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A regional analysis of supply in the Canadian pulp and paper sector Klein, Stephen Richard 1985

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A REGIONAL ANALYSIS OF SUPPLY IN THE CANADIAN PULP AND PAPER SECTOR by STEPHEN RICHARD KLEIN B.Sc, The University College of North Wales, 1983 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Faculty of Forestry) We accept this thestsias conforming to the required standards THE UNIVERSITY OF BRITISH COLUMBIA ( § ) JULY 1985 Stephen Richard Klein, 1985 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by h i s or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of F o r e s t r y The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date O c t o b e r 1 5 , 1 9 8 5 DE-6 (3/81) i i ABSTRACT The purpose of this thesis was to analyse the supply of pulp and paper products in the three major producing provinces of Canada, namely British Columbia, Ontario and Quebec. A translog restricted profit function and its first partial derivatives were estimated using the iterative seemingly unrelated regressions procedure. Derived demand equations for energy, fibre, labour and supply equations for net market pulp, newsprint and 'other paper and paperboard", (net market pulp and 'all paper and paperboard' for British Columbia) were obtained with net supplies as a function of each input and output price. The success of the model in representing the industry was mixed. Derived demand own price elasticities were, in almost all cases, negative as expected a priori. Negative own price elasticities were also found in many end product supply functions suggesting a misspecification of the supply relationship. The unexpected supply function results bring up questions about the degree of competitiveness in pulp and paper markets, and thus the validity of using the perfectly competitive market assumption in empirical studies. Finally the model was evaluated in the context of using the results in a spatial equilibrium model of the North American pulp and paper sector. i i i TABLE OF CONTENTS Page ABSTRACT ii TABLE OF CONTENTS iii LIST OF TABLES V LIST OF FIGURES vi ACKNOWLEDGEMENTS vii CHAPTER 1. INTRODUCTION 1 1.1 Statement of Purpose 1 1.2 Overview of the Canadian Pulp and Paper Sector 2 CHAPTER 2. REVIEW OF LITERATURE ON NORTH AMERICAN PULP AND PAPER SUPPLY 10 2.1 Introduction 10 2.2 Non-competitive Price Determination Models 12 2.3 Supply in Competitive Market Models 13 2.4 Derived Demand for Factors of Production 16 2.5 Summary 18 CHAPTER 3. MODEL DEVELOPMENT 19 3.1 Introduction 19 3.2 The Production Theory Approach to Modelling Industry Supply 23 3.3 Model Specification 27 3.4 Estimation Procedure 31 CHAPTER 4 DATA 33 4.1 Data Specification 33 4.2 Data Problems 36 Page CHAPTER 5. ANALYSIS OF RESULTS 38 5.1 Estimation Results 38 5.2 Discussion of Results 42 5.2.1 British Columbia 42 5.2.2 Ontario 43 5.2.3 Quebec 44 5.2.4 Summary and Comparison with Similar Studies.... 45 CHAPTER 6. CONCLUSIONS AND SUGGESTIONS FOR FURTHER RESEARCH 49 FOOTNOTES 51 LITERATURE CITED .' 52 APPENDIX A - DATA 60 APPENDIX B - ESTIMATION RESULTS 63 V LIST OF TABLES Table Page 1. Canadian Production and Exports of Selected Pulp, Paper and Paperboard Grades, 1983 3 2. Pulp, Paper and Paperboard Mills in Canada, 1985 4 3. Pulp, Paper and Paperboard Production in B.C., Ontario and Quebec, 1983 5 4. Share of Four Energy Sources in Cost of Purchased Fuel and Electricity for Canadian Pulp and Paper Mills in 1974. 6 5. Preliminary Regression Results for Quebec Newsprint Supply Function 20 6. Further Preliminary Regression Results for Quebec Newsprint Supply Function 21 7. Preliminary Regression Results for Quebec Newsprint Price Function 22 8. Further Preliminary Regression Results for Quebec Newsprint Price Function 22 9. Price Elasticity Estimates for British Columbia 38 10. Price Elasticity Estimates for Ontario 39 11. Price Elasticity Estimates for Quebec 40 v i LIST OF FIGURES Figure Page 1. Production of Net Market Pulp8, Newsprint and 'Other Paper and Paperboard'8 In British Columbia, Ontario and Quebec 7 2. Real Output Prices by Category for Ontario 9 v i i ACKNOWLEDGEMENTS I would like to thank my supervisor, Professor P. Pearse, and my other Committee members; Professors R. Uhler, D. Haley and J. Wilson for their constant support during the course of my studies in Vancouver. I also acknowledge the sound advice and guidance offered by Dean R.W. Kennedy in the initial development of my degree program. I am indebted to the Forest Economics and Policy Analysis Project researchers for their moral, technical and financial support of this study. Mr. Michael Wemerheim, Mr. Peter Morrison and Mr. Karel Jegr all contributed to this thesis by way of advice and review of initial drafts. I would particularly like to thank Mr. J. Michael Fullerton for his encouragement in the initial stages of my thesis research and Mr. Luis Constantino for his excellent technical advice which proved to be invaluable to the completion of this thesis. 1 CHAPTER 1. INTRODUCTION 1.1 Statement of Purpose The basic objective of this research was to analyse supply in Canada's pulp and paper sector in the general context of economic modelling for policy analysis. The study was conceived as a result of discussions with analysts at the Forest Economics and Policy Analysis (FEPA) Project on Canadian developments of a North American pulp and paper sector model. The model, built by Oilless and Buongiorno (1983), can be categorized as a spatial price endogenous equilbrium model formulated as a linear programming problem.1 It was developed for use in the United States Forest Service's 1985 Timber Assessment and was subsequently adopted by the FEPA Project as part of Its forest sector modelling system. Initially it was decided to estimate regional end product supply functions in Canada for use in a proposed, slightly modified version of the original model. The objective function of the present model Is of the following form: Maximize Z = ZD - Z s - ZT - Z M where: Z = Net Social Payoff (sum of producer and consumer surplus) ZD = Area under end product demand curve up to clearing quantity Z s = Area under fibre input supply curve up to clearing quantity ZT = Transportation cost ZM= Manufacturing cost 2 A feasible alternative objective function formulation is: Maximize Z = ZD - Z S E - ZT where: ZSE= Area under end product supply curve up to clearing quantity. In order to obtain end product supply curves for the industry, the restricted profit function dual to a specific production function was considered as a framework for analysis. Estimation of a specified profit function and its first partial derivatives give end product supply and derived demand functions for the industry. The latter functions are also evaluated for applications in larger industry models. 1.2 Overview of the Canadian Pub and Paper Sector The structure of the pulp and paper industry varies considerably between regions in many respects. This section aims to provide a brief description of the industry and outline Important regional differences in terms of production technology. British Columbia, Ontario and Quebec produce approximately 75 percent of national output and It is these regions which are the subject of this study. The pulp and paper sector Is the largest In Canada In terms of value added by manufacturing (Singh and Nautlyal, 1984). In 1981 more people were employed in the pulp and paper industry in Canada than any other and total shipments value was second only to the petroleum industry (Miller Freeman, 1985a). The production profile in the Canadian pulp and paper sector is heavily oriented toward newsprint and market pulp. These products are primarily produced for export with almost 90 percent of 1983 production 3 of newsprint being exported and the majority of market pulp production being destined for foreign markets. Other paper and paperboard products are less important commodities in terms of production levels and exports. Table 1 gives production of paper and paperboard and exports of pulp, paper and paperboard for 1983. In 1983 the United States was by far the largest export market accounting for 80 percent of Canada's newsprint exports and 50 percent of chemical woodpulp exports. Other major export markets were Western Europe and Asia. Table 1. Canadian Production and Exports of Selected Pulp, Paper and Paperboard Grades, 1983. Product Production Exports thousand metric tons WOODPULP bleached sulphite 255 unbleached sulphite 52 bleached softwood sulphate 4,941 bleached hardwood sulphate 541 semibleached sulphate 377 unbleached sulphate 186 mechanical 245 dissolving, special alpha 198 total 6,795 PAPER/PAPERBOARD newsprint 8,486 7,469 groundwood printing 765 636 book.writing 961 239 kraft papers 472 234 tissue 385 24 paperboard 2,344 518 total 13,413 9,120 Source : Miller Freeman (1985a). 4 In this study, pulp and paper profit functions are estimated for British Columbia, Ontario and Quebec. These regions were chosen based on the importance of these provinces in national production and considerations of data availability. The provincial distribution of pulp and paper sector activity is apparent from Table 2. Production levels of market woodpulp, newsprint and other paper and paperboard by province are given later in this section. British Columbia differs from the eastern provinces in that the industry relies heavily on market pulp rather than paper/paperboard as implied by Table 32. Table 2. Pulp, Paper and Paperboard Mills in Canada, 1985. Province Number of mill sitesft Pulp Paper/Paperboard Alberta 2 3 British Columbia 22 10 Manitoba 3 4 New Brunswick 10 6 Newfoundland 3 3 Nova Scotia 5 4 Ontario 23 32 Quebec 39 53 Saskatchewan 1 0 total 108 115 Integrated pulp and paper/paperboard mills Included In both categories. Source : Miller Freeman (1985b). 5 Table 3. Pulp, Paper and/Paperboard Production in British Columbia, Ontario and Quebec, 1983 Province Pulp Paper/Paperboard - OOO metric tons British Columbia 6,143 2,164 Ontario 4,212 3,388 Quebec 6,762 6,049 Source: Miller Freeman (1985a). The fibre input mix has varied considerably across regions and in the time period under study. In the 1950's each region utilized mainly roundwood, but with growth in the lumber and plywood industries, wood residues have become a major input, especially in British Columbia. Real3 fibre prices have shown a steady declining trend from 1950 to the early 1980's. British Columbia's fibre price has consistently remained considerably lower than prices in Quebec and Ontario over the same period. Real labour prices have risen substantially over the same period in each region, with wages In British Columbia being consistently slightly higher than in the eastern provinces. Energy source mixes also vary between regions and these are highlighted in Table 4. In the present study, purchased electricity prices and quantities are used as a proxy for all energy consumption due to the lack of more comprehensive data. These prices fluctuate In real terms but the trend Is fairly constant over the period In all regions up until 1974. As would be expected, after 1974, electricity prices rose In each region with Ontario facing the highest prices4. Further comparisons of regional 6 manufacturing costs in Canada and the United States for the pulp and paper sector are given in Sandwell (1977). Table 4. Share of Four Energy Sources in Cost of Purchased Fuel and Electricity for Canadian Pulp and Paper Mills in 1974. B.C. Ontario Quebec per cent Coal and Coke 0.01 5.66 3.12 Natural Gas 19.07 33.71 0.72 Liquid Hydrocarbons 52.57 14.74 53.43 Electricity 28.36 45.89 42.74 Source :Muller( 1981) Production of pulp and paper products has grown steadily in each region from 1950 to 1981. Differential production levels for outputs by region are shown in Figure 1. Prices in the three aggregated categories of pulp and paper products vary little between regions. Real market pulp prices fell steadily from 1953 to 1972. The 1973 oil shock caused real pulp prices to rise dramatically from 1973 to 1975 and resulted in part in greater fluctuations in pulp prices into the 1980's. Real price fluctuations in the newsprint and 'other paper and paperboard' categories follow a similar pattern though annual price changes in these products tend to be less dramatic. Figure 2 shows these price trends for Ontario. 7 Figure 1. Production of Net Market Pulpft, Newprint and 'Other Paper and Paperboard'8 In British Columbia, Ontario and Quebec. B.C. Production (OOO metric tons) 0 I i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i I -1950 1955 1960 1965 1970 1975 1980 Year Ontario Production (000 metric tons) 0 I i I I i i i i i i i I I I I I I I I I I I I I i i i i I I I I • -1950 1955 1960 1965 1970 1975 1980 Year 8 1950 1955 1960 1965 1970 1975 Year newsprint paper/board •** pulp production production production A « see Chapter A for definition B = total paper/paperboard in the case of B.C. Source: Statistics Canada (1950-1981). 9 Source: Statistics Canada (1950-1981). 10 CHAPTER 2. REVIEW OF LITERATURE ON NORTH AMERICAN PULP AND PAPER SUPPLY 2.1 Introduction When attempting to model supply in an industry the researcher is forced to make important and potentially controversial assumptions about industry/market structure. The North American pulp and paper industry is not easily categorized in this regard. Significantly different views are expressed in the available literature. For example, Armstrong (1975), believes that pulp and paper best approximates the structure of an oligopoly, while Slatin (1975) states that the industry is highly competitive. The industry structure varies considerably between geographical regions and from product to product. A number of authors contend that the North American newsprint industry is an oligopoly with a price leadership system (Guthrie 1941, 1972, Eastman and Styholt 1967, Moore 1970, Irland 1976). Rich (1978) provides evidence of target return pricing behaviour in newsprint. Gilless (1985), however, contends that discounts on list prices are commonplace and that in fact price competition is quite strong. Concentration ratios in the industry vary from unconcentrated to highly concentrated depending on product aggregation. Different authors draw conflicting conclusions from this evidence (eg. Irland 1976, Leahey 1978). Eastman and Styholt (1967) believe eastern Canadian newsprint producers are collectively dominant with a single firm setting prices. The fine paper and paperboard industry in Canada is traditionally highly tariff protected and the bulk of these products are domestically consumed 11 (Haviland e± al. 1968). Tariff protection reduces foreign competition in domestic markets and can promote oligopolistic behaviour, though Muller (1979) argues that there is enough competition from the United States to prevent a price leadership system. The market for Canadian woodpulp is generally believed to be distinctly competitive (Muller 1978, Gilless 1985). The level of competitiveness in an industry can be gauged from a number of indicators. Two common indicators are, the number of firms in an industry (usually measured by its concentration ratio) and gains from capturing economies of scale. Study of the product markets also provides useful evidence in this regard. Pricing patterns, discount and dealing activity, sales and distribution channels and buying mechanisms can all provide insights into market structure. Alternatively, formal tests for price-taking behaviour can be applied to certain empirical studies (Applebaum 1979). Numerous studies in the literature on the pulp and paper sector assume a market structure, develop an empirical model to estimate price formation in the market, and infer from the success of the model, the validity of the initial assumption (eg. Muller 1979). This review aims at summarizing the methodologies and results of past supply side studies in the North American pulp and paper sector. Models of end product price determination under competitive and non-competitive market assumptions are reviewed in the following two sections while studies of derived demand for factors of production in the industry are discussed in the final section. 12 2.2 N o n - c o m p e t i t i v e P r i c e D e t e r m i n a t i o n M o d e l s A number of econometric models of price determination in the North American pulp and paper sector under non-competitive market assumptions have been developed in recent years. McLeod (1975) developed a recursive econometric model of the United States' paper industry consisting of six blocks : demand, production, employment and earnings, prices, profit and investment. He hypothesized that paper prices are primarily a function of input prices specifying prices of labour, wastepaper, woodpulp and chemicals as independent variables in regression equations. Dagenais (1976) described a model of price formation for newsprint in eastern North America. He based his study on an oligopolistic model with the price leader constrained in price setting by the desire to discourage entry into the industry and reduce the temptation for price cutting behaviour among industry members. The final equation derived expressed price as a function of operating costs (which determine entry preventing price) and the average operating rate of producers (which influences the probability of price cutting behaviour from firms in the industry). Muller (1976,1978) discusses a model developed to simulate the impacts of pollution control on the Canadian pulp and paper industry. In agreement with the Dagenais model, Muller specifies newsprint prices as a function of unit costs and capacity utilization. Leahey (1978), working on pollution control impacts in the United States, dissagregated unit costs in the price function, and again used capacity utilization as an independent variable. 13 Buongiorno and Oilless (1980) and Buonglorno el al. (1983) estimated price functions from the cost function dual of a generalized Cobb-Douglas production function assuming cost minimization for O.E.C.D. countries5 and the United States respectively. Buongiorno el al. (1983) found capacity utilization rates had no effect on the price equation In contrast with studies described previously. This study also found no evidence for economies of scale, lending weight to the competitive market hypothesis (Kaltenberg 1983). Singh and Nautiyal (1984) adopted a similar approach to model price formation in the Canadian pulp and paper Industry. They employed the Cobb-Douglas and Constant Elasticity of Substitution (CES) production function specifications. These three studies support the hypothesis that price formation is primarily based on input costs and provide evidence that capacity utilization In the industry does not significantly affect paper prices. 2.3 S u p p l y i n C o m p e t i t i v e M a r k e t M o d e l s In his pioneering study, McKlllop (1967) estimated supply and demand functions for the major forest output groups in the end product and primary product (roundwood and stumpage) sectors of the United States' forest industries. End product supply functions In the pulp and paper industry were developed for paper, paperboard, building paper and building paperboard. The results were far from satisfactory with nonsignificant coefficients for product price for two of the product groups. Only productivity in pulp and paper was significant with signs as expected a priori McKlllop suggested that high Industry concentration and 14 non-competitive markets in the industry may be the cause of the problem. Muller (1979) recognized the potential usefulness of applying profit functions to the case of the Canadian pulp and paper industry. In this paper and a later extended study, (Muller 1980), he identifies three distinct areas of weakness in certain published models (e.g. Muller 1978, Leahey 1978) which can be overcome by specification of a restricted profit function: 1. Failure to model the impact of factor price changes on output of the industry; 2. Failure to deal with multiple output industries (such as the Canadian pulp and paper industry) successfully; and 3. The assumption of market power which is debatable, particularly in an industry which is subject to significant international competition. In his 1979 paper Muller estimated normalized quadratic profit functions at the national level. He specified eight models differing in terms of which factors are fixed or variable and which price was used to normalize the functions estimated. He used annual data from 1947-1976, estimating the equation system with the iterative Zellner algorithm of the SHAZAM econometrics program (White 1978). The results of these estimations were promising; all short run own price elasticities of end product supply and factor demand being stable and of expected sign. Certain reservations were, however, noted by the author. The presence of highly autocorrelated residuals suggests important explanatory variables may have been omitted. Hessian matrices of several of the models were not positive definite, thus invalidating the profit functions' representation of production technology6. 15 The national study was disaggregated into three regions by Muller and reported in subsequent papers (Muller 1980, 1981). In his 1980 paper Muller estimated a single model with newsprint, woodpulp, energy, labour and materials/supplies as variable and capital and 'paper and paperboard' fixed. The model was estimated for Canada, British Columbia, Ontario and Quebec. Forty four of the eighty reported coefficients were found to be statistically significant. Two out of five woodpulp, and three of five newsprint supply function own price elasticities were of right sign and significant. Problems present In the national study were also apparent In regional estimation. As noted by Muller, one possible source of error may have been certain data limitations forcing the author to double count in woodpulp production data and assume 'other paper and paperboard' production in British Columbia was zero over the estimation period. As mentioned in the introduction, Oil less and Buongiorno (1983) developed a competitive, regional, price endogenous, linear programming model of the North American pulp and paper sector. The objective function is the 'net social payoff'7, or the sum of producer and consumer surplus in the sector. An arbitrarily close approximation of the 'net social payoff function is obtained using a separable programming technique developed by Duloy and Norton (1975). The objective function Is maximized yielding equilibrium quantities in each market for each commodity included. A model outlined by Guder and Buongiorno (1984) employs similar concepts and Is used to analyze Interregional trade in the North American newsprint industry. The objective function is again based on the 'net social payoff concept and a quadratic programming algorithm is used to solve the problem. 16 2.4 Derived Demand For Factors of Production As the use of production theory in empirical economic studies has become common in recent years so the understanding of demand for inputs to the production process has increased. In the pulp and paper sector early studies such as those by McKillop (1967) and Leuschner (1973) required the researcher to apply a priori knowledge of demand for fibre inputs in order to specify the appropriate function. Use of duality theory and the estimation of cost and profit functions provide a natural framework for analysis of derived demand. In general the pulp and paper industry acts as a price-taker in input markets and the market structure problems encountered on the output side are less important here. Only in the case of fibre inputs (chips and roundwood) are firms likely to be able to influence prices to any extent, and only then in a limited number of cases. Muller (1975) estimated factor demand equations and Allen elasticities of substitution from a generalized Leontief cost function. The results of this study were unsatisfactory with factor price coefficients of incorrect sign and poor estimates of elasticities of substitution. Muller (1978) dropped the price coefficients in the same function to estimate factor demands. In 1979 Muller estimated demand equations with a normalized restricted quadratic profit function at the national level with some success. Own price elasticities had correct signs for all Inputs in each model and 12 out of 14 of the price coefficients were statistically significant. In later studies, Muller (1980,1981) obtained regional 17 estimates of factor demand elasticities. With woodpulp and newsprint as variable outputs and energy and labour variable inputs own price elasticities in factor demand equations yielded five out of five right signs for labour, with only one being insignificant and three out of five right signs for labour, with two being statistically significant. Buongiorno and Gilless (1980) and Buongiorno e l al. (1983) estimated derived demand functions from the cost function dual of generalized Cobb-Douglas production functions for all O.E.C.D countries and the United States respectively. In all cases very stable, plausible results were obtained. In the United States study own price derived demand elasticities for energy, labour, woodpulp and wastepaper were all around -1.0. Own price elasticities for capital were around -0.5. Sherif (1983) specified a translog cost function and estimated the cost function, share equation system In order to analyse the production technology in the Canadian pulp and paper industry. Right signs were obtained for each own price derived demand elasticity though they were very low for wood, labour and capital at under -0.1. The energy price elasticity was about -0.25. Nautlyal and Singh (1983) estimated a CES production function and its roundwood derived demand function for the Ontario forest industries. Partial price elasticity estimates for roundwood in pulp and paper were 0.16 for capital, 0.13 for labour and -0.29 for roundwood. These elasticities are all of expected sign and very stable. Similar estimations were undertaken at a national level by Singh and Nautiyal (1984). Using Cobb-Douglas and CES functions for different product groups very consistent, plausible derived demand elasticities were obtained. 18 Finally Martinello (1985) estimated a translog cost function and derived demand functions for all Canadian forest Industries. Correct signs were obtained for all own price elasticities in the pulp and paper sector. 2.5 S u m m a r y From this review it Is clear that a number of approaches have been taken to analyse supply in the North American pulp and paper sector. There is considerable disagreement expressed in the literature on the price setting mechanisms acting in pulp and paper markets. Studies dealing directly with the market structure of the industry have tended to be qualitative in nature, while most empirical work has developed around a specific market structure assumption. From the relative success of these models one can speculate about the validity of the assumption, though, since no formal tests for price-taking behaviour are commonly employed, no firm conclusions can be drawn. In this study, as described in the following chapter, simple models of supply based on competitive and non-competitive market assumptions are specified and estimated. Finally a profit-maximising competitive model of the sector is developed and evaluated for use in larger models. 19 CHAPTER 3. MODEL DEVELOPMENT 3.1 Introduction As discussed in the statement of purpose, the aim of this study was to analyse supply in Canada's pulp and paper sector with a view to using the results in an alternative formulation of the pulp and paper model developed by Gilless and Buongiorno (1983). The profit function model provides a particularly convenient framework for the analysis of supply in the present case. Its ability to model multiple input, multiple output industries makes it especially useful in the pulp and paper industry which is characterized by diverse output commodities and important differences in regional commodity production mixes 8. For this reason in particular the profit function was employed in this study, though Lopez (1982) outlines certain theoretical advantages of the profit function over the more frequently used cost function. Before specifying and estimating a profit function some preliminary regressions were run with annual regional factor input and end product output price and quantity data. M &fl£ derived demand and end product supply functions were f irst specified as dependent solely on own price. These functions gave poor results and were difficult to interpret due to the problem of identification 9. Supply functions for pulp, newsprint and other paper and paperboard were next specified as functions of end product and factor prices. By observing changes in price coefficients with certain variables present and absent in the model it became evident that there was very l i t t le stability in the parameter estimates. By way of 20 example, the following Quebec newsprint supply functions were estimated by OLS, with results listed in Tables 5 and 6: Model 1: NQ = p 0 + PiNPd + p"2PPd + P W 1 + v Model 2: NQ - ^ 0 + * lNP d + r2PPd + *3UP d + f^P* * y 5 E P d + y 6 L P d + w Where: NQ = Newsprint production NP = Newsprint price PP = "Other paper and paperboard' price UP = Net market pulp price FP = Fibre price EP = Energy price LP - Labour price v, w = Stochastic error terms Note: d = Deflated by GNP deflator. Table 5. Preliminary Regression Results for Quebec Newsprint Supply Function. Independant Coefficient Elasticity at mean Variable model 1 model 2 model 1 model 2 NPd 2827 -4876* 0.340 -0.588 ppd -7203* 2815 -1.316 0.514 UPd -976 -573 -0.132 -0.077 FPd -46121* -0.510 Epd 907 0.004 L p d 92658* 0.465 * = significant at 5% level 21 Table 6. Further Preliminary Regression Results for Quebec Newsprint Supply Function Model F-Value Degrees of Adjusted Freedom R-Square 1 490 27 0.28 2 41.79 24 0.89 Similar instability and counter-intuitive signs were found in coefficients of supply functions for pulp and other paper and paperboard and in other regions. As discussed in the literature review, numerous authors have hypothesized that prices for outputs from the Canadian pulp and paper industry are not formed in a competitive market but by a variety of oligopolistic price setting systems. The newsprint industry is frequently accused of mark-up pricing. It was decided to experiment by specifying simple price functions with pulp, newsprint and other paper and paperboard expressed as functions of input prices. Again the results were far from satisfactory with many nonsignificant coefficients and unexpected signs. Details of the regressions for newsprint price in Quebec in linear and log-linear forms are reported below and in Tables 7 and 8 : Model 3: NP = S0 + 6,FP + 5 2EP + 6 3LP + z Model 4: InNP = d)0 + <J>,lnFP + 4»2 InEP + <J>3lnLP + x Where : z,x = Stochastic error terms 22 Table 7. Preliminary Regression Results for Quebec Newsprint Price Function Independant Coefficient Elasticity at mean Variable model 1 model 2 model 1 model 2 FP/lnFP -0.00002* -0.182 -1.565 -0.182 EP/lnEP -0.00003 0.024 0.949 0.024 LP/lnLP 16.114 0.813 0.650 0.813 * » significant at 5% level Table 8. Further Preliminary Regression Results for Quebec Newsprint Price Function Model F-Value Degrees of Adjusted Freedom R-Square 3 20.56 29 0.65 4 77.64 29 0.88 These preliminary investigations are not encouraging for either the competitive supply representation or the price setting model of price determination. It was decided to go ahead with estimation of restricted profit functions along with end product supply and derived demand equations. In the remainder of this chapter, background to the profit function approach and details of the final model specification and estimation procedure employed are given. 23 3.2 The Production Theory Approach to Modelling Industry Supply In recent years duality theory has been used extensively by applied researchers in modelling the production technology of industries. Duality theory has its origins in Minowski's theorem of 1911 (Diewert 1974), which states that every closed convex set can be characterized by its supporting half spaces10. The theory has been stated or proven by various authors in different contexts (eg. Hotelling 1932, Hicks 1946, Samuelson 1953-1954 and Shepherd 1953). The concept of duality is perhaps most easily demonstrated in terms of cost and production functions. Assume a firm faces a production function Y=f(x) where Y is the maximum output the firm can produce in a given time period using x, a vector of input quantities. If the production function satisfies certain regularity conditions, then the firm's minimum cost function C(Y;p) can be calculated, where p is a vector of input prices, as the solution to the following constrained minimization problem: C(Y;p) = min x {pT x: f(x)> Y) (1) In other words, the firm, taking input prices as given, attempts to minimize costs in producing an exogenous output level, Y. The production function f determines the cost function C through definition (1). As pointed out by Diewert (1974) It Is also true that the cost function, 1f it satisfies certain regularity conditions, determines the production function; there is, thus, a duality between cost and production functions. An analogous result is reached when demonstrating the duality 24 between the firm's variable profit function Tf(p,v), where p is a vector of variable input and output prices and v is a vector of fixed input quantities, and the firm's production possibilities set, T (Diewert 1982). The production possibilities set, T, is the set of all feasible combinations of inputs and outputs where outputs are denoted by positive numbers and inputs are denoted by negative numbers. Variable input and output quantities are denoted by the vector u with fixed input quantities denoted by the vector -v. The profit function is formally defined as: TT(p,v) m max u {pTu: (u,-v) € T] (2) The principal practical relevence of duality is that dual functions are simply related to derived demand and end product supply equations. Hotelling (1932) was the f irst to recognize this relationship in terms of the profit function: Hotelling's Lemma (1932) states that if a restricted profit function is differentiate with respect to variable quantity prices and satisfies certain regularity conditions then its f irst partial derivatives represent profit maximizing net supplies. dTr (p ;v)/dpj = u,<p;v) (3) By specifying a flexible functional form output supply and Input demand equations are expressed as a function of each input and output price. Also no a prjpri restrictions on substitution possibilities between inputs and between outputs are Imposed on the model. Any equation giving a second order Taylor's approximation to an arbitrary functional form is 25 flexible. In recent years a number of flexible functional forms have been developed and applied in empirical analyses. Three frequently employed flexible functional forms are the generalized Leontief (Diewert 1971), the transcendental logarithmic (Christensen et a i 1971) and the quadratic function. These forms are related in that the transcendental logarithmic (translog) is quadratic in logarithms of all variables and the generalized Leontief is quadratic in square roots of exogenous variables. For the sake of brevity only the translog and quadratic functional forms wi l l be considered here. Denny (1974), Diewert (1974), Woodland (1976) and Berndt and Khaled (1979) all provide examples of a number of functional forms and discuss the relationships between them. Denny (1974) and Woodland (1976) consider the superiority of flexible functional forms over simpler Cobb-Douglas, Leontief and constant elasticity of substitution forms in terms of their ability to represent a wide range of technologies and substitution possibilities. The translog functional form was introduced by Christensen et a i (1971), expanded in Christensen et a i (1973) and further discussed by Diewert (1974). The form is quadratic in logarithms: lnti(p;v) = tv 0 + Scamp i + 1/2 XX ^ l n p j l n P h + X X fiylnpjlnVj + S f y l nV j + 1/2 X X <pj<lnVjlnvk Where: y^, = y h i <l>jk = 4>kj (4) This form has perhaps been the most frequently employed in 26 recent applied studies. Berndt and Wood (1975) estimated a translog cost function and derived demand equations for the manufacturing industry in the United States. Common to many of these analyses the paper concentrates on a particular input demand equation, in this case, derived demand for energy. Berndt and Christensen (1973) used a translog production function to analyse the substitution possibilities of equipment, structures, and labour in United States manufacturing. Kohli (1978) developed a translog GNP function for Canada with domestic input and import prices and dutput for domestic production and export prices as arguments. By differentiating the GNP function with respect to prices and estimating the system, derived demand for imports and supply of exports were investigated. Finally Wills (1979) estimated a dual cost function for the United States primary metals Industry in order to study the degree of technical change in the sector. Lau (1974) f i rst proposed the use of the quadratic form as a normalized profit function. The normalized quadratic profit function is shown below: TTlp'iV) m OCQ + SarjPi' + 1/2 X £ r^Pj' Ph" + ESS J JP J 'VJ Where: r f ( p ; v ] = TT(p ' ;v] Pi p* - P/Pi = ?b = * J bp (5) 27 Examples of empirical work based on the normalized restricted profit function are Muller (1979), Shumway (1983) and Swamy and Binswanger (1983). 3.3 Model Specification The translog functional form (4) was arbitrarily chosen to represent production technology in the Canadian pulp and paper industry. The final specification is given below: ln7T[p';v]' • oc0 + X CVJ lnpj' + 1/2 X X fh Inp/ lnp h ' + X X lnpj' lnVj + X Pj InVj + 1/2 £ X d)j< InVj lnv k Where: fh = y w TT'(p';v) = normalized restricted profit Pj' = normalized prices of fibre, energy, labour, market pulp, newsprint and 'other paper and paperboard' (B.C., outputs of market pulp and total paper/paperboard). v i = capital stocks and year (time trend variable) Note: Profits and prices normalized by the price of market pulp. (6) The symmetry conditions stated in (4), y h = y h i , 6g = 5jj > and 28 ^jk = ^kj w e r e directly imposed on the model. Normalization of the translog function is achieved by dividing variable quantity prices in the profit function and the net supply equations by any input or output price, in this case, the price of pulp. By normalizing, a number of the variables in the system, namely the pulp prices, are lost from each equation and the number of parameters to be estimated is reduced11. If we assume homogeneity of degree one in pf then the lost estimates can be recovered from the remaining equation system from the following: (1) Sa, - 1 (ii) - 0 for i - 1, , I (iii) £ $ j j = 0 for j = 1, J (Diewert 1974) (7) Using Hotelling's Lemma (3) a system of end product supply and derived demand equations can be obtained by taking first partial derivatives of the profit function with respect to the relevant output and input prices. The analogy of this result for the translog function is a set of profit share equations derived in the following way: glnTT'(p'v) = aTf(p';v) Pj = XjPj = 5j 6W 5PiTT'(p';v) TT'(p';v) Where: S, = share of profits attributed to net supply i Thus: (8) 29 (9) Input profit shares are constrained to be negative and output shares positive. This leads to the following result: Since the share equations sum to one they cannot be jointly estimated and thus one equation must be dropped from the system. Once the reduced system is econometrlcally estimated it can be used to derive the parameters of the omitted share equation (Diewert 1974). Utilizing Zellner's iterative SURE procedure gives parameter estimates that are invariant to the share equation dropped from the system (Berndt and Christensen 1973). In this study, the market pulp share was arbitrarily chosen to be omitted. Own and cross price elasticities of supply or demand are derived from share equations. The own price elasticity is defined as: SS, - 1 (10) Ii + Sj - 1 (12) Cross price elasticities are defined as: (13) 30 Having specified and estimated the above model for British Columbia, Ontario and Quebec it was decided to test the sensitivity of the model to functional form. By estimating a normalized restricted quadratic profit function (5) with the same variables as the translog model (6), it was possible to compare elasticities with (6) and with the results of Muller (1980, 1981). In the case of the quadratic, symmetry conditions are imposed as in the translog, but linear homogeneity is imposed through normalization with the price of market pulp. The quadratic function estimated is (5). Again, the profit function (5), using Hotel lings' Lemma (3) can be differentiated with respect to Input and output prices in order to obtain a system of net supply functions: u, = 5TT'(P';V) (13) The derivative of the profit function with respect to the price used to normalize (In this case the net market pulp price) is non-linear and thus must be dropped from the system. The own and cross price elasticities of net supply are defined as: S||= * i i Pi and: (14) 31 e U - * u Pj Where: i * j (15) Estimations of the translog and quadratic models were carried out for each region and both with and without the profit functions in the equation system. The large number of parameters in the profit function, given a limited data time series, forced omission of a small number of variables in each case. Detailed estimation results for the translog model are presented in Appendix B. These results and calculated elasticities are discussed in Chapter 5. 3.4 Estimation Procedure The equation systems described in the previous section were all estimated using the iterative Seemingly Unrelated Regression Equations (SURE) procedure developed by Zellner (1962). The SURE method involves estimating each equation in the system separately by OLS and using the vectors of residuals to construct an estimator of the residual variance -covariance matrix of the system. This matrix is then substituted into the Generalized Least Squares (GLS) estimator of the equation system. The Zellner method is based on the premise that there is correlation between residuals of different equations in the system. The efficiency gain achieved from using the Zellner method over OLS increases as the degree of between equation residual correlation increases (Johnston, 1984). 32 Intuitively one might expect the share equation systems estimated in this study to exhibit between equation residual correlation if there is some degree specification error. Since this is distinctly likely, the method used should result in more efficient parameter estimators. Gains in efficiency are also achieved using this system as a result of across equation symmetry restrictions which reduce the number of parameters to be estimated (Doran and Williams 1982). By iterating the SURE procedure parameter estimates converge to the Maximum Likelihood (ML) estimates which are invariant to the choice of share equation dropped from the system (Berndt and Christensen, 1973). The iteration process involves recomputing the variance-covariance matrix of residuals after each iteration for use in the following GLS parameter estimation. The iterative SURE procedure (SYSTEM command) in the SHAZAM program (White 1978) was employed for all estimations. 33 CHAPTER 4 DATA 41 Data Specification In this section the data used in the study are described in detail. Regional data on the pulp and paper sector are significantly inferior to national data. In some cases where regional data were not obtainable national data were used. The time series extended from 1950 to 1981 and data were obtained for British Columbia, Ontario and Quebec. Fibre input price and quantity data were obtained from Statistics Canada's annual Census of Manufacturers (Pulp and Paper Mills, Catalogue 36-204). Implicit prices were obtained by dividing the total value of a particular fibre input by the quantity purchased. Fibre input price was taken as the mean implicit price of roundwood (softwood and hardwood) and wood residue weighted by the quantity used and measured in dollars per cubic meter. Fibre quantity was taken as the sum of total roundwood and wood residue used, measured in cubic meters. Electricity prices and quantities were obtainable for each region in the desired time series. Regional data on other energy forms were not available for the bulk of the period under study. It was subsequently decided to use data on purchased electricity as a proxy for all energy inputs. Implicit price and quantity data were reported regional for pulp and paper mills in the Census of Manufacturers from the following Statistics Canada Catalogues: 1950-61 - Electric Power Statistics Vol. II, 57-202, Annual. 34 1962-74 - Consumption of Purchased Fuel and Electricity by the Manufacturing, Mining and Electric Power Industries, 57-506, Occasional. 1975-81 - Consumption of Purchased Fuel and Electricity by the Manufacturing, Mining, Logging and Electric Power Industries 57-208, Annual. Labour input data were obtained from the Census of Manufacturers, Statistics Canada Catalogue 36-204. The number and total wage bill of 'Production and Related Workers' were used to obtain implicit prices and quantities. Regional capital stock data were obtained from Statistics Canada, Vancouver. These data were split into construction and 'machinery and equipment'. For the purposes of this study the total mid year net stock was considered most suitable. The time period for these data was 1955-1981. National capital stock data for the pulp and paper industry are reported in Fixed Capital Flows and Stocks, Statistics Canada Catalogue 13-563 from 1936-1983. By calculating the percentage of the national capital stock in each region for the period 1955-1960 it was ascertained that regional variations in the national stock were minimal. In order to extend the data to 1950, the mean regional percentage of national capital stock was obtained for the above time period. By multiplying this mean percentage by the national capital stocks for 1950-1954, estimates of regional stocks were obtained and subsequently used. Newsprint and other "paper and paperboard' production and implicit price data for Ontario and Quebec were easily obtained from the 35 Census of Manufacturers, Pulp and Paper Mills Catalogue 36-204 Production quantity and value data are only reported up to 1961 and so implicit prices were obtained from value and quantity of shipments data in the usual way. Production quantities were used. The difference between production and shipments of the industry is the change in inventories in the year in question. For British Columbia only total paper and paperboard data were available and thus this aggregation was employed in the British Columbia model. The greatest difficulty was encountered in attempting to obtain market pulp output time series. Census of Manufacturing, Pulp and Paper Mills Catalogue 36-204 gives regional pulp produced and pulp used data from 1958-1982 for Ontario and Quebec. Since much of the pulp produced is used within the province in manufacture of newsprint and other paper products, to use this data would result in considerable double counting. Pulp produced less pulp used gives a measure of net exports of market pulp from the region. Unfortunately only chemical pulp used is reported for British Columbia and so total pulp production less chemical pulp used was employed in this region. Total national exports of market pulp are reported in Statistics Canada Catalogue 36-204 for the period 1950-1962. In order to extend the regional pulp output data to 1950 the regional pulp produced less pulp used percentage of national exports was calculated for the period 1958-1962. Again the mean percentage multiplied by the national exports for 1950-1957 gave a simple estimate of regional net exports for the period. Implicit pulp price data could not be computed from the Census of Manufacturers since values of pulp output were not reported. Regional 36 implicit export prices for pulp were obtained from purchased Statistics Canada data for the period 1966-1981. Common implicit prices calculated from the national export data referred to above were used for the period 1950-1962. For prices in the period 1963-1965 a national industry price index from Industry Price Indices, Statistics Canada Catalogue number 62-011 was used. 4 2 Data Problems Obtaining data on inputs into the pulp and paper manufacturing industry presented problems. The required time series and regional breakdown in energy inputs were only available for purchased electricity. This information fails to represent the true cost of energy since other purchased energy sources' 2 are ignored and since much of the energy consumed is internally generated. Energy generated from within the pulping process became particularly important in the 1970's after the rise in oil prices. The correct treatment of such an input requires detailed information about the opportunity cost of using waste liquor as an energy source, and whether the energy generated could readily be transfered to local grid systems. This Information is not readily available over the time period in question. Chemicals have represented approximately 10 percent of total national pulp and paper input costs over the past 30 years. Unfortunately Statistics Canada only reports quantity and value data on these on a national basis and hence they could not legitimately be included here. 37 Materials and supplies used other than fibre input and chemicals presently represent slightly less than 20 percent of total manufacturing costs. Due to the diverse nature of these materials and supplies and the lack of data recorded for these, price and quantity indices could not be developed and again they were omitted from the model. Regional capital stock was estimated for the period 1950 to 1954, though due to the stability of this series it is unlikely to be a significant source of error. Problems with output data focussed on one product, market pulp and one region, British Columbia. Regional net market pulp quantities were estimated for the period 1950-1957 as described in the previous section. A potential source of data error is evident in the market pulp price series employed in the estimations. As described in the previous section the data used were constructed from three different price series. British Columbia output data problems focussed on the aggregation of newsprint and 'other paper and paperboard' into 'total paper and paperboard". As a result of this a two output model was run for British Columbia, thus reducing its usefulness and causing difficulties in regional comparisons. Adding to the market pulp problems discussed above, for British Columbia only chemical pulp used data was available and thus the quantity of market pulp produced in this region was overstated. Again this increases estimation biases in the model and reduces the potential for comparing this region with others in the present study, and for comparisons with other studies. 38 CHAPTER 5. ANALYSIS OF RESULTS 5.1 Estimation Results Tables 9, 10 and 11 show price elasticity estimates at the mean of the data for each model in British Columbia, Ontario and Quebec. Table 9. Price Elasticity Estimates for British Columbia Equation Variable Translogft Translog8 Quadratic0 Quadratic1 FIBRE fibre - 0 . 7 4 - 0 . 3 6 - 0 . 2 3 * 0 . 0 3 energy - 0 . 0 1 0 . 0 5 0 . 0 2 0 . 0 4 * labour 0 . 0 9 - 0 . 2 7 0 . 1 0 * 0 . 1 4 mlct. pulp 0 . 2 9 0 . 0 9 tot . paper 0 . 3 7 1.44 - 0 . 0 6 0 . 3 4 * ENERGY energy 0.01 - 0 . 2 7 - 0 . 6 2 * - 0 . 6 5 * fibre - 0 . 1 1 - 0 . 6 4 0 . 1 7 0 . 4 0 * labour 0 . 8 0 0 . 2 2 - 0 . 1 0 0 . 1 5 mkt. pulp 0 . 5 0 0 . 3 2 tot. paper 1 .20 0 . 3 7 - 0 . 0 2 0 . 3 2 LABOUR labour - 0 . 2 3 - 0 . 9 3 0 . 1 8 " - 0 . 0 1 fibre 0 . 1 4 - 0 . 4 4 0 . 1 9 * 0 . 2 8 * energy 0 . 1 0 0 . 0 3 - 0 . 0 2 0 . 0 3 mkt. pulp 0 . 3 0 0.31 tot . paper - 0 . 3 1 1 .03 - 0 . 1 1 0 . 1 3 rflCT. PULP m k t . pulp - 0 . 1 0 - 0 . 1 8 fibre - 0 . 1 0 - 0 . 0 4 energy - 0 . 0 1 - 0 . 0 1 labour - 0 . 0 6 - 0 . 0 8 tot. paper 0 . 2 8 0.31 TOT. PAPER tot .paper - 0 . 4 5 0 . 8 0 - 0 . 1 1 0 . 0 3 fibre - 0 . 2 2 - 0 . 8 3 - 0 . 0 4 0 . 2 3 * energy 0 . 0 6 - 0 . 0 2 >-0.01 0 . 0 2 labour - 0 . 0 4 - 0 . 3 7 - 0 . 0 4 - 0 . 0 5 m k t . pulp 0 . 5 0 0.41 B ft= full model,B = reduced model (without profit function), * = significant at five percent with infinite degrees of freedom. Note: see Appendix B for translog coefficient t values. 39 Table 10. Price Elasticity Estimates for Ontario Equation Variable Translog0 Translog8 Quadratic0 Quadratic' FIBRE f i b r e - 0 . 7 3 - 0 . 8 5 - 0 . 7 4 * - 0 . 4 7 * energy <0.01 0.01 0.01 0 . 0 2 labour 0 . 0 8 0 . 0 8 - 0 . 0 2 0 . 1 5 * mkt. pulp 0 . 1 9 0 . 2 5 newsprint 0 . 4 6 0 . 4 9 < 0 . 0 1 * 0 . 1 8 * other paper/bd. - 0 . 0 1 0 . 0 5 1 . 0 3 * 0.21 ENERGY energy - 0 . 6 7 - 0 . 4 5 <0.01 - 0 . 2 9 * fibre 0 . 0 3 - 0 . 0 8 0 . 0 5 0 . 1 4 labour 0 . 2 8 0 . 2 5 - 0 . 0 6 0 . 1 2 mkt. pulp - 0 . 0 6 - 0 . 0 1 newsprint 0 . 3 3 0 . 4 3 0 . 0 8 0 . 4 3 * other paper/bd. - 0 . 0 9 - 0 . 1 4 0 . 1 3 - 0 . 3 3 LABOUR labour - 0 . 4 7 - 1 . 0 5 - 0 . 3 2 * - 0 . 2 9 * fibre 0 . 1 0 0.11 - 0 . 0 3 - 0 . 2 0 * energy 0 . 0 5 0 . 0 5 - 0 . 0 1 0 . 0 2 mkt. pulp 0 . 0 6 0 . 0 9 newsprint - 0 . 0 6 0 . 1 9 - 0 . 3 9 * - 0 . 1 7 * other paper/bd. 0 . 3 4 0 . 2 6 0 . 9 2 * 0 . 3 1 * M K T . P U L P mkt. pulp - 0 . 0 8 0 . 0 2 fibre - 0 . 2 3 - 0 . 3 1 energy 0 . 1 0 <0.01 labour - 0 . 0 5 - 0 . 0 8 n e w s p r i n t - 0 . 0 6 - 0 . 0 5 other paper/bd. 0 . 4 3 0.41 NEWSPRINT newsprint - 0 . 2 7 - 0 . 1 0 - 0 . 6 2 " - 0 . 3 5 * fibre - 0 . 2 8 - 0 . 3 1 < 0 . 0 1 * 0 . 1 1 * energy - 0 . 0 3 - 0 . 0 4 0.01 0 . 0 4 * labour 0 . 0 3 - 0 . 9 0 - 0 . 1 8 * - 0 . 0 8 * mkt. pulp - 0 . 0 3 - 0 . 0 2 other paper/bd. - 0 . 5 9 0 . 9 8 1 . 1 8 * 0 . 4 5 * OTHER P A P E R / o t h e r paper/bd. - 0 . 6 5 - 0 . 6 1 - 2 . 2 5 * - 0 . 9 8 * BD. fibre - 0 . 0 1 - 0 . 0 3 0 . 6 0 * 0 . 1 2 energy 0.01 0.01 0.01 - 0 . 0 3 labour - 0 . 1 7 - 0 . 1 2 0 . 4 0 * 0 . 1 4 * mkt. pulp 0 . 2 2 0.21 newsprint 0.61 0 . 9 6 1 . 0 8 * 0 . 4 3 * fi,B," = See Table 9 40 Table 11. Price Elasticity Estimates for Quebec Equation Variable Translog0 Translog8 Quadratic0 Quadratic1 FIBRE fibre - 1 . 8 4 - 0 . 9 4 - 0 . 6 4 " - 0 . 5 6 * energy 0 . 0 6 0 . 0 4 0 . 0 4 0 . 0 3 labour - 0 . 1 6 - 0 . 2 5 0 . 0 2 0 . 0 6 mkt. pulp 0.61 0 . 8 2 newsprint 0 . 8 2 0 . 6 3 < 0 . 0 1 * 0 . 2 2 other paper/bd. - 0 . 2 1 - 0 . 0 1 0 . 3 9 * 0 . 0 4 ENERGY energy - 0 . 8 9 - 1 . 0 4 <0.01 - 0 . 7 3 * fibre 0 . 2 3 0 . 2 5 0.21 0 . 2 0 labour - 0 . 4 2 - 0 . 9 1 - 0 . 2 0 - 0 . 0 5 mkt. pulp - 0 . 4 2 - 0 . 4 0 newsprint 1 .46 1.91 0 . 9 1 * 0 . 6 4 * other paper/bd. 0 . 0 2 0 . 1 9 - 0 . 9 0 * 0 . 1 6 LABOUR labour - 0 . 4 7 - 0 . 4 9 - 0 . 3 1 * - 0 . 2 6 * fibre - 0 . 1 7 - 0 . 3 2 0 . 0 3 0.91 energy - 0 . 1 1 - 0 . 1 8 - 0 . 0 5 - 0 . 0 1 m k t . pulp - 0 . 1 0 - 0 . 0 1 newsprint 0 . 6 4 0 . 6 7 0 . 1 8 0 . 2 0 * other paper/bd. 0 . 1 9 0 . 3 2 0 . 0 9 - 0 . 0 8 M K T . P U L P mkLpulp - 0 . 4 4 - 0 . 0 8 fibre - 0 . 9 4 -1 .17 energy 0 . 1 6 0 . 1 4 labour 0 . 1 5 0.01 newsprint 0 . 6 9 0 . 7 2 other paper/bd. 0 . 3 6 0 . 3 9 NEWSPRINT newsprint 0 . 5 0 0 . 4 5 - 0 . 3 4 * - 0 . 3 3 * fibre - 0 . 3 4 - 0 . 2 7 < 0 . 0 1 * 0 . 1 0 energy - 0 . 1 5 - 0 . 1 3 0 . 0 8 * 0 . 0 5 * labour - 0 . 2 6 - 0 . 2 3 0 . 0 6 0 . 0 6 * mkt. pulp 0 . 1 9 0 . 1 4 other paper/bd. - 0 . 3 3 - 0 . 3 6 0 . 1 0 - 0 . 0 2 OTHER PAPER/ other paper/bd. - 0 . 3 3 - 0 . 3 6 - 0 . 6 0 * - 0 . 5 4 * BD. fibre 0 . 1 8 0.01 0 . 3 7 * 0 . 0 4 energy - 0 . 0 1 - 0 . 0 4 - 0 . 1 5 * 0 . 0 3 labour - 0 . 1 5 - 0 . 2 9 0 . 0 6 - 0 . 0 5 mkt. pulp 0 . 2 0 0.21 newsprint 0 . 0 8 0 . 4 7 0 . 2 0 - 0 . 0 4 41 Full estimation results for the translog model are given in appendix B. Net supply price elasticities are presented in this section and discussed in section 5.2. For the restricted profit function to be dually related to the underlying transformation function it must satisfy the properties of symmetry, homogeneity of degree one in prices, monotonicity and convexity in prices. Symmetry conditions are directly imposed on the model by restricting the relevant parameters in the equation system to be equal. Linear homogeneity is directly imposed in the quadratic model through normalization and implicitly imposed on the translog model in calculating the missing parameters (from (7)]. Monotonicity requires that the profit function be increasing in output prices and decreasing in input prices. Practically, this can be tested by ascertaining whether the first partial derivatives of the function, the predicted shares in the translog, are positive at all data points for outputs and negative at all data points for Inputs. This condition is satisfied for all translog models estimated. Profit maximization behaviour in the Industry implies the profit function is convex in variable quantity prices. A sufficient condition for convexity is that the matrix of second order partial derivatives of the profit function with respect to variable prices, the Hessian matrix, is positive definite. The Hessian matrix [H] is written in terms of coefficients and shares of the estimated equations as: yn + S A - U y ^ + ^ S s ^ffi+^Se 42 y 2 1 + S 2 S 1 y22 + 52<52- 1) *26 + S2S 6 IH]- : ^ 6 i + S 6 S , y 6 2 + S 6 S 2 y 6 6 + S 6 ( S 6 - 1 ) (16) Gordon (1984) By calculating eigenvalues of the Hessian at the mean of the data the positive definiteness can be tested. For the matrix to be positive definite all eigenvalues must be greater than zero. For each translog model estimated eigenvalues were not all positive and thus the convexity condition was violated. 5.2 Discussion of Results In this section the results summarized in the previous section and presented in more detail in appendix B are f irst discussed fully on a regional basis. Finally a more general discussion of regional differences and comparisons to other studies is given in summary to the discussion section. Estimation results for British Columbia are discussed first. 5.2.1 British Columbia Share equations of the translog model in this region had poor predictive results with very low adjusted R2 's in both the model with and without the profit function. Significance of price coefficients in many of the share equations was also low. Own price elasticities for labour and 43 fibre in both models were negative with magnitudes of around 0.5. The energy own price elasticity was negative in the reduced model and just positive in the full model. Own price elasticities for 'al l paper and paperboard' and pulp were not consistent with a priori expectations as only the all paper category in the reduced model had a positive sign. The quadratic models for British Columbia had high R2 's and generally highly significant parameter estimates in net supply equations. Only the energy derived demand equation had expected signs on elasticities for both the full and reduced model. Cross price elasticity estimates in all models were low as might be expected due to relatively rigid short run production substitution possibilities in the industry. Cross price elasticities for pulp in the paper equation and visa versa were positive suggesting these outputs may be complements in production. Input cross price elasticities In derived demand functions were commonly positive and low which is consistent with a small degree of substitutability amongst inputs. In most cases cross price elasticity estimates suggest that as output commodity prices rise the consumption of inputs rises. Consistently negative input cross price elasticities In supply equations show that input price changes have small negative effects on production levels. 5.2.2 Ontario The translog models in Ontario offer plausible results on the derived demand side but again supply equation estimations are contrary to 44 a priori expectations. Both the full and reduced model share equations have good explanatory power and consistently significant coefficient estimates. Only three of 50 variables in these equations were not significant at the five percent level with infinite degrees of freedom. Own price elasticities for fibre, energy and labour were all negative in both the full and reduced models and ranged from about -0.5 to -1.0. End product supply equations showed unexpected negative signs for both models in newsprint and 'other paper and paperboard' while in the reduced pulp model a very low positive elasticity estimate was obtained. Most cross price elasticities were small and similar in sign to those obtained for British Columbia. Net supply equations of the quadratic model again tended to have high FPs with two notable exceptions in the full model. Significance levels were quite high with 31 out of 50 elasticities being significant at the five percent level. Derived demand own price elasticities were all negative except in the energy equation of the full model which was zero. Again, as with the translog, end product supply own price elasticities were negative. 5.2.3 Quebec Net supply equations in the full and reduced translog model gave signs expected a priori on own price elasticities for fibre, energy, labour and newsprint. Newsprint price elasticity estimates were about 0.5 for the full model and 0.45 for the reduced model. Own price elasticities for 45 the other two outputs were negative in both models. With a few notable exceptions, R 2 values for share equations were quite high and over 70 percent of parameter estimates were significant at the five percent level. Considerable stability in elasticities between the full and reduced model was evident with the same signs for each variable In each equation. The quadratic gave similar results to the translog with notable exceptions being a zero own price elasticity estimate in the full model and negative newsprint own price elasticities. Again R^s tended to be high and approximately half of the estimated coefficients were significant at the five percent level. 5.2.4 Summary and Comparison With Other Studies Certain trends run through the regions considered in this study. Generally, own price elasticities of derived demand were found to be negative and usually of magnitude between 0.5 and 1.0. Thus we can postulate that in each region, and for each of the major inputs, quantities consumed in the production process are responsive, in the short run, to input prices. From the translog model fibre demand appears, on average, to be slightly more price elastic than energy and labour demand. Another feature of the model estimations common to all regions is the high frequency of negative signs on own price in end product supply functions. This result causes a violation of the convexity condition on the restricted profit function which is a serious weakness of the model. 46 There are a number of possible explanations for this result: 1. There may be a time lag before producers are able to react fully to output price changes. If this is the case, and it seems quite likely given the relatively fixed nature of pulp and paper production processes, that the positive relationship expected between output price and quantity w i l l not be captured in the present model; 2. There may be a problem of specification bias. For example, if a variable that significantly affects supply is left out of the model, then changes in this variable could override the effects of price changes on output levels. Thus the positive relationship expected between price and quantity in supply equations could be masked as a result of specification bias; 3. Data inaccuracies could be the cause of the incongruous results; 4. Simultaneous equations bias could potentially create problems. Al l supply and demand equations in the system have common independent variables and thus it is not clear whether a supply or demand function has been estimated. This identification problem could lead to biased estimates of the model's parameters; and 5. If the end product markets are not perfectly competitive then a measurable market supply function does not exist and thus cannot be estimated. Given the body of literature supporting this hypothesis the absence of price-taking behaviour in the industry is a likely explanation of the results obtained. 47 Good comparisons can be made between the results reported here and a study by Muller (1980). As described in Chapter 2, Muller estimates a regional normalized quadratic restricted profit function with materials and supplies, energy and labour as variable inputs and woodpulp and newsprint as variable outputs. Capital and 'other paper and paperboard' are considered fixed and included in the model. Muller estimated the full and reduced version of the equation system for British Columbia, the full model for Canada as a whole and the reduced model for Ontario and Quebec. Expected signs on own price elasticities were only obtained in all models for the energy input. Labour own price elasticities were positive in both British Columbia models. Newsprint own price elasticities were positive in all but the Quebec case while woodpulp output was positively related to price only in the Canada and British Columbia models. Muller's research differed from the present study in terms of certain data assumptions, input categories chosen, the specification of variables as fixed or variable and the time period used. Given these differences there appear to be many similarities in the results. End product supply equations in particular gave unexpected results in both cases for most regions while derived demand equations in both studies were more successful. Derived demand elasticity estimates showed considerable similarity to notable past studies of Buongiorno and Gilless (1980), Buongiorno et al- (1983), Sherif (1983), Singh and Nautiyal (1984), and Martinello (1985). All of the above studies used cost functions with various functional forms to estimate derived demands in the sector. As 48 noted in the literature review, each obtained expected signs and magnitudes similar to those estimated here on own price elasticities in demand equations. 49 CHAPTER 6. CONCLUSIONS AND SUGGESTIONS FOR FURTHER RESEARCH As discussed in the statement of purpose, the aim of this study was to develop and evaluate regional end product supply functions and derived demand functions for possible incorporation into an existing North American pulp and paper spatial equilibrium market model. From the previous chapter it is clear that certain major reservations must be expressed about using elasticities from these estimations in such a model. In many cases negative end product supply own price elasticities were obtained. This result is contrary to a priori expectations and since no theoretical justification can be postulated for "wrong' signs, the supply functions estimated should not be incorporated in larger models. Negative own price elasticities of supply result in violation of the convexity condition which is required for the profit function to be dually related to the production possibilities set (Diewert 1974). The frequency of estimated downward sloping supply functions in the present study raises questions about the competitiveness of markets in the pulp and paper sector. As discussed in the literature review, various authors (eg. Guthrie 1972, Dagenais 1976 and Rich 1978) contend that North American pulp and paper producers are not price-takers but operate as an oligopoly. The problems encountered here and by Muller (1980) in obtaining 'right' signs on supply functions could be due to the lack of a competitive market. Derived demand equations generally offered plausible results. Use of these results is, however, not advised since estimates w i l l 50 undoubtedly be biased by the poor supply results. Cost function estimates, in preliminary investigations give low, negative and significant own price elasticity estimates. Further studies on these lines could yield a model capable of dealing with policy questions relating to the impacts of input price changes on demands for fibre, energy and labour. Further research could be aimed at evaluating possible causes of the negative supply elasticities in the present study. A simple partial adjustment model could be developed in order to ascertain whether a lag in producer's reaction time is important. Further work on identifying data problems and missing variables should also be considered. A test for price-taking behaviour described by Applebaum (1979) could be applied to the present study in order to provide evidence of market structure and thus gain a further insight into an appropriate model of supply in the industry. Finally, if the competitive model is rejected, on the basis of the investigations described above, then consideration could be given to various oligopolistic pricing models. 51 FOOTNOTES 1. The model is briefly described in section 2.3 of the literature review. 2. Since the quantity of pulp used to make a tonne of paper/board varies by grade, no firm conclusion can be drawn from the data in Table 3. However, this variation is not substantial and thus the bias towards market market pulp production in British Columbia is clearly implied. 3. In all cases in the text real prices are nominal prices deflated by the GNP deflator. 4 Ontario electricity prices have risen above British Columbia and Quebec prices since electricity generation in this province is based more on thermal sources (oil and coal) whereas hydro power provides the bulk of the electricity in the latter provinces. 5. O.E.C.D. is the Organization for Economic Cooperation and Development of which there are eighteen member countries including the most of the major Western economies. 6. For discussion see section 5.2. 7. Samuel son (1952) developed the concept of 'net social payoff. 8. See Section 1.2, Chapter 1 for discussion. 9. For discussion see Theil (1971). 10. See Pope (1982) for discussion of Minkowski's theorem. 11. Hence increasing the efficiency of estimation. 12. See Table 4, Section 1.2 for detailed regional energy type consumption figures. LITERATURE CITED 5 3 LITERATURE CITED Applebaum, E. 1979. T e s t i n g P r i c e Taking Behaviour. 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Econometrica. 1 : 2 3 9 - 2 4 0 . 5 9 W i l l s , J . 1979. T e c h n i c a l Change i n the U.S. P r i m a r y Metals Industry. Journal of Econometrics 1 0 : 8 5 - 9 8 . Woodland, A.D. 1976. Modelling the Production S e c t o r of an Economy: A S e l e c t i v e Survey and A n a l y s i s . U n i v e r s i t y of B r i t i s h Columbia D i s c u s s i o n Paper No. 7 6 - 2 1 . Zellner, A. 1962. An E f f i c i e n t Method of E s t i m a t i n g Seemingly Unrelated Regressions and T e s t s f o r Aggregation B i a s . Journal of the American S t a t i s t i c a l A s s o c i a t i o n . 5 7 : 3 4 8 - 3 6 8 . 50 APPENDIX A . . DATA T a b l e A . l . B r i t i s h Columbia Data a o a. o u Q. 3 _ o. K> <D E o O O fO O o CA (A to _. o CO CO to o CO (Si _. o o f> o O eo to (SJ . 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( s j t o o o t o o c » i o i n — o i D i ^ - ' d - o o t o t r i n - — — » » a o m i © t o o o t O f O ( s i c n t o f > * - ( s j — r>r>io o « - « - — e n o o c n o o r « . t > i > . t s . i o i o c v . o o o o r v o o o > o o o — i n i o i n « - < o i n o o £> «<• — — — — — — — — — — — — — (SJ(\J iZ « o — ( s i t o ^ i n o r > o o c n o — ( s i t o « - i n i o i > ( o c n o — ( s i t o ' T i o f ^ o o c n o — S l / l l / l m l n l O l n l n l n l o u ^ l f l l O l O l O l O l O l O l O l O l 0 ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ o o o v~ cn cn cn cn cn cn cn cn cn o> cn cn cn cn cn cn cn cn cn cn cn cn cn on cn cn cn cn cn cn Y e a r F i b r e p r . F i b r e q u . E n e r g y p r $ / m 3 m 3 S/000 kwh 1950 1 0 . 1 3 7182120 3 . 0 2 1951 1 1 . 8 2 7 7 6 8 9 1 0 3 . 1 6 1952 1 2 . 5 1 6 9 6 7 4 4 0 3 . 1 7 1953 1 2 . 6 2 7 0 8 6 7 7 0 3 . 2 6 1954 1 2 . 0 4 7 3 8 8 Z 4 0 4 . 1 0 1955 1 1 . 5 5 7 9 7 0 1 5 0 4 . 3 4 1956 1 1 . 9 5 8 3 8 7 3 3 0 4 . 8 2 1957 1 2 . 6 6 8 4 3 6 9 6 0 4 . 8 6 1958 1 3 . 0 8 8177110 4 . 7 7 1959 1 2 . 9 6 8 3 0 5 2 9 0 4 . 5 5 1960 1 2 . 3 1 8 9 5 3 3 6 0 4 . 7 4 1961 1 2 . 5 4 8 9 3 2 7 9 0 5 . 0 9 1962 1 2 . 3 9 9 3 1 5 9 1 0 5 . 4 9 1963 1 2 . 3 9 9 3 6 7 5 7 0 5 . 1 9 1964 1 2 . 1 0 9 8 9 5 2 9 0 5 . 1 7 1965 1 2 . 2 9 9 8 1 4 4 0 0 5 . 2 3 1966 1 2 . 7 3 10697440 5 . 1 6 1967 1 2 . 0 4 12305880 5 . 3 6 1968 1 3 . 9 8 11057320 5 . 3 8 1969 1 4 . 1 2 11972420 5 . 9 5 1970 1 6 . 8 1 10263110 6 . 8 0 1971 1 7 . 5 1 9 7 9 1 7 4 0 7 . 4 8 1972 1 7 . 3 7 10346450 7 . 3 0 1973 1 8 . 0 6 10486980 8 . 3 5 1974 2 1 . 0 8 11204560 8 . 7 4 1976 2 3 . 4 3 11472000 1 2 . 2 3 1977 2 4 . 7 0 13820000 1 6 . 0 9 1978 2 6 . 3 3 14544000 16.11 1979 2 8 . 4 5 15299000 1 7 . 9 7 1980 3 0 . 3 8 15872000 2 0 . 0 2 1981 3 4 . 6 1 15735000 2 1 . 8 8 n e r g y q u J _ a b o u r p r . l a b o u r q u . N e w s p r 000 k w h 000 $/W n o . w * 0 0 0 $/(1T / y e a r 1851000 3 . 0 3 14003000 1 0 6 . 3 0 2 0 6 1 0 0 0 3 . 5 2 15196000 1 1 4 . 0 0 2 0 5 7 0 0 0 3 . 5 4 15675000 1 1 6 . 4 0 2 1 6 9 0 0 0 3 . 7 3 15547000 1 2 2 . 6 0 2111000 3 . 7 8 15950000 1 2 1 . 3 0 2173000 4 . 0 5 15796000 1 2 4 . 0 0 2120000 4 . 1 6 16835000 1 2 7 . 0 0 2 4 3 4 0 0 0 4 . 3 3 16976000 1 2 7 . 5 0 2 6 7 6 0 0 0 4 . 4 5 16551000 1 2 7 . 5 0 3 0 0 8 0 0 0 4 . 5 0 16753000 1 2 6 . 9 0 3 1 3 7 0 0 0 4 . 8 5 16615000 1 3 1 . 6 0 3 1 4 2 0 0 0 5 . 0 1 16416000 1 3 2 . 0 0 3154000 5 . 1 9 16358000 1 3 8 . 7 0 3 4 3 3 0 0 0 5 . 3 0 16609000 1 3 9 . 4 0 3 6 5 9 0 0 0 5 . 4 5 17162000 1 3 7 . 4 0 3 7 5 6 0 0 0 5 . 6 4 17365000 1 3 7 . 2 0 4 0 5 6 0 0 0 6 . 2 4 17945000 1 4 0 . 2 0 3 9 2 6 0 0 0 6 . 5 2 17830000 1 4 3 . 8 0 4 0 5 4 0 0 0 7 . 0 1 17537000 1 4 7 . 9 0 4 2 8 6 0 0 0 7 . 5 7 17936000 1 4 7 . 8 0 4 2 1 5 0 0 0 8 . 0 3 17832000 1 4 5 . 6 0 4 2 4 3 0 0 0 8 . 4 4 17132000 1 5 1 . 0 0 4 5 9 2 0 0 0 9 . 3 0 16970000 1 5 5 . 7 0 4 5 2 4 0 0 0 1 0 . 1 0 17326000 1 6 5 . 7 0 4 8 9 3 0 0 0 1 1 . 4 8 17753000 2 0 3 . 4 0 3 9 9 5 0 0 0 1 3 . 7 4 17302000 3 0 5 . 9 0 4787000 1 7 . 0 5 17329000 3 4 4 . 5 0 5 0 5 4 0 0 0 1 8 . 0 0 17797000 3 6 7 . 7 0 5118000 1 9 . 4 9 17881000 4 2 4 . 9 0 5 0 8 7 0 0 0 2 0 . 8 6 18328000 4 7 7 . 0 0 5029000 2 3 . 8 8 17879000 5 3 3 . 6 0 News q u . MT 0 . P a p e r p r 0 . P a p e r q u P u l p p r . $/MT MT $/MT P u l p q u . MT C a p i t a l s t . 000 $ 1125000 1167000 1178000 1178000 1221000 1295000 1335000 1349000 1329000 1356000 1459000 1448000 1453000 1421000 1555000 1581000 1677000 1647000 1596000 1745000 1685000 1608000 1624000 1770000 1778000 1410000 1610000 1663000 1743000 1734000 1743000 1 5 2 . 5 0 1 7 8 . 7 0 1 8 0 . 7 0 1 8 2 . 0 0 1 8 9 . 3 0 1 9 0 . 0 0 1 9 7 . 1 0 1 9 9 . 4 0 1 9 8 . 0 0 2 0 0 . 2 0 2 0 1 . 9 0 2 0 9 . 8 0 2 1 1 . 2 0 2 1 4 . 4 0 2 1 4 . 4 0 2 1 3 . 6 0 2 2 4 . 1 0 2 2 7 . 7 0 2 2 9 . 9 0 2 3 2 . 3 0 2 3 6 . 6 0 2 3 2 . 4 0 2 3 7 . 0 0 2 7 7 . 2 0 3 7 4 . 6 0 4 4 1 . 4 0 4 6 3 . 7 0 4 8 9 . 7 0 5 7 0 . 5 0 6 3 4 . 9 0 6 9 4 . 7 0 6 0 1 0 0 0 6 5 7 0 0 0 6 0 4 0 0 0 6 4 6 0 0 0 6 5 6 0 0 0 7 1 5 0 0 0 7 8 4 0 0 0 7 6 5 0 0 0 8 0 7 0 0 0 8 5 0 0 0 0 8 7 6 0 0 0 7 7 8 0 0 0 8 6 5 0 0 0 9 0 3 0 0 0 9 5 5 0 0 0 9 7 6 0 0 0 1027000 1 0 2 6 0 0 0 1 0 8 0 0 0 0 1140000 1 1 9 8 0 0 0 1 2 2 0 0 0 0 1311000 1 4 6 2 0 0 0 1 6 2 5 0 0 0 I 182000 1 4 7 6 0 0 0 1 6 5 3 0 0 0 1 8 0 9 0 0 0 1 7 8 7 0 0 0 1 8 1 9 0 0 0 1 2 5 . 0 0 1 7 9 . 0 0 1 6 6 . 0 0 1 4 1 . 0 0 1 3 7 . 0 0 1 3 9 . 0 0 1 4 1 . 0 0 1 4 1 . 0 0 1 4 2 . 0 0 1 4 0 . 0 0 1 3 8 . 0 0 1 3 3 . 0 0 1 3 4 . 0 0 1 3 3 . 0 0 1 4 0 . 0 0 1 4 7 . 0 0 1 5 0 . 0 0 1 4 9 . 0 0 1 4 5 . 0 0 1 4 9 . 0 0 1 6 1 . 0 0 1 5 9 . 0 0 1 5 2 . 0 0 1 8 8 . 0 0 3 0 3 . 0 0 3 7 0 . 0 0 3 8 4 . 0 0 3 6 7 . 0 0 4 7 0 . 0 0 5 7 7 . 0 0 6 0 3 . 0 0 4 0 4 0 0 0 4 9 1 0 0 0 4 2 4 0 0 0 4 2 6 0 0 0 4 7 7 0 0 0 5 1 7 0 0 0 5 1 9 0 0 0 4 9 9 0 0 0 4 5 6 0 0 0 4 4 0 0 0 0 6 6 3 0 0 0 6 6 7 0 0 0 6 6 9 0 0 0 6 9 8 0 0 0 7 5 1 0 0 0 6 7 7 0 0 0 7 5 4 0 0 0 7 8 8 0 0 0 8 3 4 0 0 0 9 2 0 0 0 0 9 2 9 0 0 0 8 6 8 0 0 0 9 4 4 0 0 0 8 4 4 0 0 0 8 9 6 0 0 0 7 3 3 0 0 0 9 4 4 0 0 0 9 2 8 0 0 0 9 6 5 0 0 0 1037000 1131000 191664 2 2 4 5 7 6 2 5 5 6 2 5 2 7 6 4 8 5 2 8 7 0 1 2 2 9 9 0 8 3 3 4 2 6 2 2 3 9 6 1 2 7 4 2 6 8 5 0 4 4 3 1 4 5 4 5 3 3 4 3 4 4 9 4 2 3 4 4 6 2 8 7 4 6 0 7 8 8 4 9 7 4 1 3 5 6 8 0 6 2 6 2 9 4 5 7 6 4 3 0 0 6 6 2 8 7 4 8 6 4 2 0 9 6 6 8 9 3 0 4 7 5 5 3 4 9 811341 8 5 9 4 9 4 1011246 1460365 1700807 1881779 2 0 8 1 7 6 7 2 4 0 8 2 5 3 2 9 6 6 1 1 8 Y e a r F i b r e p r . F i b r e q u . E n e r g y p r . E n e r g y q u . L a b o u r p r . L a b o u r q u . News p r $ / m 3 m 3 $ / 0 0 0 0 0 0 kwh 0 0 0 $/W n o . w * 0 0 0 $/MT kwh / y e a r 1950 1 0 . 1 0 11768540 2 . 8 8 5 5 8 9 0 0 0 2 . 9 9 19236000 1 0 4 . 1 0 1951 1 1 . 8 4 13027780 2 . 8 4 6 0 4 9 0 0 0 3 . 4 7 2 0 5 3 8 0 0 0 1 1 0 . 9 0 1952 1 3 . 1 5 12740690 2 . 9 1 6 7 1 7 0 0 0 3 . 6 6 2 0 0 4 1 0 0 0 1 1 5 . 4 0 1953 1 2 . 8 7 12625320 3 . 0 6 7 0 8 4 0 0 0 3 . 7 8 2 0 2 7 9 0 0 0 1 2 0 . 5 0 1954 1 2 . 0 5 13182110 2 . 8 5 7 6 4 5 0 0 0 3 . 8 1 2 1 6 8 0 0 0 0 1 2 0 . 5 0 1955 1 1 . 4 4 13949990 3 . 1 6 7 2 6 0 0 0 0 3 . 8 7 2 2 9 3 6 0 0 0 1 2 1 . 8 0 1956 1 2 . 0 7 14559590 3 . 5 9 6 5 3 9 0 0 0 4 . 2 4 2 4 2 0 4 0 0 0 1 2 6 . 0 0 1957 1 2 . 5 0 13639570 3 . 4 7 7 2 8 6 0 0 0 4 . 3 4 2 3 2 9 3 0 0 0 1 2 6 . 6 0 1958 1 2 . 2 1 12303860 3 . 1 2 8 9 0 4 0 0 0 4 . 3 2 2 2 4 0 7 0 0 0 1 2 7 . 6 0 1959 1 2 . 0 3 12806340 3 . 2 1 8 9 1 8 0 0 0 4 . 5 0 2 2 5 2 3 0 0 0 1 2 6 . 4 0 1960 1 2 . 0 3 13000840 3 . 0 1 9 9 6 0 0 0 0 4 . 8 1 2 1 9 0 9 0 0 0 1 2 7 . 9 0 1961 1 1 . 8 9 13445060 3 . 1 2 9 7 4 4 0 0 0 5 . 0 5 2 1 8 4 1 0 0 0 1 3 0 . 1 0 1962 1 1 . 3 9 13542500 3 . 3 8 9 2 1 9 0 0 0 5 . 2 4 2 1 6 6 7 0 0 0 1 3 2 . 3 0 1963 1 1 . 7 7 13955030 3 . 7 0 8 1 0 5 0 0 0 5 . 3 9 2 1 4 6 7 0 0 0 1 3 1 . 1 0 1964 1 1 . 8 1 15218850 3 . 9 0 8 3 0 1 0 0 0 5 . 5 8 2 2 3 7 6 0 0 0 1 3 0 . 0 0 1965 1 1 . 9 8 15798030 4 . 0 8 8 2 2 9 0 0 0 5 . 7 9 2 2 8 4 2 0 0 0 1 2 9 . 7 0 1966 1 2 . 5 4 17557860 4 . 3 2 8 4 4 0 0 0 0 6 . 3 4 2 4 0 2 3 0 0 0 1 3 2 . 7 0 1967 1 1 . 9 8 17451500 4 . 5 3 7 9 7 8 0 0 0 6 . 6 1 2 3 9 0 5 0 0 0 1 3 4 . 5 0 1968 1 3 . 6 9 17444840 4 . 4 4 8 3 7 9 0 0 0 7 . 1 1 2 3 2 6 4 0 0 0 1 3 5 . 2 0 1969 1 3 . 8 4 19250660 4 . 6 7 9 0 9 2 0 0 0 7 . 7 0 2 4 1 7 2 0 0 0 1 3 6 . 1 0 1970 1 6 . 4 7 16362340 4 . 6 8 9 2 6 4 0 0 0 8 . 1 3 2 4 2 8 2 0 0 0 1 4 0 . 3 0 1971 1 6 . 6 9 15538350 4 . 7 5 9 3 0 1 0 0 0 8 . 6 2 2 3 3 5 1 0 0 0 1 4 1 . 9 0 1972 1 7 . 0 5 15687080 4 . 5 6 10275000 9 . 5 8 2 2 8 8 5 0 0 0 1 4 4 . 5 0 1973 1 8 . 4 6 14915390 4 . 5 0 10720000 1 0 . 1 2 2 1 7 2 7 0 0 0 1 5 9 . 9 0 1974 2 2 . 4 2 17237030 5 . 2 0 11588000 1 1 . 5 4 2 4 6 1 2 0 0 0 2 1 2 . 2 0 1976 2 2 . 2 5 2 0 5 2 1 0 0 0 6 . 4 1 12029000 1 4 . 8 5 2 5 3 8 2 0 0 0 2 6 4 . 5 0 1977 2 4 . 3 7 2 0 8 7 3 0 0 0 7 . 4 4 11962000 1 6 . 4 0 2 4 2 7 9 0 0 0 3 1 1 . 0 0 1978 2 5 . 1 1 2 3 3 6 3 0 0 0 8 . 9 3 13225000 1 8 . 1 3 2 4 6 0 4 0 0 0 3 4 1 . 8 0 1979 2 7 . 3 1 2 5 6 1 6 0 0 0 1 0 . 1 2 13250000 1 9 . 2 5 2 5 0 8 6 0 0 0 3 8 2 . 5 0 1980 2 8 . 3 7 2 4 0 5 3 0 0 0 1 1 . 2 5 13926000 2 0 . 9 9 2 3 9 9 2 0 0 0 4 5 5 . 1 0 1981 3 2 . 4 2 2 4 8 3 5 0 0 0 1 3 . 1 2 15000000 2 4 . 3 6 2 5 1 4 0 0 0 0 5 0 5 . 7 0 News q u . MT 0 . P a p e r p r 0 . P a p e r q u P u l p p r . $/MT MT $/MT P u l p q u . MT C a p i t a l s t . 0 0 0 $ 2 5 0 9 0 0 0 1 5 7 . 6 0 2617000 1 7 4 . 7 0 2693000 1 8 1 . 4 0 2 6 8 7 0 0 0 1 7 6 . 2 0 2794000 1 8 4 . 8 0 2 8 6 8 0 0 0 1 8 3 . 8 0 3 0 2 2 0 0 0 1 7 9 . 4 0 2974000 1 8 6 . 0 0 2698000 1 8 9 . 8 0 2764000 1 9 4 . 0 0 2 8 6 3 0 0 0 1 9 8 . 9 0 2 8 5 5 0 0 0 1 8 2 . 6 0 2 8 2 9 0 0 0 2 2 3 . 3 0 2811000 2 1 9 . 7 0 3107000 2 2 1 . 0 0 3 2 4 5 0 0 0 2 2 0 . 8 0 3 5 7 9 0 0 0 2 1 8 . 7 0 3440000 2 2 4 . 1 0 3 5 0 1 0 0 0 2 1 4 . 4 0 3777000 2 2 4 . 6 0 3 7 6 6 0 0 0 2 2 5 . 3 0 3 6 0 9 0 0 0 2 2 6 . 1 0 3793000 2 2 8 . 0 0 3670000 2 5 4 . 6 0 4079000 3 5 3 . 2 0 3 9 3 0 0 0 0 3 8 1 . 3 0 3726000 3 9 6 . 6 0 4124000 4 1 6 . 5 0 4075000 4 7 9 . 1 0 3790000 5 5 3 . 9 0 4 4 5 2 0 0 0 6 0 1 . 6 0 5 4 9 4 7 2 125 6 2 6 7 9 2 179 5 4 6 5 6 6 166 5 8 0 9 9 0 141 5 8 7 7 4 6 137 6 2 8 4 8 1 139 7 4 3 6 9 9 141 6 9 3 9 4 1 141 7 1 3 8 2 8 142 7 7 2 0 0 0 140 7 5 0 0 0 0 138 6 2 2 0 0 0 133 7 3 7 2 6 9 134 8 4 1 0 1 4 121 7 8 2 9 7 5 128 8 7 6 4 4 4 133 1 0 8 1 8 3 3 138 1132173 145 1171788 146 1 3 0 4 2 8 7 148 1372830 159 1375830 158 1530231 146 1514643 178 1 6 1 6 4 0 6 3 1 9 1270348 321 1 3 9 6 0 8 0 3 2 5 1 6 8 4 9 6 6 3 3 8 1995381 4 6 8 1763612 5 6 9 1 6 9 8 5 5 0 5 9 2 3 8 8 0 0 0 184536 4 7 2 0 0 0 2 1 6 2 2 4 4 0 8 0 0 0 2 4 6 1 1 8 4 1 0 0 0 0 2 6 6 2 0 3 4 5 9 0 0 0 2 7 6 3 3 8 4 9 8 0 0 0 3 2 0 9 5 7 4 9 9 0 0 0 3 6 8 1 9 0 4 8 0 0 0 0 4 1 2 5 1 2 4 1 2 0 0 0 4 4 4 7 2 9 4 1 5 0 0 0 4 6 1 3 1 4 6 2 3 0 0 0 4 8 1 9 1 2 6 5 7 0 0 0 506581 6 9 1 0 0 0 5 2 5 3 2 5 7 5 7 0 0 0 5 5 8 6 8 5 8 1 4 0 0 0 6 1 8 9 5 2 6 5 3 0 0 0 7 0 3 7 3 0 6 5 1 0 0 0 7 8 8 0 4 0 6 0 4 0 0 0 8 5 6 9 7 6 5 9 3 0 0 0 9 0 3 8 4 5 6 7 3 0 0 0 9 7 7 3 8 0 6 2 8 0 0 0 1 0 5 4 4 0 9 6 6 4 0 0 0 1101747 5 8 1 0 0 0 1158146 4 5 0 0 0 0 1 2 8 6 5 0 3 5 7 6 0 0 0 1 5 9 2 6 8 3 7 6 1 0 0 0 2 1 6 1 3 1 6 6 2 3 0 0 0 2 3 8 3 1 1 4 6 9 1 0 0 0 2 6 4 6 4 8 2 8 8 6 0 0 0 2 9 9 0 4 2 6 7 9 8 0 0 0 3 4 6 2 0 1 3 8 6 5 0 0 0 4 0 6 9 8 1 9 APPENDIX B. ESTIMATION RESULTS Table B.I. British Columbia Full Translog model results. Estimated Estimated Equation Variable Coefficient t-value Equation Variable Coefficient t-yalMe Profit L -99.53 -0.80 function F -113.73 -0.54 E 17.96 0.51 A 234.80 0.48 K -610.39 -2.42 T -796.94 -1.52 LL -0.20 -11.69 LF -0.10 -7.48 LE -0.03 -3.62 LA 0.18 6.89 FF -0.20 -4.43 FE -0.01 -0.82 FA 0.06 0.92 EE -0.03 -1.85 EA 0.05 13.72 AA -0.01 -0.03 KL -0.04 -0.47 TL 13.05 0.79 KF -0.12 -0.80 TF 15.06 0.53 KE 0.01 0.60 TE -2.41 -1.00 KA 0.10 0.27 TA -30.95 -0.47 KK -1.00 -2.75 KT 82.18 2.42 INTERCEPT 5976.60 1.51 R2 0.69 D.W. 0.85 Total Paoer A -0.01 -0.05 shflre F 0.06 0.91 E 0.05 3.18 L 0.16 5.83 U -0.29 K 0.10 0.27 T -30.93 -0.47 INTERCEPT 234.67 0.48 R2 -0.09 D.W. 1.14 Fibre F -0.20 -4.43 share E -0.01 -1.07 L -0.10 -7.45 A 0.06 0.91 U 0.23 K -0.12 -0.80 T 15.06 0.53 INTERCEPT - 113.72 "0,54 R2 0.23 D.W. 0.85 Energy E -0.03 -5.28 share F -0.01 -1.07 L -0.03 -5.41 A 0.05 3.18 U 0.01 K 0.09 0.50 T -2.42 -0.69 INTERCEPT 17.98 0.69 R2 0.62 D.W. 1.29 Labour L -0.20 -12.51 share F -0.10 -7.45 E -0.03 -5.41 A 0.18 5.83 U 0.15 K -0.04 -0.47 T 13.04 0.76 INTERCEPT -99.48 -0.80 R2 0.18 D.W. 1.30 Pulo U -0.11 share F 0.23 E 0.01 L 0.15 A -0.29 K 0.06 T 5.25 INTERCEPT -38.45 Table B.2. British Columbio Reduced Translog Model results Estimated Eauotlon Variable Coefficient t-value Fibre F -0.09 -1.81 share E 0.01 1.19 L 0.01 0.15 A -0.30 -2.68 u 0.38 K -0.40 -2.55 T 62.89 2.19 INTERCEPT -471.99 -2.19 R2 0.36 D.W. 1.66 Energy E -0.03 -5.18 share F 0.01 1.19 L -0.02 -2.86 A 0.01 0.73 U 0.02 K -0.02 -1:04 T 2.77 0.79 INTERCEPT -20.92 -0.79 R2 0.69 D.W. 1.57 Estimated Equation Variable Coefficient t-value Total oaoer A 0.76 2.69 share F -0.3 -2.68 E 0.01 0.73 U -0.42 K 0.76 2.06 T -147.78 -2.19 INTERCEPT 1109.8 2.19 R2 0.17 D.W. 1.68 Pulo U -0.16 share F 0.38 E 0.02 L 0.18 A -0.42 K -0.12 T 39.69 INTERCEPT -296.71 Labour L -0.09 -3.12 share F 0.01 0.15 E -0.02 -2.86 A -0.08 -0.99 U 0.16 K -0.22 -2.43 T 42.43 2.50 INTERCEPT -319.18 -2.50 R2 0.43 D.W. 1.66 Table B.3. Ontario Full Translog Model results Estimated Estimated Eauation Variable Coefficient t-value Eauation Variable Coefficient t-value ProfU L -239.8 -6.90 Fibre F -0.36 -8.99 funrtipn F -254.21 -5.10 share E -0.04 -3.94 E -15.51 -0.18 L -0.22 -8.93 N 461.76 12.20 N 0.16 4.42 p 2.59 8.63 P 0.36 9.02 K -1.01 -3.72 U 0.1 T 293.77 6.66 K -0.12 -2.58 LL -0.36 -9.29 T 33.37 4.64 LF -0.22 -10.20 INTERCEPT -253.74 -4.7 LE -0.05 -0.46 LN 0.34 3.02 R2 0.75 LP 0.17 1.51 D.W. 1.46 FF -0.36 -9.96 FE -0.04 -4.36 Energy E -0.04 -5.07 FN 0.16 5.90 share F -0.04 -3.94 FP 0.36 2.62 L -0.05 -4.09 EE -0.04 -0.37 N 0.03 2.53 EN 0.03 2.95 P 0.06 4.27 EP 0.06 0.56 U 0.03 -1.12 NN -0.05 -0.19 K -0.1 1.19 NP -0.14 -0.83 T 1.8 -1.23 PP -0.32 -1.00 INTERCEPT -13.99 KL -0.13 -3.60 TL 31.55 6.08 R2 0.89 KF -0.12 -2.81 D.W. 1.31 TF 33.44 7.52 KE -0.01 -0.66 Labour L -0.36 -11.04 TE 2 0.07 share F -0.22 -8.95 KN 0.2 3.33 E -0.05 -4.09 TN -60.93 -9.01 N 0.33 11.87 INTERCEPT -2208.9 -9.08 P U 0.17 0.13 6.01 R2 0.86 K -0.13 -3.44 D.W. 1.98 T INTERCEPT 31.6 -240.19 5.22 -5.28 R2 0.69 D.W. 1.84 Table B.3. Confd Estimated Equation Variable Coefficient t-value Herfsorlnt N -0.05 -0.83 share F 6.16 4.42 E 0.03 2.53 L 0.33 11.87 p -0.14 -2.63 u -0.34 K 0.2 3.98 T -60.84 -7.77 INTERCEPT 461 7.84 R2 0.85 D.W. 1.85 Estimated Equation Variable Coefficient t-value Other pooer P -0.32 -3.74 share F 0.36 9.02 E 0.06 4.27 L 0.17 6.01 N -0.14 -2.63 U -0.13 K 0.04 3.2 T -0.08 -3.81 INTERCEPT 2.58 10.75 R2 0.82 D.W. 1.27 PulD U 0.21 share F 0.1 E 0.03 L 0.13 N -0.34 P -0.13 K 0.02 T -5.86 INTERCEPT 45.34 Table B.4. Ontario Reduced Translog Model results Estimated Estimated Equation Variable Coefficient t-value Equation Variable Coefficient t-value F -0.3 -5.79 0.11 1.4 E -0.03 -2.44 share F 0.13 2.29 L -0.21 -4.61 E 0.02 1.47 N 0.13 2.29 L 0.21 3.99 P 0.35 7.58 P -0.16 -2.48 U 0.07 U -0.31 K -0.07 -1.08 K 0.08 1.17 T 25.44 2.56 T -36.4 -3.44 INTERCEPT -194.11 -2.59 INTERCEPT 291.98 3.47 0.76 R 2 0.87 1.51 D.W. 1.86 Energy. E share F L N P U K T INTERCEPT R 2 0.9 D.W. 1.36 -0.04 -4.99 -0.03 -2.44 -0.04 -2.96 0.02 1.47 0.07 4.25 0.03 <0.01 0.08 0.3 1.86 -2.69 14.00 Other paner P share F E L N U K T INTERCEPT R 2 0.83 D.W. 1.32 -0.3 -3.48 0.35 7.58 0.07 4.25 0.19 4.19 -0.16 -2.48 -0.14 0.06 1.24 -5.11 -0.61 40.4 0.64 Labour share L -0.25 -4.75 Pulp U 0.24 F -0.21 -4.81 share F 0.07 E -0.04 -2.96 E 0.03 N 0.21 3.97 L 0.11 P 0.19 4.19 N -0.31 U 0.11 P -0.14 K -0.03 -0.61 K -0.05 T 13.13 1.51 T 4.64 ERCEPT -100.99 -1.54 INTERCEPT -33.57 R2 0.73 System R2 0.9996 D.W. 1.82 Chi 2 245.59 with 25 D F . Table B.5. Quebec Full Translog Model results Estimated Estimated Equation Voriable Coefficient t-value Equation Variable Coefficient t-value Profit L -415.04 -5.09 Fibre F -0.17 -2.34 function F 195.02 1.64 share E -0.08 -5.74 E -92.85 -2.92 L -0.15 -3.5 N 1.88 5.05 N 0.17 1.91 P 2.60 7.34 P 0.38 7.43 K -0.76 -1.94 U -0.14 T 308.29 4.50 K 0.25 3.17 LL -0.47 -7.43 T -26.42 -1.87 LF -0.15 -7.25 INTERCEPT 195.01 1.84 LE -0.01 -0.25 LN 0.25 4.61 R2 0.64 LP 0.18 3.98 D.W. 1.14 FF -0.17 -2.69 FE 0.08 -5.75 Energy E -0.03 -2.71 FN 0.17 1.94 share F -0.08 -5.74 FP 0.38 8.05 L -0.01 -0.28 EE -0.03 -1.52 N -0.03 -1.48 EN -0.03 -1.32 P 0.06 3.07 EP 0.06 3.12 U 0.09 NN 0.39 3.11 K -0.07 -2.84 NP -0.62 -9.85 T 12.31 2.64 PP 0.06 0.72 INTERCEPT -92.85 -2.65 KL -0.21 -3.88 TL 54.80 5.11 R2 0.22 KF 0.25 3.32 D.W. 1.2 TF -26.42 -2.14 KE -0.07 -2.70 Labour L -0.47 -7.55 TE 12.31 2.16 share F -0.15 -3.5 INTERCEPT 2321.60 -4.50 E -0.01 -0.28 N 0.25 4.75 R2 0.85 P 0.18 3.96 D.W. 1.30 U 0.2 K -0.21 -3.86 T 54.8 5.07 INTERCEPT -415.04 -5.11 R2 -415.04 D.W. -5.11 Table B.5. Cont'd Estimated Estimated EflUSiM Variable Coefficient t-value Eouation Variable Coefficient t-value Newsorint N 0.39 3.11 QUierDflDer P 0.06 0.66 share F 0.17 1.91 share F 0.38 7.43 E -0.03 -1.48 E 0.06 3.07 L 0.25 4.75 L 0.18 3.96 P -0.62 -8.69 N -0.62 -8.69 U -0.15 U -0.07 K -0.18 -7.94 K 0.68 3.71 T 0.41 0.04 T -0.17 -5.95 INTERCEPT 1.88 5.03 INTERCEPT 2.6 7.34 R2 0.64 R2 0.89 D.W. 1.35 D.W. 1.65 PUlD share u 0.081 F -0.14 E 0.09 L 0.2 N -0.15 P -0.07 K 0.14 T -40.94 INTERCEPT 309.4 Table B.6. Quebec Reduced Translog Model Results Estimated Estimated Eguqtipn, Variable Coefficient H a l U E Equation Variable Coefficient t-value F -0.40 -4.42 Newsprint N -0.1 -0.6 E -0.08 -4.66 share F 0.46 4.34 L -0.14 -2.56 E -0.05 -2.16 N 0.46 4.34 L 0.34 5.34 P 0.31 5.20 P -0.47 -4.62 U -0.16 -1.94 U -0.18 K -0.12 -0.78 K 0.49 2.39 T 36.24 1.30 T -118.96 -3.22 INTERCEPT -275.52 -1.32 INTERCEPT 898.85 3.24 0.66 R2 0.74 1.24 D.W. 1.65 E -0.01 -0.45 Other oaoer P 0.07 0.65 F -0.08 -4.66 share F 0.03 5.2 L 0.04 1.92 E 0.03 1.52 N -0.05 -2.16 L 0.09 1.99 P 0.03 1.52 N -0.47 -4.62 U 0.06 U -0.03 K -0.02 -0.71 K -0.12 -0.96 T 0.50 0.10 T 37.31 1.63 INTERCEPT -3.70 -0.10 INTERCEPT -279.56 -1.63 0.44 R2 0.87 1.31 D.W. 1.27 Labour  share L -0.47 -6.47 PulD U 0.18 F -0.14 -2.56 share F -0.16 E 0.04 1.92 E 0.06 N 0.34 5.34 L 0.13 P 0.09 1.99 N -0.18 U 0.13 P -0.03 K -0.23 -2.96 K <0.01 T 57.67 3.82 T -12.75 INTERCEPT -436.27 -3.84 INTERCEPT 95.2 R2 0.85 D.W. 1.69 Table B.7. Description of Variables. ble description variable description L Labour price NP newsprint pr. * other paper price F Fibre price PP other paper price * other paper price E Energy price LK labour pr. * capital A Total peper&paperb.price LT labour pr. * time trend N Newsprint price FK fibre pr. * capital P Other paper&paperb.prtce FT fibre pr. * time trend U Net mrkt. pulp price EK energy pr. * capital K Capital stock ET energy pr. * time trend T Time trend AK Total paper&paperb. price * capital LL labour pr. * labour pr. AT Totol paper&paperb. price * time trend LF labour pr * fibre pr. NK newsprint pr. * capital LE labour pr. * energy pr. NT newsprint pr. * time trend LA labour pr. * totol paper pr. PK other paper pr. * capital LN labour pr. * newsprint pr. PT other paper pr. * time trend LP labour pr. * other paper pr. FF fibre pr. " fibre pr. FE fibre pr. * energy pr. FA fibre pr. • total paper pr. FN fibre p r . " newsprint pr. FP fibre pr. • other paper pr. EE energy pr. • energy pr. EA energy pr. * total paper pr. EN energy p r . « newsprint pr. EP energy pr. » other paper pr. AA total paper pr. * total paper pr. NN newsprint p r . " newsprint pr. note: 1. A l l prices are normalized by the price of pulp. 2. A l l prices expressed as natural logarithms of nominal prices. 

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