6 9 1 5 E - 0 1 i • 1 4 9 o 7 7 7 0 1 0 . 7 6 3 7 7 o 1 3 2 4 7 E - O I i • 1 5 0 o 8 6 1 3 4 O . 6 4 8 5 9 o I 2 7 5 4 E - 0 1 i * 1 5 1 . 0 5 7 4 1 . 0 5 6 2 0 I 2 0 5 0 E - 0 2 1 5 2 . 2 3 6 2 1 . 2 4 6 5 - o 1 0 3 5 5 E - 0 I * i 1 5 3 . 3 6 1 2 1 . 3 6 B 3 - 0 7 0 7 2 4 E - 0 2 * i 1 5 4 1 . 3 1 3 4 1 . 3 2 1 7 - 0 8 3 4 8 5 E - 0 2 * i 1 5 5 - 0 5 2 1 7 0 - 0 . 5 8 5 6 4 0 6 3 9 4 3 E - 0 1 i * 1 5 6 - 0 4 6 8 6 1 - 0 . 5 1 2 7 3 0 4 4 1 1 4 E - 0 1 i + 1 5 7 - 0 3 9 7 6 8 - 0 . 4 4 0 4 5 0 4 2 7 7 6 E - 0 1 i * 1 5 8 - 0 4 0 8 2 5 - 0 . 4 5 9 9 6 0 5 I 7 0 8 E - 0 1 j * 1 5 9 - 0 3 7 2 4 6 - 0 . 4 1 6 7 2 0 4 4 2 6 5 E - 0 1 i • 1 6 0 - 0 3 2 2 5 5 - O . 3 7 1 5 5 0 4 0 9 9 B E - 0 1 i * 1 6 1 - o 2 1 4 8 8 - 0 . 2 G 5 5 4 0 5 O G 6 3 E - 0 I i * 1 6 2 - 0 1 7 2 3 8 - 0 . 2 0 8 5 3 ' 0 3 6 1 5 3 E - 0 1 i * 1 6 3 - 0 1 0 2 6 1 - 0 . 1 1 9 1 6 0 1 6 5 5 1 E - 0 1 i • 1 6 4 - 0 5 4 8 8 9 E - 0 1 - 0 . 7 3 1 7 4 E - 0 1 0 1 8 2 8 4 E - 0 I i * 1 6 5 0 0 0 . 2 0 0 0 9 E - 0 2 - 0 2 0 0 0 9 E - 0 2 1 6 6 0 1 6 2 7 3 0 . 2 0 1 9 2 - o 3 9 1 9 2 E - 0 1 * i 1 6 7 0 2 8 6 5 0 0 . 3 2 0 6 8 - 0 3 4 1 7 8 E - 0 1 • i 1 6 8 0 7 2 4 7 2 0 . 7 1 7 9 9 0 6 7 3 3 9 E - 0 2 i * 1 6 9 0 9 3 6 9 2 0 . 9 1 0 8 5 0 2 6 0 7 0 E - 0 1 i • 1 7 0 0 9 3 2 8 2 0 . 9 7 3 1 0 - 0 4 0 2 7 5 E - 0 1 * i 1 7 1 0 9 4 3 6 1 0 . 9 4 0 3 8 0 3 2 3 5 0 E - 0 2 1 7 2 . 0 2 6 8 1 . 0 1 5 3 0 1 1 4 9 8 E - 0 1 i * 1 7 3 . 0 9 3 0 1 . 0 5 9 2 0 3 3 7 2 0 E - 0 1 i • 1 7 4 . 2 1 7 4 1 . 2 0 8 4 0 9 0 5 6 7 E - 0 2 i * 1 7 5 . 3 3 4 0 1 . 3 1 5 0 0 1 9 0 0 5 E - 0 1 i * 1 7 6 . 3 5 3 1 1 . 3 3 2 5 0 2 0 6 2 0 E - 0 1 i * 1 7 7 - 0 4 1 4 6 7 - 0 . 4 3 5 4 2 0 2 0 7 5 2 E - 0 1 i * ' 1 7 8 - 0 3 5 9 7 5 - 0 . 3 7 0 8 7 0 1 1 1 1 7 E - 0 1 '* 208 Table A3.1. Estimated Residuals from Total Cost Function Equation, Final Model, (cont'd) Canadian Food Manufacturing Industries, 1961-1982  Observed Predicted Observation Value Value Calculated Plot of Calculated Number {in C) (hiC) Residual Residuals around zero 1 7 9 - O . 3 1 0 6 4 - 0 3 3 3 8 1 O 2 3 1 7 5 E - 0 1 I • 1 8 0 - 0 . 2 3 5 1 0 - 0 2 6 2 2 1 0 2 7 1 1 1 E - 0 1 I * 1 8 1 - 0 . 1 8 3 4 4 - 0 2 1 8 2 0 0 3 4 7 5 4 E - 0 1 I 1 8 2 - 0 . 1 3 4 9 4 - 0 1 8 5 4 7 0 5 0 5 3 I E - 0 1 I * 1 8 3 - 0 . 8 9 1 9 2 E - 0 1 - 0 1 2 7 2 8 0 3 8 0 8 4 E - 0 1 I * 1 8 4 - 0 . 7 4 1 2 0 E - 0 1 - 0 9 1 9 5 9 E - 0 1 0 1 7 8 3 8 E - 0 1 I * 1 8 5 - 0 . 5 2 3 7 8 E - 0 1 - 0 7 8 2 8 5 E - 0 1 0 2 5 9 0 7 E - 0 1 I 1 8 6 - 0 . 9 3 8 3 9 E - 0 2 - 0 1 6 1 1 7 E - 0 1 0 6 7 3 3 5 E - 0 2 I 1 1 8 7 0 . 0 0 2 0 0 0 9 E . - 0 2 - 0 2 0 0 0 9 E - 0 2 1 8 8 0 . 5 7 5 7 1 E - 0 1 0 7 0 5 2 2 E - 0 1 -o 1 2 9 5 2 E - 0 1 * I 1 8 9 0 . 1 1 6 9 2 0 1 3 2 4 3 - 0 1 5 5 1 0 E - 0 1 * j 1 9 0 0 . 2 9 1 2 7 0 3 1 0 8 2 - 0 1 9 5 5 8 E - 0 1 * I 1 9 1 0 . 4 1 8 5 1 0 4 2 6 5 5 - 0 8 0 3 4 I E - 0 2 * 1 1 9 2 0 . 4 8 9 1 4 0 5 1 9 7 4 - 0 3 0 6 0 1 E - 0 1 « j 1 9 3 0 . 5 4 1 6 9 0 5 7 8 6 4 -o 3 6 9 5 3 E - 0 1 * 1 1 9 4 0 . 6 1 6 1 4 0 6 4 4 0 7 - 0 2 7 9 3 0 E - 0 1 * I 1 9 5 0 . 7 3 3 8 1 0 7 5 1 3 1 - 0 1 7 4 9 7 E - 0 1 * | 1 9 6 0 . 8 2 9 3 3 0 8 4 6 8 5 -o 1 7 5 1 3 E - 0 1 * I 1 9 7 0 . 9 4 5 9 0 0 9 5 7 4 6 - 0 1 1 5 6 0 E - 0 1 * j 1 9 8 0 . 9 6 9 5 7 0 9 8 9 2 6 - 0 1 9 6 9 2 E - 0 1 * I 1 9 9 - 0 . 5 7 4 4 9 - 0 5 3 0 5 6 - 0 4 3 9 3 0 E - 0 1 * I 2 0 0 - 0 . 5 1 0 6 3 - 0 4 8 9 7 0 - 0 2 0 9 2 2 E - 0 1 » I 2 0 1 - 0 . 4 0 8 2 5 - 0 4 0 0 8 6 - 0 7 3 9 3 2 E - 0 2 * I 2 0 2 - 0 . 3 4 9 8 4 - 0 3 5 0 4 5 0 6 0 9 3 1 E - 0 3 2 0 3 - 0 . 2 9 0 S 4 - O 2 9 9 3 9 0 8 8 4 8 9 E - 0 2 I * 2 0 4 - 0 . 2 3 4 8 7 - 0 2 4 0 9 3 0 6 0 5 3 3 E - 0 2 I * 2 0 5 - 0 . 1 8 0 2 2 - 0 1 8 6 6 6 0 6 4 4 0 4 E - 0 2 I • 2 0 6 - 0 . 1 1 4 1 5 - 0 1 1 2 8 6 -o 1 2 9 3 5 E - 0 2 2 0 7 - 0 . G 1 0 0 3 E - 0 1 - 0 5 4 7 4 1 E - 0 1 - 0 6 2 6 2 I E - 0 2 « i 2 0 8 - 0 . 2 4 9 3 8 E - 0 1 - 0 1 4 8 0 9 E - 0 1 -o 1 0 1 3 0 E - 0 1 * I 2 0 9 0 . 0 0 2 0 0 0 9 E - 0 2 - 0 2 0 0 0 9 E - 0 2 2 1 0 0 . 5 8 5 2 4 E - 0 1 0 5 4 1 6 9 E - 0 1 0 4 3 5 4 6 E - 0 2 I * 2 1 1 0 . 1 6 9 3 0 0 1 5 9 8 9 0 9 4 1 8 1 E - 0 2 I * 2 1 2 0 . 4 6 7 2 6 0 4 7 5 1 4 -o 7 8 7 3 9 E - 0 2 ' I 2 1 3 0 . 5 9 4 2 0 0 5 9 3 8 9 0 3 1 4 0 1 E - 0 3 • 2 1 4 0 . 6 1 2 0 2 0 6 1 7 3 6 - 0 5 3 3 8 7 E - 0 2 • I 2 1 5 0 . 7 1 7 3 1 0 7 2 0 7 0 - 0 3 3 8 9 0 E - 0 2 * 2 1 6 0 . 8 3 5 0 3 0 8 3 3 9 9 0 1 0 3 9 5 E - 0 2 * 2 1 7 0 . 9 0 5 2 1 0 9 0 7 6 3 - 0 2 4 2 8 6 E - 0 2 * 2 1 8 1 . 0 9 8 2 . 0 7 4 2 0 2 4 0 3 7 E - 0 1 I * 2 1 9 1 . 2 2 5 6 . 2 0 3 5 0 2 2 0 1 9 E - 0 1 I * 2 2 0 1 . 2 0 6 2 . 1 8 2 1 0 2 4 0 9 8 E - 0 1 I * 2 2 1 - 0 . 5 6 6 0 7 - 0 5 5 4 8 2 - 0 1 1 2 5 5 E - 0 1 * I 2 2 2 - 0 . 5 0 6 5 3 - 0 4 9 8 6 9 - 0 7 8 4 5 2 E - 0 2 * I 2 2 3 0 . 4 5 4 2 3 E - 0 1 0 5 4 2 3 6 E - 0 1 - 0 8 8 1 3 6 E - 0 2 ' I 2 2 4 0 . 3 1 9 0 6 E - 0 1 0 3 5 9 0 0 E - 0 1 - 0 3 9 9 4 I E - 0 2 2 2 5 - 0 . 4 5 2 0 2 - 0 4 6 0 6 1 0 8 5 B 5 9 E - 0 2 I • 2 2 6 - 0 . 4 G 2 5 4 - 0 4 6 B 6 2 0 6 0 7 3 6 E - 0 2 I * 2 2 7 - O . 4 9 7 1 4 - 0 5 2 0 9 3 0 2 3 7 9 4 E - 0 1 I • 2 2 8 - 0 . 4 1 7 1 2 - 0 4 5 0 3 3 0 3 3 2 0 4 E - 0 1 I • 2 2 9 - O . 2 3 0 6 7 -o 2 3 8 4 3 0 7 7 5 7 7 E - 0 2 I • 2 3 0 - 0 . 1 3 0 1 8 - 0 1 2 9 6 8 - 0 4 9 8 9 1 E - 0 3 2 3 1 O . O 0 2 0 0 0 9 E - 0 2 -o 2 0 O 0 9 E - O 2 2 3 2 0 . 2 4 5 3 6 0 2 6 4 5 7 - 0 1 9 2 1 6 E - 0 1 • j 2 3 3 0 . 3 4 6 1 1 0 3 7 9 6 9 - 0 3 3 5 7 5 E - 0 1 * 1 2 3 4 1 . 0 7 3 2 . 0 8 0 0 - 0 6 8 6 3 4 E - 0 2 * I 2 3 5 1 . 0 9 3 3 . 0 2 9 7 0 6 3 5 5 8 E - 0 1 I 2 3 6 0 . 7 7 0 2 5 0 7 4 4 6 0 0 2 5 6 5 6 E - 0 1 I * 2 3 7 0 . 7 6 4 4 8 0 7 5 5 3 5 0 9 1 2 8 3 E - 0 2 I • 2 3 8 0 . 7 2 8 1 9 0 7 3 5 5 0 - 0 7 3 1 6 5 E - 0 2 ' I 209 Table A3.1. Estimated Residuals from Total Cost Function Equation, Final Model, (cont'd) Canadian Food Manufacturing Industries, 1961-1982  Observed Predicted Observation Value Value Calculated Plot of Calculated Number (/»C) (/»C) Residual Residuals around zero 2 3 9 0 . 8 8 4 2 8 0 . 8 8 3 8 0 0 4 8 0 3 6 E - 0 3 * 2 4 0 1 . 3 9 8 1 1 . 3 8 7 1 0 1 1 0 0 6 E - 0 1 I + 2 4 1 1 . 3 9 9 0 1 . 3 8 0 6 0 1 8 4 6 5 E - 0 1 1 * 2 4 2 0 . 9 6 2 5 6 0 . 9 4 1 9 0 0 2 0 6 5 7 E - 0 1 I * 2 4 3 - 0 . 7 6 9 2 5 - 0 . 7 4 7 6 7 - 0 2 1 5 8 4 E - 0 1 * I 2 4 4 - 0 . 6 8 8 8 8 - 0 . 6 6 9 4 5 - 0 1 9 4 3 1 E - 0 1 * I 2 4 5 - 0 . 5 4 8 8 2 - 0 . 5 3 5 2 1 - 0 1 3 6 1 5 E - 0 1 * I 2 4 6 - 0 . 5 1 3 9 3 - 0 . 4 9 5 4 9 - 0 1 8 4 4 4 E - 0 1 * I 2 4 7 - 0 . 3 7 5 9 6 - 0 . 3 5 6 5 3 - 0 1 9 4 2 6 E - 0 1 * I 2 4 8 - 0 . 3 3 0 6 7 - 0 . 3 1 3 9 2 - 0 1 6 7 5 6 E - 0 1 * I 2 4 9 - 0 . 2 9 5 1 6 - 0 . 2 7 9 1 2 - 0 1 6 0 4 1 E - 0 1 * I 2 5 0 - 0 . 3 7 5 3 6 - 0 . 3 5 7 8 9 - 0 1 7 4 6 8 E - 0 1 * I 2 5 1 - 0 . 3 1 3 2 1 - 0 . 2 9 5 9 3 - 0 1 7 2 7 8 E - 0 1 * I 2 5 2 - 0 . 1 4 6 3 9 - 0 . 1 3 6 3 8 - 0 1 0 0 1 0 E - 0 1 * I 2 5 3 0 . 0 O . 2 0 0 0 9 E - 0 2 - 0 2 0 0 0 9 E - 0 2 2 5 4 0 . 1 6 6 8 2 0 . 1 5 9 0 5 0 7 7 7 2 3 E - 0 2 I * 2 5 5 0 . 4 9 7 4 3 0 . 4 8 6 2 4 0 1 1 1 8 9 E - 0 1 I * 2 5 6 0 . 7 9 4 6 1 0 . 7 9 4 0 2 0 5 8 8 5 7 E - 0 3 2 5 7 0 . 7 2 2 0 7 0 . 7 2 3 6 3 - 0 1 5 6 3 7 E - 0 2 2 5 8 O . 8 1 6 4 0 O . 8 2 8 7 9 - 0 1 2 3 8 3 E - 0 I * I 2 5 9 1 . 1 8 9 9 1 . 2 1 5 0 - 0 2 5 0 7 0 E - 0 1 » I 2 6 0 1 . 3 3 7 3 1 . 3 3 5 9 0 1 3 2 8 2 E - 0 2 2 6 1 1 . 5 3 9 9 1 . 5 2 4 0 0 1 5 8 9 5 E - 0 1 I * 2 6 2 1 . 6 8 1 7 1 . 6 5 6 7 0 2 4 9 2 3 E - 0 1 I * 2 6 3 1 . 8 0 5 6 1 . 8 0 6 2 -o 5 7 4 3 6 E - 0 3 2 6 4 1 . 7 4 8 7 1 . 7 1 6 3 0 3 2 3 7 6 E - 0 1 I 2 6 5 1 . 0 9 3 7 - 0 . 1 1 4 1 5 . 2 0 7 9 1 2 6 6 - 0 . 6 2 2 8 2 - 0 . 1 3 8 2 6 -o 4 8 4 5 6 X I 2 6 7 - 0 . 5 6 0 3 7 - 0 . 1 4 8 6 2 - 0 4 1 1 7 4 X I 2 6 8 - 0 . 4 5 9 0 6 - 0 . 1 2 8 7 1 - 0 3 3 0 3 4 X I 2 6 9 - 0 . 4 1 8 7 6 - 0 . 1 4 4 2 8 - 0 2 7 4 4 8 X I 2 7 0 - 0 . 3 6 6 4 5 - 0 . 1 4 8 3 9 -o 2 1 8 0 6 * I 2 7 1 - 0 . 3 1 0 7 5 - 0 . 3 1 1 8 6 t - 0 1 - 0 2 7 9 5 6 X I 2 7 2 - 0 . 2 4 9 1 7 - 0 . 1 5 0 6 2 - 0 9 8 5 4 3 E - 0 1 • I 2 7 3 - 0 . 1 8 7 3 9 - O . 1 2 0 1 9 - 0 6 7 1 9 8 E - 0 1 * I 2 7 4 - O . 5 7 9 O 5 E - 0 1 - 0 . 3 7 4 4 8 E - O 1 - 0 2 0 4 5 7 E - 0 1 * I 2 7 5 0 . 0 0 . 2 0 0 O 9 E - 0 2 - 0 2 0 0 0 9 E - 0 2 2 7 6 0 . 7 5 1 9 1 E - 0 1 0 . 5 6 7 1 7 E - 0 1 0 1 8 4 7 4 E - 0 1 I * 2 7 7 0 . 2 1 7 3 5 0 . 1 5 2 6 1 0 6 4 7 3 7 E - 0 1 I 2 7 8 0 . 5 5 3 3 0 0 . 4 4 6 0 7 0 1 0 7 2 4 1 2 7 9 0 . 6 2 9 0 6 0 . 5 1 6 3 1 ' 0 1 1 2 7 5 I 2 8 0 0 . 7 2 3 6 9 0 . 6 1 1 1 9 0 1 1 2 5 0 I 2 8 1 0 . 9 3 7 8 6 0 . 8 6 0 1 1 0 7 7 7 5 3 E - 0 1 I 2 8 2 1 . 0 4 3 9 1 . 0 1 8 8 0 2 5 1 3 6 E - 0 1 I * 2 8 3 1 . 1 5 2 2 1 . 1 4 8 5 0 3 6 6 9 6 E - 0 2 2 8 4 1 . 2 8 6 2 1 . 2 8 3 3 0 2 9 2 5 5 E - 0 2 2 8 5 1 . 3 5 8 8 1 . 3 6 8 9 - 0 1 0 1 0 6 E - 0 1 * I 2 8 6 1 . 3 5 7 2 1 . 3 8 1 6 - 0 2 4 4 5 1 E - 0 1 . * I 2 8 7 - 1 . 0 0 8 8 - 1 . 0 9 4 7 0 8 5 9 8 0 E - 0 1 I 2 8 8 - 0 . 9 4 9 4 1 - 1 . 0 2 5 6 0 7 6 2 1 3 E - 0 1 I 2 8 9 - 0 . 8 2 8 0 3 - 0 . 8 8 8 6 2 0 6 0 5 9 0 E - 0 1 I 2 9 0 - 0 . 7 7 2 5 8 - 0 . 8 3 1 2 6 0 5 8 6 7 7 E - 0 1 I 2 9 1 - 0 . 7 1 0 6 4 - 0 . 7 5 8 2 3 0 4 7 5 9 1 E - 0 1 I 2 9 2 - 0 . 5 6 5 7 0 - 0 . 6 2 0 3 7 0 5 4 6 7 1 E - 0 1 I 2 9 3 - 0 . 4 4 5 7 6 - 0 . 4 9 7 1 1 0 5 1 3 5 8 E - 0 1 I 2 9 4 - 0 . 3 5 6 6 6 - 0 . 4 2 0 9 3 0 6 4 2 7 4 E - 0 1 I 2 9 5 - 0 . 2 3 1 0 5 - 0 . 2 8 4 0 4 0 5 2 9 9 4 E - 0 1 I 2 9 6 - 0 . 1 2 2 1 1 - 0 . 1 5 6 1 4 0 3 4 0 3 2 E - O I I 2 9 7 0 . 0 0 . 2 0 0 O 9 E - O 2 - 0 2 0 0 0 9 E - 0 2 . * 2 9 8 0 . 6 5 3 9 4 E - 0 1 0 . 9 6 4 1 0 E - 0 1 - 0 3 1 0 1 6 E - 0 1 I 210 Table A3.1. Estimated Residuals from Total Cost Function Equation, Final Model, (cont'd) Canadian Food Manufacturing Industries, 1961-1982 )bservation Number Observed Value (l«C) Predicted Value (inC) Calculated Residual Plot of Calculated Residuals around zero 299 0 1957 1 0 . 2 9 0 7 7 - 0 9 5 0 5 9 E - 0 1 * I 300 0 39957 0 . 4 3 6 1 5 - 0 3 6 5 8 0 E - 0 1 * I 301 0 56788 0 . 6 0 4 7 6 - 0 3 6 8 8 1 E - 0 1 » J 302 0 6 4 2 6 0 0 . 7 1 2 1 6 - 0 6 9 5 5 9 E - 0 1 * I 303 0 72934 0 . 8 1 6 5 3 - 0 8 7 1 8 4 E - 0 1 * I 304 0 8 1320 0 . 9 0 4 4 0 - 0 9 1 1 9 3 E - 0 1 * I 305 0 9 5 6 6 0 1.0738 - 0 1 1724 * I 306 . 0 5 1 0 1.1429 - 0 9 1 8 6 8 E - 0 I * I 307 . 1758 1 .2820 - 0 106 19 * I 308 . 2 2 2 5 1.3757 - 0 15323 * I 309 - 0 8 7 3 3 0 - 0 . 8 4 0 6 2 - 0 3 2 6 8 2 E - 0 1 * J 3 1 0 - 0 8 3 4 6 0 - 0 . 7 9 4 0 5 - 0 4 0 S 4 4 E - 0 1 * I 31 1 - 0 76973 - 0 . 7 1 7 8 7 - 0 5 1 8 5 8 E - 0 1 t J 312 - 0 69377 - 0 . 6 3 6 8 5 - 0 5 6 9 2 1 E - 0 1 * I 313 - 0 58733 - 0 . 5 5 7 6 8 -o 2 9 6 4 5 E - 0 1 * J 314 - 0 43869 - 0 . 4 1 4 1 6 - 0 2 4 5 2 8 E - 0 1 * I 315 - 0 34 143 - 0 . 3 3 4 5 1 - 0 6 9 2 8 8 E - 0 2 * I 316 - 0 27723 - 0 . 2 6 5 1 1 - 0 12123E-01 * I 317 - 0 16650 - 0 . 1 4 3 4 9 - 0 2 3 0 1 2 E - 0 1 * I 3 18 -o 76S2SE -01 - 0 . 7 7 2 5 8 E -01 0 7 3 3 7 5 E - 0 3 319 0 0 0 . 2 0 0 0 9 E -02 - 0 2O009E-02 3 2 0 0 13054 0 . 1 3 8 7 1 - 0 8 1 7 2 3 E - 0 2 * I 321 0 29608 0 . 3 3 8 8 6 - 0 4 2 7 7 7 E - 0 1 * I 322 0 3 8 0 4 0 0 . 4 0 5 8 2 - 0 2 5 4 I 5 E - 0 1 * I 323 o 56468 0 . 6 0 8 6 4 -o 4 3 9 6 7 E - 0 1 * I 324 0 52723 0 . 5 3 8 9 6 - 0 11735E-01 * I 325 0 62677 0 . 6 7 3 9 6 -o 4 7 1 9 4 E - 0 1 * I 326 0 65482 0 . 6 9 5 0 2 - 0 4 0 2 0 2 E - 0 1 * I 327 0 8 1268 0 . 8 5 2 3 2 - 0 3 9 6 3 2 E - 0 1 * J 328 , 0 92191 0 . 9 4 1 8 9 - 0 1 9 9 7 4 E - 0 I * J 329 . 0 2 7 8 1.0398 - 0 1 1994E-01 * j 3 3 0 . 0 3 7 0 1.0237 0 13311E-01 I * 331 - 0 57414 - 0 . 6 0 1 3 4 0 2 7 2 0 0 E - 0 I I * 332 - 0 5224 1 - 0 . 5 4 3 6 2 0 2 1 2 0 9 E - 0 1 I * 333 - 0 48198 - 0 . 5 0 3 8 9 0 2 1 9 1 4 E - 0 1 I * 334 - 0 43383 - 0 . 4 5 5 7 2 0 2 1 8 8 6 E - 0 1 I * 335 - 0 37622 - 0 . 4 1152 0 3 5 2 9 4 E - 0 1 I *• 336 - 0 31233 - 0 . 3 2 5 2 1 0 12878E-01 I * 337 - 0 27199 - 0 . 2 8 8 4 0 0 16407E-01 I * 338 - 0 18732 - 0 . 2 2 5 1 1 0 3 7 7 9 4 E - 0 1 I * 339 -o 13563 - 0 . 1 5 9 5 3 0 2 3 9 1 0 E - O I I * 340 - 0 74702E -01 - 0 . 8 3 8 B 5 E -01 0 9 1 8 2 8 E - 0 2 I * 34 1 0 0 0 . 2 0 0 0 9 E -02 - 0 2 0 0 0 9 E - 0 2 342 0 7BB20E -01 0 . 9 1 0 9 4 E -01 - 0 12273E-01 * I 343 0 20935 0 . 2 2 4 8 1 - 0 15456E-01 * I 344 0 4 1404 0 . 4 2 8 8 5 - 0 14809E-01 * I 345 0 57877 0 . 5 B 3 5 7 - 0 4 8 0 0 0 E - 0 2 * I 346 0 66333 0 . 6 6 7 0 4 - 0 3 7 1 I 5 E - 0 2 347 0 73968 0 . 7 2 5 2 8 0 14403E-01 I * 348 0 824 15 0 . 8 1 9 5 4 0 46 140E-02 I * 349 0 95497 0 . 9 5 5 8 1 - 0 8 4 8 0 1 E - 0 3 350 . 1298 1 .1033 0 2 6 5 0 2 E - 0 1 I * 351 . 3 0 2 7 1.2864 0 16336E-01 j * 352 . 4 0 2 5 1.37 16 0 3 0 9 2 0 E - 0 1 j * 3 5 3 - . 1 165 - 1. 1158 - 0 6 3 9 7 0 E - 0 3 354 - . 0214 - 1 .0200 - 0 13521E-02 355 - 0 94729 - 0 . 9 5 7 8 9 0 10S95E-01 I * 356 - 0 91497 - 0 . 9 0 9 3 7 - 0 S 6 0 0 8 E - 0 2 • I 357 - 0 81925 - 0 . 8 1 2 4 4 - 0 6 8 1 1 1 E - 0 2 M 35B - 0 72107 - 0 . 7 2 1 4 3 0 3 6 0 3 1 E - 0 3 * 211 Table A3.1. Estimated Residuals from Total Cost Function Equation, Final Model, (cont'd) Canadian Food Manufacturing Industries, 1961-1982 Observed Predicted Observation Value Value Calculated Plot of Calculated Number O C ) O C ) Residual Residuals around zero 3 5 9 - 0 6 0 6 1 4 - 0 . 6 3 8 3 7 0 3 2 2 2 9 E - 0 1 3 6 0 - 0 5 5 3 1 9 - 0 . 5 8 8 4 0 0 3 5 2 0 4 E - 0 1 3 6 1 - 0 38666 - 0 . 4 2 5 1 4 O 3 B 4 7 9 E - 0 1 3 6 2 - 0 2 3 9 3 4 - 0 . 2 4 6 6 9 0 7 3 4 9 2 E - 0 2 3 6 3 0 0 0 . 2 0 O 0 9 E - 0 2 - 0 2 0 0 0 9 E - 0 2 3 6 4 0 1 2 1 2 0 0 . 9 4 4 8 5 E - 0 1 0 2 6 7 1 4 E - 0 1 3 6 5 0 2 4 5 9 1 0 . 1 9 4 6 7 0 5 1 2 3 3 E - 0 1 3 6 6 0 4 1 0 8 8 0 . 3 8 0 0 2 0 3 0 B 6 3 E - 0 1 3 6 7 0 4 4 5 0 4 0 . 4 1 3 1 9 0 3 1 8 4 7 E - 0 1 3 6 8 0 5 2 5 1 2 0 . 4 6 0 4 4 0 G 4 6 8 6 E - 0 1 3 6 9 0 5 0 2 8 0 0 . 4 3 3 4 7 0 6 9 3 3 6 E - 0 I 3 7 0 0 8 1 0 4 2 0 . 8 1 3 7 1 - 0 3 2 9 4 9 E - 0 2 3 7 1 0 9 5 3 7 6 0 . 9 3 7 4 3 0 1 6 3 2 9 E - 0 1 3 7 2 . 0 8 8 4 1 . 1 0 4 6 - 0 1 G 2 6 5 E - 0 1 * I 3 7 3 . 2 3 2 5 1 . 2 3 8 0 - 0 5 S 4 8 5 E - 0 2 * I 3 7 4 . 2 9 4 2 1 . 2 9 6 5 - 0 2 2 5 1 3 E - 0 2 * 212 Table A3.2. Residual Summary Statistics lor the Final Model ' Canadian Food Manufacturing Industries, 1961-1982 Summary Statistic Total Cost Production Labour Share Non-Production Labour Share Energy Share Materials Share Durbin-Walson 1.76 0.37 0.38 0.61 0.36 First-Order/) 0.12 0.81 0.81 0.69 0.82 Runs Test: -9.92 -12.52 -10.56 -11.49 -12.11 Normal Statistic2 (92;52) (167;48) (86;51) (77;49) (71;49) Estimated Coefficient 7.10 0.14 -0.07 0.67 -0.12 of Skewness3 (yi) (0.13) (0.13) (0.13) (0.13) (0.13) Estimated Coefficient 127.76 0.71 • 6.28 2.04 1.61 of Kurtosis 3 (y2) (0.25) (0.25) (0.25) (0.25) (0.25) 1 The final model is the system of equations (42') and (43). 2 The number of runs is given below the value of the statistic: it is the first value in parentheses. The second value is the percentage of positive error terms. The estimated deviation of this statistic is given below its value in parentheses. 

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