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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 p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  requirements f o r an advanced degree a t the  the  University  o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make it  f r e e l y a v a i l a b l e f o r reference  and  study.  I further  agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may  be granted by the head o f  department o r by h i s or her r e p r e s e n t a t i v e s .  my  It i s  understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l gain  s h a l l not be allowed without my  permission.  Department o f  Forestry  The  U n i v e r s i t y o f B r i t i s h Columbia  1956  Main M a l l  Vancouver, Canada V6T  1Y3  Date  DE-6  (3/81)  October  15,  1985  written  ii  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 CHAPTER 1. INTRODUCTION  vii 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 3.1 Introduction  19 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 LITERATURE CITED  51 .'  52  APPENDIX A - DATA  60  APPENDIX B - ESTIMATION RESULTS  63  V  LIST OF TABLES  Table 1.  Page 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  Share of Four Energy Sources in Cost of Purchased Fuel and Electricity for Canadian Pulp and Paper Mills in 1974.  6  Preliminary Regression Results for Quebec Newsprint Supply Function  20  Further Preliminary Regression Results for Quebec Newsprint Supply Function  21  Preliminary Regression Results for Quebec Newsprint Price Function  22  4.  5.  6.  7.  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  vi  LIST OF FIGURES  Figure  1.  Page  Production of Net Market Pulp , Newsprint and 'Other Paper and Paperboard' In British Columbia, Ontario and Quebec  7  Real Output Prices by Category for Ontario  9  8  8  2.  vii  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. It was developed for use in the United 1  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 = Z - Z - Z - Z D  where:  s  T  M  Z = Net Social Payoff (sum of producer and consumer surplus) Z = Area under end product demand curve up to clearing quantity Z = Area under fibre input supply curve up to clearing quantity Z = Transportation cost Z = Manufacturing cost D  s  T  M  2  A feasible alternative objective function formulation is: Maximize Z = Z - Z D  where:  E S  - Z  T  Z = Area under end product supply curve up to clearing quantity. E  S  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  WOODPULP bleached sulphite unbleached sulphite bleached softwood sulphate bleached hardwood sulphate semibleached sulphate unbleached sulphate mechanical dissolving, special alpha total PAPER/PAPERBOARD newsprint groundwood printing book.writing kraft papers tissue paperboard total Source : Miller Freeman (1985a).  Production Exports thousand metric tons  255 52 4,941 541 377 186 245 198 6,795 8,486 765 961 472 385 2,344 13,413  7,469 636 239 234 24 518 9,120  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 3 . 2  Table 2. Pulp, Paper and Paperboard Mills in Canada, 1985.  Province  Number of mill sites Pulp Paper/Paperboard  Alberta British Columbia Manitoba New Brunswick Newfoundland Nova Scotia Ontario Quebec Saskatchewan  2 22 3 10 3 5 23 39 1  total  ft  108  3 10 4 6 3 4 32 53 0 115  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  British Columbia Ontario Quebec  6,143 4,212 6,762  Paper/Paperboard - OOO metric tons 2,164 3,388 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. Real  3  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 prices . Further comparisons of regional 4  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 Pulp , Newprint and 'Other Paper and ft  Paperboard' In British Columbia, Ontario and Quebec. 8  B.C. Production (OOO metric tons)  0 I i 1950  i  i  i  i  i  i  i  1955  i  i  i  i  1960  i  i  i  i  i  i  1965 Year  i  i  i  i  i  1970  i  i  i  i  i  1975  i  i  I-  1980  Ontario Production (000 metric tons)  0 I i 1950  I I  i i i  1955  i  i i i  I I  1960  I I  I I  1965 Year  I I  I I  I I I  1970  i i i i  1975  I I  I I  1980  • -  8  1950  1955  1960  1965  1970  1975  Year newsprint production  paper/board production  A « see Chapter A for definition B = total paper/paperboard in the case of B.C. Source: Statistics Canada (1950-1981).  •** pulp production  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 aggregation.  concentrated depending on product  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  Non-competitive  Price Determination  Models  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. countries and the United States respectively. Buongiorno el al. (1983) 5  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 market hypothesis (Kaltenberg 1983).  competitive  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  Supply in Competitive Market Models  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 technology . 6  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' , or the sum of producer and consumer surplus in 7  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 . For this reason in particular the 8  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 first specified as dependent solely on own price. These functions gave poor results and were difficult to interpret due to the problem of identification . Supply functions for pulp, newsprint 9  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 little 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 + PiNP  Model 2:  NQ -  d  p" PP  +  0  ^  + 0  + y LP 6  *lNP d  d  +  2  d  +  r PP  d +  2  PW  1  v  +  *3UP  d  +  f^P*  * y EP  d  5  +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 Variable NP ppd d  UP FP pd  d  Coefficient model 2 model 1 2827 -7203* -976  d  E  L p  d  * = significant at 5% level  -4876* 2815 -573 -46121* 907 92658*  Elasticity at mean model 2 model 1 0.340 -1.316 -0.132  -0.588 0.514 -0.077 -0.510 0.004 0.465  21  Table 6. Further Preliminary Regression Results for Quebec Newsprint Supply Function  Model  F-Value  1 2  Degrees of Freedom  490 41.79  Adjusted R-Square  27 24  0.28 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 EP + 6 LP + z 2  Model 4: InNP = d)  0  3  + <J>,lnFP + 4»2 InEP + <J>lnLP + x  Where : z,x = Stochastic error terms  3  22  Table 7. Function  Preliminary Regression Results for Quebec Newsprint Price  Independant Variable  Coefficient model 1 model 2  FP/lnFP -0.00002* -0.182 EP/lnEP -0.00003 0.024 LP/lnLP 16.114 0.813 * » significant at 5% level  Elasticity at mean model 1 model 2 -1.565 0.949 0.650  -0.182 0.024 0.813  Table 8. Further Preliminary Regression Results for Quebec Newsprint Price Function  Model  F-Value  3 4  20.56 77.64  Degrees of Freedom 29 29  Adjusted R-Square 0.65 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 spaces . The theory has been stated or proven by 10  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) = m i n {p x : f(x)> Y)  (1)  T  x  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 {p u: (u,-v) € T]  (2)  T  u  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 i r s t 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 first 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 w i 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 + S c a m p i + 1/2 XX 0  +XX Where:  y^, = <l>jk  =  y  fiylnpjlnVj  ^lnpjlnPh  + SfylnVj +  1/2 X X <pj<lnVjlnv  k  h i  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 r s t proposed the use of the quadratic form as a normalized profit function. The normalized quadratic profit function is shown below:  TTlp'iV)  Where:  m  OCQ  + SarjPi' + 1/2 X £ r^Pj' P"  rf(p;v]=  TT(p';v]  p*  -  P/Pi  =  ?b  =  *J  bp  h  +  ESSJJPJ'VJ  Pi  (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  + X X  Where:  f  =  h  y  Inp/ lnp ' h  lnpj' lnVj + X Pj InVj + 1/2 £ X d)j< InVj lnv  k  w  TT'(p';v) = normalized restricted profit Pj' =  normalized prices of fibre, energy, labour, market pulp,  v  newsprint and 'other paper and paperboard' (B.C., outputs of market pulp and total paper/paperboard). capital stocks and year (time trend variable)  i  =  Note: Profits and prices normalized by the price of market pulp.  The symmetry conditions stated in (4), y  h  (6)  = y , 6g = 5jj and h i  >  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 reduced . 11  If we assume  homogeneity of degree one in p then the lost estimates can be recovered f  from the remaining equation system from the following:  (1)  Sa,  (ii) (iii)  - 1 - 0  £$jj=0  f o r i - 1,  ,I  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) 6W  Where: Thus:  =  aTf(p';v) Pj 5PiTT'(p';v)  =  XjPj  =  5j  TT'(p';v)  S, = share of profits attributed to net supply i  (8)  29  (9)  Input profit shares are constrained to be negative and output shares positive. This leads to the following result:  SS, - 1  (10)  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:  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||=  and:  * i i Pi  (14)  31  e  Where:  U -  * u Pj  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  comparisons with other studies.  in the present  study, and for  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 FIBRE  Variable fibre energy labour mlct. pulp tot. paper  ENERGY  LABOUR  energy fibre labour mkt. pulp tot. paper labour fibre energy mkt. pulp tot. paper  rflCT. PULP  TOT. P A P E R  mkt. pulp fibre energy labour tot. paper tot .paper fibre energy labour mkt. pulp  Translog  Translog  -0.74 -0.01 0.09 0.29 0.37 0.01 -0.11  -0.36 0.05 -0.27 0.09 1.44 -0.27 -0.64 0.22 0.32 0.37 -0.93 -0.44 0.03 0.31 1.03 -0.18 -0.04 -0.01 -0.08 0.31 0.80 -0.83 -0.02 -0.37 0.41  ft  0.80 0.50 1.20 -0.23 0.14 0.10 0.30 -0.31 -0.10 -0.10 -0.01 -0.06 0.28 -0.45 -0.22 0.06 -0.04 0.50  8  Quadratic Quadratic B 0  1  -0.23* 0.02 0.10*  0.03 0.04* 0.14  -0.06 -0.62* 0.17 -0.10  0.34* -0.65* 0.40* 0.15  -0.02 0.18"  0.32 -0.01 0.28* 0.03  0.19* -0.02 -0.11  -0.11 -0.04 >-0.01 -0.04  0.13  0.03 0.23* 0.02 -0.05  = full model, = reduced model (without profit function), * = significant at five percent with infinite degrees of freedom. Note: see Appendix B for translog coefficient t values. ft  B  39  Table 10. Price Elasticity Estimates for Ontario Equation Variable FIBRE  fibre energy labour  ENERGY  mkt. pulp newsprint other paper/bd. energy  -0.01 -0.67  fibre labour  0.03 0.28 -0.06 0.33  0.05 -0.45 -0.08 0.25 -0.01 0.43  fibre energy  NEWSPRINT  labour newsprint other paper/bd. newsprint fibre energy labour mkt. pulp  other paper/bd. OTHER P A P E R / o t h e r paper/bd. BD. fibre energy labour mkt. pulp newsprint  fi,B,"  =  S  Translog -0.85 0.01 0.08 0.25 0.49  newsprint other paper/bd. labour fibre energy mkt. pulp newsprint other paper/bd. mkt. pulp  MKT.PULP  0  -0.73 <0.01 0.08 0.19 0.46  mkt. pulp  LABOUR  Translog  ee Table 9  -0.09 -0.47 0.10 0.05 0.06 -0.06 0.34 -0.08  -0.14 -1.05 0.11 0.05 0.09 0.19 0.26 0.02  -0.23  -0.31  0.10  <0.01  -0.05 -0.06 0.43 -0.27 -0.28 -0.03 0.03 -0.03 -0.59 -0.65 -0.01 0.01 -0.17 0.22  -0.08 -0.05 0.41 -0.10  0.61  -0.31 -0.04 -0.90 -0.02 0.98 -0.61 -0.03 0.01 -0.12 0.21 0.96  8  Quadratic Quadratic' 0  -0.74* 0.01 -0.02  -0.47* 0.02 0.15*  <0.01* 1.03* <0.01 0.05 -0.06  0.18* 0.21 -0.29* 0.14 0.12  0.08 0.13 -0.32*  0.43* -0.33 -0.29*  -0.03 -0.01  -0.20* 0.02  -0.39* 0.92*  -0.17* 0.31*  -0.62" <0.01* 0.01 -0.18*  -0.35* 0.11* 0.04* -0.08*  1.18* -2.25* 0.60* 0.01 0.40*  0.45* -0.98* 0.12 -0.03 0.14*  1.08*  0.43*  40  Table 11. Price Elasticity Estimates for Quebec Equation Variable FIBRE  fibre energy labour  ENERGY  LABOUR  MKT.PULP  0  Translog  8  Quadratic  Quadratic  0  1  -1.84 0.06 -0.16  -0.94  -0.64"  -0.56*  0.04 -0.25  0.04 0.02  0.03 0.06  mkt. pulp newsprint other paper/bd. energy  0.61 0.82  0.82 0.63  <0.01*  -0.21 -0.89  -0.01 -1.04  0.39* <0.01  0.22 0.04 -0.73*  fibre labour  0.23 -0.42  0.25 -0.91  0.21 -0.20  0.20 -0.05  mkt. pulp newsprint  -0.42 1.46  -0.40 1.91  0.91*  0.64*  other paper/bd. labour  0.02 -0.47  0.19 -0.49  -0.90* -0.31*  fibre energy  -0.17 -0.11  0.03 -0.05  m k t . pulp newsprint other paper/bd. mkLpulp  -0.10 0.64  -0.32 -0.18 -0.01 0.67 0.32 -0.08  0.16 -0.26* 0.91 -0.01  0.18 0.09  -0.08  fibre energy labour newsprint NEWSPRINT  Translog  other paper/bd. newsprint fibre energy labour mkt. pulp  other paper/bd. OTHER PAPER/ other paper/bd. fibre BD. energy labour mkt. pulp newsprint  0.19 -0.44 -0.94 0.16 0.15 0.69 0.36 0.50 -0.34 -0.15 -0.26 0.19 -0.33 -0.33 0.18 -0.01 -0.15 0.20 0.08  0.20*  -1.17 0.14 0.01 0.72 0.39 0.45 -0.27 -0.13 -0.23 0.14  -0.34* <0.01* 0.08* 0.06  -0.33* 0.10 0.05* 0.06*  -0.36 -0.36 0.01 -0.04  0.10 -0.60* 0.37* -0.15*  -0.02 -0.54* 0.04 0.03  -0.29 0.21 0.47  0.06  -0.05  0.20  -0.04  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  convexity in prices.  of  degree one in prices, monotonicity  and  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^+^Ss  ^ffi+^Se  42  y 1 S S +  2  IH]-  2  1  y22 52<52+  1)  *26 S2S +  6  : ^6i S S, +  6  y 2 S S  y66 S (S -1)  +  6  6  +  2  6  6  (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 i r s t 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 R 's in both the model with and 2  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 'all 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 R 's and 2  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.  All  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 consumption figures.  1.2 for detailed regional  energy type  LITERATURE CITED  53  LITERATURE CITED  Applebaum, E. 1979. Testing Econometrics. 9: 2 8 3 - 2 9 4 .  Price  Taking  Behaviour.  Journal  of  Armstrong, G.R. 1975. Conduct i n the Pulp and Paper Industries. In Rumsey, F. and W.A. Duerr, eds. Social Sciences i n Forestry: A Book of Readings. Philadelphia: W B . Saunders and Company. 409pp. Berndt, E.R. and L.R. Christensen. 1973. The Translog Function and the Substitution of Equipment, Structures and Labor i n U.S. Manufacturing 1929-68. Journal of Econometrics. 1 : 8 1 - 1 1 3 . Berndt, E.R. and M S . Khaled. 1979. Parametric Productivity Measurement and Choice Among Flexible Functional Forms. Journal of P o l i t i c a l Economy. 87(6): 1221-1245. 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An E f f i c i e n t Method of Estimating Seemingly Unrelated Regressions and T e s t s f o r Aggregation Bias. Journal of the American Statistical Association. 57:348-368.  50  APPENDIX A . . DATA  Table A . l .  a  o  a. o  u  Q. tt  _  £ S^"  _ *»  Q. 3  B r i t i s h Columbia Data  _. o O O fO O o C CO (Si _A (A to ID o— CO CO to o OO (SI (SJ to OI ID ISI to r» cn —. cn ID CO CA cn t>- (SI Ok cn o r> o fO o> ID o co o (Sl rr (O IO fO cn ID m cn t"» in IO in <SI r» TT at ^— »— (SI (SI ro o to «• o OI (Si (SI r(Sl fO lO in IS) in to to to in to ID GO o .— o • to to o o on m in m CO rftr o r» cn VO (SI (SI cn 00 to oo o — cn on o — in cn ID _. (SJ «- to — r-— (O — — —  to o t> o o o o O o o o (SI 00 in o o o o o o o o (SJ cn « • o o o o o o o o r~ o OO flo to in to m o » (SI «— to .— f- to o o to to rsi in rr oo 0O m — o to — — — •on— CSI (SI (SI • _ _ (SJ o 00 rr to o rr. «• «• to to to — — — — — to — _ _ to _ _ _  _. o o f> oo rin o in o <»- o fO to rin in r» IO to o (SI OO ro r (SI to in  o o o o o o o o o o o o o o o o o o ID oo rr 00 in t> rr r— 00 to (SI to IO to to (SI to to to to in to to (SI to m rr to — to to — _ _ m _ in _  .  CO m T o O eo to (SJ 00 an V" on r> cn (Si in (SJ ID cn «.— to 00 in — r— ID .— oo (SI ID to oo in o O oo r- o to t> oo (SI (V to cn (SI r» to to (SI (SJ to o o o o o O o o o o o o o o o o o o o o orr o o o o o o cn to ID t-» o r» to cn m o<0o in o (SJ r> oo cn r» o m r_. in _ cn to to to LO o OO (SJ in — in OO — c s i t sm j t o t oto « - to L o r*. m  o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o  _ _  ffl H  a. to  Q.  o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o  N i n O K ) O e O O K l M - K l l O O » l D ( D - i n i \ J « - i n i O K l « > - N ( y N » N i n  lnlO»^Nlno3^lr)lo*-01^l^l<IlK)lOlo<r^^llo^Jl/>^lnlOlr)«•N * f v i n i o i o i o i D N O i o o o - N i ' ) i o i o i n N i D « i o o a i o i o i - - - a i — — — — — — — — — — — — — (SJ — — — ( S J ( S J ( S I _  • !r t— t_ n <D ^  -ioiooo«-ir«-*ioinooo(JiNiDfl-o-o-ineo-i/>oiioinoNOicntoo —N O iDcnco — o o o c o o t o ^ r c n o — t o m K > c n < r t > i n o o c n ( s i c o to oo r- o>co — — o t o ( s i v o o c n ( s i ( S i » ^ t o i D O ( \ j — r>to — fO(si(si(sjtooo  2. § eg l _ * 3 v o j3 ' §  o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o i n ID I - oo — — 5 i - i n « 0 ( s j o > i o ^ - o c n i s j i n c n o o t o a > _ ^ - c s i i o i o o t o c s i o o « o o to * io - o o c ^ i n t o < o i n o o o t o o 5 r o o c n i o ( s j t o c n f O ( s i o v i ^ r ^ — cn — ooi^-cnisjin^aor^iocn^cntoiotooooton-oinincnioisjcnt^oisjtoo t o < - ^ - i n i n m i n i n m i n i o i D r * t > « o c n c n o o — o<- — (siio(si(sjtotototo  Q. •» (0  ^ ( M N N N M M I O I O I O I O T T T V I O M N I O T T V T I O n O I O N r - I ' l l O — — — — — — — — — — — — — — — — — — — — — — — — ( S J ( S J K ) ( O K ) T T ^  - (sjincnr<in^-ooinoor»«0(si(sj(sj(Oio«— to o — ( s j i n ^ - t o o t o t o t o i o o o i s i i n o i o — ioo» — to m r~ oo to cn — o i s i n n V V V ^ V V i n i n i o i n i n i n i d i d ^ N o o i o d d — — — — — — (vjrsirsjtsj  K ) » O N O ( D O O O O I I O N -  => " ? 2 2  X> O is. a  O  O" -G " > >- ^ o _ «-2 • S C O  o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o lOlnol^^-^oo^5NlOtOln-N^•lOlrtlOOlnMM^lfl-lOto-vlO(o io o in N <- t o i ^ t o t o r s i o o i n — l o t o c j t o v i s j c n c n o v o i o t o ' a o t o a o t o i n ——( s j i r > i r > t o ^ r ^ o o ( s j » i o i n o ^ r » o t o o i ^ r j i > i n ( \ i i s j ^ - o o r » — — (SJ(SJ(SltOt04-tO«-tOfOV«-«-<«-«-«-  k _ 2 >»2-£ o o > l_ ^  p^onisitoisjoto —© ( s j t o o r - c n m c n i n — N N « - t o i o o i N O N » « N i n i^iDioooto(sj(sjcnto(sjini^iooocnv^in^(sjtoint>in~ioinin'«-too « - v v « - v » « - i n i n i n i n i n i n i n i A i n i n m i n i n v i o * i o N » o - Ninon _ _ _ _ _  _  o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o t o —(siinr--tsjintoor^too(sj —t o < s j t o > i r o o « - o t o o o o o o o voooinrsir^oinoor-pvjvoofvj — o t s i r - f s i c j t o c v i i s j p j o i s j o o o o o o i n i s i o o i D c s i i n i n t o — o i s i o o m — oo on <M oo to to — o o o < - « - i n ( s i o t O ( s j o ( O _ r * i o m o n r > . t o — — in — r - o o v o — o — r ^ o o o o o o o o o o v i o v o o o — cn <sj CM to on o — O ( s i o o o i n t o i o o t « > — o n o t o t o o o o o o o t o o o o t o r r — _ (vj(\j(sjtoininmin(v.r><oa>cn — ( s j « - r - c o c n m t o r » - o o « 0 " i r < o t * . o o i n — — — — — — — — — rsj<sjrsi<\j<\j»\jr>i<sj  «> v» C  m • cc t_ — uo.  <D  K>  E  inmor-entovr-cntor^iovr*- — veocntomtots-r«.(sjtoootooc»ioin — 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 « - « - —enoocnoor«.t>i>.ts.ioiocv.oooorvooo>ooo  — inioin«-<oinoo  £> «<•  — — — —  — — — — — — — — — (SJ(\J  iZ « S v~  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 —(sito'Tiof^oocno — l/ll/lmlnlOlnlnlnlou^lfllOlOlOlOlOlOlOlOl0^^^^^^^^^^ooo 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  Year Fibre p r . Fibre qu. $/m3  m3  Energy pr S/000  n e r g y quJ_abour p r . l a b o u r q u . N e w s p r 000 k w h  kwh  0 0 0 $/W  no.w*000  $/(1T  News q u . 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 $/MT  Pulp q u . Capital s t . MT 000 $  / year  1950  10.13  7182120  3.02  1851000  3.03  14003000  106.30  1125000  152.50  601000  125.00  404000  1951  11.82 12.51  7768910  3.16  2061000  15196000  114.00  1167000  178.70  657000  179.00  491000  224576  6967440  3.17  2057000  3.52 3.54  15675000  116.40  1178000  180.70  604000  166.00  424000  255625  1952  191664  12.62 12.04  7086770  3.26  2169000  3.73  15547000  122.60  1178000  182.00  646000  141.00  426000  276485  1954  7388Z40  4.10  2111000  3.78  15950000  121.30  1221000  189.30  656000  137.00  477000  287012  1955  11.55  7970150  4.34  2173000  4.05  15796000  124.00  1295000  190.00  715000  139.00  517000  299083  1956  11.95  8387330  4.82  2120000  4.16  16835000  127.00  1335000  197.10  784000  141.00  519000  342622  1957  12.66  8436960  2434000  4.33  16976000  127.50  1349000  199.40  765000  141.00  499000  396127  1958  13.08  8177110  4.86 4.77  2676000  4.45  16551000  127.50  1329000  198.00  807000  142.00  456000  426850  1959  12.96  8305290  4.55  3008000  4.50  16753000  126.90  1356000  200.20  850000  140.00  440000  443145  1960  12.31  8953360  4.74  3137000  4.85  16615000  131.60  1459000  201.90  876000  138.00  663000  453343  1961  12.54  8932790  5.09  3142000  5.01  16416000  132.00  1448000  209.80  778000  133.00  667000  449423  1962  12.39  9315910  5.49  3154000  5.19  16358000  138.70  1453000  211.20  865000  134.00  669000  446287  1963  12.39  9367570  5.19  3433000  5.30  16609000  139.40  1421000  214.40  903000  133.00  698000  460788  3659000  17162000  137.40  1555000  214.40  955000  140.00  751000  497413  3756000  17365000  137.20  1581000  213.60  976000  147.00  677000  568062  224.10  1027000  150.00  754000  629457  1953  1964  12.10  9895290  5.17  1965  12.29  9814400  5.23  5.45 5.64  1966  12.73  10697440  5.16  4056000  6.24  17945000  140.20  1677000  1967  12.04  12305880  5.36  3926000  6.52  17830000  143.80  1647000  227.70  1026000  149.00  788000  643006  1968  11057320  5.38  4054000  7.01  17537000  147.90  1596000  229.90  1080000  145.00  834000  628748  1969  13.98 14.12  11972420  5.95  4286000  7.57  17936000  147.80  1745000  232.30  1140000  149.00  920000  642096  1970  16.81  10263110  6.80  4215000  17832000  145.60  1685000  236.60  1198000  161.00  929000  689304  1971  17.51  9791740  7.48  4243000  8.03 8.44  17132000  151.00  1608000  232.40  1220000  159.00  868000  755349  1972  17.37  10346450  7.30  4592000  9.30  16970000  155.70  1624000  237.00  1311000  152.00  944000  811341  1973  18.06  10486980  4524000  10.10  1770000  277.20  1462000  188.00  844000  859494  21.08  11204560  4893000  11.48  17326000 17753000  165.70  1974  8.35 8.74  203.40  1778000  374.60  1625000  303.00  896000  1011246  1976  23.43  11472000  12.23  3995000  13.74  17302000  305.90  1410000  441.40  I 182000  370.00  733000  1460365  1977  24.70  13820000  16.09  4787000  17.05  17329000  344.50  1610000  463.70  1476000  384.00  944000  1700807  1978 1979  26.33  14544000  18.00 19.49  367.70  1663000  489.70  1653000  367.00  928000  1881779  15299000  5054000 5118000  17797000  28.45  16.11 17.97  17881000  424.90  1743000  570.50  1809000  470.00  965000  2081767  1980  30.38  15872000  20.02  5087000  20.86  18328000  477.00  1734000  634.90  1787000  577.00  1037000  2408253  1743000  694.70  1819000  603.00  1131000  2966118  1981  34.61  15735000  21.88  5029000  23.88  17879000  533.60  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 $/m3  m3  $/000  0 0 0 kwh  kwh 1950  10.10  0 0 0 $/W  no.w*000  $/MT  News q u . 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  $/MT  Pulp qu. Capital s t . MT 000 $  / year  11768540  2.88  5589000 6049000  2.99 3.47  19236000  104.10  2509000  157.60  20538000  110.90  2617000  174.70  549472 626792  125 179  388000  184536  472000  216224  1951  11.84  13027780  2.84  1952  13.15  12740690  2.91  6717000  3.66  20041000  115.40  2693000  181.40  546566  166  408000  246118  1953  12.87  12625320  3.06  7084000  3.78  20279000  120.50  2687000  176.20  580990  141  410000  266203  1954  12.05  13182110  2.85  7645000  120.50  2794000  184.80  587746  137  459000  276338  11.44  13949990  3.16  7260000  3.81 3.87  21680000  1955  22936000  121.80  2868000  183.80  628481  498000  320957  3.59 3.47  6539000  4.24  24204000  126.00  3022000  179.40  499000  368190  7286000  4.34  23293000  126.60  2974000  186.00  743699 693941  139 141 141  480000  412512  1956  12.07  14559590  1957  12.50  13639570  1958  12.21  12303860  3.12  8904000  4.32  22407000  127.60  2698000  189.80  713828  142  412000  444729  1959  12.03  12806340  8918000  4.50  22523000  126.40  2764000  194.00  772000  140  415000  461314  1960  12.03  13000840  3.21 3.01  9960000  4.81  21909000  127.90  2863000  198.90  750000  138  623000  481912  1961  11.89  13445060  3.12  9744000  21841000  130.10  2855000  182.60  622000  506581  11.39  13542500  3.38  9219000  21667000  132.30  2829000  223.30  691000  525325  1963  11.77  13955030  3.70  8105000  5.39  21467000  131.10  2811000  219.70  737269 841014  133 134  657000  1962  5.05 5.24  121  757000  558685  1964  11.81  15218850  3.90  8301000  5.58  22376000  130.00  3107000  221.00  1965  11.98  15798030  4.08  8229000  5.79  22842000  129.70  3245000  1966  12.54  17557860  4.32  8440000  6.34  24023000  132.70  1967  17451500  4.53  7978000  134.50  17444840  8379000  23264000  1969  13.84  19250660  4.44 4.67  6.61 7.11  23905000  1968  11.98 13.69  9092000  7.70  24172000  1970  16.47  16362340  4.68  9264000  8.13  24282000  1971  16.69  15538350  4.75  9301000  8.62  23351000  141.90  3609000  1972  17.05  15687080  4.56  10275000  9.58  22885000  144.50  3793000  128  814000  618952  220.80  782975 876444  133  653000  703730  3579000  218.70  1081833  138  651000  788040  3440000  224.10  1132173  145  604000  856976  135.20  3501000  214.40  1171788  146  593000  903845  136.10 140.30  3777000  224.60  1304287  148  673000  977380  3766000  225.30  1372830  159  628000  1054409  226.10  1375830  158  664000  1101747  228.00  1530231  146  581000  1158146  1973  18.46  14915390  4.50  10720000  10.12  21727000  159.90  3670000  254.60  1514643  178  450000  1286503  1974  22.42  17237030  11588000  11.54  24612000  212.20  4079000  353.20  1616406  319  576000  1592683  1976  22.25  20521000  5.20 6.41  12029000  14.85  25382000  264.50  3930000  381.30  1270348  321  761000  2161316  1977  24.37  20873000  7.44  11962000  16.40  24279000  311.00  3726000  396.60  1396080  325  623000  2383114  1978  25.11  23363000  8.93  13225000  18.13  24604000  341.80  4124000  416.50  1684966  338  691000  2646482  1979  27.31  25616000  13250000  19.25  25086000  382.50  4075000  479.10  1995381  468  886000  2990426  1980  28.37  24053000  11.25  13926000  20.99  23992000  455.10  3790000  553.90  1763612  569  798000  3462013  1981  32.42  24835000  13.12  15000000  24.36  25140000  505.70  4452000  601.60  1698550  592  865000  4069819  10.12  APPENDIX B.  ESTIMATION RESULTS  Table B.I. British Columbia Full Translog model results.  Equation Variable L Profit function F E A K T LL LF LE LA FF FE FA EE EA AA KL TL KF TF KE TE KA TA KK KT INTERCEPT 0.69 R2 D.W. 0.85 Total Paoer shflre  R2 D.W.  Estimated Coefficient -99.53 -113.73 17.96 234.80 -610.39 -796.94 -0.20 -0.10 -0.03 0.18 -0.20 -0.01 0.06 -0.03 0.05 -0.01 -0.04 13.05 -0.12 15.06 0.01 -2.41 0.10 -30.95 -1.00 82.18 5976.60  A -0.01 F 0.06 E 0.05 L 0.16 U -0.29 K 0.10 T -30.93 INTERCEPT 234.67 -0.09 1.14  t-value -0.80 -0.54 0.51 0.48 -2.42 -1.52 -11.69 -7.48 -3.62 6.89 -4.43 -0.82 0.92 -1.85 13.72 -0.03 -0.47 0.79 -0.80 0.53 0.60 -1.00 0.27 -0.47 -2.75 2.42 1.51  -0.05 0.91 3.18 5.83 0.27 -0.47 0.48  Estimated Equation Variable Coefficient Fibre F -0.20 share E -0.01 L -0.10 A 0.06 U 0.23 K -0.12 T 15.06 INTERCEPT - 113.72 R2 0.23 D.W. 0.85 E -0.03 Energy share F -0.01 L -0.03 A 0.05 U 0.01 K 0.09 T -2.42 INTERCEPT 17.98 R2 0.62 D.W. 1.29 Labour L -0.20 share F -0.10 E -0.03 A 0.18 U 0.15 K -0.04 T 13.04 INTERCEPT -99.48 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  t-yalMe -4.43 -1.07 -7.45 0.91 -0.80 0.53 "0,54  -5.28 -1.07 -5.41 3.18 0.50 -0.69 0.69  -12.51 -7.45 -5.41 5.83 -0.47 0.76 -0.80  Table B.2. British Columbio Reduced Translog Model results  Estimated Eauotlon Variable Coefficient Fibre share  R2 D.W. Energy share  R2 D.W. Labour share  R2 D.W.  t-value  -0.09 F 0.01 E 0.01 L A -0.30 u 0.38 K -0.40 T 62.89 INTERCEPT -471.99 0.36 1.66  -1.81 1.19 0.15 -2.68  -0.03 E 0.01 F L -0.02 A 0.01 U 0.02 K -0.02 T 2.77 INTERCEPT -20.92 0.69 1.57  -5.18 1.19 -2.86 0.73  L -0.09 F 0.01 E -0.02 A -0.08 U 0.16 K -0.22 T 42.43 INTERCEPT -319.18 0.43 1.66  -3.12 0.15 -2.86 -0.99  -2.55 2.19 -2.19  -1:04 0.79 -0.79  -2.43 2.50 -2.50  Estimated Equation Variable Coefficient Total oaoer share  R2 D.W. Pulo share  A 0.76 F -0.3 E 0.01 U -0.42 K 0.76 T -147.78 INTERCEPT 1109.8 0.17 1.68 -0.16 U F 0.38 E 0.02 L 0.18 A -0.42 K -0.12 39.69 T INTERCEPT -296.71  t-value 2.69 -2.68 0.73 2.06 -2.19 2.19  Table B.3. Ontario Full Translog Model results Estimated Eauation Variable Coefficient t-value Eauation ProfU  funrtipn  L  F E  N p K T LL LF LE LN LP FF FE FN FP EE EN EP NN NP PP KL TL KF TF KE TE KN TN INTERCEPT R2 D.W.  -239.8 -254.21 -15.51 461.76 2.59 -1.01 293.77 -0.36 -0.22 -0.05 0.34 0.17 -0.36 -0.04 0.16 0.36 -0.04 0.03 0.06 -0.05 -0.14 -0.32 -0.13 31.55 -0.12 33.44 -0.01 2 0.2 -60.93 -2208.9  -6.90 -5.10 -0.18 12.20 8.63 -3.72 6.66 -9.29 -10.20 -0.46 3.02 1.51 -9.96 -4.36 5.90 2.62 -0.37 2.95 0.56 -0.19 -0.83 -1.00 -3.60 6.08 -2.81 7.52 -0.66 0.07 3.33 -9.01 -9.08  Fibre share  Variable  Estimated Coefficient  F -0.36 E -0.04 L -0.22 N 0.16 P 0.36 U 0.1 K -0.12 T 33.37 INTERCEPT -253.74  R2 D.W.  0.75 1.46  Energy share  E F L N P U K T INTERCEPT  t-value -8.99 -3.94 -8.93 4.42 9.02 -2.58 4.64 -4.7  -0.04 -0.04 -0.05 0.03 0.06 0.03 -0.1 1.8 -13.99  -5.07 -3.94 -4.09 2.53 4.27 -1.12 1.19 -1.23  R2 D.W.  0.89 1.31  Labour share  L -0.36 F -0.22 E -0.05 N 0.33 P 0.17 U 0.13 K -0.13 T 31.6 INTERCEPT -240.19  -11.04 -8.95 -4.09 11.87 6.01  0.86 1.98  R2 D.W.  0.69 1.84  -3.44 5.22 -5.28  Table B.3. Confd Estimated Equation Variable Coefficient t-value Herfsorlnt share  N F E  L p u K T INTERCEPT  R2 D.W. PulD share  -0.05 6.16 0.03 0.33 -0.14 -0.34 0.2 -60.84 461  0.85 1.85 U F E L N P K T INTERCEPT  -0.83 4.42 2.53 11.87 -2.63  Estimated Equation Variable Coefficient Other pooer P share F E  L N  U K  3.98 -7.77 7.84  T INTERCEPT  R2 D.W. 0.21 0.1 0.03 0.13 -0.34 -0.13 0.02 -5.86 45.34  0.82 1.27  -0.32 0.36 0.06 0.17 -0.14 -0.13 0.04 -0.08 2.58  t-value -3.74 9.02 4.27 6.01 -2.63 3.2 -3.81 10.75  Table B.4. Ontario Reduced Translog Model results  Equation Variable  Estimated Coefficient  -0.3 -0.03 L -0.21 N 0.13 P 0.35 0.07 U K -0.07 T 25.44 INTERCEPT -194.11 0.76 1.51 F  E  Energy. share  E  F L N P  U K T INTERCEPT R2 D.W.  Labour share  R2 D.W.  -0.04 -0.03 -0.04 0.02 0.07 0.03 <0.01 0.3 -2.69  t-value -5.79 -2.44 -4.61 2.29 7.58  -0.25 -0.21 E -0.04 N 0.21 P 0.19 U 0.11 K -0.03 T 13.13 ERCEPT -100.99 0.73 1.82 F  share  L P  U K T INTERCEPT R2 D.W.  -4.99 -2.44 -2.96 1.47 4.25  E  L N  U K T INTERCEPT R2 D.W.  -0.61 1.51 -1.54  Pulp share  t-value  0.11 0.13 0.02 0.21 -0.16 -0.31 0.08 -36.4 291.98  1.4 2.29 1.47 3.99 -2.48  -0.3 0.35 0.07 0.19 -0.16 -0.14 0.06 -5.11 40.4  -3.48 7.58 4.25 4.19 -2.48  1.17 -3.44 3.47  0.87 1.86  Other paner P share F  0.08 1.86 14.00  -4.75 -4.81 -2.96 3.97 4.19  F E  -1.08 2.56 -2.59  0.9 1.36 L  Estimated Equation Variable Coefficient  0.83 1.32 U F  0.24 0.07 0.03 0.11 -0.31 -0.14 -0.05 4.64 -33.57  E L N P K T INTERCEPT System R 2 0.9996 Chi 2 245.59 with 25 D F .  1.24 -0.61 0.64  Table B.5. Quebec Full Translog Model results  Equation  Profit  function  R2 D.W.  Estimated Estimated Voriable Coefficient t-value Equation Variable Coefficient  L  F E N P K T LL LF LE LN LP FF FE FN FP EE EN EP NN NP PP KL TL KF TF KE TE INTERCEPT  -415.04 195.02 -92.85 1.88 2.60 -0.76 308.29 -0.47 -0.15 -0.01 0.25 0.18 -0.17 0.08 0.17 0.38 -0.03 -0.03 0.06 0.39 -0.62 0.06 -0.21 54.80 0.25 -26.42 -0.07 12.31 2321.60  -5.09 1.64 -2.92 5.05 7.34 -1.94 4.50 -7.43 -7.25 -0.25 4.61 3.98 -2.69 -5.75 1.94 8.05 -1.52 -1.32 3.12 3.11 -9.85 0.72 -3.88 5.11 3.32 -2.14 -2.70 2.16 -4.50  Fibre share  R2 D.W.  Energy share  R2 D.W.  Labour share  0.85 1.30  R2 D.W.  F E L N P U K T INTERCEPT  t-value  -0.17 -0.08 -0.15 0.17 0.38 -0.14 0.25 -26.42 195.01  -2.34 -5.74 -3.5 1.91 7.43  -0.03 -0.08 -0.01 -0.03 0.06 0.09 -0.07 12.31 -92.85  -2.71 -5.74 -0.28 -1.48 3.07  3.17 -1.87 1.84  0.64 1.14 E F L N P U K T INTERCEPT  -2.84 2.64 -2.65  0.22 1.2 L F E N P  -0.47 -0.15 -0.01 0.25 0.18 U 0.2 K -0.21 T 54.8 INTERCEPT -415.04 -415.04 -5.11  -7.55 -3.5 -0.28 4.75 3.96 -3.86 5.07 -5.11  Table B.5. Cont'd  Estimated EflUSiM Variable Coefficient t-value Eouation Variable Newsorint share  R2 D.W. PUlD share  N F E L P U K T INTERCEPT  0.39 0.17 -0.03 0.25 -0.62 -0.15 -0.18 0.41 1.88  0.64 1.35 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  3.11 1.91 -1.48 4.75 -8.69 -7.94 0.04 5.03  Estimated Coefficient  QUierDflDer P 0.06 share F 0.38 E 0.06 L 0.18 N -0.62 U -0.07 K 0.68 T -0.17 INTERCEPT 2.6 R2 D.W.  0.89 1.65  t-value 0.66 7.43 3.07 3.96 -8.69 3.71 -5.95 7.34  Table B.6. Quebec Reduced Translog Model Results  Estimated Eguqtipn, Variable Coefficient H a l U E F -0.40 E -0.08 L -0.14 N 0.46 P 0.31 U -0.16 K -0.12 T 36.24 INTERCEPT -275.52 0.66 1.24 E F L N P U K T INTERCEPT 0.44 1.31 Labour share  R2 D.W.  -4.42 -4.66 -2.56 4.34 5.20 -1.94 -0.78 1.30 -1.32  Equation Variable Newsprint share  -0.45 -4.66 1.92 -2.16 1.52  L -0.47 F -0.14 E 0.04 N 0.34 P 0.09 U 0.13 K -0.23 T 57.67 INTERCEPT -436.27 0.85 1.69  -6.47 -2.56 1.92 5.34 1.99  -0.71 0.10 -0.10  -2.96 3.82 -3.84  t-value  N -0.1 F 0.46 E -0.05 L 0.34 P -0.47 U -0.18 K 0.49 T -118.96 INTERCEPT 898.85 0.74 1.65  -0.6 4.34 -2.16 5.34 -4.62  Other oaoer P 0.07 share F 0.03 0.03 E L 0.09 N -0.47 U -0.03 K -0.12 T 37.31 INTERCEPT -279.56 R2 0.87 D.W. 1.27  0.65 5.2 1.52 1.99 -4.62  R2 D.W.  -0.01 -0.08 0.04 -0.05 0.03 0.06 -0.02 0.50 -3.70  Estimated Coefficient  PulD share  U F E L N P K T INTERCEPT  0.18 -0.16 0.06 0.13 -0.18 -0.03 <0.01 -12.75 95.2  2.39 -3.22 3.24  -0.96 1.63 -1.63  Table B.7.  ble L F E A N P U K T LL LF LE LA LN LP FF FE FA FN FP EE EA EN EP AA NN  Description of Variables.  description  variable  Labour price NP Fibre price PP Energy price LK Total peper&paperb.price LT Newsprint price FK Other paper&paperb.prtce FT Net mrkt. pulp price EK Capital stock ET Time trend AK labour pr. * labour pr. AT labour pr * fibre pr. NK labour pr. * energy pr. NT labour pr. * totol paper pr. PK labour pr. * newsprint pr. PT labour pr. * other paper pr. fibre pr. " fibre pr. fibre pr. * energy pr. fibre pr. • total paper pr. fibre p r . " newsprint pr. fibre pr. • other paper pr. energy pr. • energy pr. energy pr. * total paper pr. energy p r . « newsprint pr. energy pr. » other paper pr. total paper pr. * total paper pr. newsprint p r . " newsprint pr.  description newsprint pr. * other paper price other paper price * other paper price labour pr. * capital labour pr. * time trend fibre pr. * capital fibre pr. * time trend energy pr. * capital energy pr. * time trend Total paper&paperb. price * capital Totol paper&paperb. price * time trend newsprint pr. * capital newsprint pr. * time trend other paper pr. * capital other paper pr. * time trend  note: 1. All prices are normalized by the price of pulp. 2. All prices expressed as natural logarithms of nominal prices.  

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