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Modelling wood quality, productivity, demands and supplies in the sawmilling industry : British Columbia… Constantino, Luis Fragoso 1986

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M O D E L L I N G W O O D Q U A L I T Y ; P R O D U C T I V I T Y , D E M A N D S A N D S U P P L I E S IN THE S A W M I L L I N G INDUSTRY; BRITISH C O L U M B I A C O A S T A N D PACIF IC N O R T H W E S T W E S T S I D E by LUIS F R A G O S O C O N S T A N T I N O L ic .Eng.S i lv . , L i s b o n Techn ica l Un ivers i ty , 1978 A T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L L M E N T OF T H E R E Q U I R E M E N T S FOR T H E D E G R E E OF D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y OF G R A D U A T E S T U D I E S (Department of Forest ry ) W e accept this thes is as c o n f o r m i n g to the r e q i i H ^ d standard THE UNIVERSITY OF BRITISH C O L U M B I A M a y , 1986 ® Luis F r a g o s o C o n s t a n t i n o , 1986 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 o f the requirements f o r an advanced degree a t the U n i v e r s i t y 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 i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r 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 of 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 my department or by h i s o r her r e p r e s e n t a t i v e s . I t 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 g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . r Department of The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 ii ABSTRACT The main purpose of this thesis is to empi r ica l ly evaluate the impacts of s a w l o g s c a r c i t y , revealed in the increasing pr ices and d e c r e a s i n g qual i ty , on the s a w m i l l i n g industr ies of the Brit ish C o l u m b i a (BC) Coas t and the Uni ted Sta tes P a c i f i c Nor thwest (PNW) W e s t s i d e . The ob jec t ives of the research are: (1) to test whether w o o d qual i ty has dec l ined o v e r t i m e ; (2) to evaluate the extent to which lagging product iv i ty per fo rmance of the industry can be expla ined through dec l in ing w o o d qual i ty ; and, (3) to m o d e l the industry e c o n o m e t r i c a l l y in order to measure s h o r t - r u n input and output r e s p o n s e s to changes in w o o d price and qual i ty . W o o d qual i ty is def ined as the ratio of a quantity index of the s a w l o g input to the total vo lume of w o o d c o n s u m e d . The quantity index is an aggregate of grades and s p e c i e s harvested and t raded. Qual i ty change is d e c o m p o s e d into two e f f e c t s : a grade e f fec t and a s p e c i e s e f f e c t . It is s h o w n that f r o m 1925 through 1980/1982 the qual i ty of w o o d harvested and traded in B C dec l ined on average , wi th both the s p e c i e s and grade e f f e c t s contr ibut ing to the qual i ty dec l ine . F r o m 1957 through 1982 w o o d qual i ty remained stable in B C whi le it d e c l i n e d c o n s i d e r a b l y in the P N W . The qual i ty level of the w o o d traded is c o n s i d e r a b l y higher, on average, in the P N W , but this reg ion is los ing its qual i ty advantage relat ive to B C . Regional d i f f e r e n c e s in average w o o d pr ices are c o m p l e t e l y expla ined away by qual i ty d i f f e r e n c e s , and s o there is no ev idence that the BC industry benef i ts f r o m a w o o d c o s t advantage relat ive to the P N W o n e . A measure of total factor product iv i ty is d e v e l o p e d f r o m a product ion f u n c t i o n . It is s h o w n that in the P N W the rate of technical p r o g r e s s is c lear ly higher when the w o o d qual i ty decl ine is accounted for . W h e n rates o f technical iii p rogress are c o m p a r e d , it is found that B C lags behind the P N W , and that the relat ive product iv i ty l o s s e s in BC are even greater when w o o d qual i ty changes are c o n s i d e r e d . When product iv i ty leve ls are c o m p a r e d , it is found that the P N W industry is the m o s t e f f ic ient o f the two reg ions . H o w e v e r , when w o o d quality d i f f e r e n c e s are accounted for , B C b e c o m e s the most e f f ic ient of the t w o reg ions on average. The regional industr ies are m o d e l l e d e c o n o m e t r i c a l l y using a stat ic t ranslog restr ic ted prof i t f u n c t i o n . Lumber and pu lpchips are var iable outputs and s a w l o g s and labour are var iable inputs, whi le capital is a f ixed fac tor . W o o d qual i ty and technical p rogress are exogenous sh i f te rs . Annual observa t ions f r o m 1957 through 1981 are ut i l ized for es t imat ion . The P N W mode l ou tper fo rms the B C m o d e l in te rms o f its theoret ical c o n s i s t e n c y with the prof i t max imiz ing h y p o t h e s i s . The h y p o t h e s e s that w o o d quality d o e s not be long in the m o d e l , or that it is suf f ic ient to use qual i ty adjusted p r i c e s , are both s ta t is t ica l ly re jec ted . Constant returns to sca le can not be re jected in the P N W , whi le increas ing returns are f o u n d in B C . Constant output d e m a n d and constant input supp ly e las t ic i t i es are c o m p u t e d in addi t ion to total s h o r t - r u n e las t ic i t ies . It is f o u n d that shor t - run input subst i tut ion e f f e c t s are negl ig ib le when c o m p a r e d with the v e r y large output e f f e c t s . The p r o p o r t i o n of pu lpchips in output is pr ice r e s p o n s i v e . In both reg ions , a dec l ine in w o o d qual i ty m o v e s the industry to a more pulpchip intensive region o f the output s p a c e and to a more labour intensive region of the input s p a c e . In the P N W , the es t ima ted rate o f technica l p rogress is three t i m e s lower when w o o d qual i ty is o m m i t t e d f r o m the m o d e l , but in B C , where w o o d qual i ty changed l e s s , the rate of technical p r o g r e s s is not not iceab ly a f f e c t e d . iv TABLE OF CONTENTS ABSTRACT ii TABLE OF CONTENTS ; iv LIST OF TABLES vii LIST OF APPENDIX I TABLES x LIST OF APPENDIX II TABLES xi LIST OF FIGURES xii AKNOWLEDGEMENTS xiv 1. INTRODUCTION 1 1.1 Objectives and Relevance of the Research 1 1.2 Main Research Hypotheses 8 1.3 Related Literature 9 1.4 Plan of the Thesis 18 Footnotes 21 2. THE SAWMILLING INDUSTRY ON THE BRITISH COLUMBIA COAST AND PACIFIC NORTHWEST WEST 22 2.1 Introduction 22 2.2 Summary of the Data Utilized _ 23 2.3 Factor and Output Markets .28 2.4 Regulations 31 2.5 Historical Trends in the Regional Industries 33 2.6 Trends in Innovations in the Sawmilling Industry .42 Footnotes .„. , .49 3. MEASURING WOOD QUALITY 50 3.1 Introduction 50 3.2 Approaches for the Measurement of Quality Change 53 3.3 The Measurement of Sawlog Quality 55 3.4 Trends and Levels of Sawlog Quality on the BC Coast and PNW West .66 3.5 Conclusions .86 Footnotes 89 V 4. IMPACTS OF CHANGING WOOD QUALITY ON TOTAL FACTOR PRODUCTIVITY COMPARISONS 90 4.1 Introduction 90 42 Total Factor Productivity Model 92 4.3 Growth Rates and Relative Levels of Total Factor Productivity in the Regional Sawmilling Industries .95 4.4 Conclusions 100 Footnotes 104 5. AN ECONOMETRIC MODEL OF THE SAWMILLING INDUSTRY ON THE BC COAST AND PNW WEST 105 5.1 Introduction 105 5.2 The Theoretical Model 109 5.3 The Empirical Model 121 5.4 The Statistical Model ~ 136 Footnotes 138 6. EMPIRICAL RESULTS 139 6.1 Introduction 139 6.2 Experiments 139 6.3 Parameter Estimates, Summary Statistics, Profit Function Properties and Test Results 143 6.4 Elasticities and Rates of Technical Progress 163 6.5 Global Assessment of Econometric Model and Test of Research Hypotheses 178 7. EXTENSIONS OF THE RESEARCH 188 7.1 Introduction 188 7.2 Determinants of Trends in Relative Regional Lumber Outputs 189 7.3 Determinants of Trends in Relative Regional Lumber Recoveries and Chip/Lumber Proportion 192 7.4 Impacts of Quality Change on Unit Production Costs, Returns to Capital and Log Utilization Patterns 195 7.5 Log Export Restrictions „ 202 7.6 Tariffs on Canadian Lumber Exports to the US 203 7.7 One Area for Further Research; Measuring the Size of the BC Economic Timber Inventory 204 7.8 Other Areas for Further Research 206 8. SUMMARY AND CONCLUSIONS ; 209 BIBLIOGRAPHY 220 APPENDIX I - DATA DESCRIPTION 238 1. INTRODUCTION 238 vi 2. BRITISH COLUMBIA COAST 238 2.1 Lumber and Shingle Price Index 238 2.2 Lumber and Shingle Revenue and Implicit Volume 240 2.3 Pulpchip Price ' 240 2.4 Pulpchip Revenue and Implicit Volume 241 2.5 Sawlog Price 242 2.6 Sawlog Volume and Expenditures with Wood 242 2.7 Labour Wage Index 243 2.8 Expenditures with Labour and Implicit Labour Input 244 3. PACIFIC NORTHWEST WESTSIDE 244 3.1 Lumber and Shingles Price Index 244 3.2 Lumber and Shingle Revenue and Implicit Volume 247 3.3 Pulpchip Price .'. 249 3.4 Pulpchip Revenue and Volume 249 3.5 Sawlog Price 254 3.6 Sawlog Volume and Expenditures with Wood 255 3.7 Labour Wage Index 256 3.8 Expenditures with Labour and Implicit Labour Input 257 4. CAPITAL STOCK 258 4.1 Real Capital Stock in BC and in the PNW 258 4.2 User Cost of Capital in BC and in the PNW 261 4.3 Aggregate Capital Stock in the BC Coast and PNW West 264 5. A CRITIQUE OF THE DATA 265 6. DATA LISTINGS 266 Footnotes 268 APPENDIX II - RESULTS OF ALTERNATIVE SPECIFICATIONS OF THE ECONOMETRIC MODEL -.276 vii LIST OF TABLES 1.1 Wood Products Industry Studies in North America - Description, Model Specification and Assumptions 11 1.2 Wood Products Industry Studies in North America - Results: Labour Productivity, Technical Progress and Biases of Technical Progress 16 1.3 Wood Products Industry Studies in North America - Results: Elasticities of Substitution, Constant Output Demand Elasticities and Degree of Returns to Scale 19 2.1 Distribution of Sawmilling Manufacturing Costs by Major Components in BC and PNW, Selected Years 24 2.2 Description of the Data Utilized 27 2.3 Average Growth Rates and Relative Levels of Quantities and Nominal Prices of the Several Sawmilling Inputs and Outputs, 1957-1982: BC, PNW and BC Relative to the PNW 35 2.4 Average Growth Rates and Relative Levels of Single Factor Productivities. Input and Output Ratios and Relative Prices, 1957-1982: BC, PNW and BC Relative to the PNW 37 2.5 Trends in the Supply of Innovations in BC and PNW .45 2.6 Machinery Demanded in Mills Visited in BC .47 3.1 Discrete Equations Utilized in the Construction of Quality Indices 64 3.2 Components of the Log Aggregate for the Vancouver Log Market 68 3.3 Components of the Log Aggregate for the Pacific Northwest Log Market ....69 3.4 Components of the Log Aggregate for the Vancouver Forest Region 73 3.5 Average Growth Rates of Wood Quality and Relative Wood Quality Levels in the Vancouver Forest Region and Vancouver Log Market (Statutory Grades, Board Foot Log Scale) 75 3.6 Average Growth Rates of Wood Quality in the Vancouver and Pacific Northwest Log Markets (All Grades and Sawlog Grades, Board Foot Log Scale) .82 3.7 Average Growth Rates of Wood Quality, Relative Wood Quality Levels and Board Foot Scale Effect in the Vancouver and Pacific Northwest Log Markets (Sawlog Grades, Cubic Meters) .82 4.1 Average Growth Rates of Total Factor Productivity and Input Contributions to Output Growth 96 4.2 Average Relative Levels of Total Factor Productivity and Input Contribution to Output Differences 99 viii 5.1 Summary of the Properties of the Profit Function Imposed and Checked ..126 5.2 Summary of Tests on the Characteristics of the Profit Function 127 5.3 Expected Signs for Some of the Relationships 135 6.1 Initial Model - British Columbia Parameter Estimates and Summary Statistics 145 6.2 Initial Model - Pacific Northwest Parameter Estimates and Summary Statistics 146 6.3 Initial Model - Violations of Properties of the Regional Profit Functions ..148 6.4 Initial Model - Violations of Expected Signs of Economic Relationships ....151 6.5 Results of Tests on the Characteristics of Regional Profit Functions -Wood Quality 153 6.6 Results of Tests on the Characteristics of Regional Profit Funcitons -Homogeneity and Technical Progress . .....154 6.7 Results of Tests on the Characteristics of Regional Profit Functions -Regional Differences 155 6.8 Alternative Model Specifications - Violations of Properties of the BC Profit Function 159 6.9 Alternative Model Specifications - Violations of Properties of the PNW Profit Function 160 6.10 Alternative Model Specifications - Violations of Expected Signs of the BC Profit Function 161 6.11 Alternative Model Specifications - Violations of Expected Signs of the PNW Profit Function 162 6.12 Initial Model - Demand and Supply Elasticities 164 6.13 Initial Model - Elasticities of Selected Input and Output Ratios 167 6.14 Initial Model - Constant Output Demand Elaticities 169 6.15 Initial Model - Constant Input Supply Elasticities 173 6.16 Comparison Between Initial and Alternative Model Specifications - Own Elasticities of Demands and Supplies 177 6.17 Comparison Between Initial and Alternative Model Specifications -Elasticities with Respect to Capital and Wood Quality 179 6.18 Comparison of Rate of Technical Progress Estimates of the Models With and Without Wood Quality 185 ix 7.1 Causes Behind the Increasing BC/PNW Relative Lumber Production 191 72 Causes Behind the Declining BC/PNW Relative Lumber Recovery 194 8.1 Summary of Tests of Main Research Hypotheses 210 X LIST OF APPENDIX I TABLES A.1.1 BC Coast - Lumber and Shingle Price Index, Implicit Quantity Index and Revenue; Pulpchip Price, Volume and Revenue 269 A.l .2 BC Coast - Average Sawlog Price, Sawlog Volume, Sawlog Expenditure and m3/Mfbm (BC Log Scale) Conversion Factor 270 A.1.3 BC Coast - Wage Index, Implicit Index of Man-hours Paid and Expenditures with Labour Index of the User Cost of Capital, Index of Real CapitalStock and Expenditures with Capital 271 A.1.4 PNW West - Lumber and Shingle Price Index, Implicit Quantity Index and Revenue; Pulpchip Price, Volume and Revenue 272 A.1.5 PNW West - Average Sawlog Price.Sawlog Volume, Sawlog Expenditure and mVMfbm (Scribner Log Scale) Conversion Factor 273 A.1.6 PNW West - Wage Index, Implicit Index of Man-hours Paid and Expenditures with Labour; Index of User Cost of Capital, Index of Real Capital Stock and Expenditures with Capital 274 A.1.7 Wood Quality Indices (one-stage) - Vancouver Forest Region, Vancouver Log Market and PNW Log Market 275 xi LIST OF APPENDIX II TABLES A.2.1 No Wood Quality - British Columbia Parameter Estimates and Summary Statistics 277 A.2.2 No Wood Quality - Pacific Northwest Parameter Estimates and Summary Statistics 278 A.2.3 Across Region Retrictions on Wood Quality and Time Trend - Britsh Columbia Parameter Estimates and Summary Statistics 279 A.2.4 Across Region Restrictions on Wood Quality and Time Trend -Pacific Northwest Parameter Estimates and Summary Statistics 280 A.2.5 Homogeneous of Degree One in Capital - British Columbia Parameter Estimates and Summary Statistics 281 A.2.6 Homogeneous of Degree One in Capital - Pacific Northwest Parameter Estimates and Summary Statistics 282 A.2.7 No technical Progress - British Columbia Parameter Estimates and Summary Statistics 283 A.2.7 No technical Progress - British Columbia Parameter Estimates and Summary Statistics 284 A.2.9 No Wood Quality - Demand and Supply Elasticities 285 A.2.10 Across Region Restrictions on Wood Quality and Time Trend -Demand and Supply Elasticities 286 A.2.11 Homogeneous of Degree One in Capital - Demand and Supply Elasticities 287 A.2.12 No Technical Progress - Demand and Supply Elasticities 288 xii LIST OF FIGURES 2.1 Lumber and Shingle Implicit Quality Index - BC and PNW 34 2.2 Aggregate Capital Stock - BC and PNW ; 34 2.3 Trends in Lumber Recovery - BC and PNW 38 2.4 Trends in Chip Recovery - BC and PNW 38 2.5 Trends in Labour Productivity - BC and PNW 39 2.6 Trends in Capital Productivity - BC and PNW 39 2.7 Trends in the Wood Consumed per Unit of Laoubr - BC and PNW .40 2.8 Trends in the Wood/Labour Relative Price - BC and PNW .40 3.1 Wood Quality and Species and Grade Effects in the Vancouver Forest Region (Statutory Grades, BC Board Foot Log Scale) .77 3.2 Wood Quality of Individual Species in the Vancouver Forest Region: Douglas-fir, Cedar and Hemlock (Statutory Grades, BC Board Foot Log Scale) .77 3.3 Wood Quality in the Vancouver Forest Region and Vancouver Log Market (Statutory Grades, BC Board Foot Log Scale) 78 3.4 Sawlog Quality in the Vancouver Log Market: Cubic Meter Index, Board Foot Index and Log Scale Effect (Sawlog Grades) .78 3.5 Wood Quality in the Vancouver and Pacific Northwest Log Markets (Sawlogs, Cubic Meters .85 3.6 Average and Quality Adjsuted Sawlog Prices in the Vancouver and Pacific Northwest Log Markets 85 5.1 Average Gross Lumber Recovery Factor for Various Small-Log Feed-works and Heading Combinations, 16-ft (4.88m) Straight Logs, Random Length Dimension 2 in. (50mm) Only 126 5.2 Lumber and Chip Values per Unit Related to Tree DBH for Risk Group 1 Trees 126 6.1 Own Elasticities of Lumber Supply 176 6.2 Own Elasticities of Sawlog Demand 176 7.1 Impacts of Wood Quality on Unit Lumber Production Costs 196 7.2 Impacts of Wood Quality on Returns to Capital 196 7.3 Impacts of Wood Quality on Log Utilization Patterns in British Columbia .198 xiii 7.4 Impacts of Wood Quality on Log Utilization Patterns in the Pacific Northwest 198 7.5 Trends in the Marginal Profitability of Wood Quality in the Pacific Northwest During the Period 1957-1973 200 7.6 Simulation of PNW Production Costs Under BC Economic Conditions 200 AKNOWLEDGEMENTS xiv Many people contributed invaluable advice and support during this seemingly never ending project. Dr. D. Haley helped to identify the research boundaries and to keep my mind on track, while at the same time trusting me with enough space to pursue my own research interests. Drs. W. Schworm and M. Slade offered their knowledge, time and patience in answering many questions and provided an essential support to the initial research proposal. Thanks are also due to Drs. P. Pearse, R. Barichello, G. Schreuder and J. Dobie for their suggestions during various phases of this project. I benefitted imensely from my close collaboration with the staff of the Forest Economics and Policy Analysis Project and I am indebted to Dr. P. Pearse for having encouraged the use of its considerable resources. Dr. T. Heaps provided a light in the tunnel in several moments of intellectual agony and was always available for discussions concerning my thesis work. All the other staff at FEPA helped in one way or another. In particular I wish to express my thanks to Dr. R. Uhler, M. Fullerton, M. Wernerheimer and S. Klein. G. Townsend gave me valuable assistance with the data collection and preliminary data analysis. K. Todd also provided computational help. I benefitted from discussions with Dr. B. Abt, M. Luckert, L. Hamdi, S. Caghill, P. Cardellichio and in particular Dr. D. Gordon,-who taught me a lot. Dr. R. Haynes, C. Jackson and F. Ruderman gave essential help with the collection of PNW data. S. Chow devoted her skill, persistence and knowledge of hieroglyphs to the typing of several versions of this thesis. At last, I wish to thank Dr. D. Tait, J. Hacket and G. Townsend for their supporting friendship during my staying at UBC. Financial support for this research was provided by a grant from the National Sciences and Engineering Research Council of Canada and by the Forest XV Economics and Policy Analysis Project which is funded by the Canadian Forestry Service. A scholarship from the Ministry of External Affairs / World University Service of Canada is also gratefully aknowledged. Above all, I wish to express my deep gratitude to llza, who made most of the sacrifices and to Sara and Rosa, who created many smiles and did not let me exagerate the importance of this effort. 1 1. INTRODUCTION 1.1 OBJECTIVES AND RELEVANCE OF THE RESEARCH The main purpose of this research is to empirically evaluate the economic and technological impacts of sawlog scarcity, revealed in the increasing sawlog prices and declining sawlog quality, on the sawmilling industries of the BC Coast (BC) and PNW Westside (PNW).1 The context which gave rise to this objective can best be described through a quotation from Pearse et aj.. (1984): "The adequacy, cost and changing composition of future domestic timber supply is a major concern. Historically, Canada's vast endownment of high quality timber gave domestic producers an economic advantage over international competitors. However, as exploitation of the original forest has progressed into more remote and less accessible areas, the costs of recovering timber have increased dramatically. At the same time, the volume and quality of the timber on the frontier, and hence its value have declined. Much of the best timber has now been harvested. Thus production costs in the Canadian forest industry are projected to increase significantly over the next several decades. The economic stream resulting from these trends in Canada and the subsequent loss of comparative advantage and competitiveness on world markets will be further aggravated by relatively stable (e.g. Europe) or only slightly rising (e.g. United States) real cost for some of our major trading partners." For some time, researchers have dealt with the problems of physical and economic scarcity of natural resources and the relationships between scarcity and economic growth (Barnett and Morse, 1963). It is now the general consensus that economic scarcity can be mitigated through the substitution of other goods, in production or in consumption, for natural resources, and through technical progress (Solow, 1977, 1978). Rosenberg (1977) presents an illuminating discussion of some of these issues, in the context of the timber economy. Since the early 70's many studies have empirically analyzed the relationships between natural resources and other inputs and outputs in various 2 industries. The objective in most of these studies was to measure the degree of substitutabiiity of labour and capital for the natural resource and the rates of technical progress. These studies benefitted from developments in economic theory, in particular in duality theory (Shephard, 1958; Diewert, 1974; McFadden, 1978) and the derivation of flexible functional forms (Diewert, 1971). Many of these studies originated with the energy crisis of the mid 1970's and analyzed the impacts of rising energy prices on the economy (Berndt and Wood, 1975; Griffin and .Gregory, 1976; Denny et al., 1978; Halvorsen and Ford, 1979; Pindyck and Rotenberg, 1983). Other studies have concerned themselves with natural resources in general (Humphrey and Moroney, 1975; Jorgenson and Fraumeni, 1981; Taher el si. 1983). If it is true that wood costs will rise in the future and wood quality will decline, one can expect several readjustments to take place in the industry. Labour and capital will be substituted for wood with resulting increases in lumber recoveries and new techniques introduced to cope with the changing characteristics of sawlogs. But one can also expect a decline in the size of the industry, production and eventually a loss in its market share, particularly if competitive regions do not face the same problems. Recently, several studies analyzing some of these issues in the wood products industries both in Canada and the US have appeared in the literature (Stier, 1980a, 1980b; Merrifield and Haynes, 1983; Nautiyal and Singh, 1983; Abt, 1984; Martinello, 1984b, 1985a). These studies dealt with the wood products industries at various levels of industrial and regional disaggregation and have varied considerably in terms of methodology and the data base utilized. Although these studies have already produced a rich variety of models that provide insights into the characteristics of sawmilling - in particular the 3 substitution possibilities between wood and other inputs and rates of technical progress - they still leave many questions unanswered. They have, for example, consistently shown, with few exceptions, that sawmilling has been undergoing technical recess and not technical progress (as measured through a residual or time trend), or ranking close to last with respect to this indicator of technical performance when compared with other industries, both in Canada and the US. Their results also suggest, albeit less consistently, that substitution possibilities between wood and other inputs are limited, so that increases in wood prices will have a large impact on production costs. A plausible, but never tested, explanation for the estimated low rates of technical progress in the sawmilling industry is the declining quality of the resource harvested. The incorrect measurement of the wood input, due to the omission of adjustments for quality change, is a problem in all the studies analyzed and may also introduce biases on the measures of substitution and of other characteristics of production. Although it is popular consensus that the quality of wood has been declining in BC and in the PNW, no study has yet looked rigorously into this problem, possibly due to lack of data and the difficulties inherent in defining and deriving an indicator of wood quality. The first goal of this research, then, is to derive a measure of wood quality for BC and the PNW and test whether it is true that wood quality has declined. A commonly used measure of technical performance in industry studies, including those on the wood products industries, is Total Factor Productivity (TFP). it is usually defined as output per unit of aggregate input, where the aggregate includes all the inputs utilized in the production process. Its use as a measure of productive efficiency has been advocated in the economic literature (National 4 Academy of Sciences, 1979; Kendrick and Vaccara, 1980; Berndt and Watkins, 1981) instead of the usual single factor productivity measures such as labour productivity, (or lumber recovery in the case of the wood products industries). This is because the latter do not allow the separation of substitution effects from changes in technical efficiency. TFP growth, or the growth in output not explained by the growth in aggregate input, is usually interpreted as a measure of technical progress in the industry. A drawback of such a measure, which is due to its residual nature, is that it will incorporate any factors not taken into account in the aggregation procedure, such as ignored variations in input quality. A second goal of this research, therefore, is to measure technical progress in the BC and PNW sawmilling industries using this residual approach and to analyze the contribution of changing wood quality to TFP growth. Existing studies of the structure of the wood products industries still leave many questions unanswered. First, no study has yet analyzed the impacts of changing wood quality on sawmilling technology and the input/output choices of producers. A visit and study of 25 sawmills carried out by the author throughout BC showed that wood quality is an important variable, likely to affect the relative employment of other factors of production and outputs produced. Engineering characteristics of sawmilling suggest that although labour and wood might be substitutes, labour and wood quality are likely to be complements in production. For example, if the wood price increases, mills may attempt to reduce wood consumption through the use of more labour intensive techniques that increase lumber recoveries. On the other hand, if wood quality declines, high throughput capital intensive techniques, which save on the labour input, may become the most profitable. A comparison of the BC Coast technology, where high quality sawlogs are available, with the BC Interior one, where wood quality is lower, lends support to this hypothesis. 5 Second, sawmilling has always been treated as a single output industry, and residue production ignored.2 Pulpchips are becoming a very important secondary output of the industry (Nilsson, 1985). In particular, declines in wood quality are likely to impact noticeably on the proportion of residue produced, and the same could be said about changes in output relative prices (the proportion of pulpchips in the output is likely to be higher if pulp prices are high and the lumber prices low than otherwise), and technical progress (development of chipping machinery). These types of relationships have never been modelled, and instead a fixed proportion assumption between lumber and pulpchips in the output mix is usually utilized. Third, with the exception of Abt (1984), all studies have treated capital as a variable input, i.e., they have assumed that it can be instantaneously adjusted to its optimum level. Because such an assumption seems quite inappropriate, the results provided by such studies may not only be biased, but are also inconsistent with the short-run responses of the industry, and useless for short-run policy analysis. Fourth, most studies used dual cost functions and limited themselves to the measurement of constant output elasticities. These elasticities measure the substitution possibilities between the several inputs (movements along an isoquant), but they do not tell the complete story of what happens when exogenous shocks occur. This is because such models usually do not explain variations in output, which is treated as exogenous, and so output effects (movements from one isoquant to another one) are not endogenously modelled. For policy analysis purposes, it is important to obtain estimates of the total effects (Field and Berndt, 1981; Field and Allen, 1981). In this way one can evaluate the full impacts of specific policies, or of the rising wood prices and declining quality. 6 The third goal of this research is to develop an econometric model of the sawmilling industry for BC and the PNW, which will generalize and extend the results of existing studies by taking the above features into account. The objective is to analyze the relationships between wood prices and wood quality and the other inputs and outputs of the industry in a static framework when (1) the capital stock is held fixed, i.e., the relationships are short-run, (2) two outputs are considered, lumber and pulpchips, and (3) the output levels are allowed to vary in response to exogenous shocks, i.e., both substitution and output effects will be modelled. In particular, sawmilling firms will be assumed to maximize profits and a restricted (fixed capital) profit function, which has never been utilized in lumber industry modelling, will be specified and estimated. Such a model will suit itself for policy analysis purposes. An additional contribution of this research is the comparison between BC and the PNW. There are several reasons why this comparison is important. Evidence suggests that the existence of a competitive market for stumpage in the PNW has resulted in higher wood costs (Haley, 1980) and that this has led the industry to operate in a less wood intensive region of the input space. Also, most of the wood quality changes in the PNW probably stem from a shift to second growth timber, and less from the cutting at the extensive margin as in BC. By pooling the two regions together, a richer sample from which to derive economic and technological parameters of the sawmilling industry will be obtained. Because the resource type, markets and historical development of the two regions are very similar, the major differences being institutional, the inter-regional comparison will provide insights on the impacts of differing policies between the two regions such as timber pricing arrangements. 7 Furthermore, the PNW is one of BC's main competitors in terms of lumber production. The seriousness of the impacts of sawlog scarcity in BC will also be a function of what is happening in competing regions. It is useful to compare the two regions with respect to their relative technical efficiencies which is an important determinant of competitiveness, after explaining away wood quality and factor intensity differentials. This thesis is also relevant to current research directed at the problem of measuring the size of the economic timber stock. Timber availability (Berndt et aj.., 1979) or economic timber supply (Haley and Cooney, 1982), have been defined as the physical volume (or proportion) of the inventory that can be economically recovered (i.e., at economic profits equal to or greater than zero) at a given point in time. A considerable empirical research effort has been applied in this area in BC (Cooney, 1981; Cooney and Haley, 1982; Williams and Morrison, 1985). The amount of timber that can be economically .recovered will depend on the downstream conditions, from harvesting to consumer markets. For example, if the sawmilling industry exhibits technical progress, the price it can afford to pay for sawlogs will rise, and the economic inventory will increase. By knowing how technical progress and other variables have been shifting the demand for logs, one can draw inferences about the rate at which the economic stock is likely to increase or decrease. This is a very important issue for policy in regions such as BC where the rate of harvest is-regulated. Another area of research in forestry economics to which this thesis can contribute, is the development of large sectoral market equilibrium models. The traditional role of these models in forestry has been to provide forecasts of market conditions, that can be used to improve the resource planning process. This research effort has culminated, in the US, with spatial models such as the Timber Assessment Market Model (TAMM) (Adams and Haynes, 1980) of the US 8 wood products sector and the US Pulp and Paper Model (Giless, 1983). These models, which are now being introduced in Canada (Pearse et a_[., 1984), tend to follow traditional specifications of demands and supplies, and do not incorporate substitution effects in a theoretically consistent manner. These are dealt with through simple trend forecasts of input-output ratios and often assume fixed proportion technologies (Abt, 1984). The model to be developed in this thesis will correct some of these deficiencies and will permit an evaluation of the adequacy of the above assumptions in the case of the sawmilling industry. Its structure will allow it to benefit from, or contribute to, TAMM forecasts. In summary, the three main objectives of the research are: 1. To develop a measure of wood quality for the BC Coast and PNW West and test whether wood quality has been declining. 2. To measure technical progress in both regions using the residual approach and evaluate the contribution of wood quality change to TFP growth. 3. To model, econometrically, the sawmilling industry using a restricted profit function, and analyze the relationships between wood prices, wood quality and other inputs and outputs in the industry. 1.2 MAIN RESEARCH HYPOTHESES The main hypotheses to be tested in this research are the following: 1. The quality of wood has declined both in BC and in the PNW. 2. Wood quality has declined at a faster rate in BC than in the PNW. 3. Wood quality is higher on average in the PNW than in BC. 4. Wood quality is an important variable in lumber industry mode/ling. 5. Wood quality changes have a significant impact on measures of technical progress in the sawmilling industry. 9 6. A short-run competitive profit maximizing assumption is appropriate for modelling input and output choices of sawmilling producers both in BC and the PNW. 7. The PNW industry exhibits a higher rate of technical progress than the BC industry. 8. Technical progress has been wood using, labour saving in BC, and wood saving, labour using in the PNW. 9. In the short-run, a decline in wood quality will increase the amount of wood utilized per unit of labour. 10. The proportion of pulpchips in sawmilling output responds positively to increases in the pulpchip to lumber relative price. 11. The proportion of pulpchips in sawmilling output increases with a decline in wood quality. 12. Input demands are characterized by large expansion effects and small substitution effects. 1.3 RELATED LITERATURE Twenty-two studies that dealt directly or indirectly with the topic of this thesis were identified in the literature.5 These studies attempted to characterize aspects of production technologies of the wood products industries in Canada and the US and in many cases included several additional manufacturing sectors. The studies varied greatly in terms of aggregation detail, model sophistication, variable specifications and data base and also, in terms of the results obtained. Constantino and Haley (1985) provide a review of technical progress studies both in the wood products and in the pulp and paper industries in Canada and the US. The main methodological features of these studies have been systematically summarized in Table 1.1. Historically, they have followed the theoretical 10 developments in production economics, and range from simple labour productivity analyses, to the more sophisticated econometric models utilizing non-homothetic dual cost functions which provide measures of elasticities of substitution, rates and biases of technical progress, and economies or biases of scale. They fall into four main categories: 1. Studies providing simple labour productivity estimates: 1 to 3. 2. Studies whose main objective was to measure technical progress and used either an index number or accounting approach (residual TFP) or an econometric model with a time trend: 4 to 11. 3. Studies that attempted to measure substitution, technical progress, biases of technical progress, and/or returns to scale, using either a cost function or a production function; 12 to 19. 4. Studies whose main objective was to model market equilibrium but, as a by-product, provided a characterization of the structure of production; 20 to 22. The earlier studies (1 through 3) looked at single factor productivity ratios, defined in physical units, and provided non-formal explanations for their behaviour. Kendrick's study (1973) is one of a series of major studies, by the same author, of Total Factor Productivity (TFP) for the several US manufacturing industries. TFP is defined as the ratio of real value added to an aggregate of labour and capital inputs. Studies 5 through 8 attempted to decompose labour productivity growth into several sources, using either an index number or an econometric approach. All of them start by postulating a production function. Robinson (1975) and Rao (1978) used the Solow-Divisia index (Solow, 1957) to decompose growth in real value added per unit of labour into growth of the capital to labour ratio and technical progress. Auer (1979) postulated labour quality and industrial structure as additional causal factors of labour productivity growth, Table 1.1; Wood Products Industry Studies in North America - Description, Model Specification and Assumptions. N o Author /Year Main Objective Country / Period I n d u s t r i e s ^ Method M o d e l ^ F u n c t i o n a l ^ Single Factor T e c h n i c a l ^ Substitution Other Outputs Inputs Main Data Region Form Productivity Progress Indicators Characteristics ' Source Indicators of Production 1 Kaiser ( 1 9 7 1 ) Labour Productivity Measurement US 4 7 - 67 W o o d Products , Pulp and Paper (further disaggregated) Index Number Output / Labour Employee hour Productivity Labour NBER 2 Porter ( 1 9 7 3 ) Labour Productivity Measurement Canada 4 9 6 8 Sawmilling, Pulp and Paper, Others (3 digit) Index Number N A Output / Labour Employee hour Productivity Value Added Labour S C 3 Sandoe and Labour and Wayman Capital ( 1 9 7 6 ) Productivity Canada 65 72 Sawmilling, P lywood , Pulp and Paper (3 digit) Index Number Output / Employee hour; Output/Real Capital Stock Labour and Capital Productivity Physical Output Labour Capital : SC(CM) 4 Kendrick ( 1 9 7 3 ) Technical Progress US 4 8 - 66 Lumber, Pulp and Paper, Others (2 digit) Index Number Production Kendrick index Labour Function Productivity C E S Residual TFP Real Value Labour Capital Several Added 5 Robinson ( 1 9 7 5 ) Technical Progress US 49 7 0 W o o d Products (2 digit) Index Number Labour Productivity Function S o l o w index (Cobb -Douglas) Labour Productivity Residual TFP Time trend Real Value Added Labour Capital A S M IRS 6 Rao ( 1 9 7 8 ) Technical Progress 7 Rao ( 1 9 7 9 ) 8 Auer ( 1 9 7 9 ) Gol iop and Jorgenson ( 1 9 8 0 ) 10 Denny et at. ( 1 9 8 1 b ) Denny and Fuss ( 1 9 8 1 ) Technical Progress Labour Productivity (sources), Technical Progress Sources of Economic Growth, Technical Progress Technical Progress, Regional Cost Eff ic iencies Sources Labour Productivity Growth Canada Canada Canada Provinces 57 - 74 US Canada Provinces Canada Provinces 7 1 - 7 3 61 73 6 1 - 7 5 W o o d Products , Pulp and Paper, Others (2 digit) W o o d Products, Pulp and Paper, Others (2 digit) Forestry W o o d Products , Pulp and Paper, Others (2 digit) W o o d Products, Pulp and Paper, Others (2 digit) W o o d Products, Pulp and Paper, Others (2 digit) W o o d Products , Pulp and Paper, Others (2 digit) Index Number Econometric Index Number Econometric index number Econometric Index Number Index Number Index Number Labour Productivity Function Labour Productivity Function Labour Productivity Function Production Function (CRTS) Cost Function (CRTS) Labour Productivity. Function Cobb-Douglas Labour Productivity Cobb-Douglas Truncated Translog Labour Productivity Cobb-Douglas Labour Productivity Tornquist (Translog) Tornquist (Translog) Tornquist (T ranslog) Labour Productivity Labour Productivity Residual TFP Residual TFP Time trend Time Trend Real Value Added Labour Capital Residual TFP Residual TFP (cost eff iciency growth) Residual TFP Gross Output Capital, Labour Energy, Materials, Unemployed Capacity, Labour Quality Real Value Added Aggregate Output Constant Value of Shipments Constant Value of Shipments Labour, Capital, , Materials Labour, Capital, Materials S C S C S C Labour, Capital, Labour Quality, Industrial Structure Labour, Capital, Several Materials (further disaggregated) S C S C Table 1.1 cont'd. 12 N o Author /Year Main Objective Country / Period Industries^ ^ Method Model *• ^ F u n c t i o n a l ^ Single Factor T e c h n i c a l ^ Substitution Other Outputs Inputs Main Data Region Form Productivity Progress Indicators Characteristics Source Indicators of Production 12 J o r g e n s o n and Production Fraumeni Structure, ( 1 9 8 1 ) Technical Progress and Biases US W o o d Products, Pulp and Paper, Others (2 digit) Econometric Index Number Unit Cost Function (CRTS) Translog Tornquist Residual TFP Time trend Elasticities Substitution Capital, Labour Energy, Materials USNIPA 13 Greber and Biases of W h i l e ( 1 9 8 2 ) Technical Progress US 5 1 - 7 3 W o o d Products (2 digit) Econometric Production Function C E S Ef f ic iency of Biases of Elasticity of Labour and Technical Substitution Capital Progress Value added Labour Capital ,USDP(CM) 14 Slier (1980a) Biases of Technical Progress US 5 8 Logging, Sawmill ing , P lywood, Paper (3 digit) Econometric Unit Cost Function Translog Time trend Elasticity of substitution and constant output demands N A Labour Capital A S M 15 Slier ( 1 9 8 0 b ) Substitution, ~ Technical Progress and Biases US 5 0 74 W o o d Products (2 digit) Econometric Unit Cost Function (CRTS) Translog Time trend Elasticity of substitution and constant output demand Lumber Labour, Capital, U S D C , USDL, Materials IRS 16 Rao and Preston ( 1 9 8 3 ) Substitution, Technical Progress and Biases Canada 79 W o o d Products , Others (2 digit) Econometric Production and Translog index Number Cost Function Time trend Residual TFP Elasticity of substitution Gross Output Labour, Capital, S C Energy, Materials 17 Abt ( 1 9 8 4 ) 18 Martinello ( 1 9 8 4 b ) 19 Martinello (1985a) 2 0 Nautiyal and Singh ( 1 9 8 3 ) Substitution, Marginal Product of Capital Substitution, Technical Progress and Biases Substitution, Technical Progress and Biases, Biases of Scale Demand Elasticities 21 Merrif i e l d ^ Demand and Haynes Elasticities, ( 1 9 8 3 ) Market Adjustments US State groups BC Canada 63 78 Ontario Pacif ic Northwest 63 63 - 8 2 5 2 / 5 3 Sawmilling (3 digit) W o o d Products (further disaggregated) Logging, Sawmilling, Pulp and Paper (3 digit) 8 0 Lumber, P lywood , Pulp and Paper (3 digit) Econometric 5 0 - 76 W o o d Products (2 digit) Restricted C o s t Function (K f ixed) Translog Time trend Econometric Cost Function Translog Econometric Cost Function Econometric Econometric Production Function Production Function Translog (non-homothetic) Cobb-Douglas C E S Translog Time trend Time trend Elasticity of substitution and constant output demands Constant output demand elasticities Returns scale Returns to scale Constant value of shipments/ aggregate lumber output index Aggregate Outputs Elasticities of Returns to and Aggregate substitution and constant output demands Elasticities of demand Demand and supply elasticities biases of scale Returns to scale Outputs Physical Outputs Physical Outputs Labour, Capital, W o o d Labour, Capital, W o o d , Energy (and Materials) Capital, Labour, W o o d , Energy (incl. materials) Capital, Labour, W o o d Capital, Labour, W o o d A S M S C S C S C U S F S 2 2 Martinello (1984a) Labour Market Equilibrium BC 63 - 79 W o o d Econometric Cost and Products Profit Function (aggregate of (several 3 digit) specif ications) Several Time trend Elasticities of Returns to Aggregate Capital, Labour, substitution scale Outputs Energy, W o o d and constant output demand S C Table 1.1 Cont'd. V) The digit number refers to the level of industrial disaggregation in (2) CRTS - Constant Returns to Scale (3) CES - Constant Elasticity of Substitution (4) TFP - Total Factor Productivity (5) NBER - National Bureau of Economic Research SC - Statistics Canada CM - Census of Manufacturers ASM - Annual Survey of Manufacturers IRS - Internal Revenue Service USDP - US Department of Commerce USDC - US Department of Labour USFS - US Forest Service USNIPA US National Income and Product Accounts (6) Another study by these authors (Merrifield and Haynes, 1984) was review. 14 while Rao (1979) extended his earlier results by defining output as gross output and including materials as an input. Both these authors utilized an econometric model. Gollop and Jorgenson (1980) (study 9) decomposed output growth into several sources, including variations in input quality and technical progress, in a major inter-industry comparison of US manufacturing. Studies 10 and 11 (Denny et a].., 1981b; Denny and Fuss, 1981) provide an equivalent analysis for Canadian manufacturing, including the measurement of inter-regional variations in TFP. These three later studies incorporate the recent developments in index number theory, through the use of less restrictive functional forms for the aggregators. Study 13 (Greber and White, 1982) utilizes the procedure developed by Sato (1970) to measure the biases of technical progress, assuming a constant elasticity of substitution production function, defining output as real value added, and including labour and capital as inputs. Studies 20 (Nautiyal and Singh, 1983) and 21 (Merrifield and Haynes, 1983) modelled market equilibria by econometrically estimating the first order conditions for profit maximization together with a production function. While study 20 utilized a Cobb-Douglas and a CES production function, study 21 utilized a translog.4 All the other studies made use of duality theory, specified a cost-function, and utilized a translog functional form. Study 22 (Martinello, 1984a) utilized other functional forms in addition to the translog. With the exception of study 22, their main objective was to characterize the structure of the technology by measuring one or several of the following parameters: elasticities of substitution, constant demand elasticities, rate of technical progress, bias of technical progress, degree of returns to scale, biases of scale. Martinello (1984a) modelled the wage-setting 15 process between the BC forest industry and the IWA (International Woodworkers of America) using alternative theoretical and empirical specifications for the industry and the union models. Some of the studies treated the sawmilling industry at a level of regional disaggregation pertinent to this thesis. Studies 8, 10 and 11 measured technical progress in the wood products industry in BC. Study 18 provided a characterization of the structure of production for the BC wood products industry using a translog cost function.5 Study 22" modelled the wood products labour market in BC. Study 17 characterized the lumber industry in the US West using a translog restricted cost function, while study 21 modelled wood market equilibra in the PNW industry using a translog production function. The results of the studies reviewed with respect to single factor productivity, technical progress and biases of technical progress are summarized in Table 1.2. It is convenient to highlight some of the findings which are relevant to this thesis. Lagging productivity growth (lower rate of technical progress) in the wood products industry is the rule in most studies that provide inter-industry comparisons. Study 9 (Gollop and Jorgenson, 1980), found that the US wood products industry exhibited technical recess, i.e., a negative rate of technical progress between 1947 and -1973. Wood products had the fourth worst performance among the 44 industries studied, surpassing only agricultural services, metal mining, rail and bus lines, and transportation. Technical recess was found for the US wood products industry by Stier (1980b) (study 15), and by Jorgenson and Fraumeni (1981) (study 12), for the BC wood products industry by Martinello (1984b) and for the Canadian sawmilling industry by Martinello (1985a). Rao (1978 and 1979) (studies 6 and 7) estimated positive rates of technical progress, but Table 1.2; Wood Products Industry Studies in North American - Results: Labour Productivity, Technical Progress and Biases of Technical Progn (3) N o Industry Region/Per iod Labour Productivity Rate of Technical B iases v ot Growth Rate (%/Year) Progress (%/Year) Technical Progress W o o d Products Sawmilling Sawmilling P l y w o o d W o o d Products W o o d Products W o o d Products W o o d Products W o o d Products 1 0 / 1 1 W o o d Products 12 W o o d Products 13 W o o d Products 14 Sawmilling P lywood 15 W o o d Products 16 W o o d Products IB W o o d Products 19 Sawmilling US 47 - 67 Canada 4 9 - 6 8 Canada 6 5 - 72 US 4 8 - 6 6 US 4 9 - 70 Canada 5 7 - 74 Canada 5 7 - 75 US 47 - 7 3 Atlantic Quebec Ontario Prairies B C 61 - 7 5 / 7 7 US 5 8 - 74 US 5 1 - 7 3 ' U S 5 8 - 74 US 5 0 - 74 Canada 5 7 - 79 B C 63 - 7 9 Canada 63 - 8 2 3 .20 7.80 ( 5 . 9 0 f 2.50 2 .80 3 .00 (2.90)' 1.88 (2.90) 2.44 (3.23) 2.73 2.96 2.33 3 .70 2.34 3.50 (2.50) 1.75 1.23 .4^ (1.32) -.61 .95 .85 .75 .9 I .70 - 0 . 0 0 4 8 (2) - . 0 0 5 0 (?) 2.34 (1.90)' iW'» - . 0483 - . 0 4 3 0 K using, L using E using, M saving K using, L saving K using, L saving K using, L saving K using, - L saving W using K using, L saving E using, . M using K using, L saving W saving K using, L saving . E using, W saving (1) Numbers in parenthesis are for total manufacturing (2) Reported figure is the negative of the coef f ic ient of the first order term of the time trend (3) K - capital; L - labour; W - w o o d ; E - energy; M - materials (4) this is - (dc/dt) . ( t /c) calculated at the mean of the data, where c are costs and t is year. O) 17 showed that the industry rated poorly, when compared to other industries. Study 15 (Kendrick, 1973), produced somewhat different results. The US wood products industry was shown to rank fifth, in terms of TFP growth, among the 21 industries studied. However, the study covered an earlier period - 1948 to 1966 - than those discussed above, and output was defined as real value added.6 The other exception is study 16 (Rao and Preston, 1983), which estimates a higher rate of technical progress for the wood products industry in Canada, than for total manufacturing.7 Of particular interest are studies 10 and 11 (Denny et aj.., 1981b; Denny and Fuss, 1981), which provide inter-regional, inter-temporal and inter-industry comparisons of Total Factor Productivity (TFP). Their results indicate that, in all the Canadian provinces for the period 1961-1975, the wood products industry lagged behind most other industrial sectors in terms of their rates of technical progress. In both BC and Ontario, wood products displayed lower rates of technical progress than any of the other industries studied. Compared to other provinces, the BC wood products industry had the lowest rate of technical progress. Study 10 also analyzed regional cost efficiency levels. The BC wood products industry was the most cost efficient when compared to other regions, in spite of its poorer technical progress performance. In spite of the different - theoretical and empirical approaches, the several studies consistently indicated a poor performance for the wood products industry, with respect to technical progress indicators.' This thesis will extend those results, by trying to evaluate to what extent such a poor performance could be explained by the declining quality of the resource harvested. For example, a possible explanation for the findings of study 10 (Denny et aj., 1981b) could be the higher quality of wood in BC, which would make manufacturing costs .lower, 18 but a faster rate of decline in quality, which would lead to a faster rate of increase in costs, when compared to other regions. With respect to the biases of technical progress, the accumulated evidence would seem to suggest a predominantly labour saving, capital using and energy using bias. The results for the biases with respect to wood or materials, are inconsistent. Table 1.3 summarizes the results of the studies providing estimates of elasticities of substitution, constant output demand elasticities and degree of returns to scale. Although results tend to vary considerably between studies, as one would expect given the different model specifications and data bases utilized, they suggest the existence of some, but low (less than 1), substitution possibilities between wood and labour, and wood and capital. The same conclusion is obtained from the constant output elasticities reported. What these results do not show are the changes in input levels due to variations in outputs induced by changes in input prices. Given the low substitution possibilities, one would expect an increase in wood costs to have an important negative effect on production, its magnitude depending, of course, on the shape of the production function. This information is important for policy analysis. This problem will be analyzed in this thesis, as well as the relationships between wood quality and the several inputs and outputs. Finally, the studies reviewed seem to indicate approximately constant returns to scale at the industry level. 1.4 PLAN OF THE THESIS The thesis is organized as follows. In Chapter 2, the sawmilling industries in BC and in the PNW are briefly described, characterized and compared using several simple statistics. A summary of the data utilized throughout the thesis is included in this Chapter. In Chapter 3, a measure of wood quality is derived and Table 1.3: Wood Products Industry Studies in North America - Results: Elasticities of Substitution, Constant Output Demand Elasticities and Degree of Returns to Scale. Elasticities^ ) of Constant Output Returns Substitution Demand Elasticities to Scale No. aLW aKL £WW eLW eKW 13 - - 0.14 - - - - -14 - - 0.11 - - - - - -0.20 4.16 0.16 -0.30 -0.16 -2.79 0.13 2.68 -17<3Ss 0.20 -0.08 -0.11 0.11 0.96 0.73 - - -0.25 -0.47 — 0.47 — 1.00 W 0.59 - - -0.20 -0.39 - 0.39 - 1.00 18 0.44 0.16 1.17 -0.12 -0.46 -0.39 0.27 0.10 1.10 19 0.00 0.58 23 -0.37 -0.24 -0.30 0.00 0.24 1.11 (1) L - labour; K - capital; W - wood or materials. (2) This study reported the results of two models; the non-homothetic model was chosen. (3) H - Hardwood region; S - Softwood region; W - West region. In this model K is a fixed factor. 20 applied to data from the Vancouver Forest Region, Vancouver Log Market and the six log markets in the Pacific Northwest West. Trends and levels in wood quality are analyzed and discussed. In Chapter 4, a measure of Total Factor Productivity is developed through the specification of a production function, and the impacts of wood quality on this measure are analyzed. In Chapter 5, the theoretical and empirical models of the industry are developed and estimation procedures are described. In Chapter 6, parameter and test results are reported, discussed and interpreted. In Chapter 7, the results of Chapter 6 are utilized to carry out some simulations of the industry and analyze some historical trends in demands, supplies, productivities and input or output ratios. The conclusions of the thesis are summarized in Chapter 8. A detailed description of the data is given in an Appendix. 21 Footnotes 1. Hereinafter, the British Columbia Coast will be referred to as BC, and the Pacific Northwest Westside as PNW. 2. Martinello (1984a, 1984b, 1985a) included pulpchips in an output aggregate, but the assumption that pulpchips and other outputs are separable from the several inputs, technical progress and wood quality appears to be too simplistic. 3. There are other studies available in non-published form (Bible, 1983; Nautiyal and Singh, 1984a, 1984b; Merrifield and Singleton, 1985; Merrifield and Haynes, 1985; Martinello, 1985b). Because these consist of discussion drafts and are still in mimeo form, and do not add very significant information for the topic of this thesis, it was decided not to include them in the review. There is also a considerable number of studies dealing with the pulp and paper industry (e.g. Manning and Thornburn, 1971; Muller, 1979; Sherif, 1982; Nautiyal and Singh, 1984c; Klein, 1985) and other forest related industries (Doran and Williams, 1982; Andersson et aj.., 1985). These were also excluded from this literature review. 4. Translog is an abbreviation for the transcendental logarithmic functional form, developed by Christensen et al. (1973). which is today one of the most popular functional forms in industrial econometric models. 5. Martinello (1985b) extended this study by looking at the BC Coast and the BC Interior, and increased the level of industrial disaggregation. 6. Berndt and Watkins (1981) show that when labour and capital amount to a small share of total costs as in sawmilling, value added based TFP measures considerably overstate the rate of technical progress. 7. The results reported for study 16 are for a non-homothetic non-constant returns to scale cost function. As will be discussed in Chapter 6, these models tend to do a bad job in separating scale from technical progress effects, due to multicolinearity problems between the time trend and output. This issue is discussed by Fuss (1983). 8. It is interesting to notice that technical progress estimates based on production functions usually exhibited a positive sign, while those based on cost functions were negative. Also, those derived from index numbers were much larger in absolute value than those utilizing econometric estimation. 22 2. THE SAWMILLING INDUSTRY ON THE BRITISH COLUMBIA COAST AND PACIFIC NORTHWEST WEST 2.1 INTRODUCTION The definition of the sawmilling industry in this study includes sawmills, planing mills and shingle mills. It is equivalent to Statistics Canada Standard Industrial Classification 2513 and 2511 and to the US Census of Manufacturers Standard Industrial Classification 242. The -US definition also includes Hardwood Dimension and Flooring Mills (SIC 2426), but because these are negligible in the US West, the two definitions are closely comparable. Although the data available allows the separate treatment of sawmills and shingle mills, aggregation of the two industries increases the confidence in the sawlog quality measure to be developed in Chapter 3, because it is difficult to distinguish between sawlogs going to sawmills and to shingle mills. Throughout this thesis, the industrial aggregates will be interchangeably referred to as the lumber industry, or the sawmilling industry. This Chapter is organized as follows. In Section 2.2, a brief description of the data utilized in this Chapter and throughout the thesis is given. The data are more exhaustively described in Appendix I. In Section 2.3, factor and output markets are discussed, while in Section 2.4 important policies which have affected the structure of the industry are" briefly mentioned. In Section 2.5, the industry in both regions is characterized and compared in terms of several relevant and simple statistics. In Section 2.6, some features of sawmilling technology are described. 23 22 SUMMARY OF THE DATA UTILIZED The lumber or sawmilling industry processes sawlogs which are extracted from the forest by the logging or harvesting industry. It produces two main outputs: lumber of varying characteristics, mainly used in construction, shipping and manufacturing, and pulpchips, used as a raw material by the pulping industry. It produces other residues that sometimes have market value, namely for the production of energy. These include bark, hog fuel and sawdust. In the PNW, sawmilling residues are also an important raw material for the board industry. Sawmilling utilizes three main inputs: wood, labour and capital. A distribution of costs by major category is shown in Table 2.1. Energy costs are a very minor proportion of total costs. According to Sandwell Management Consultants (1977), in BC this proportion varied between 0 and 1.5% in 1977 and in the PNW between 1% and 2% for the same year. There are other miscellaneous non-wood inputs (other materials), of which the main component is expenditures on repairs and alterations. Difficulties in obtaining data for BC and PNW on production and prices of residues other than pulpchips, resulted in these factors being ignored. Due to unavailability of data on energy and miscellaneous non-wood inputs for the PNW these were also ignored. Repairs and alterations expenditures, which are a component of this latter category, are partially accounted for in the depreciation patterns assumed for the capital stock, and the remaining miscellaneous inputs (e.g. containers and packaging materials) amount to only a very minor proportion of total costs. Abt (1984) has justified this procedure for US sawmilling industry data. Table 2.1: Distribution of Sawmilling Manufacturing Costs by Major Components in BC and PNW, Selected Years. BC Coast^1) PNW^1) BC Coast1?) PNw( 3) Category (1977) (1977) (1980) (1980) % % % % Wood 49 Labour 32 Energy 1 Other Materials 6 Administration 10 Depreciation 1 66 61 68 17 21 23 2 1 3 9 7 4 3 8 3 3 2 -(1) Sandwell Management Consultants (1977); this source reports high and low costs; the percentages are based on arithmetic averages. (2) Ministry of Industry and Small Business Development (1981). (3) Baiter and Berg (1985); these costs are based on Data Resources Inc. estimates and apply to high cost US West mills, operating mostly from public timber; depreciation costs were not reported. 25 Table 2.2 describes the several variables analyzed and lists the main data sources. All indices referred in Table 2.2 are inter-temporal and inter-regional Tornqvist index numbers (Diewert, 1976) and the two regions were linked through the 1971 cross-section. This procedure is discussed in more detail in Appendix I. Where appropriate, the indices were rebased so that the BC indices in 1971 would equal the average value of the variable on the BC Coast for that year. Conversion factors derived in Chapter 3 were utilized to convert sawlog prices in dollars per rvlfbm (BC or Scribner.log scales) to cubic meters. Two data series for sawlog price and revenue in BC (A and B), and for sawlog price and volume in the PNW (A and B) were developed. The reason for this was that there was some uncertainty concerning the most appropriate data for BC, and also there was some interest in checking the sensitivity of results to changes in the data. There are several weaknesses in the data, which are more exhaustively discussed in Appendix I. They are briefly mentioned here. The major weakness is in the way the capital stock measure was derived. There are well known theoretical and empirical problems inherent in the measurement of aggregate capital. These were aggravated because raw investment tiata could not be obtained for BC, and so a capital stock estimate provided by Statistics Canada had to be utilized. This estimate is based on the perpetual inventory method and straight line depreciation, and its main flaw is the assumed service life for equipment (26 years) which is likely to be too long. The PNW capital stock was built consistently with the BC one, and so both measures probably overstate the capital input in sawmilling. An additional problem occurred because capital stock estimates were developed for the whole of BC and for the entire PNW. These had to be Table 2.2; Description of the Data Utilized. Variable*1 ^ Definition Main Data Sources B C ( 2 ) P N W ( 3 ) Lumber price Price Index; aggregate of the average prices of lumber of Douglas-fir, hem-fir, cedar, spruce, other species and shingles SC(CM) WWPA, USDAfS), TAMM, USDLfBLS), RL Lumber revenue Value of shipments SC(CM) USDC (ASM,CM), TAMM Lumber quantity Implicit quantity index; Lumber revenue/Lumber price - -Pulchip price Average Price per O.D. Ton SC(CM) NWPPA, USDAfS) Pulpchip quantity Volume in O.D. Tons SC(CM) WWPPA, APA, USDAfS), NPA Pulpchip revenue Pulpchip price * pulpchip quantity - -BC wood price (A) Average price per m' of wood purchased or transferred SC(CM) n.a. PNW wood price (A) •Delivered wodd cost per m>; stumpage cut + average logging cost n.a. TAMM BC, PNW wood expenditure (A) Total cost of wood SC(CM) USDC(ASM,CM), TAMM, Abt (1984) BC, PNW wood volume (A) Implicit volume; wood expenditure (A)/wood price (A) - -BC, PNW wood price (B) Average price per mJ in the log markets COFI IFA BC wood expenditure (B) Wood volume (A) • wood price (B) - n.a. PNW wood expenditure (B) Total cost of wood n.a. USDC (ASMCM) TAMM Abt(1984) BC, PNW wood volume (8) Implicit volume; wood expenditure (B)/wood price (B) n.a. -Labour price Price Index; aggregate of the average wages per manhour employed of production and non-production workers (with some fringe benefits) SC(CM) USDC (ASM.CM), WWPA, BLS Labour expenditure Expenditures with production and non-production workers SC(CM) USDC (ASM.CM), WWPA, USFS Labour quantity Implicit quantity index; labour expenditure/labour price - -Capital price User cost of capital, including adjustments for corporate income tax, interest and depreciation deductions and assuming static expectations SC, and various authors USDL(BLS), USDC(BEA), USDT(IRS) and various authors Capital stock Quantity index; aggregate of the net stocks of structures and equipment based on perpetual inventory method, with straight line depreciation and SC assumed lives SC (unpublished data) BLS, USDC(BEA) (unpublished data) Capital expenditure Capital price • Capital stock (sum of structures and equipment) - -Table 2.2 Continued. (1) All prices were converted to Canadian nominal dollars. (2) SC(CM) - Statistics Canada (Census of Manufacturers) (3) WWPA - Western Wood Products Association USDA(FS) - US Department of Agriculture (Forest Service) TAMM - Data base for the Timber Assessment Market Model (Adams et a}. (1980), and unpublished data from the same author) USDL(BLS) - US Department of Labour (Bureau of Labour Statistics) RL - Random Lengths Yearbook USDC - US Deparment of Commerce (ASM,CM) - (Annual Survey of Manufacturers, Census of Manufacturers) APA - American Pulpwood Association NWPPA - Northwest Pulp and Paper Association NPA - National Particleboard Association COFI - Council of Forest Industries of British Columbia IFA - Industrial Forestry Association ' USDC(0EA) - US Department of Commerce (Office of Economic Analysis) USDT(IRS) - US Department of Treasury (Internal Revenue Service) 28 allocated between BC Coast and Interior and PNW West and Eastside. Several procedures were utilized: the region proportion of the capital stock is equal to the regional proportion of (1) profits, (2) physical production, (3) capacity, (4) energy consumption at full capacity. Because (1) did not appear theoretically sound (it implies equal average rates of return to capital in both subregions), (2) and (4) led to time series that showed unreal short-run fluctuations and (4) could not be used in the PNW, due to lack of energy data, (3) was chosen. All series yielded comparable long-run trends. Because the BC Coast is less capital intensive than the BC Interior, procedure (3) probably led to an overestimate of the capital stock on the BC Coast. Additional weaknesses in the data are first, the failure to measure labour in hours worked instead of hours paid, due to lack of such information in BC. Second, the impossibility of accounting for changes in inventories of lumber, pulpchips and sawlogs. The lumber inventories series were incomplete in the PNW, and were inconsistent with the shipment series in BC, and so correction of shipments for changes in inventories could not be carried out. The third weakness is the measurement of the pulpchip output in the PNW. Because such data is not available, it had to be computed using indirect information (see Appendix I), and several measurement errors are likely to have been introduced. In addition a considerable number of adjustments were made to the other PNW data, for reasons to be discussed in the Appendix. Because there was ample opportunity to check the final data against data from other sources, the comparisons giving support to the procedures utilized for the adjustments, these data deserve some confidence. 29 2.3 FACTOR AND OUTPUT MARKETS The sawmilling industry processes logs which are extracted from the forest by the logging industry. In both BC and in the PNW there are log markets, where sawlogs are traded. However, the forest industry in both regions is highly integrated both vertically and horizontally and most log transactions consist of intra-firm transfers. The largest companies today include logging operations, sawmills, shingle mills, pulp and paper mills and veneer and plywood mills. The trend towards greater integration has reduced the relative importance of log trading and the representativeness of the log markets has been declining (Pearse et al, 1974). In a study carried out by the author of the Vancouver Log Market,1 the agents involved in log market transactions were classified into four main categories: independent (non-integrated) sellers, independent buyers, integrated firms and log brokers. Integrated firms were the dominant group. Log trading was carried out either through free market operations: auction bids, direct sales or sales through a log broker; or through direct trades: logs for chips or logs for logs. Direct trades (logs for logs) are particularly common between integrated companies who claim that current log market prices are used for trading purposes. About 15% of the BC Coastal harvest is traded in the log market. In the PNW this proportion is probably lower than 10%. Due to lack of data on the volume of the harvest, it was impossible to correctly evaluate the representativeness of the PNW log markets. In spite of the integration of the industry, and given the existence of the log markets, it was decided, in this research, to treat sawmilling as a non-integrated industry, and assume that sawmills (at the firm level) are price takers in the log markets. Although this choice may be questionable, it has been 30 used in every study of sawmilling found in the literature, even in regions, such as the BC Interior and eastern Canada where log markets are non-existent or negligible. Also, several representatives of large companies interviewed in BC claimed that log market prices are used in the internal valuation of wood transfers. Most of the labour force on the BC Coast is unionized in the IWA (International Woodworkers of America), which is also the dominant union in the PNW. However, in the PNW there appears to be more non-unionized mills than in BC. In BC, wages are set through a bargaining process between the IWA and representatives of the industry (Forest Industry Relations). This process has been modelled by Martinello (1984a). Following Martinello's results (Martinello, 1984b and 1985a), it was decided to assume that sawmilling firms are price takers in the labour market given that sawmilling labour is not highly specialized, and that it is relatively integrated with the Canadian and US labour markets. Sawmilling is a book example of a competitive industry in the North-American dimension lumber market. A majority of lumber produced in the two regions consists of dimension lumber, and this tends to be a fairly homogeneous product with a high degree of substitutability between the several grades and sizes. The BC coastal industry also supplies several off-shore markets. Some of the markets, particularly those for higher grades of lumber, are less competitive. However, given that these markets account for a relatively small proportion of total lumber output, this problem will be ignored in this research, and sawmilling firms will be treated as price takers in the lumber market. In the case of integrated companies, pulpchips are usually internally transferred from sawmills to pulpmills. Pulpchip trading is also a common procedure between non-integrated sawmills and pulpmills but it was impossible to 31 quantify the importance of this practice in BC and in the PNW. In this research, price-taking behaviour of sawmills in the pulpchip market will also be assumed. 2.4 REGULATIONS In BC, existing log and chip export restrictions, lower the prices of these two products relative to world levels. These restrictions have been discussed by Pearse (1976), Davies (1977) and Trebett et al. (1983). In the PNW, existing log export restrictions have a smaller impact because a smaller proportion of the timber harvested is affected. No log exports are allowed from Federal forest land. After 1963 log exports from state-owned lands in Oregon were also restricted, while they are permitted in Washington (Lindell, 1978). According to this author, in 1975, 17.8% of all the timber harvested in Washington, and 44.8% of all the timber harvested in Oregon were affected. In the PNW, there are no chip export restrictions in effect. Although in BC no other important regulations bear directly on the markets for inputs or outputs of sawmills, the complex institutional arrangements affecting timber ownership and the amount and quality of timber harvested, have affected the sawmilling industry. These institutional arrangements have been extensively described and discussed by Pearse (1976). Their importance results because 95% of the timber is owned by the province. Some pertinent features of these arrangements are the following: 1. Timber is mainly allocated to firms through a system of long-term cutting rights which take various forms. As a rule, rights to harvest timber are not transferred, except through the merging of firms. According to Pearse (1976), merging has led to increasing concentration in the control of harvesting rights, which are now in the hands of a small number of integrated companies. 32 Firms pay a price, or stumpage, for the timber harvested, which (on the BC Coast) is calculated as the residual value after harvesting costs are subtracted from the market price of the extracted resource (logs). An allowance for risk and profits is included in the calculations. Given the system of cutting rights, there is no bidding on the appraised stumpage, and so a stumpage market does not exist. 2 This stumpage appraisal system has been discussed by Pearse et a|. (1974). Several criticisms to it have been advanced, due to its apparent failure to truly appraise the economic rent accruing to the timber resource. Problems that have been mentioned are: lack of competitiveness of the Vancouver Log Market, from which price data are derived; the use of lagged harvesting costs, which may not reflect actual costs; and the calculation of the allowance for risk and profits, which is a percentage of the selling price of logs. The volume of timber each firm can harvest in a given year is regulated through lower and upper limits. This follows from the sustained yield policy which is in effect on BC public lands. The harvest is regulated through the Annual Allowable Cut (AAC), with the objective of sustaining, in the long-run, an even flow of production. Some flexibility is introduced in the AAC constraint, by permitting firms to cut above or below the harvest (within a 50% deviation) in a given year, but requiring that the average cut over a period of 5 years be within a 5% deviation of the AAC. What and where firms harvest must," in most cases, follow a plan approved by the government. The old growth timber must generally be harvested first. The limiting quality to which timber must be harvested (but not processed) is imposed through regulations. These are called the utilization standards and are specified in terms of a minimum diameter, above which all trees have to be removed. 33 In the PNW, the cut on public lands is more constrained. This results because there is not as much flexibility as in BC for deviations from the AAC. On the other hand, there is not a system of long-term cutting rights equivalent to the BC one. On public lands, a stumpage appraisal system is also in effect, but bidding for timber takes place above a minimum appraised stumpage. Thus, a market for stumpage can be said to exist in the PNW. Also, the importance of the non-regulated ownership types is greater in this region. According to Haley (1980), 42% of the forest land in Washington and Oregon is privately owned, 6% is under State jurisdiction, 1% is controlled by county and municipal governments and 51% is under Federal jurisdiction (in BC 94% is Provincial, 1% Federal and 5% private). 2.5 HISTORICAL TRENDS IN THE REGIONAL INDUSTRIES In Figure 2.1, an index of lumber and shingle production in the two regions is shown for the period 1957-1982. Production varied considerably with the business cycle as did sawlog consumption and labour demand. The capital stock has grown more or less steadily over time (Figure 2.2). The average growth rates of quantities and prices of the several inputs and outputs are reported in Table 2.3.3 In BC, all demands and supplies increased during the period, while in the PNW the demand for labour and wood declined. These results reflect to a. certain extent the fact that BC has increased its market share relative to the PNW. For example, in 1957 the BC value of lumber and pulpchip shipments amounted only to 24% of total shipments in both regions, but in 1982 the BC share had increased to 34%. The sharp increase in pulpchip production in both regions reflects the growth of the pulp and paper industries and its increasing use of mill residues relative to roundwood as a raw material. FIGURE 2.1 Lumber and Shingle Implicit Quantity Index - BC and PNW 34 16000 BC C o o s t PNW West 1965 1970 1975 1980 1985 FIGURE 2.2 Aggregate Capital Stock - BC and PNW IOOOOOO T ; : ; : Table 2.3; Average Growth Rates and Relative Levels of Quantities and Nominal Prices of the Several Sawmilling Inputs and Outputs, 1957-1982: BC, PNW and BC Relative to the PNW.* 1* Average Growth Rates Relative Growth Rates Relative Levels BC PNW BC/PNW BC PNW INPUT/OUTPUT Quantity Price Quantity Price Quantity Price Quantity Price Quantity Price (%/Year) Lumber (index) 1.62 7.45 0.34 6.61 1.28 0.84 100 100 247.4 99.0 Chips 5.19 6.15 6.41 7.12 -1.22 -0.97 100 100 159.3 119.2 Wood* ' • 1.61 7.66 -0.34 8.31 1.95 -0.65 100 100 189.8 122.5 Labour (index) 0.51 8.47 -0.26 7.28 0.77 1.19 • 100 100 226.0 101.3 Capital (index) 3.92 6.58 2.07 7.61 1.85 -1.03 100 100 296.1 95.9 SOURCES: See Appendix I and Table 2.2. (1) see footnote (3) of this Chapter for an explanation of how growth rates and levels were calculated. (2) based on average log market sawlog price. 36 The growth rate differential between the two regions shown in columns 5 and 6 of Table 2.3 is a measure of the growth in the spread of the variable in question between BC and the PNW. Lumber supply, wood consumption, labour consumption and capital stock increased in BC relative to the PNW, while the pulpchip relative production declined. According to Table 2.3, labour prices in BC have grown faster than the prices of other major inputs, while in the PNW the biggest increase occurred in wood prices. Pulpchip and wood prices declined in BC relative to the PNW and so did the user cost of capital. The average levels of the several variables for the whole period 1957-1969 in the PNW relative to BC, which was taken as a basis, are shown in the last two columns of Table 2.3. While the average wage and lumber prices were identical, the user cost of capital was 5% lower in the PNW, and the pulpchip and wood price considerably higher (19% and 23% respectively). The PNW industry utilized, on average, 3 times the BC capital stock, 2.3 times the BC labour and 1.9 times the BC wood to produce 2.5 times more lumber and shingles and 1.6 times more pulpchips. It should be mentioned that these summary statistics hide the different patterns in growth rates and relative levels that occurred in different periods, and that they are considerably affected by "abnormal" situations, such as the post-1980 recession. In Table 2.4, growth rates of several single factor productivity indicators*, as well as input ratios and relative prices, are shown. Some of the statistics shown in Table 2.4 are also displayed in Figures 2.3 through 2.7. Because logarithmic scales were used in the figures, the slopes of the trend lines equal the average growth rates reported in the table. The difference between the two trend lines measures the logarithmic difference between the variable in the two Table 2.4; Average Growth Rates and Relative Levels of Single Factor Productivities, Input and Output Ratios and Relative Prices, 1957-1982; PNW and BC Relative to the PNW.*1) Average Growth Rates Relative Growth Rates Relative Levels BC PNW BC/PNW BC PNW PNW RATIO Quantity Price (2> Quantity Price Quantity Price Quantity Price Quantity Price (%/Year) Wood Productivity 0.31 -0.29 1.01 -1 44 -0.70 1.15 100. 100. 126.2 82.2 Labour Productivity 1.41 -1.10 0.92 -0.41 0.49 -0.69 100. 100. 106.0 99.3 Capital Productivity -1.99 0.79 -1.41 -0.75 0.58 1.54 100. 100. 80.9 105.0 Lumber Recovery 0.00 -0.21 0.68 -1.69 -0.68 1.48 100. 100. 130.2 80.8 Chip Recovery ! 3.58 -1.51 6.75 -1.19 -3.17 -0.32 100. 100. 83.8 97.3 Wood/Labour 1.10 -0.81 -0.09 1.03 1.19 -1.84 .. 100. 100. 84.0 120.9 Wood/Capital -2.30 1.08 -2.41 0.69 0.1 1 0.39 100. 100. 64.2 127.9 Labour/Capital -3.41 1.89 -2.33 -0.34 -1.08 2.23 100. 100. 76.3 105.7 SOURCES; See Appendix I and Table 2.2. (1) The same equation reported in footnote (3) of this Chapter was utilized to compute trends and relative levels, with the dependent variable a quantity or price ratio. (2) The price ratio corresponding to wood productivity is aggregate output price index divided by average sawlog prices; the price ratio corresponding to lumber recovery is lumber and shingle price index divided by average sawlog price; the other price ratios are defined in a similar way. v i 2 0 0 FIGURE 2.3 Trends in Lumber Recovery - BC and PNW Logarithmic Scale A BC C o a s t X PNW West 1 9 5 5 1 9 6 0 1 9 6 5 1 9 7 0 1 9 7 5 1 9 8 0 1 9 8 5 4 0 0 -O o o IT r v i n cn O m a> </> o m 100-40-FIGURE 2.4 Trends in Chip Recovery - BC and PNW Logarithmic Scale A A A A « A A. A" 1 9 5 5 X 1 9 6 0 1 9 6 5 1 9 7 0 1 9 7 5 1 9 8 0 A BC Coast X PNW West 1 9 8 5 200 q o" o tv in cn o m <D W o m 100 90-FIGURE 2.5 Trends in Labour Productivity - BC and PNW Logarithmic Scale X x x X A T A BC Coast x PNW West 1955 1960 1965 1970 1975 1980 1985 FIGURE 2.6 Trends in Capital Productivity — BC and PNW Logarithmic Scale 200 o o o ¥ tv in cn o co aj (A o CD 100-40-A BC Coast X PNW West 1955 1960 1965 1970 1975 1980 1985 40 FIGURE 2.7 Trends in the Wood Consumed per Unit of Labour - BC and PNW Logarithmic Scale 2 0 0 1 1 A BC Coost X PNW West 1955 1960 1965 1970 1975 1980 1985 FIGURE 2.8 Trends in the Wood/Labour Relative Price - BC and PNW Logarithmic Scale 200 A BC Coost X PNW West 1955 1960 1965 1970 1975 1980 1985 41 regions, which roughly approximates the percentage difference. Given the current concern in BC over the increasing scarcity of wood, it is interesting to observe what has been happening to wood productivity. If wood productivity increases, the same output can be produced with less wood, and so declines in wood availability are translated into smaller declines in output. While lumber recoveries remained constant on average in BC during the period, they grew in the PNW at approximately 0.68%/year (Figure 2.3). Wood productivity grew slightly in BC (due to the increasing pulpchtp output) and at a considerably faster rate in the PNW. Labour productivity (Figure 2.5) increased at a faster rate in BC. Chip recovery increased in both regions, but at a faster rate in the PNW (Figure 2.4). While the amount of wood consumed per unit of labour input has increased in BC, it has remained constant in the PNW (Figure 2.7), and this phenomenon can in part explain the different productivity patterns between the two regions. The behaviour of relative prices, also summarized in Table 2.4, can suggest explanations for these trends. While the price of wood has been declining relative to the wage rate in BC (-0.81%/year), i.e., labour is becoming more expensive relative to sawlogs, the opposite has been happening in the PNW (1.03%/year) (Figure 2.5). It is a prediction of the microeconomic theory of the firm that cost minimizing producers will respond to changes in relative prices by substituting abundant (and inexpensive) inputs for the more scarce (and expensive) ones. The behaviour of the industry in both regions seems to be consistent with the theory, by becoming more wood and less labour intensive in BC, and more labour and less wood intensive in the PNW. Both regions are becoming more capital and less labour and wood intensive. Capital productivity (Figure 2.6) declined in both regions but at a faster rate in BC. 42 Columns 5 and 6 of Table 2.4 show the average growth of the spread between the two regions with respect to the ratios in question. Lumber recovery in BC relative to the PNW has declined at an average rate of 0.68% per year, while the lumber/wood price ratio has increased at 1.48%. This can be loosely interpreted as meaning that wood is becoming relatively scarcer in the PNW than in BC. The last four columns of Table 2.4 show the average levels (over the period analyzed) of single factor productivities, input and output ratios, and relative prices, in the PNW relative to BC, which is taken as a basis ( = 100.00). It is interesting to note, that in spite of the increasing trends in labour productivity in BC, the average level of labour productivity was 6% higher in the PNW, and that this region used on average less wood per unit of labour. Wood productivity was 26% higher and lumber recovery 30% higher on average in the PNW than in BC. Capital productivity, the wood/capital and labour/capital ratios were lower, probably reflecting the fact that the PNW industry is considerably more capital intensive than the BC one.5 2.6 TRENDS IN INNOVATION IN THE SAWMILLING INDUSTRY As preliminary work for this research, a study of trends in innovations in the sawmilling industry was undertaken.* This study involved a review of the technical literature, visits" and interviews with management in 25 sawmills throughout BC (17 in the Interior, 8 on the Coast), and interviews with 6 equipment manufacturers, most of which were suppliers in BC and in the PNW. Some of the findings of the study, which are relevant to the topic of this thesis, are reported here. Most of the technological innovations introduced in sawmills during the last 30 years, have been through improved machinery or plant design. According to 43 several authors, the three main factors that have been shaping sawmilling technology in the leading lumber producing regions of the world are (1) relatively increasing wage rates, (2) relatively increasing wood prices, and (3) declining sawlog quality (McBride, 1963; Fraser, 1975; Hartman, 1975). Increasing wages are common to all regions, but increasing log prices seem to be particularly critical in the PNW (Hallock, 1978), and declining log sizes in BC and in the PNW. Until the 1960's, the main objective of technical innovation was labour reduction (Willinston, 1979). Stumpage prices were low and increasing real wages put an upward pressure on manufacturing costs. This led to a drive towards mechanization with the objective of increasing labour productivity. Examples of developments were push button setworks to eliminate the carriage rider, limit switches on log and lumber decks to eliminate deckmen, limit switches on lumber sorting machines and automatic lumber stackers (Hallock, 1979). More recently, scrag saws, multiple saw trimmers and automated sorting systems have been implemented. Increasing real log prices seems to be a phenomenon peculiar to the PNW. As a consequence, a great deal of attention in this region has been paid to improvements in lumber recoveries (Hallock, 1978), and new machinery was developed that served this purpose, benefiting from the developments in the electronics industry (Willinston, 1979). Examples are the recent precision cutting devices and log holding systems (Halliday, 1976), computer controlled scanning devices, the optimization of log, cant and board breakdown and the use of thinner kerf saws made of more resistant materials, in order to reduce the proportion of sawdust in output (Thasher, 1977; Kirbach, 1980). Large log mill technology is inappropriate to the processing of small logs, because of higher unit costs (Hobbs, 1968). As log sizes have declined, mills have 44 attempted to increase lineal throughputs by adding a small log line to the existing mill. High speed, small log mills have been built, featuring chipper headrigs, multiple bandsaw headrigs, slab chippers, chipping edgers and automated sorting and packaging systems (Willinston, 1975). In several cases, a high speed stud mill was added to an existing large log mill, permitting the standardization of output (Faughender, 1981). Another area in which improvements have been introduced are energy saving systems. Waste burning became a eommon practice during the 1970's, in order to reduce pollution levels, or for the production of energy. This latter practice is more popular in the US than in BC (Lefcort, 1982). There are also examples of innovations made available that increase the value of output, such as finger-jointing (Strickler and Kennedy, 1980) or machine stress rating (Pellerin, 1980). In Table 2.5, the main technological innovations in sawmilling, as supplied by equipment manufacturers in 1982 are summarized. Table 2.5 is interpreted as indicating innovations supplied both in BC and in the PNW. These innovations have been classified according to the main impact they are likely to have on the existing variable input and output mix in the mill. Innovations were considered to save labour per unit of output if their main effect was to increase labour productivity, to save wood if they increased wood productivity and to save energy if they increased energy productivity. They were considered to increase output if, as a result of their introduction, an increase in the productivity of all inputs could be expected (i.e., the dominant input could not be identified). This classification was based on the author's judgement and advice provided by manufacturers. Examination of Table 2.5 indicates a clear dominance of innovations that permit the saving of wood, except for the front-end and back-end of the sawmill where labour saving characteristics still appear important. Table 2.5; Trends in Supply of Innovations in BC and the PNW. AREA INNOVATIONS RESULT CLASSIFICATION OBSERVATIONS LOG HANDLING Sophisticated log haulers reduce log jams save labour mainly on ponds also in yards Log singulators reduce log jams, increase throughput save labour Double arbor cut off saw reduce size and width of saws save wood save labour (maintenance) Log scanning and value driven bucking increases potential value of short logs increase output Robust barkers reduce maintenance and downtimes save labour Automatic centering of barkers reduced lumber damage and chip upgrading save wood increase output Faster barkers with ring preparing in advance for log diameter increased throughput save labour Automatic log bin sorters (merchandizer) lumber upgrade and reduction of manpower save labour increase output HEADRIG High strain band saws pneumatic or rubber strain systems more accurate thin kerf saws through reduced response time (damping effect) save wood Log scanning systems upgrade, less waste save wood increase output Log scanning for sweep upgrade, less waste save wood increase output -Log scanning for quality upgrade increase output non-existent yet Chipping headrigs with log scanning and computer controlled setting of knives reduces proportion of chips save wood Very fast chipping headrigs increased throughput save labour Hidraulic setting of knees in carriages greater cutting accuracy save wood Sidedogs, enddogs, overhead carriage precision sawying infinite taper save wood increase output EDGERS Double arbor rotary gangs -spline arbor instead of color smaller saws reduced kerf save wood increases maintenance requirements Less wearable saws through carbide saw tipping improves accuracy, reduces kerf save wood Sideboarder optimizers for wane reduced wastes at the edger save wood not in BC yet Sideboard optimizers for defect upgrades boards increase output in use in Scandinavia Cant optimizers save wood LUMBER HANDLING SYSTEMS Automated bin and tray sorters save labour CHIPPERS Drum chippers upgrades chips increase output Drum chippers with screen for recycling upgrades chips increase output ENERGY Systems for production of energy from wood wastes energy used mainly in kilns save energy NOTE: table is based on information provided by equipment suppliers. 46 Table 2.6 summarizes recent and planned investment in machinery in the sawmills visited in BC. It is interpreted as indicating the innovations demanded by the BC sawmills. The same criterion of classification used in Table 2.5 was also used in Table 2.6. According to the results in Table 2.6, the demand for high throughput, labour saving equipment appears to be clearly dominant when compared with equipment whose main effect is to increase lumber recoveries. This dichotomy between innovations supplied, dominantly wood saving, and innovations demanded in BC, clearly labour saving, can perhaps be best interpreted by means of the theory discussed by Rosenberg (1972). The basic idea is that the demand for an innovation will be affected by the firm expectations about trends in relative factor and product prices. A change in relative factor prices will induce the substitution of one factor for another, and a specific technology will be demanded. If equipment manufacturers behave also in a profit maximizing manner, they will concentrate their inventive capacity in developing those innovations for which demand can be expected to grow the most. The supply of technical progress will depend upon the expected profits to be made from supplying the innovation. Thus, a change in relative factor prices will also stimulate the development of appropriate technology, that will make substitution between factors in processing feasible. Given that most of the equipment manufacturers interviewed were suppliers both in BC and in the PNW, the supply, of wood saving innovations is probably responding to the economic environment facing sawmills in the PNW. As was shown in the previous Section, in this region wood prices have grown the fastest, reflecting the increasing wood scarcity. On the other hand, in BC, labour prices increased the most, and so demand for labour saving innovations appeared to be the most important. Table 2.6; Machinery Demanded in Mills Visited in BC. MILL RECENT INVESTMENT REASON CLASSIFICATION BOTTLENECKS PLANNED INVESTMENT CLASSIFICATION debarkers chipper headrig chippers band mill single band edger double arbor edger increase throughput with small logs and produce chips increase throughput increase throughput save labour increase output save labour save labour save wood small planer, low throughput manual sorting and stacking, too much manpower bigger planer automatic green and dry sorter save labour save labour chipper headrig automatic bin sorter and stacker dry kiln log yard sidewise bucking barkers double arbor edger chipping headrig MSR eliminate studmill eliminate 6 workers per shift increased throughput replace pond replace powersaw, increase throughput increase throughput with small logs increase throughput with small logs and produce chips increase value of stress lumber save labour save labour save labour save labour save labour save wood save labour increase output increase output downtimes of barkers small log deck after bandsaw, low throughput manual sorting and stacking, too much manpower barker larger deck automatic green sorter save labour save labour save labour 6 edger in 1 line small line with chipping headrig automatic bin sorter computerized CNS automatic trim, merchandizer log singulator 8 chipping slabber optimized CNS speed converter in CNS 1 1 two saw circular headrig chipping system automatic log sorter automatic lumber sorter finger jointing 13 edger 14 machine for cabin logs 15 automatic green sorter 16 automatic sorter 18 twin band resaw automatic bin sorter new building 19 log merchandizer eliminate resaw, increase throughput increase throughput, produce chips reduce manpower automatic setting of knives and saws, increase throughput reduce log jams produce chips reduce wastes increase throughput produce chips increase throughput save manpower upgrade output reduce manpower reduce manpower increase throughput save labour save labour increase output save labour save wood save labour save labour save labour save labour increase output save wood save labour increase output save labour save labour increase output increase output save labour labour saving save labour save labour save wood save labour band and cant edger in one line trim optimizer, limited log supply, limited backend bad design of mill: small decks, log jams, low throughput large log barkers too many workers at the planer mill edger, one machine instead of two reduce overtrimming new mill small log barkers automatic bin sorter and stacker save labour save wood save labour save labour 22 automatic bin sorter quad edgers laser machine double band headrig upgrading increase throughput save labour save wood save wood save labour 23 overtrimming trimmer optimizer save wood 48 This study seems to reinforce the trend analyses carried out in the previous section. In particular, it confirms the fact that in response to market forces (labour prices increasing the most), the BC industry does not appear too concerned with improving recovery standards, but that most of the emphasis has been on substituting capital for manpower, with subsequent increases in labour productivity. Such would be the predicted behaviour of profit-maximizing, competitive producers. If the prediction that wood prices in BC will escalate, due to rising harvesting costs, holds (see quotation in the Introduction to the thesis), one can expect this trend to reverse, and the BC industry to embark in more programs to improve the recovery standards. 49 Footnotes 1. Constantino, L. (1983) - The Vancouver Log Market, A Quantitative Analysis. Paper Presented as Part of the Requirements for Forestry 519, Faculty of Forestry, University of British Columbia, 71pp. + graphs and tables. 2. An exception are the small business sales which are 5% of the cut annually. 3. Average growth rates and level differentials for the period 1957-1982 were estimated by running the regression In Xj = a„ + dfD + o2-T + a3-T-D where Xj is a price or a quantity, D is a dummy variable (PNW = 1, BC=0), T is year, a 2 is the average growth rate in BC, a2 + a2 is the average growth rate in the PNVV -a 3 is the difference in growth rates between BC and the PNW, and e f l l + J •100, where T is the mean year, is used to compute the average level of the variable in the PNW relative to BC which is taken as a basis (=100.0). 4. Single factor productivity is defined as aggregate output, where the aggregate includes lumber, shingles and pulpchips, divided by the quantity employed of the factor of production. 5. In the analysis carried out so far, average log market sawlog prices (Series (A) in Table 2.2) were used as a measure of the opportunity cost of logs, together with the corresponding series for sawlog consumption. The same analysis was carried out with the alternative series for sawlog price (Series (B) in Table 22) and consumption, but the results were qualitatively identical to the ones discussed above. Quantitatively they were also close, with a noticeable difference in the levels of wood productivity (136.), lumber recovery (141.) and wood/labour (78.) ratios in the PNW relative to BC (100.). The time trends were identical. 6. Constantino, L. (1983) - Trends in Innovations in the BC Lumber Industry. Paper submitted as part of the requirements for Forestry 580, Faculty of Forestry, University of British Columbia, 82pp. 3. MEASURING WOOD QUALITY 50 3.1 INTRODUCTION Wood quality is an important variable that affects both productivity and profitability of logging (Erickson, 1978; Cooney, 1981) and milling (Mcintosh, 1964; Dobie, 1971 and 1972; Dobie et aj., 1975). It is a popular belief that wood quality has declined and that this has had important impacts on industry efficiency and structure (Hartman, 1975; Fahey and Starosto'vic, 1978; Zobel, 1984). Studies looking at" patterns of wood quality change are very scarce in the literature, and this dimension of forest production has been overlooked, when compared with the analysis of the quantity dimension. The existing research is of two main types; (1) analyses of the relationships between wood characteristics, mill technology and product recoveries (e.g. Willinston, 1981; Dobie, 1972; Dobie et ai. 1975), and (2) analyses of the patterns of change in the characteristics of the forest inventory. LaBau and Knight (1978), an example in the latter group, looked at historic changes in sawtimber volume by DBH class and by species in the United States. By using average diameter as a proxy for quality, they found that while the quality of the inventory is improving in the eastern states, it has been declining in the west, due to the depletion of preferred species (Douglas-fir and redwoods) and the liquidation of large, high-quality, old growth timber. According to these authors, the quality decline has been more pronounced on public lands than in private ownerships. Declining quality overtime is consistent with the predictions of standard Ricardian theoretical models of resource exploitation (Barnett and Morse, 1963). Inter-temporal profit maximization in deterministic models suggests that those stands yielding the highest net revenue will be depleted first (if one looks at the 51 forest as a mine, i.e., no growth). There is a close relationship between the value and cost of logging of a particular stand and the quality of logs that can be extracted. Higher quality logs not only have higher value, but they tend to be located, as a rule, on the best and most accessible sites, thus yielding lower harvesting costs. In general, one would expect the overall quality to exhibit a declining trend overtime. However, cycles and short-run fluctuations in the quality of the harvest can also be expected. In good lumber markets, the quality of the marginal log is likely to be lower, thus reducing average log quality. On the other hand, if a poor lumber market coincides with a good pulp market, the opposite may result. Average quality will decline because more pulpwood is harvested. Also, pools of higher quality timber may be made economically recoverable as new regions are made accessible, for example through the opening of roads, or due to the installation of plants in remote areas. Variations in quality will also be affected by changes in the expectations of the industry concerning the relative prices of end products. Stands of higher quality timber may not be harvested for some time, if capital gains are expected when compared with stands of lower quality timber. In other words, if the prices of the final products that can be recovered from top quality timber are expected to grow in the future at a faster rate than the prices of lower quality products (ignoring relative processing costs), high -quality wood may be left appreciating in the stand. In BC, several public policies have affected the quality of the resource being extracted. The most important was the introduction of closer utilization standards in the mid 60's. The increases in annual allowable cuts, resulting from closer utilization, were allocated to companies whose sawmills processed smaller 52 logs and agreed to sell their chip production to specific pulp companies. The result was a burst of sawmilling capacity aimed at processing smaller logs (Pearse, 1980). Consequently, the average size of logs harvested declined. According to Pearse (1976), these effects were felt in the Interior, but had less impact on the Coast. Another important policy affecting average log quality is the regulation that the old growth timber must be harvested first. Although old growth timber may, on average, be of higher physical quality,' it may not necessarily be the least cost, and so this regulation is likely to affect the quality of. wood extracted, when compared with the resulting pattern in the absence of such a constraint. This constraint does not exist in the PNW, where second growth timber has been harvested for some time. There are two basic problems in the analysis of the impacts of wood quality change. The first problem, discussed in this Chapter, is to define and measure wood quality. The second problem, which is closely related to the first one and will be discussed in Chapter 5, is how to incorporate quality variables in economic models of the industry in order to analyze the impacts of quality change on processing technology, demands and supplies. The objective of this Chapter is to derive a measure of the quality of wood harvested in BC and in the PNW that can be used to test the hypothesis that wood quality has declined overtime. In Section 3.2, the literature on quality measurement is briefly reviewed. In Section 3.3, a log quality measure is derived. In Section 3.4, the log quality measure is applied to data from the Vancouver Forest Region, the Vancouver Log Market and the six log markets in the PNW. In Section 3.5, some conclusions are drawn. 53 32 APPROACHES TO THE MEASUREMENT OF QUALITY CHANGE Economists have long been concerned with the measurement of the quality of goods. Quality is viewed as an important variable due to its impacts on both consumer and producer choices. Much of the earlier interest in quality measurement was related to the development of cost of living indices. It was considered, for example, that if the cost of a good bought by a consumer remained unchanged but its quality increased, the cost of living had in fact declined, although conventional price indices often failed to reflect this change. These issues are discussed, among others, by Triplett (1976) and Deaton and Muellbauer (1980). In principle, if data disaggregated enough by prices and quantities of goods are available, so that quality variations within each category of good are either negligible, or can be ignored due to the low resolution of the analysis, quality change can be measured through the use of conventional price and quantity indices. On the quantity side, a measure of quality is obtained by defining aggregate quantity as the product of two terms: the sum of the quantities of the several goods (e.g. total volume) and quality. Aggregate quantity can be measured using index numbers. Deflating aggregate quantity by total quantity (volume) yields a measure of quality. Growth in aggregate quantity is the sum of two terms -growth in total quantity (volume)- and growth in quality. On the price side, an equivalent measure of quality is obtained by deflating the average (composite) price of the several goods by the aggregate price. This price index measures the price level or the so called pure price. Growth of the average (composite) price of the good is also the sum of two terms - growth in the price level (pure price, price index), and growth in quality. Under certain conditions, the quality indices derived from the quantity or price sides will be 54 equal (see Section 3.3). Obviously this approach only makes sense when the quantities of the several goods can be measured through a common unit (e.g. volumes of different sawlog grades). This index number approach to the measurement of quality change has been widely used in the explanation of productivity change and economic growth (Jorgenson and Griliches, 1967; Gollop and Jorgenson, 1980; Gollop and Roberts, 1981; Chinloy, 1980, 1981, 1983). By decomposing quality change into several factors, related to different labour characteristics, Chinloy (1981,1983), in two extensive studies of the quality of labour in the US and Canada, was able to quantify the sources of labour quality growth. When disaggregated data is not available so that price and quantity indices cannot be constructed, or when each good cannot be assumed to be of homogeneous quality, an alternative method is required. This is a common situation with capital assets (e.g. houses, automobiles). The most popular approach in dealing with this situation in the consumer context has been the hedonics methodology (Griliches, 1971a). The problem is to derive the unknown prices of the characteristics, which can then be used to build price indices. Once this is done, the analysis of quality change is carried out in an identical way to the one discussed above. In order to derive these "hedonic" price indices, a hedonic price equation is estimated, usually for several cross-sections of a time series. The dependent variable is the observed price of a good (e.g. sawlogs), and the independent variable its characteristics (e.g. average diameter, species, etc.). The estimated coefficients of the characteristics variables measure the implicit prices of the characteristics. When two cross-sections corresponding to two different time periods are compared, the change in the observed price, not accounted for by 55 changes in the characteristics valued at the estimated implicit prices, measures the price change, i.e., the pure price change or change in the price level. Such pure price change is conceptually equivalent to the price change measured through price indices. Quality change can then be measured as the change in the average (composite) price of the good minus the pure price change. This method has been widely applied in the study of automobiles (Dhrymes, 1967; Griliches, 1971b), housing (Chinloy, 1977), residential property (Ridker and Henning, 1967), trucks (Hall, 1971) etc. The hedonics methodology has been analyzed from a theoretical point of view by Rosen (1974), who, using a supply-demand framework, deduced the hedonic price equation as the envelope of bid and offer curves for various quality characteristics. Theoretical interpretations of the hedonics equation have also been provided by Lancaster (1971), Lucas (1975), Muellbauer (1975) and Ladd (1983). Brannman et a[. (1981), applied the hedonics methodology to data on prices and characteristics of Douglas-fir stumpage sold in the Pacific Northwest, and were able to decompose the change in average stumpage price into a pure price and a quality effect. For the period 1968 through 1978, the authors found a very small declining trend in the quality of Douglas-fir, not statistically different from zero. But year-to-year variations in quality were important. 3.3 THE MEASUREMENT OF SAWLOG QUALITY The measure of log quality utilized in this research is derived through the index number approach mentioned above as opposed to the hedonics approach. The choice was made based on the data available (prices and volumes by grades), which facilitate this method. 56 Although the hedonics approach could be used with the same data, it would not yield any additional information. The main disadvantage of the approach chosen, is that each log grade will have to be assumed to be of homogeneous quality, which is not true. If data on the average characteristics of the wood harvested were available, or if average charateristics of each grade could be easily derived from grade specifications, than there would be some advantages to using the hedonics approach. The main one would be the derivation of the shadow or implicit prices of the characteristics. However, in this case, multicolinearity problems would be likely to occur when estimating the hedonics equation, since in the case of logs the different quality characteristics are closely related and move together from grade to grade (larger diameter, more clear wood, less defects) or across time. There have been institutional attempts to classify logs according to their characteristics. These have resulted in various grading systems. According to Dobie (1971), the traditional classifications of logs into groups are related to the end products that can be recovered from them. Most of the grading systems are either based on value judgements, i.e., the grader uses his judgement when evaluating the final products that can be obtained from the log, or are based on a visible characteristic thought to be related to the product yield. Until recently there were two log grading systems in existence on the BC Coast: statutory and industrial grades. In 1981, the two systems were brought together in a single grading system. Log grading is particularly important in BC, due to the existence of an active log market and due to the stumpage appraisal system. Until 1981 there were approximately 44 different industrial grades which were used as a basis for log transactions. Logs were classified in specific grades if they could "pass" certain minimum requirements or specifications, usually defined in terms of species, length, diameter, potential yield of clear lumber. 57 knots, spiral grain, pathological and other defects. Prior to 1981 statutory grades were the official grades utilized for stumpage appraisal. They were also defined in terms of minimum requirements to enter the grade, but were less refined and each one usually comprised several industrial grades. Until 1981 there were approximately 30 different statutory grades in use. A grading system equivalent to the BC industrial grades is also used in the PNW for log transactions. This system comprises 57 different grades. The volume of wood harvested is composed of a mix of species and grades. Different species and grades possess different qualities (i.e., characteristics) in the sense that they contribute differently to production. If the species and the grade mix changes from one year to another, there is a change in the characteristics, and, therefore, in the average quality of logs. It is this change that one wants to measure. Suppose sawmilling can be represented by a production function of the type (3.3.1) M = F(L| tp.UI.K) where M is the volume of lumber produced, the Ij .are the volumes of grades i (i = 1, ,n) of sawlogs, and W and K are the quantities of labour and capital employed. If the marginal products of the several log grades differ, because of different characteristics, a change in the grade mix will lead to a change in output, even when the total wood volume (V=Llj) and the quantities of labour and capital are held constant. Under certain assumptions, it is possible to replace the Ij by a single number L, an aggregate measure of the log input. The required assumption is that the sawlog grades are weakly separable in the lumber production function. This 58 implies empirically that the marginal rates of substitution between the several grades are independent of the levels of other factors of production employed. L is defined as (3.3.2) L = G(LV. , g and is a quality corrected measure of the wood input, which captures not only the effect of volume changes, but also the effect of changes in the grade mix. In the same way that F(.) in (3.3.1) is a production function aggregating or transforming the quantities of the several sawmilling inputs into an output M, G(.) in (3.3.2) is a production" function aggregating or transforming the quantities of a subset of the inputs, the volumes of different sawlog grades, into an aggregate measure of the wood input L. An obvious definition of wood quality is therefore (3.3.3) Q = L/V Q is a quality index, that converts the wood volume V (e.g. cubic meters) into a quality adjusted wood input measure L. The growth rate in quality is obtained by differentiating (3.3.3) with respect to time and dividing by the quality level: (3.3.4) (5Q/5t) • (1/QJ = ieU5t) • (1/D- (5V/tft) • (1/V) = ti \m/ei) • (tfl/flt))) • (1/L) - [SW/St) • (1/V) The profit on the choice of the grade mix is (3.3.5) p.Ga^.Lpl-ZpjL where P is the value of one unit of quality adjusted log volume and Pj (e.g. $/cubic meter) is the value of one unit of grade i log volume. 59 The first order conditions for profit maximization imply that (3.3.6) P • (*G/*l,| - p{ for alii and (3.3.4) can be written as (3.3.7) («Q/«| • (1/Q) - [I ap,l/PD • m/8l) • (1/1,11) - l*V/*t) • (l/V) or Q= ZZI-V =L-V (3.3.8) 1 1 Z, - PjL/Zpjlj where Z.j is the share of grade i in total log expenditure and a dot over a variable denotes a growth rate. Assuming the aggregator G(.) is linearly homogeneous, this implies that P-G(l 1,...,ln)=Zpjlj, and that the cost shares Zj sum to one, which explains equation (3.3.8). (3.3.8) is a Divisia index number and it is the basic equation utilized for the measurement of wood quality in this thesis. The growth rate of total quality equals the sum of the growth rates of the volumes of each grade, weighted by their shares of total expenditure, minus the growth rate in total volume. Implicit in the above equation is the idea that those grades with higher marginal products, i.e., which are more efficient, will also be more valuable, so that it is appropriate to use market information (i.e. prices) when weighting the relative contributions of the several grades to lumber production. The definition of quality change (3.3.8) has an intuitive meaning. Suppose that from year t to year t + 1, more of grade 1 of Douglas-fir and more of a pulpwood grade of hemlock were consumed, but that the volume of the pulpwood grade increased at a faster rate. Then, although the total volume increased, there would be an increase in the proportion of lower quality grades, and average quality would have declined. Equation (3.3.8) allows one to separate this change in 60 the grade composition or quality, from the change in volume. In order to better study the anatomy of wood quality change, the above analysis is repeated for each species separately, and then the several species are aggregated into an overall quality measure. Each species is composed of several grades. Define the species aggregate (Sj) in year t as (3.3.9) S j - F t l J , . l j Z Ijrv1 where Ijj is the volume of grade i of species j and F is a positive linearly homogeneous aggregator function. The log aggregate is composed of several species. Define the log aggregate (L) in year t as (3.3.10) L - G(S,.Sz.....Sm) where Sj is the volume of species j and G is a positive linearly homogeneous aggregator function. The growth rates of the two aggregates are respectively (3.3.11) S j - H j f j j (3.3.12) L - ZZjSj where Sj - SlnS^/St - IfiSy*t) • fl/Sj) = Slnlj/tft = (0Lj/ftt) • HAJP and z j r WnSj/^nljjJMPjjl/tlPjiljj) Zj = (5lnL/*LnSj) • IpjSjj/ttpjSj) = [2p^/[ZZp^ In words, Zyf is the share of expenditure with grade i of species j in the total expenditure with species j. Zj is the share of expenditure with species j in total log expenditure, p.. is the average price of grade i of species j, p. is the 61 average price of species j, and a dot over a variable means growth rate. Define the average quality of species j (Q|) at time t as (3.3.13) q t j -s t j /v 1 , where Vj is the volume of species j at time t. Define the average quality of the log aggregate (Q*) at time t as (3.3.14) Q U L W where V* is the total volume of logs at time t. The growth rates of quality are; (3.3.15) Qj'Sj-Vj (3.3.16) Q . L - V Substituting (3.3.12) into (3.3.16) yields, (3.3.17) Q=SZjSj-V Substituting (3.3.11) into (3.3.15) yields, (3.3.18) Q= ZZjtSZjiLjj-V) Add and subtract V^ , the growth rate of the volume of species j to (3.3.18) : (3.3.19) Q = ZZj IZ (Zjjr Vj * Vj)) - V (3.3.20) Q. ZZjttlZjrj|-Vj»'* XZjVj-V or (3.3.21) Q= ZZjQj-IZjVj-V and 62 (3.3.22) Q - QT • Os The total change in quality equals the sum of two effects: a grade effect (Q|) and a species effect (Qs). The grade effect reflects the change in the mix of grades within each species. It is the share weighted sum of the quality change of each species. The species effect reflects the change in the mix of species in the log aggregate. It is the change in the quality of the aggregate due to changes in species composition. Suppose that from one year to another, the volume of hemlock increased at a faster rate than that of Douglas-fir, and that everything else, including the grade composition of those two species, remained the same. Then, the volume would have increased, but the average quality would have declined, because there was a shift to a less valuable species (lower marginal product). In this case the species effect (Q g) accurately measures the total quality change, because there is no grade effect (Q| =0). Now suppose that in addition to the change in the species composition, grade 3 Douglas-fir also grows at a faster rate than grade 1. In addition to the species effect, there would be a grade effect, and the decline in quality correspondingly greater. Equation (3.3.22) only measures the true quality change if the grades themselves do not change in quality. Because this is not likely to be the case, this method yields only an approximate measure of quality change. The error of the approximation will depend on the variability of log characteristics within each grade. With a high number of grades, the approximation error is likely to be minor, because grade quality variations are likely to lack economic significance in studies of the industrial aggregates. Divisia index numbers are appropriate for continuous data, but an approximation must be used with discrete data. The Tornqvist translog index is 63 very popular in the literature and was also used here. Its properties have been discussed by Diewert (1976). Diewert has argued for the use of indices such as the Tornquivst, because they imply the assumption of a flexible functional form for the aggregator, and so the substitution possibilities between the components are not restricted. The discrete index was applied to equation (3.3.8), which measures total quality change in a single stage and to equation (3.3.21) which decomposes total quality change into two effects. Although equations (3.3.8) and (3.3.21) were shown to be equivalent, the same does not apply with the discrete measure; a discrete Divisia index is not necessarily a discrete Divisia index of the components (Diewert, 1978). To obtain consistency in aggregation, the aggregator function in one of the stages would have to be Cobb-Douglas, i.e., shares remain constant overtime. Still, according to Diewert, if indices are constructed by chaining observations in successive periods, the measures resulting from single and two stage aggregation should be approximately equal. The formulae used are shown in Table 3.1. Equations (3.3.23) through (3.3.27) were used for the log quality measurement. Quality change within each species is measured with equation (3.3.24). The grade effect is the species share weighted sum of the growth rates of the qualities of each species and is measured in equation (3.3.25). Equation (3.3.26) measures the species effect and equation (3.3.27) the total quality change as the sum of the two effects. Equation (3.3.23) measures total quality change using a single effect. One still needs to justify the use of the above equations for inter-regional quality comparisons. The above derivation cannot be used, because of the discrete nature of regional comparisons, which invalidates the use pf derivatives. The one-stage discrete formula (3.3.23) can be alternatively obtained by assuming that Table 3.1: Discrete Equations Utilized in the Construction of Quality Indices. No. Equation 0) Definition 3.3.23 AlnQt + 1 , t Aln^* 1-* 3.3.24 AlnQt + 1,t J 3.3.25 AlnQj + 1,t 3.3.26 AlnQj + 1,t 3.3.27 AlnQt + 1 , t ZZ 0.5(Zt-Zt. + Zt + 1-Zt.+ 1)-Alnlt.+ 1,t - Total Quality J J l J J l J l Change (one stage) = Z 0.5(Zt. + Zt+1)-Alnlt.+ 1,t - AlnVt + 1,t Species j J Quality Change Grade Effect J' Z 0.5(Zj + Zj + 1)-AlnQj + 1,t Z 0.5(Zt + Zt + 1-AlnVt-i-1,t - AlnV1"1"1*1 Species J J J Effect AlnQt + 1,t AlnQL+1,t + Total Quality Change (two stage) (1) AlnXt + 1 > t = ^ ( X ^ V x 1 ) where X is any variable and t is year. Alternatively, t + 1 is taken as referring to the PNW and t to BC. 65 the aggregator L=G(l.|,...,ln) has a translog form. By utilizing the quadratic approximation lemma (Diewert, 1976), the linear homogeneity assumption and the first order conditions for profit maximization, the equation can be derived. This approach has been utilized by Denny and Fuss (1980) in the context of inter-regional and inter-temporal total factor productivity comparisons and is used in the present context by Constantino (1985b). It implies the assumption that the two regional aggregators have identical parameters. Caves et aj (1982b) have generalized the use of such formulae to discrete comparisons of aggregators, in which only the second order parameters are required to be equal. Thus, the discrete equation (3.3.23) can also be used for interregional comparisons between two regions, just by reinterpreting t + 1 as referring to one region and t as referring to the other region. The two stage equations (3.3.24) - (3.3.27) were not utilized in interregional comparisons. Given the assumptions utilized to derive the quality measure (linear homogeneity of the aggregator and price taking profit maximizing behaviour with respect to the components of the log aggregate), an identical quality measure can be obtained from the price side. To see this, note that1 (3.3.28) P • V = P-L = Ip^ where SP j I j is total sawlog expenditure, P is the value per unit of volume (the average price - $/cubic meter, given by total wood costs divided by total wood volume), and P is the value per unit of quality adjusted log input (the quality adjusted price, or price index, given by total wood costs divided by the aggregate wood input L). Quality was defined above as Q=L/V and so (3.3.29) Q = p/P or in terms of growth rates, • • • (3.3.30) Q = P-P 66 Differentiating (3.3.28) with respect to time yields (3.3.31) L • 13P/SI) * P • lei/St) = 2l,tffp/fft) • Zp^L/St) or (3.3.32) P • L = Z (lp(L/PL) • {1/pj) • [dp/St)] * Z UPjtj/PL) • (I/I,) • l*l/*t)) = and (3.3.33) P - 2ZjPi (3.3.34) Q = P - ZZ,?, P is a quality adjusted price, i.e., a price index which measures the price level. Quality change equals the growth rate of the value per unit of volume (the change in the average price) minus the expenditure share weighted sum of the growth rates of the prices of the several grades (the change in the quality adjusted price). 3.4 TRENDS AND LEVELS OF SAWLOG QUALITY ON THE BC COAST AND PNW WEST Three sets of wood quality indices were built; (A) Vancouver Forest Region Quality Indices (1925-1980) (B) Vancouver Log Market Quality Indices (1925-1982) (C) PNW Log Market Quality Indices (1957-1982) The Vancouver Log Market allows one to observe prices and quantities of the several statutory and industrial grades traded on the BC Coast. There is a rich set of data collected by the British Columbia Council of Forest Industries 6 7 which includes this information on a weekly, monthly, quarterly, half-yearly and yearly basis, some of which dating back to 1924.2 Six similar markets operate in the PNW West: Puget Sound, Grays-Willapa Harbors, Columbia River, Willamette Valley, Oregon Coast and Southern Oregon. The Industrial Forestry Association compiles quarterly data for water, inland and export sales by grade for each of the six markets.5 In the quality indices developed, it is assumed that log market prices of the several grades reflect the relative value's of their marginal products. This will happen if processing firms behave competitively in the log market. As discussed in Chapter 2, the importance of log trading has been declining due to the backward integration of manufacturing and logging firms. On average, about 15% of the BC Coastal harvest and less than 10% of the PNW West4 harvest are traded. The declining importance of the Vancouver Log Market has raised questions about its competitiveness (Pearse et ai., 1974). An important one is that because log market prices are used as a basis for stumpage appraisal, integrated firms involved in log trading may have an incentive to collude in order to lower log prices. But, in spite of these doubts, the hypothesis of competitiveness has never been formally rejected.5 Similar objections could be raised about the several PNW log markets. Oslen and Terpstra (1981) investigated and did not reject the hypothesis that the Willamette Valley log market was competitive. The Vancouver Log Market (VLM) and Pacific Northwest Log Market (PLM) data are summarized in Tables 3.2 and 3.3 respectively. A third data set consisting of volumes of several statutory grades harvested in the Vancouver Forest Region was obtained.6 The grade volumes for 1961-1973 and 1976-1977 were missing and these were estimated by regressing the shares of each grade in each species harvest on the shares of each grade in each species volume in the VLM and on time. Table 3.4 describes the components Table 3.2; Components of the Log Aggregate for the Vancouver Log Market. SPECIES STATUTORY GRADE INDUSTRIAL GRADE DATA AVAILABLE FOR INDUSTRIAL GRADE DATA AVAILABLE FOR STATUTORY GRADE OR SPECIES #1 Peeler #1 Standard # 1 Select #1 1943 - 1982 1943 - 1982 1947 1924 - 1982 DOUGLAS- FIR #2 Peeler #2 Peeler #3 Peeler #4 Standard #2 Select #2 1943 - 1982 1946 - 1982 1954 - 1982 1943 - 1982 1943: 1946 - 1953 1924 - 1982 #3 Standard #3 Select #3 Lumber Reject 1943 -1982 1942; 1946 - 1948; 1952 - 1958 1974 1982 1924 - 1982 HEMLOCK #1 #2 #3 Standard # 1 Standard #2 Standard #3 Lumber Reject 1947 1947 1947 1974 1982 1982 1982 1982 1924 - 1982 CYPRESS #1 #2 #3 Standard #1 Standard #2 Standard #3 Lumber Reject 1974 1974 1974 1974 1982 1982 1982 1982 1974 - 1982 B A L S A M #1 #2 #3 Peeler Lumber Pulp Lumber Reject 1947 - 1948; 1952; 1956 - 1982 1947 - 1982 1947 - 1982 1974 - 1982 1947 - 1982 SPRUCE #1 #2 #3 Standard # 1 Standard #2 Standard #3 Lumber Reject 1934; 1936 - 1982 1934; 1936 - 1982 1974 - 1982 1974 - 1982 1934; 1936 - 1982 #1 Lumber # 1 Shingle # 1 Select #1 Merch # 1 1943 - 1982 1943 - 1982 1943; 1946 1959 -- 1947 1982 1924 - 1982 CEDAR #2 Lumber #2 Shingle #2 Select #2 Tie #2 Merch #2 1943 - 1982 1943 - 1982 1943 ; 1947 - 1948 1949 - 1953 1959 - 1982 1924 - 1982 #3 Shingle #3 Select #3 Tie #3 Merch #3 Lumber Reject 1943 - 1982 1943 ; 1947 - 1948 1949 - 1958 1959 - 1982 1974 - 1982 1924 - 1982 PINE #1 #2 #3 Standard # 1 Standard #2 Standard #3 Lumber Reject 1934; 1936 - 1982 1934; 1936 - 1982 1974 - 1982 1974 - 1982 1934; 1936 - 1982 O) CO Table 3.3: Components of the Log Aggregate for the Pacific Northwest Log Markets. SPECIES GRADE DATA AVAILABLE FOR GRADE DOUGLAS-FIR HEMLOCK NOBLE FIR WHITE FIR SPRUCE CEDAR PINE Peeler #1 Peeler #2 Peeler #3 Special Mill Sawlog #1 Sawlog #2 Sawlog #3 Sawlog #4 Mixed Ungraded Peeler Special Mill Sawlog #1 Sawlog #2 Sawlog #3 Sawlog #4 Mixed Ungraded Peeler Special Mill Sawlog #1 Sawlog #2 Sawlog #3 Sawlog #4 Mixed Ungraded Peeler Special Mill Sawlog # 1 Sawlog #2 Sawlog #3 Sawlog #4 Mixed Ungraded Select Special Mill Sawlog # 1 Sawlog #2 Sawlog #3 Sawlog #4 Mixed Ungraded Sawlog #1 Sawlog #2 Sawlog #3 Sawlog $4 Mixed Ungraded Peeler Special Mills Sawlog # 1 Sawlog #2 Sawlog #3 Sawlog #4 Mixed Ungraded 1957 - 1982 1957 - 1982 1957 - 198-2 1963 - 1982 1957 - 1982 1957 - 1982 1957 - 1982 1969 - 1982 1969 - 1982 1957 - 1982 1957 - 1982 1963 - 1982 1957 - 1982 1957 - 1982 1957 - 1982 1969 - 1982 1969 - 1982 1957 - 1982 1957 - 1982 1963 - 1982 1957 - 1982 1957 - 1982 1957 - 1982 1969 - 1982 1969 - 1982 1957 - 1982 1957 - 1982 1963 - 1982 1957 - 1982 1957 - 1982 1957 - 1982 1969 - 1982 1969 - 1982 1957 - 1982 1957 - 1982 1963 - 1982 1957 - 1982 1957 - 1982 1957 - 1982 1969 - 1982 1969 - 1982 1957 - 1982 1957 - 1982 1957 - 1982 1957 - 1982 1969 - 1982 1969 - 1982 1957 - 1982 1957 - 1982 1963 - 1982 1957 - 1982 1957 - 1982 1957 - 1982 1969 - 1982 1969 - 1982 1957 - 1982 70 of the aggregate for the Vancouver Forest Region. For all data sets there were problems of missing observations. These arose mainly due to the introduction of new grades in the middle of the series. This "new good" issue is a well known problem in the index number literature. Diewert (1980) has recommended ways of dealing with this problem, but these were not used due to their complexity. Instead, it was chosen to drop any observation adjacent to a zero (missing) volume, for any of the grades. In other words, in each two adjacent years, identical samples' were compared. For example, lumber rejects started being reported in 1974. 1973 was compared with 1974 excluding lumber rejects and 1974 was compared with 1975 including lumber rejects. An additional problem occurred with the PNW data set due to variations in the sample coverage, which for some years did not cover all quarters or all regional markets.6 Important discontinuities happened in 1963-1964, in 1966-1967, in 1967-1968 and 1968-1969. Because in all cases overlapping samples (equivalent for adjacent years) were obtained, in every year to year comparison the samples were identical. Thus, if quality change in a subset of the markets or quarters is representative of quality change in the entire set, this procedure avoided biases introduced by inter-seasonal or inter-regional quality variations. A last and more serious problem, which affected all indices, is due to the way log scales are defined both in BC and in the PNW. In the PNW, and until 1971 in BC, the log volume was measured based on potential output, i.e., the number of board feet that may be cut (Scribner Log Scale in the PNW and Board Foot Log Scale in BC). Conversion to a scale that measures the actual volume of the log, either in cubic feet or cubic meters, varies with log diameter and other log characteristics (e.g. defects) (Forestry Undergraduate Society, 1983; Tan, 1983). Because conversion factors from the board foot scales to cubic meters or cubic Table 3.4: Components of the Log Aggregate for the Vancouver Forest Region. SPECIES STATUTORY DATA DATA GRADE AVAILABLE FOR AVAILABLE FOR STATUTORY SPECIES GRADE^1) #1 1924 - 1980 DOUGLAS- FIR . #2 1924 - 1980 1924 - 1980 #3 1924 - 1980 #1 1947 1980 HEMLOCK #2 1947 - 1980 1924 - 1980 #3 1947 - 1980 #1 1974 1980 CYPRESS #2 1974 - 1980 1974 - 1980 #3 1974 - 1980 #1 1947 1980 BALSAM #2 1947 - 1980 1924 - 1980 #3 1947 - 1980 #1 1934 1980 SPRUCE #2 1934 - 1980 1934 - 1980 #3 1934 - 1980 #1 1924 1980 CEDAR #2 1924 - 1980 1924 - 1980 #3 1924 - 1980 . #1 1934 1980 PINE #2 ' 1934 - 1980 1934 - 1980 #3 1934 — 1980 includes years 1961 - 1973 and 1976 1977 for which statuto grade volume shares in each species were predicted by regressing this variable on statutory grade volume shares in the VLM and time. 72 feet are grade dependent, the quality index will be affected by the measurement units utilized. This can be easily seen by rewriting equation (3.3.8) in the following way: (3.4.1) i f . ziZjZjjdjj+Cjjl-V-C where Ijj is the growth rate of the volume of grade i of species j expressed in board feet, is the growth rate of the conversion factor of board feet into cubic meters for grade i of species j, V=EZIjj is the total volume in board feet, V its growth rate, .and C the growth rate of the average (weighted) conversion factor. Q c would be the growth rate of total quality if volumes were expressed in cubic meters. Assuming that Cjj =0, i.e., the average conversion factors for each grade remains unchanged (there are no variations in quality within each grade), equation (3.4.1) can be rewritten in the following manner; (3.4.2) if = j; ((Z-SJ™) • (S^ flBj - QF -c where ZF is the share of grade i in total sawlog expenditure with all species, sP c the share of grade i in total board feet volume, Si is the share of grade i in total cubic meter volume, h the growth rate of the volume of grade i (in cubic meters or board feet). The difference in the quality growth rates defined in cubic * c • F meters (Q ) and in board feet (Q ) is C, the growth rate in the average conversion factor. Quality change in cubic meters is the sum of two effects. The first is the quality effect incorporated in the log scales (the inverse of the Mfbm/cubic meter m c • conversion factor) measured by Z(S I-S I)- IJ. In general, for a low quality grade, c m S I > S I . This is because low grades receive a smaller weight in the log scale than 73 in the firmwood scale, and so in the presence of quality declines, this effect is negative (C is positive). The second is the quality effect not incorporated in the log scale, measured by L(Zj-S m-lj. In general, for a low quality grade, S mi>Z|. Although low grades receive smaller weight in the log scale, its relative value will, as a rule, be even smaller, so in the presence of quality declines, this effect (Q^) will also be negative. If the log scale considerably underestimates the board feet that may be cut from low quality logs, a pervasive result may occur and S mi<Zj. This would lead to a positive contribution of this term to quality change, even in the presence of quality declines. The relative sizes of the grade and species effects in the two stage index will also depend on the scale utilized, as can be seen in the following two equations: (3.4.3) Q,C =Q,F-2ZjCj (3.4.4) QsC =Q s F-(C-IZjCj) where Cif is the grade effect in cubic meters, ClF the grade effect in board feet, and -ZZj-Cj the grade effect incorporated in the log scale. oJj is the species effect in cubic meters, til the species effect in board feet and -(C-LZj-Cj) the species effect incorporated in the log scale. In general, the greater the quality decline (or increase), the greater the difference between the two measures. The cubic meter based measure will exhibit sharper variations than the board foot based one. If the BC and PNW log scales m c differ in the way quality effects are incorporated (i.e. (Si - Si) in equation 3.4.2), the comparison of growth rates of quality between the two regions using board feet or cubic meters will yield different results. The same applies to inter-regional comparisons of quality levels. The board foot based quality index measures quality change, net of the effect already incorporated in the log scale. 74 A cubic meter based index would be intuitively more appealing, but unfortunately it could not be utilized for all indices derived in this research, because most of the data were expressed in board feet (80% of the observations for BC; 100% of the observations for the PNW). The grade specific conversion factors obtained for BC (Sitter et ai., 1982) were derived for recent years. Their use in earlier years would introduce unquantifiable biases.8 The compromise utilized here was to derive quality indices for the whole time series in board feet, and for a subsarnple of the data in cubic meters. This subsample covers the period 1947 - 1982 for the Vancouver Log Market and 1957 1982 for the Pacific Northwest log markets. During this period, grade specifications did not change considerably, and so the conversion procedure is less arbitrary. In this way, one also obtains estimates of the quality effects incorporated in the log scales. Also, in general, the sign of the quality change will not be affected by the scale utilized, and so a qualitative analysis will still be valid. In Table 3.5, quality indices for the Vancouver Forest Region and Vancouver Log Market are summarized.' There was some interest in comparing indices for the two data sets because first, there were some doubts concerning the representativeness of the log market for deriving information on trends in the quality of the harvest, and second, because the grade information for the Vancouver Forest region was less detailed, and thus the biases due to quality variations within each grade likely to be more severe. It was considered that if the two indices produced similar results, the above two problems could be ignored. Both indices are based on statutory grades (board foot log scale), so they are comparable. They were linked through the 1980 cross-section. Table 3.5; Average Growth Rates of Wood Quality and Relative Wood Quality Levels in the Vancouver Forest Region and Vancouver Log Market (Statutory Grades, Board Foot Log Scale) - percentage per y e a r P ' ^ VFR LEVEL LEVEL RELATIVE RELATIVE TO TO VLM VANCOUVER FOREST REGION VANCOUVER LOG MARKET VLM (One Stage) (1925-1946) PERIOD Grade Species Two One Grade Species Two One VLM VFR VLM VFR Effect Effect Stage Stage Effect Effect Stage Stage 1925 - 1980 -0.20 -0.28 -0.48 -0.48 -0.13 -0.22 -0.35 -0.34 100.0 100<2> 1925 - 1956 -0.38 -0.18 -0.55 -0.57 -0.28 -0.28 -0.55 -0.51 100.0 101.7 - -1957 - 1980 -0.I2 -0.26 -0.37 -0.35 0.04 -0.12 -0.08 -0.08 100.0 97.7 - -1925 - 1946 -0.50 -0.21 -0.71 -0.71 -0.41 -0.35 -0.76 -0.66 100.0 102.1 100.0 102.1 1947 - 1956 -0.29 -0.23 -0.51 -0.58 -0.56 -0.06 -0.62 -0.68 100.0 101.0 93.5 94.4 1957 - 1970 -0.05 -0.49 -0.54 -0.49 0.05 -0.45 -0.40 -0.39 100.0 98.9 89.9 88.9 1971 - 1980 -0.1 1 0.13 0.02 0.04 0.32 0.69 1.01 1.02 100.0 96.1 88.8 85.3 (1) average growth rates and relative levels were calculated by running a regression such as InQ = a„ + «jPj + e„J + 0J.D..T where the D. are region and period specific dummies and T is time. (2) differed on the 5th digit. (3) the two time series were linked through the 1980 cross-section. 76 The results for the one- and two-stage indices were very close, a feature of all inter-temporal comparisons. In the VFR from 1925 through 1980, log quality declined at an average rate of 0.48% per year, with the decline in the quality of the grade mix contributing 0.20% per year and the decline in the quality of the species mix contributing 0.28%. For the same period, log quality in the VLM declined at an average rate of 0.34% per year, with the grade effect contributing 0.13% and the species effect 022%. For both indices, the effect of changes in the species mix was greater than the effect of changes in the grade mix. These average growth rates disguise what happened in different periods. For both indices the quality decline slowed down during the latter part of the period, with quality actually increasing after 1971. This increase in quality was sharp in the VLM (1.01% per year), with the species effect contributing 0.69% per year and the grade effect contributing 0.32% per year. In the VFR, the quality of the grade mix declined in all subperiods, but the quality of the species mix increased after 1971, leading to a net quality increase. The relative importance of the grade and species effects varied, with changes in the grade mix dominating prior to 1956 for both indices, and changes in the species mix dominating after 1957. The quality level was slightly higher in the VFR than in the VLM during the earlier part of the period, and slightly lower during the second part of the period. The behaviour of these two quality indices can also be observed in Figures 3.1, 3.2 and 3.3. In the VFR, all the most important species (Douglas-fir, hemlock and red cedar) declined in quality, with hemlock displaying the lowest decline. The lowest quality level in the VFR was achieved in 1975, while in the VLM this occurred in 1972. Both indices show similar year-to-year fluctuations. Because sawmills are likely to rely more on the log market than pulpmills, one could expect the log market index to be less affected by changes in the demand for pulpwood. This may in part explain the different quality trends observed after FIGURE 3.1 Wood Quality and Species and Grade Effects in the Vancouver Forest Region Statutory Grades, BC Board Foot Log Scale 105-1 70 H 1 1 1 1 1 I 1920 1930 1940 1950 1960 1970 1980 1990 FIGURE 3.2 Wood Quality of Individual Species in the Vancouver Forest Region: Douglas-fir, Cedar and Hemlock Statutory Grades, BC Board Foot Log Scale 1920 1930 1940 1950 1960 1970 1980 1990 FIGURE 3.3 Wood Quality in the Vancouver Forest Region and Vancouver Log Market Statutory Grades, BC Board Foot Log Scale 110 I 70-60-Voneouvtr Log Mqrfc«t Vancouver Fcvei^Rtqlon 1920 1930 1940 1950 1960 1970 1980 1990 FIGURE 3.4 Sawlog Quality in the Vancouver Log Market: Cubic Meter Index, Board Foot Index and Log Scale Effect Sawlog Grades 110 I 105-79 1971, although in the earlier periods the two indices behaved identically. The similarity between the two indices suggests that the quality trends of logs traded are representative of the quality trends of logs harvested. This fact had already been noticed by Pearse et a[. (1974), who compared the proportions of several grades in the total volume traded with the proportions of several grades in the total volume harvested for selected years. This result gives support to the procedure utilized later in the thesis, of using a log market quality index as a proxy for the quality of logs going to sawmills. Table 3.6 summarizes the average growth rates for the Vancouver and Pacific Northwest log market quality indices (board foot log scale). Two sets of indices were built, one using information on all industrial grades and one using infomation on sawlog industrial grades alone.10 The sawlog index eliminates peeler and pulp grades. The reason for building the two indices (all grades and sawlog grades) is that there is a considerable overlap between the grades utilized by different industries. According to several log brokers, log sellers and log buyers interviewed in BC, both sawmills and plywood mills compete for peeler grades, and many sawmills do acquire and resort pulp grade log booms. The extent of the overlapping depends on the market conditions. In good lumber markets, sawing a low quality pulp log may become profitable. This same problem also occurs in the PNW log markets (Adams, 1974). Given that for this research it was important to measure the quality, of logs going to sawmills, the two indices were built in order to evaluate the sensitivity of the quality measure to changes in the grades included. The first aspect to notice in Table 3.6 is that the all grade and sawlog grades one-stage quality indices produced comparable results in terms of the direction of the change for each region. Comparing the results of Table 3.6 with those of Table 3.5 for the VLM indices, one is led to the conclusion that all Table 3.6: Average Growth Rates of Wood Quality in the Vancouver and Pacific Northwest Log Markets (All Grades and Sawlogs, Board Foot Log Scale) - percentage per year/ ' VANCOUVER LOG MARKET PNW LOG MARKET PERIOD All Grades Sawlogs All Grades Sawlogs One Stage Grade Species Two Stage One Stage One Stage Grade Species Two Stage One Stage Effect Effect 'Effect Effect 1925 - 1982 -0.26 -0.13 -0.14 -0.28 -0.26 1925 - 1956 -0.49 -0.31 -0.18 -0.50 -0.44 - - - - -1957 - 1982 0.02 0.04 -0.02 0.01 0.03 -0.42 -0.43 0.29 -0.15 -0.16 1925 - 1946 -0.64 -0.41 -0.33 -0.74 -0.64 - - - - _ 1947 - 1956 -0.85 -0.47 0.00 -0.46 -0.53 - •. - _ _ _ 1957 - 1970 -0.17 -0.06 -0.49 -0.54 -0.53 -0.80 -0.77 0.21 -0.56 -0.51 1971 - 1982 0.85 0.34 0.54 0.88 0.90 -0.25 -0.42 0.29 -0.13 -0.08 (1) see footnote (1) of Table 3.5 for an explanation of how growth rates and relative levels were calculated. 00 o 81 VLM board foot indices yielded similar results, so the quality measure appears to be quite insensitive to changes in the grade specification, i.e., utilization of statutory or industrial grades and inclusion of all grades or just sawlog grades. The VLM sawlog quality index shows a declining trend for the period 1925 -1982 (-0.26%) with the grade and species effect contributing equally on average to this decline. In terms of the several subperiods, all the quality decline occurred before 1971, and in the following years quality increased at an average rate of 0.90% per year. Before 1956 most of the decline was due to changes in the grade mix, while between 1957 and 1970 the degradation of the species mix was the dominant factor. Log quality declined at a much faster rate in the PNW than in BC. While in the VLM quality remained unchanged on average between 1957 and 1982 (0.03% per year), it declined in the PNW log market at an average rate of 0.16% per year. The rate of quality decline slowed down after 1971, as in BC, but it remained negative. In the PNW all the quality declines appear to arise from changes in the grade mix. The species effect was positive from 1957 through 1982. One hypothesis for the faster decline in quality in the PNW could be the increasing use of second-growth timber. On the BC Coast, most of the harvest is still on old growth timber. Table 3.7 shows the results for the cubic meter based quality measure. The indices include only sawlog grades. These can be compared with the sawlog indices of Table 3.6, the difference between them measuring the quality change incorporated in the board foot log scale (scale effect in the table). The results for the two-stage index were very close to the one-stage index, and so the former was omitted from the table. The scale effect has the same sign as the quality effect (with the exception of the grade effect for the 71-82 subperiod in the PNW), and is smaller in absolute value (with the exception of 71-82 in the Table 3.7: Average Growth Rates of Wood Quality. Relative Wood Quality Levels and Board Foot Scale Effect in the Vancouver and Pacific (1) (2) Northwest Log Markets (Sawlog Grades, Cubic Meters) - percentage per year.v ' v ' VANCOUVER LOG MARKET PNW LOG MARKET PNW LEVEL LEVEL RELATIVE RELATIVE TO TO VLM VLM 1947-1956 PERIOD Grade Effect Species Effect One Stage Grade Effect Species Effect One Stage One Stage One Stage Scale. m> Scale m' Scale m> Scale m> Scale m 1 Scale VLM PNW VLM PNW effect effect effect effect effect effect m' m' m' m' 1947 - 1982 0.01 -0.10 -0.08 1957 - 1982 0.09 0.05 0.03 0.05 0.15 0.12 -0.93 -0.56 0.36 0.07 --0.59 -0.43 100.0 136.7 - -1947 - 1956 -0.76 -0.29 0.09 0.09 --0.74 -0.21 - - - -" - 100.0 - 100.0 -1957 - 1970 -0.19 -0.13 -0.41 0.08 --0.59 -0.06 -1.90 -1.13 0.32 0.1 1 -•1.53 -1.02 100.0 147.6 95.3 140.7 1971 - 1982 0.52 0.18 0.57 0.03 1.13 0.23 -0.30 0.12 0.44 0.15 0.19 0.27 100.0 135.1 97.6 131.9 (1) see footnote (1) of Table 3.5 for an explanation of how growth rates and relative levels were calculated. (2) The two time series were linked through the 1982 cross-section, after converting the PNW grades to BC grades. co ho 83 PNW), so as noted above, the board foot and cubic meter indices generally move in the same direction and the former is smoother. Figure 3.4 shows the VLM sawlog quality index (one-stage) in cubic meters as well as the VLM sawlog quality index (one-stage) in board feet and the index for the board foot scale effect. The board foot scale effect was computed by subtracting the rate of change in the board feet index from the rate of change in the cubic meter index (equation 3.4.2). It is an index of the conversion factor rebased to 1947 = 100. The two quality indices trace each other closely and the quality effect incorporated in the BC Board Foot Log Scale appears to be minor. This is probably due to the fact that quality did not change very much in the VLM during the period. The scale effect might have been more important prior to 1947. The scale effect appears to be more important in the PNW, which could be due to the sharper variations in quality observed in that region. From 1947 through 1982 log quality declined in the VLM at an average rate of 0.08% per year, with all the decline due to changes in the composition of the species mix. Quality change varied considerably between time periods with all the declines occuring in the first two subperiods. Between 1971 and 1982 a sharp increase in quality occurred (1.13% per year). Quality declined at a faster rate in the PNW than in BC between 1957 and 1970 and increased at a slower rate between 1971 and 1982. In the PNW, while the grade composition deteriorated in both subperiods, the species mix improved. Given the popular belief concerning the declining quality of wood, it is surprising to find that all indices increased after 1971. In BC, this fact is due to the increase in the volume shares of statutory grades #1 and #2 relative to grade #3 that occurred after this year. This happened with two of the most important species: Douglas-fir and red cedar. The shares of statutory grades #1 84 and #2 of hemlock declined, but at a slower rate than prior to 1971. Unfortunately, no explanation for this increasing trend in the quality of wood could be advanced, and this constitutes one area for further research. One possible speculation is that declining lumber real prices after 1971, coupled with the low productivity performance of sawmilling (see Chapter 4.), led the industry to the use of higher quality wood in order to secure its competitive position in output markets. Given that higher quality timber will be eventually depleted, the increasing quality trend will not be sustainable in the long-run. The VLM and PNW time series were linked through the 1982 cross-section. Conversion matrices which expressed each PNW grade in terms of several BC grades were obtained for that year.10 Quality was on average 37% higher in the PNW than in BC, but the quality gap is diminishing (48% in 1957-1970; 35% in 1971-1982). The VLM and PNW sawlog quality indices (one-stage) in cubic meters are compared in Figure 3.5. The results of this Section can be used in connection with an important and actual policy issue. In 1981, the PNW sawmilling industry began complaining that the Canadian wood products industries were capturing part of the US market due to government subsidies, in particular subsidized stumpage. As a consequence of this process, usually known as the "Countervailing Duty Case Relating to Certain Forest Products from Canada",11,1S American producers sought countervailing tariffs on some wood product imports from Canada. Although the initial round of investigations led to a decision of no countervailing duties, the process still continues today under new forms. One of the arguments advanced by the BC industry in its defense was that stumpage cannot be compared between the several regions due to the different qualities of wood. 85 FIGURE 3.5 Wood Quality in the Vancouver and Pacific Northwest Log Markets Sawlogs, Cubic Meters 180 o 6 o TT CT) 160-140 120-a> O 100 m 80 60 : • • • VLM PLM 1945 1950 1 , 1 , 1 , 1955 1960 1965 1970 1975 1980 1985 FIGURE 3.6 Average and Quality Adjusted Sawlog Prices in the Vancouver and Pacific Northwest Log Markets 80-© 60-o '3 D a k. <u CL V> 40 -O O c g g 20-a o VLM Ouolltv *dluit»d PLM Quality Adjusted VLM Non-odju«t«d PLM Non-od|utt«d 1955 1960 1965 1970 1975 1980 1985 86 The question posed in this research is to what extent can the relative PNW/BC sawlog price be explained by the relative sawlog quality in the two regions. This is not a test of whether stumpage is subsidized. It is rather a test of whether the average market price of sawlogs, the input to the sawmilling industry, differs due to quality differences or due to any other factors, which could include stumpage differences. In order to test this, the relative average sawlog prices in the Vancouver and PNW log markets were adjusted for quality differences by rewriting equation (3.3.34) as follows; (3.4.5) AlnP = AlnP - AlnQ. where P is the quality corrected price, P~ is the average price and Q is sawlog quality. The results are shown in Figure 3.6. The quality adjusted prices are expressed in terms of the VLM 1957 quality level. Average prices were also plotted for comparison. While the quality adjusted and average prices are almost identical in the VLM (quality changed very little), it was found that the difference in log quality between the two regions more than explains the average price differential, for most observations. The quality corrected price was lower in the PNW for most of the years, probably due to lower logging costs. Only in 1981 did the PNW price clearly rise above the VLM one. The results of this analysis suggest that the BC industry is no more subsidized via wood prices than the PNW one, and give support to the hypothesis that all differences in wood prices arise mostly from differences in wood quality. This interregional price comparison is more extensively discussed in Constantino (1985b). 87 3.5 CONCLUSIONS In this Chapter, a sawlog quality measure was developed and applied to three data sets for the Vancouver Forest Region, Vancouver log market and Pacific Northwest log markets. Quality change was expressed as the sum of two effects: a species effect and a grade effect. It was also shown that the quality measure depends an whether volumes are measured through a cubic meter or board foot log scale. The VFR and VLM indices based on the BC Board Foot log scale show that quality declined on average between 1925 and 1980/1982, but that all the decline occurred prior to 1971. During the period 1971-82 average quality increased. Both the degradation of the species and grade mix contributed to the quality decline. The VLM index based on the firmwood scale confirmed these results for 1947-1982. The quality effects incorporated in the log scale were minor during this period. All the quality indices utilizing BC data yielded similar results, and appear quite insensitive to changes in the grades utilized. Quality in the PNW declined at a considerably faster rate than in BC during fhe period 1957-82 with all the decline due to changes in the grade mix. The species effect contributed positively to quality change. According to the cubic meter quality index, the quality decline occurred prior to the 1970's, and during the last decade quality increased on average, as in BC, but at a lower rate. Year-to-year quality fluctuations were found to be more important in the PNW. In BC, there is a constraint that the old growth must be cut first, and the BC cut has mostly occurred at the extensive margin. In the PNW, such a constraint does not exist, and second growth timber has now been cut for some time. These facts could explain the faster decline and sharper yearly fluctuations in quality in the PNW, as well as the fact that most of the quality decline results from 88 changes in the grade mix in this region. From 1957 through 1982 quality was on average 35% higher in the PNW than in BC. The quality gap between the two regions is diminishing. This quality gap more than explains the average price gap. With the exception of 1981, the quality corrected sawlog price was either slightly lower in the PNW or approximately equal in the two regions. This suggests that the BC industry is not any more subsidized via wood costs than the PNW one. With respect to hypothesis (1) of this research, it was found that although wood quality has declined on average in both regions, during the period analyzed, in the last decade quality shows an increasing trend. The hypothesis that quality declined at a faster rate in BC (2) is rejected, while the hypothesis that quality is higher in the PNW (3) is accepted. 89 Footnotes 1. The author is greatful to Dr. T. Heaps for suggesting the the following derivation. 2. Council of Forestry Industries of British Columbia, Average Log Prices Report (1924-1982), Vancouver, BC. 3. Industrial Forestry Association. Composite Log Sales, Quarterly (1957-1982) Portland, Oregon. Export sales data was excluded from the sample. For 1969-1982 annual compilations of this data were obtained from the Pacific Northwest Forest and Range Research Station, USDA, Portland. For 1957-1962 annual compilations were obtained from the Industrial Forestry Association. There were regional gaps in this data, which are discussed in the text. 4. Because it was impossible to correctly measure the volume of the harvest in the PNW West, this figure is just a rough estimate. 5. Sitter et al.. (1982) report 143 different buyers and 45 different sellers involved in log market transactions in 1980. 6. BC Ministry of Forest, unpublished compilations, 1924-1960 and 1978-1980; Pearse et al. (1974), 1974-1975; BC Ministry of Forests Annual Reports, 1925-1980 (Volumes of each species). 7. Due to its cost, not all data available was acquired. 8. For the BC earlier years (1925 - 1946), statutory grades are utilized. To derive an average conversion factor for these grades using recent information would be an arbitrary procedure. 9. The periods 1925-1946, 1947-1956, 1957-1970 and 1971-1980 were chosen to compute average growth rates because (1) in 1947 new grades were introduced, (2) 1957-1982 is the sample utilized later in the thesis, (3) after 1971 the indices exhibit a different pattern of behaviour. 10. The all grade PNW index included a mixed grade between 1969 and 1982; the sawlog index excluded the mixed grade. 11. Council of Forest Industries of BC/Timberline Computing Services (1982) -Scribner/BC Log Grading Comparison Study: System Design, Implementation and Testing. Mimeo, COFI, Vancouver, B.C. 12. Canadian Softwood Lumber Committee (1983) - Collected Proceedings of the Countervailing Duty Case Relating to Certain Forest Products from Canada, Vol. 1 - Vol. V (October 1982 - May 1983); Compiled by Canadian Softwood Lumber Committee. 13. Luckert, M. (1984) - A Synopsis of Collected Proceedings of the Countervailing Duty Case Relating to Certain Forest Products from Canada. Paper submitted for Forestry 519, University of British Columbia, Faculty of Forestry. 90 4. IMPACTS OF CHANGING WOOD QUALITY ON TOTAL FACTOR PRODUCTIVITY COMPARISONS 4.1 INTRODUCTION The objective of this Chapter is to evaluate the magnitude of the bias introduced in total factor productivity (TFP) comparisons in the sawmilling industry, when the changing quality of wood is not taken into account. In other words, the objective is to test whether the incorporation of wood quality in the TFP model will result in significantly different TFP estimates, both in inter-temporal and inter-regional comparisons. Section 4.2 describes the model utilized in this research. One of the most popular models found in the literature was also used here. In Section 4.3, empirical results are discussed, and in Section 4.4, the main conclusions of this Chapter are presented. In the remainder of this Section a brief review of the main approaches to TFP measurement is given. Empirical studies of TFP and technical progress in the wood products industries were discussed in Chapter 1. There is a very large body of theoretical and empirical literature on the measurement of TFP, technical progress and contribution of technical progress to economic growth. The earlier literature was reviewed by Nadiri (1970), and Kennedy and Thirwall (1972). Technical progress, or change in technical efficiency, has been defined as a shift in the production function brought about by increases in the state of knowledge (Stigler, 1961). Single factor productivity measures such as labour productivity have been criticized as a measure of technical efficiency, on the grounds that they will be affected not only by technical progress, but also by substitution effects, which cause changes in factor proportions, for example in the labour/capital ratio. The same criticism applies to measures common in the forest industries, such as lumber recoveries. Constantino and Haley (1985) present a discussion of these issues in the context of productivity 91 measurement in the forest industries. There are two main approaches to the measurement of technical progress -the econometric approach and the accounting or index number approach. Diewert (1981) has shown that under certain conditions these two approaches are equivalent. The simplest form of the econometric approach is to statistically estimate a production function with a time trend. The coefficient on the time trend measures technical progress, or the change in output overtime not explained by the change in inputs. The index number ~ approach usually starts by defining TFP as the ratio of aggregate output to aggregate input. Technical progress is measured by determining how TFP changes overtime, i.e., differences in aggregate output not explained by differences in aggregate input. Because the aggregation procedure allows for substitution effects between outputs and/or inputs, such measures allow, to a certain extent, technical progress (shifts in isoquants overtime) to be separated from changes in input proportions (movements along isoquants). The aggregation procedure is critical in this TFP measure. Diewert (1976) has derived the relationships between the form of the index chosen to aggregate inputs and/or outputs and the implied form of the production function. Different functional forms imply different substitution patterns. The development of flexible functional forms since the early 70's and the identification of the corresponding index numbers, gave productivity analysts less restricted ways (in terms of the substitution possibilities) of building aggregate input and output. Because the non-explained growth in output is a residual, many effects are captured in it, including changes in the quality of inputs or outputs not accounted for in the aggregation procedure, specification and measurement errors. 92 Following the developments in duality theory, it is very popular to use cost functions rather than production functions. Cost functions are based on the assumption that firms are price-takers in input markets and minimize costs of producing an exogenous output level. Technical progress introduces shifts in the cost function. The costs of producing a given level of output, for fixed prices, are reduced. Technical progress can be measured econometrically through a time trend in a cost function. Alternatively, it can be measured using index numbers as the change in the ratio of an aggregate input price index relative to an index of unit costs. If the technology exhibits constant returns to scale the production or cost function approaches should yield identical results. 4.2 TOTAL FACTOR PRODUCTIVITY MODEL The TFP measure utilized in this research is identical to the ones derived by Jorgenson and Nishimizu (1978), Caves et aj. (1980), Denny and Fuss (1980), Denny et al. (1981b) and Caves et al. (1982a; 1982b). It starts with the assumption that the sawmilling technology in each year and in each region can be characterized with a translog production function, that does not differ in the second order terms between regions or from year to year (Denny et aj., 1981b; Caves et ai., 1982a). Adding the assumptions of constant returns to scale, price-taking behaviour in input and output markets, revenue maximizing for given input levels and cost minimizing for given output levels, one can write the logarithmic difference in TFP (AlnTFPjj) between two time periods or regions i and j as: (4.2.1) _ _ _ _ AlnTFP J r R^Lnr^j^HcijAlnL-j-S^ALnV^Aln^ - S^AlnliJjj-SK.jAlnKij where AlnMjj measures the logarithmic difference in lumber output, AlnCjj the logarithmic difference in the pulpchip output, AlnV- the logarithmic difference in 93 the v o l u m e of the w o o d input, A lnQj j the logar i thmic d i f f e r e n c e in w o o d qual i ty , AlnWjj the logar i thmic d i f fe rence in the labour input and AlnKjj the logar i thmic d i f fe rence in the capital input. The "R.^  are the ar i thmet ic averages of revenue shares of the severa l outputs and the S~jj are the ar i thmetic averages of cos t shares of the severa l inputs. If i is taken to refer to the P N W industry in 1980 and j to the B C industry in 1980, the equat ion measures the T F P d i f ferent ia l be tween the two reg ions in 1980. A l te rna t ive ly , if i is taken to refer to the B C industry in 1980 and j to the B C industry in 1979, the .equat ion measures T F P growth or technical p r o g r e s s be tween the two y e a r s . The above f o r m u l a d o e s not imply separabi l i ty o f inputs nor neutral d i f f e rences in product iv i ty (Caves et a[., 1982a). The term AlnWjj - fAlnQj j measures the change in the aggregate log input and is obta ined by inverting the procedure used to der ive the quality index in Chapter 3. It is a measure of the w o o d input in constant e f f i c i e n c y uni ts , i.e., adjusted for quality change. The inclusion of the log input in the product ion funct ion as the product of log v o l u m e and log qual i ty imp l ies that the e last ic i t ies o f lumber product ion with respect to log v o l u m e or qual i ty are equal . The term A l n G ^ is usual ly not k n o w n , due to unavai labi l i ty of data , and the w o o d input i s , in most s tud ies , impl ic i t ly or expl ic i t ly measured in v o l u m e units . Th is int roduces b iases in the T F P measure . Th is can be seen by just adding Sjj -AlnQjj to both s ides of equat ion (4.2.1): AlnTFPjj •S U J j jAlnQ 1 j= R ^ j A l n ^ + F»C (jALnCij-SujjjAlnUJjj-S^AtnLij-^jjAlnKy If, in one reg ion , w o o d qual i ty dec l ined and this is not taken into account , the in te r - tempora l change in T F P as measured through equation (4.2.2) wi l l understate the "true" technical p r o g r e s s . The magni tude of the bias wil l depend o f 94 course on the change in quality and the cost share of the wood input. If either one is negligible the bias will be very small. The same applies to inter-regional TFP comparisons. If quality is much higher in one region when compared with another one, equation (4.2.2) will overstate the efficiency differential between regions. It should be emphasized that the same applies to quality change in any of the other inputs or outputs. In the case of sawmilling, only the omission of quality change in lumber output measures appears to be important, and usually output data is available in disaggregated enough form to take this factor into account (at least partially). Labour quality does not appear to be very important in sawmilling and the pulpchip and capital shares are relatively small. From equation (4.2.1), the impacts of quality change on wood or labour productivity, or on lumber recovery can also be measured. Utilizing lumber recovery as an example, one can add and subtract AlnWjj to equation (4.2.1), obtaining (4.2.3) AlnlM./Ljj = AlnTFPjj • B ^ M ^ j ^^Inl^/l,] • S ^ l n t ^ y * after rearranging and making use of "R^ = 1 - R"cj  and S~L + 5~K + S w = 1. The interpretation of this equation is that the logarithmic difference in lumber recovery is the sum of several- terms: the TFP difference, the difference in the lumber to pulpchip ratio weighted by the pulpchip share in total revenue, the difference in the labour to wood ratio weighted by the labour cost share, the difference in the capital to wood ratio weighted by the capital cost share, and the difference in log quality weighted by the wood cost share (all differences are logarithmic). Lumber recovery will rise in the presence of increases in technical efficiency, declines in the proportion of pulpchips in output, increases in the 95 amount of labour or capital per unit of wood input, or increases in quality. 4.3 GROWTH RATES AND RELATIVE LEVELS OF TOTAL FACTOR PRODUCTIVITY IN REGIONAL SAWMILLING INDUSTRIES Equations (4.2.1) and (4.2.2) were utilized for the inter-temporal and inter-regional TFP comparison. The data utilized in this Chapter were summarized in Chapter 2 and are detailed in Appendix I. A crucial assumption is that quality change (sawlog grades, cubic meters) in the log markets approximates the quality change in logs going to sawmills and that the quality differential between the logs traded in the two regions approximates the quality differential in wood consumed. Table 4.1 shows the average growth rates in TFP and the average share weighted growth rates of inputs, quality and output. Results are shown for the periods 1957-1982, 1957-1970 and 1971-1982 for BC, PNW and BC relative to the PNW.1 During the period 1957-1982, the rate of technical progress or TFP growth in BC was on average 0.35% per year. The quality corrected rate of technical progress was slightly lower and equal to 0.24% per year. This is because wood quality increased on average between 1957 and 1982 in BC. For the same period, the rate of technical progress in the PNW was higher than in BC and equal to 0.91% per year. The quality corrected rate of technical progress was considerably higher and equal to 1.25%. This is because wood quality declined on average between 1957 and 1982 in the PNW. In terms of the relative rates of technical progress between the two regions, BC is losing in its relative efficiency at an average rate of -0.56% if wood quality is not taken into account and at an average rate of -1.01% if the relative change in wood quality is considered. It should be mentioned that the rate of TFP growth fluctuates considerably from year to year, possibly due to the effects of omitted variables. Helliwell et al. Table 4.1: Average Growth Rates of Total Factor Productivity and Input Contributions to Output Growth (Percentage Per Year). BC Period Aggre- Wood Labour Capital Aggre- TFP Wood Quality gate gate Quality Corrected Output Input TFP 1957-1982 1.93 1.16 0.17 0.25 1.58 0.35 0.11 0.24 1957-1970 4.40 2.96 0.22 0.19 3.38 1.02 -0.37 1.39 1971-1982 -0.79 -0.67 -0.24 0.14 -0.77 -0.02 0.72 -0.75 PNW 1957-1982 0.67 -0.31 -0.09 0.16 -0.25 0.91 -0.33 1.25 1957-1970 0.88 0.51 -0.79 0.08 -0.20 1.07 -0.93 2.00 1971-1982 -2.14 -2.51 -0.08 0.27 -2.32 0.18 0.17 0.01 BC RELATIVE TO PNW 1957-1982 1.26 1.47 0.26 0.08 1.83 -0.56 0.44 -1.01 1957-1970 3.52 2,47 1.01 0.11 3.58 -0.05 0.55 -0.61 1971-1982 1.44 1.60 -0.12 -0.13 1.55 -0.20 0.55 -0.76 97 (1984) discuss short-run factors which explain the cyclical behaviour of productivity in the Canadian economy. These average growth rates disguise what happened in different subperiods. From 1957 through 1970 the rate of technical progress in BC was 1.02% per year. The quality corrected rate of technical progress was higher and equal to 1.39% per year, because quality declined on average. In the PNW the quality uncorrected rate of technical progress was 1.07% per year and the quality corrected one was almost double and equal to 2.00% per year^ because quality declined considerably. During the period BC was loosing in its relative efficiency at an average rate -0.05% if wood quality is not taken into account and -0.61% if the sharper quality decline in the PNW is considered. Between 1971 and 1982, productivity growth slowed down in both regions mimicking the behaviour of the US and Canadian aggregate economies. The BC industry underwent technical recess at an average rate of -0.02% per year. If the sharp increase in wood quality during this period is taken into account this rate is -0.75%. Productivity growth also slowed down in the PNW but is still positive: 0.18% per year without quality and 0.01% per year if the increases in quality are taken into account. During this period the BC industry lost in technical efficiency to its PNW counterpart at an average rate of -0.76%, considering wood quality. In spite of benefiting -from a lower decline in wood quality, the technical performance of the BC industry has been deteriorating relative to one of its main competitors. Of course, the analysis so far has only shown how the relative positions of the two regions have been changing. Even in the presence of relative efficiency losses the BC industry could still benefit from a higher efficiency level. 98 The results for the absolute level comparison between the two regions are shown in Table 4.2. For all variables, BC was taken as a basis (=100).2 From 1957 through 1982, the efficiency level in the PNW was on average 10% higher than in BC if the wood quality differentials were not taken into account, but the efficiency gap is completely explained away by the difference in wood quality. If the higher wood quality in the PNW is considered, the efficiency level in this region becomes 11% lower (on average) than in BC.3 Accounting for wood quality changed the ranking of the two regions in terms of their average efficiency levels. These results again disguise what happened in different periods. Comparing the 1957-1970 period with the 1971-1982 period, the efficiency level in the PNW relative to BC rose from 5% higher to more than 16% higher if wood quality is not considered. If wood quality is taken into account this level rose from 11% lower to 4% lower. According to the average growth rates, the PNW industry completely eliminated the efficiency gap in 1981. Equation (4.2.3) of the previous section can be used to show the contribution of wood quality change and wood quality differences to lumber recovery growth and lumber recovery differences. This analysis is not carried out here, but it is noted that the average wood quality difference only explains 23% of the average 35% difference in lumber recoveries between the two regions. Given the assumption of constant returns to scale and cost minimizing behaviour, it can be shown that the logarithmic change in TFP equals the logarithmic change in input prices weighted by the input cost shares minus the logarithmic change in unit production costs (Denny et aj., 1981b). TFP growth, or TFP regional differentials, can also be interpreted as the rate of diminution in unit production costs or unit cost differentials (logarithmic), not explained by Table 4.2: Average Relative Levels of total Factor Productivity and Input Contributions to Output Differences (BC = 100.0). 1957 - 1982 1957 - 1970 1971 -• 1982 Variable BC PNW BC PNW BC PNW Aggregate Output 100. 239. 100. 251. 100. 227. Wood 100. 154. 100. 166. 100. 142. Labour 100. 129. 100. 131. 100. 128. Capital 100. 109. 100. 110. 100. 108. Aggregate Input 100. 218. 100. 238. 100. 196. TFP 100. 110. 100. 105. 100. 116. Quality 100. 123. 100. 126. 100. 120. Quality Corrected TFP 100. 89. 100. 83. 100. 96. 100 changes or differences (logarithmic) in input prices or in wood quality. The results of this Section show that, given the assumptions of the model utilized, if both regions were facing the same input prices and behaving optimally in input choices, unit production costs would have declined faster in the PNW than in BC. Furthermore, if both regions were utilizing the same wood quality, the BC industry would have been more cost efficient on average from 1957 through 1982, but would have lost its efficiency advantage in 1981. 4.4 CONCLUSIONS Due to its residual nature, the above measure of technical progress will be affected by errors due to the omission of relevant variables. Jorgenson and Griliches (1967) have argued that if all inputs and outputs were correctly measured, and an appropriate aggregation procedure utilized, the residual growth in output not explained by growth in inputs would be negligible. It is very unlikely that one will be able to correctly measure all inputs and outputs in efficiency adjusted units (e.g. managerial efficiency). Because sufficiently disaggregated data on the wood input is usually not available, existing studies of the sawmilling or wood products industry have measured the wood input implicitly or explicitly in volume units. The aim of this Chapter was to measure the biases introduced in inter-temporal and inter-regional TFP comparisons, by not accounting for differences in wood quality. An important point to notice is that when the wood input is measured in volume units, the results will be considerably affected by whether a cubic meter or board foot log scale is utilized, and by the type of the log scale.4 As was noted in Chapter 3, log scales embody some quality effects. Also in the presence of considerable quality change, the average conversion factors will vary, and the procedure of converting all the wood volumes to a common measure may 101 introduce considerable biases if a constant conversion factor is utilized. This problem occurs with the Statistics Canada data for BC. Although the model utilized above is not considered a very appropriate representation of sawmilling, mainly due to the assumptions that wood volume and wood quality contribute identically to production, that the industry exhibits constant returns to scale, and that the capital stock can be instantaneously adjusted to its optimum level, it was used in this research due to its popularity in the technical change literature. Also, the review of the literature in the introduction to this thesis showed that although technical progress measures tend to vary considerably between studies, different models and measurement procedures have tended to yield identical results in inter-temporal and inter-industrial comparisons. It should be emphasized that the results with respect to wood quality depend on the crucial assumptions that: (i) the growth rates in the log market wood quality indices approximate the growth rates in the quality of logs going to sawmills, and (ii) the quality differential between the log market index in the PNW and in BC approximates the quality differential of wood consumed in the PNW and BC. As was discussed in Chapter 3, hypothesis (i) could not be rejected for BC through the analysis of the log market data, but the representativeness of the PNW quality measure could not be evaluated. With respect to hypothesis (5) of this research, it was shown that for the period and regions analyzed wood quality noticeably affects the rate of technical progress as measured through a residual. The importance of the impact depending, of course, on the magnitude of the quality change, and on the share of the wood input in total costs. For the period 1957-1982 in the BC, the quality corrected TFP growth rate (0.24%/year) was slightly lower than the quality uncorrected one 102 (0.35%/year), due to the average quality increase. In the PNW, the quality corrected TFP growth rate (1.25%/year) was higher than the quality uncorrected one (0.91%/year), due to the average quality decline. The omission of quality change would considerably understate the poor technical progress performance of the BC industry relative to the PNW industry (-0.56%/year without quality; -1.03% per year with quality). The rates of TFP growth computed in this chapter are comparable in magnitude to those in the studies reviewed' that utilized an index number approach (Table 1.2 in the Introduction). In BC, quality increased on average during the period. It is very unlikely that the poor performance of this region relative to other Canadian provinces, reported by Denny et a[. (1981b), could be explained by a faster wood quality decline. However, the results of those authors are for the whole of BC, and they cover a different time period. It was found that the PNW industry evidences a higher rate of technical progress than BC. Because wood quality declined at a faster rate in this region, the rate of technical progress is even higher than in BC if quality change is accounted for. The higher rate of technical progress cannot be explained through a smaller decline in wood quality. The efficiency level comparison between the two regions has shown that on average for 1957-1982, the higher efficiency of the PNW industry could be completely explained away by the wood quality differential. When differences in wood quality were accounted for., the BC industry became, on average, the most efficient of the two regions. This latter result is important for future inter-regional comparisons of the lumber industry. Although BC and the PNW are usually considered to have a similar resource base, the results of Chapter 3 and Chapter 4 have shown that the magnitude and impacts of wood quality differences are far from negligible. 103 The magnitude of the results w o u l d probab ly be even larger if the B C C o a s t or P N W W e s t were c o m p a r e d with the BC Interior, Q u e b e c , Sour thern U S S ta tes , or S c a n d i n a v i a , due to the d i f ferent nature of the resource . In addi t ion to this the d i f ferent v o l u m e measures in ex is tence (log s c a l e s ) wi l l a l s o have an impact on the results of such c o m p a r i s o n s . F ina l ly , g iven the regional var iabi l i ty of w o o d qual i ty , var iat ions in the relat ive s izes of regional industr ies wi l l a f fect the results of national (or very aggregate) studies of the industry , b e s i d e s result ing in a cons iderab le l o s s of i n fo rmat ion . 104 Footnotes 1. Average growth rates were computed by regressing InXj, where X- is an index for the variable in question (BC 1957 = 100.0) on time and period and region specific dummies. See footnote 3 of Chapter 2. 2. The level comparison utilized the results of the regression mentioned in footnote 1. 3. The bias due to the omission of data on energy and miscellaneous inputs in the inter-regional comparison was less than 1% in 1980. 4. The same obviously applies to prices, and to constant value measures when the price indices do not correctly embody the quality effects. 105 5. AN ECONOMETRIC MODEL OF THE SAWMILLING INDUSTRY ON THE BC COAST AND PNW WEST 5.1 INTRODUCTION The aim of this Chapter is to develop an econometric model of the sawmilling industries in BC and in the PNW that can be used, among other things, to investigate the responses of the industry to increases in wood prices and declines in wood quality and to test hypothesis 4 through 12 stated in the Introduction to this thesis. . . ... . The main innovative feature of the model is the way in which the quality variable is incorporated. The approach is rather general, and could in principle be used with other inputs and in other industries. To keep the exposition intuitive, and given the empirical nature of this research, the discussions are carried out in the context of the sawmilling industry. The case has been made, throughout this thesis, that wood quality is an important variable in sawmilling. Similarly to other natural resources, wood is a very heterogeneous product, and changes in wood quality are likely to affect noticeably the optimal input and output mixes in the industry. Although the importance of wood quality has been mentioned in the literature, the existing studies did not explicitly incorporate wood quality variables in industry or market models1. One objective of this Chapter is to test the importance of wood quality in lumber industry modelling and to evaluate how changes in quality affect the input/output choices of producers, in particular the demand for labour, and the supplies of lumber and pulpchips. A second objective of this Chapter is to provide measures of the total short-run responses of the industry when exogenous shocks occur. The 106 microeconomic theory of the single ouput profit maximizing firm suggests that an increase in the price of an input, e.g. wood, will have two effects: (1) an input substitution effect, brought about by the substitution of less expensive resources for the more expensive ones; and (2) an output effect, which causes a decline in production and input consumption (Gould and Ferguson, 1980; Nagatani, 1978). The output effect has two components: (1) the effect of a change in output on factor utilization, and (2) the effect of a change in the factor price in the optimum output level. In the case of multiple outputs, a change in an output price will have equivalent effects; (1) an output substitution effect, and (2) an input effect. Studies of sawmilling have concentrated on the measurement of input substitution effects and on the effects of a change in output on factor utilization. These are important for an understanding of the structure of sawmilling technology, because they describe the shape of the isoquants, and the degree of returns to scale and homotheticity, but usually they do not provide information that can be directly used in policy analysis. This is because in industries which are not constrained in their output levels, such as sawmilling, an exogenous shock (e.g. an increase in wood prices due to increased harvesting costs) will lead to both substitution -and output effects and it is important to explain the latter in addition to the former. For example, labour and wood may be substitutes, but the total effect is likely to lead to a decline in employment if wood prices increase. The model to be developed will .allow the measurement of total effects, and their decomposition into substitution and output effects. A third objective is to model both lumber and pulpchip supply. As was mentioned in the Introduction to this thesis, sawmilling has always been treated as a single output industry, and pulpchips ignored, although they are an output of increasing importance. Pulpchips are one of the main raw materials utilized by the pulp and paper industry, and changes in pulpchip supply may have important 107 consequences for the future of the pulp and paper sector. It is of interest to investigate to what extent the relative supplies of lumber and pulpchips respond to changes in relative output prices, in relative factor costs, or in wood quality. Furthermore, the technological characteristics of sawmilling suggest that a decline in wood quality will lead to an increase in the proportion of pulpchips in output, all inputs being held constant. Thus, the sign of the relationship between the chip to lumber ratio and wood quality will provide an important test of the model performance with respect to the quality variable. The importance of carrying out this analysis for BC and .the PNW was explained in the Introduction. First, the economic environment facing the industry has been different in the two regions. While in BC wages increased the most, in the PNW wood has been the scarcer input. As a result, the technological characteristics of the industries differ and by studying the two regions a better data sample and a superior representation of sawmilling can be obtained. Second, both regions are important competitors in the lumber market. The results of the analysis can provide an explanation for their relative regional outputs. There were alternative ways of developing the industry model, all of them allowing the accomplishment of the above objectives. In the choice of the final model, an important consideration was to make it suitable for the analysis of important policies currently affecting the BC lumber producers: (1) log export restrictions; (2) tariffs on Canadian lumber exports to the US; and (3) measuring the size of economically recoverable timber inventory. There was also interest in making the model suitable for linkages with the large scale sectoral models developed in the US and currently being introduced in Canada. In particular, with the Timber Assessment Market Model (Adams et ai., 1980), so that it might utilize their forecasts. Another objective was to advance explanations for the observed trends in the BC and PNW relative shares of the lumber market. 108 In the Introduction to this thesis, related studies of sawmilling were reviewed. The most recent econometric studies made use of duality theory which provides the analyst with several theoretical and empirical advantages when characterizing production technology and modelling demands and supplies. Duality theory and its application is discussed among others by Diewert (1974, 1982), McFadden (1978) and Lau (1978). The dual approach involves the specification and estimation of cost and profit functions, which, unlike production functions, already embody the optimizing behaviour of producers. A cost function, for example, relates the minimum costs of producing a given output to input prices and the output level. The nature of the function is determined by the production characteristics, and these can be retrieved from a knowledge of its parameters. Furthermore, it is easier to derive demand and supply equations and to carry out comparative statics (e.g. how lumber supply changes with a change in wood price) from dual functions than from production functions. There is also a substantial empirical advantage in the use of dual functions. The arguments in production functions are input levels, and because these are usually endogenous to the firm, they will be correlated with the error term and biased parameter estimates will result. This problem is less likely to occur with dual functions (Varian, 1978). The dual approach was also utilized in this research. This Chapter is organized as follows. In Section 2, the theoretical model of the industry is justified. The appropriateness of the several assumptions made is discussed. In Section 3, the empirical model is specified. The tests and parameters utilized to characterize the technology and producer's choices are described. Several of the relationships are given signs a priori, in accordance with the theory and what could be expected from the engineering characteristics of the 109 industry. In Section 4, the statistical model is introduced. 5.2 THE THEORETICAL MODEL Suppose that sawmilling can be represented through a technology set T, which is a set of all input and output combinations which are feasible. For reasons to be discussed below a static restricted profit function is used to represent T. Under certain conditions, the profit function (TI) is dual to the technology T (Diewert, 1974; Lau, 1976; Russell and Wilkinson, 1979). The profit function representation is particularly convenient for multiple input multiple output industries where inputs and outputs are variable and non-regulated. Profit functions are very popular in agricultural economics (Lau and Yotopoulos, 1971 and 1972; Yotopoulos and Lau, 1973; Sidhu and Baanante, 1979 and 1981; Jamison and Lau, 1982; Weaver, 1983; Shummay, 1983; Lopez, 1984; Antle, 1984; Gordon, 1984), but in other industries they have been considerably less utilized than cost functions. Examples are the studies by Kohli (1978) in international trade and Muller (1979) and Klein (1985) of the Canadian pulp and paper industry. It is assumed that the industry can be modelled through a representative firm behaving competitively in the lumber, pulpchip, labour and sawlog markets and maximizing short-run profits, constrained by the technology set, the capital stock and "state of knowledge". The restricted profit function is defined as: (5.2.1) n = nHprV,plV.K,t) =mexm c w JmPm*cp^pWHpMm.c,uj.l,K,t)€T] where n are the maximum possible profits, given T, K and t; p m =(p7!„.ps) is a vector of the prices ($/Mfbm) and m=(m,,...,ms) is a vector of the quantities (Mfbm) of the several lumber and shingle grades which are produced; p c is the 110 average price ($/OD ton) and c the quantity (OD ton) of pulpchips; p w=(p W, p2^ is a vector of the prices ($/hour) and w=(w,,Wj) a vector of the quantities (hours) of man hours of production and non-production workers; p' =(p*1 ,...J3n) is a vector of the prices ($/cubic meter) and I =(l 1 n ) a vector of the quantities (cubic meters) of the several sawlog grades of each species; K is an aggregate measure of the capital stock; t is a time trend, which is interpreted as a proxy for technical progress in sawmilling. The following conditions are assumed for II1: (1a) II1 is twice continuously differentiate; (1b) II1 is non-decreasing in output prices, non-increasing in input prices; (1c) II1 is convex and linearly homogeneous in prices; (1d) II1 is non-decreasing in K and in t (K and t are assigned positive numbers). There is also a production function F 1 , dual to the profit function II1 and the technology set T, which relates all the feasible input and output combinations belonging to T and which are efficient (Diewert, 1974; Lau, 1976): (5.2.2) F'(m,c,uJ,l,K,t] = 0 where all the variables are as defined above. In the short-run, it is assumed that the industry can instantaneously adjust the production of the several lumber and shingle grades and pulpchips and the labour input and the volumes of the several log grades consumed to their optimum levels, without incurring adjustment costs, but that capital is a quasi-fixed input which may not be at its optimum level. The rationale for this modelling approach will be discussed below. 111 Due to the large number of different types of inputs and outputs, (5.2.1) would be difficult to estimate empirically. There is a limited number of observations in the sample, and the data does not have sufficient independent variation for the several variables, so that multicolinearity problems would result. Aggregation of the several inputs and outputs is required. The standard procedure in this case would be to alternatively specify, (5.2.3) Fl = n2lPM,Pc,PUJJPL.l<,t) where p M . ^ m ^ p U l . ^ p ui ^  p L = a , L ( p j l ^ The •l,i=M,W,L are linearly homogeneous price aggregators, and the P1 i=M,W,L are numbers indexing maximum revenues or minimum costs of attaining a given transformation frontier or isoquant (the P1 are determined up to a scaling factor). The production function dual to (5.2.3) is (5.2.4) F2(M.C.UJJ..K,t] = 0 where M=*M(ny ...mg). U J = * U J (UJ ).UJ 2I, L«$4Lr..,ln) The $',i =M,W,L are linearly homogeneous quantity aggregators, and M,W,L are numbers indexing the contribution of the aggregators in the production function (they are also determined up to a scaling factor). In order to theoretically justify this procedure, it is necessary to assume that the components of each of the aggregators are separable from the levels of the inputs/outputs outside the aggregator (Blackorby et aj..,1978). The empirical implication of this condition is that the marginal rates of substitution between components in each aggregator are independent of the levels of the inputs/outputs outside the aggregator (Deaton and Muellbauer, 1980). 112 It also implies that the optimizing behaviour of producers can be modelled in two stages. In the first stage they would maximize revenues or minimize costs of producing on a given transformation frontier or isoquant. In the second stage they would choose the transformation frontier or isoquant in order to maximize profits, subject to the fixed capital stock K and "knowledge" t. For example, choosing inputs and outputs in order to maximize profits, implies choosing the volumes of the several log grades in order to minimize costs, and given the separability restrictions, the solutions to this problem are independent of the levels of other inputs and outputs, so that the following cost function can be specif ied: (5.2.5) C=C Z (p, 1 = mirn, lJlpikj:L=o>L(Ur...ln)] C J is linearly homogeneous by assumption, so that the relative costs of attaining the isoquant indexed by L, between situations 1 and 0 would be (dropping the superscripts I): (5.2.6) cVc° = (Ldp, 1 Ph'M/d ap, 0 fyO)) = tfpV+lp0) = PVP° By specifying a functional form for or the quantity or price aggregators, one can obtain a measure of P ' / P 0 (Diewert, 1976). A.s mentioned in Chapters 2 and 3 and in Appendix I, "P^ and were assumed to be translog. The aggregation of capital cannot be-justified in this way, because it is a quasi-fixed factor (see Appendix I). Following from the definition of wood quality in Chapter 3, two equivalent definitions of L and P*" are: (5.2.7) L = o>L(L, l n ) = V . Q ( 5 ' 2 ' 8 ) P L = •L(p,l....,pnl) = C / L = C / V - Q = P ^ / Q 113 where P*~ is the value of a unit of quality adjusted sawlog volume, and is the value of a unit of sawlog volume. Volume (V) and average price (P^~) were the arguments utilized in production and cost functions in the studies reviewed and, for obvious reasons, such procedure does not appear to be theoretically defensible. In particular ~P^~ will be endogenous at the firm level, because the firm will be choosing a grade distribution. Problems resulting from the endogeneity of average prices are briefly discussed by Fuss (1977). Quiggin and Bui-lau (1984) have also criticized the use of average prices in cross-sectional estimates of profit functions for testing relative efficiency along the lines developed by Lau and Yotopoulos (1971,1972). This is because most of the interregional or interfirm price variations will be due to quality variations. The use of V-Q or P*~ as arguments in the production, cost or profit functions, can be theoretically justified, but it imposes very strong restrictions on the relationships between quality and the several inputs and outputs utilized. In particular, it implies that quality is separable in the production or profit function (Spady and Friedlaender, 1978). The profit maximizing aggregate input and output combinations are independent of the composition of the aggregate log input L. More than that, it implies that changes in wood volume or in wood quality affect the profit maximizing utilization of other inputs and production of other outputs in an identical way, so that volume and quality are logarithmic perfect substitutes and the elasticities of demand - and supply with respect to price or quality of sawlogs are equal in absolute value and of opposite signs. Because one of the objectives of this research is the analysis of the impacts of wood quality change on sawmilling, and there is no reason to suppose that wood quality and wood volume contribute to production in a similar way, a different model is required. A specification for the profit function which is more general than (5.2.3), and allows the independent analysis of quality 114 effects is: (5.2.9) n = n3(PMJPcjpu,-pL.Q,K,t) where all the variables are defined as above. The dual production function is, (5.2.10) F3(M,C,ID,L,Q,M = 0 In this formulation.the elasticities with respect to sawlog price and quality are allowed to differ. Furthermore, quality is not assumed to be separable in the production function, i.e., the profit maximizing factor and output combinations are not independent of the relative volume/quality of the wood input. This formulation is still more restrictive than the initial model (5.2.1). The quality variable is interpreted as an aggregate of the several sawlog characteristics, such as species, diameter, decay, etc. and because these characteristics are assumed separable, their relationships with other inputs and outputs are constrained. This did not happen in the initial specification, where each sawlog grade was allowed to interact freely with the other inputs or outputs. Moreover, it is implicit in the above model that quality is a fixed input, so that when modelling industry responses, these are for a constant wood quality level. The more general specification (5.2.9) could also be utilized with other inputs and outputs. A model of considerable empirical interest for sawmilling could be obtained by also including lumber quality as an unrestricted argument in the profit and production functions. Such a model would allow the measurement of the relationships between wood and lumber quality, which are likely to be important, and provide a better description of the technology. The data collected does not suit itself to such analysis, and in the conclusions of this thesis, this problem will be discussed as an area for further research. Here, the concern is 115 primarily with wood quality, and in order to keep the model simple, the relationships involving lumber quality are not analyzed. Given the interpretation of Q as an aggregate of characteristics, i.e. Q=Z(q!,...,q2) if data on characteristics q1,...qz were available, this relationship could be estimated empirically. It is noted, however, that given the nature of the sawmilling technology, average diameter is probably the most important characteristic, and Q is likely to be highly correlated with average diameter. If this is the case, Q can also be viewed as a proxy for average djameter. It is convenient to contrast the above model with the characteristics models discussed by Spady and Friedlaender (1978), Friedlaender and Spady (1981), Friedlaender et ai. (1982) and Bailey and Friedlaender (1982). Although the above authors utilized cost functions, their approach can be easily extended to profit functions. If data on the characteristics of wood going to sawmills were available, the following model could be specified: (5.2.11) n = Tl W ^ P ^ P 1 . q,. ...t^Kt) (5.2.12) pL-Gf^qUq 2) where q1,...,qz are the quantities of characteristics, e.g., species, diameter, decay, etc., "P*- is the average price of logs and p'" is the quality adjusted price. In the specification utilized in this research, the q1,...,qz were replaced by Q, the quality index. Characteristics models were also discussed by Deaton and Muellbauer (1980) and Berndt (1983) in the consumers context and by Lau (1982) in the producers' context. The major concern of these authors was to rationalize hedonic price equations (see Chapter 3) in the context of consumers or producers models. If cross section and time series data on prices and characteristics of sawlog 116 bundles were available, the following model could be specified: (5.2.13) n - n 5 ( P M , P C . P U J . P L . K . t ) (5.2.14) pL - Hf^q,.. ,q_,) where H is a tranformation of a hedonics price equation and the other variables are as defined above. The above authors discuss the assumptions implicit in such specification. The characteristics models would be' of considerable policy and modelling interest in the case of sawmilling. In particular they would allow direct links with inventory based models, which usually have access to information on the characteristics of the timber, and can provide forecasts of the future availability of such quality variables. Furthermore, they could be used to derive the shadow values of characteristics, and these could be used in assessing the economic value of the inventory. Such models could also be used in the logging industry by including characteristics such as terrain, slopes or hauling distances. Because the required characteristics data could not be obtained with the resources available for this research, this approach was not utilized. In the conclusions to this thesis, such an approach is discussed as an important area for further research. The several behavioral assumptions implicit in the theoretical model (5.2.9) should be discussed. It is assumed that the capital stock (K), wood quality (Q) and the "state of knowledge" indexed by time (t) are fixed in the short-run. It is further assumed that sawmills are price takers in the lumber, chips, logs and labour markets, and that they attempt to maximize short-run profits by optimally adjusting the quantities of these outputs and inputs in response to changes in relative prices. 117 As was dicussed in Chapter 2, the lumber market is clearly competitive at the firm level. Price taking behaviour in other markets does not appear to be a very unrealistic assumption. Wages are bargained between the IWA and representatives of the industry, but given the size of the industry and the large number of firms, the set wages can be viewed as exogenous to the firm. Also, sawmilling labour is not very specialized and regional labour markets are closely integrated with national markets. Most of the wood and pulpchips are internally allocated in integrated firms, but profit maximizing behaviour and the existence of markets for these two products will lead firms to equate their shadow prices to the market prices. Capital is treated as a fixed input in the model. This assumption appears to be more appropriate in sawmilling than the commonly used alternative of assuming that it can be instantaneously adjusted to its optimum level, without adjustment costs. Of course capital will adjust through investment, and the above model could be made dynamic to take this factor into account. There is a growing literature on this type of model (e.g. Denny et al., 1981; Berndt et ai., 1981; Pindyck and Rotenberg, 1983), including an example from sawmilling (Merrifield and Singleton, 1985). However, the capital data obtained in this research is of poor quality. Such a model would require more observations than those available, and would render econometric estimation more difficult. Fixing capital makes more plausible the existence of a profit maximizing solution to the producers' problem, because firms are likely to exhibit decreasing returns with respect to the variable inputs and outputs. Also, the investment behaviour of sawmilling producers may not be adequately represented by the dynamic models available in the literature. Although the wood input is variable in the short-run, and there is a log market, an assured 118 raw material supply is a major determinant of investment decisions. In BC, factors such as allocated cut, and characteristics of existing tenures like duration and security are likely to be important determinants of investment decisions. Because most tenures have a limited time horizon, after which the right to harvest timber may be withdrawn from the firm, the period over which maximization of the present value of profits is sought is finite and diminishing from year to year. When choosing plant capacity, a key factor is the Annual Allowable Cut (AAC). For example, a regression of the BC Coast real capital stock on the AAC yielded an RJ of 0.98. The modelling of the investment behaviour of sawmills may prove to be a complex problem and it is left as an area for further research. A last justification for fixing capital is that the above structure makes the model suitable for analyzing short-run responses in the industry which are of interest to this research. With the exception of Abt (1984), such information appears to be lacking in the literature. However, the measurement of the long-run relationships between the various inputs and outputs and wood quality would also allow the testing of interesting hypotheses. For example, Barnett and Morse (1963) hypothesized that both labour and capital could be substituted for the resource of declining quality, but although the former may be true, the latter does not appear to hold in sawmilling, given the casual evidence. Also the substitution relationships may well exhibit different signs in the short and in the long-run. Brown and Christensen (1981) developed a methodology for obtaining long-run from short-run elasticities. If decreasing returns to scale are found, their approach will be utilized in this research. Wood quality and time are also viewed in the model as exogenous shifters. Note that wood quality is a variable input which is endogenously chosen by producers. For example, if chip prices increase relative to lumber prices, the proportion of pulpchips in the output will increase, and a lower quality grade mix 119 of sawlogs utilized. But it is unclear how, given the definition of quality utilized in this research, the alternative approach of treating quality as a variable input might be implemented. The model is to be used to analyze regional industry data, although the behavioural assumptions were justified for the firm. The question arises as to whether the model truely represents, in aggregate, the optimizing decisions of individual firms. This is known in the literature as the exact aggregation problem. Blackorby and Schworm (1982) mention two conditions for exact aggregation in static optimization problems. If capita) is a variable input and is competitively distributed among firms, each one valuing its marginal product at market prices, then there is no aggregation problem. If capital is a quasi-fixed input and not competitively distributed among firms, then there are restrictions on the profit function for exact aggregation. In the above model, capital is treated as a fixed input, but exact aggregation is not modelled. Blackorby and Schworm (1982) also mention that when exact aggregation is violated, an empirical implication is that aggregate models may still do a good job simulating historical data, but that their use for predictions outside the sample range is unsafe. In this research, the industry and regional data are considerably more disaggregated than in many other studies, in which exact aggregation was also violated. As a result possible errors due to inconsistent aggregation may not be as severe. Before pursuing, it is convenient to rewrite the theoretical model to be used in the research, as well as its properties. The profit function is specified as, (5.2.15) Tl = Tl3(pM pC pUJ pL Q K t) where II are observed variable profits, which are assumed to be maximum (revenue with lumber and pulpchips minus wood and labour costs), P^ is the 120 aggregate lumber price, is the average pulpchip price, P^ is the aggregate wage rate, P*~ is the aggregate sawlog price, which is interpreted as measuring the unit value of the quality adjusted sawlog volume i.e., the pure price, Q is the index of wood quality (sawlog grades, cubic meters) derived in Chapter 3 , K is an aggregate capital stock and t is time, a proxy for the technical progress input in sawmilling. The profit function is assumed to have the following properties: (3a) Twice continuously differentiable; (3b) Non-decreasing in output prices and non-increasing in input prices; (3c) Convex and linearly homogeneous in prices; (3d) Non-decreasing in capital, wood quality and time. Demand and supply equations for the variable inputs and outputs can be obtained by simply differentiating the profit function with respect to their respective prices (Hotelling's lemma): (5.2.16 M = <?n3/*PM = M3(PM,Pc,PUJ,PL,q.K,t) (5.2.17) C = «TT3/r5Pc = C3(PM,PcjP^pL,Q-K.t'] (5.2.18) -UJ = dTp/dP® = UJ3|PM.PCJPUJ/PL,CLKJt) (5.2.19) -L = <5T13/5PL = L3|PM,Pc,pUJ,FL,Q,K,t) The shadow price of capital can be obtained by differentiating the profit function with respect to capital: (5220) P K = «n3/5K = P^PM,Pc,pW pL.q.K,t] And a measure of the marginal profitability of wood quality can be obtained in a similar way: (5221) P°- = r5n3MQ = P°iPM,PC,pW,pL>Q.K,t) 121 A measure of technical progress is obtained by differentiating the profit function with respect to time; (5.2.22) P* = 5n3/<5t = Pt(PM,PC>PUJ,PL.Q,K,t) 5.3 THE EMPIRICAL MODEL The transcendental logarithmic functional form (translog) (Christensen et aj., 1973) is used for the regional profit function discussed above. Functions like the translog have been recommended in the literature, because they can provide second order approximations to unknown forms and are not restrictive of the second order relationships between variables, from which most of the economic parameters of interest are derived. Such functions are called flexible functional forms. Other commonly used functions of this type are the normalized quadratic (Lau, 1974) and the generalized Leontieff (Diewert, 1971). Lopez (1985) has recently argued for the superiority of the translog over the normalized quadratic and generalized Leontieff for profit functions, because the latter impose quasi-homotheticity and separability restrictions, and so they are less flexible. The translog has also been the most popular functional form in the more recent sawmilling studies reviewed in the Introduction. The translog profit function is: $222) InH = ft0 • X^jlnPj • Z 3p 6LnXg • O.szVrjjlnPjlnPj * Z ^ c y n P j l n X g • o.5S 3z 3e 8 rlnM 8ln}y where Pj(i =M,C,W,L) are the prices of lumber, pulpchips, labour and sawlogs and X g (s=K,Q,T) are the capital stock, wood quality and time. The following restrictions which are implied by the properties of the profit function discussed above are imposed: (5.2.24) z 4 a . = J i = M C L j l D z 4 r M ) = o . I V Q - 0 • ^ L r 0 • ^ u i r 0 - ' - M . C L . W Z 4 5 K J =0 . Z^Qj-O . Z 4 # T i =0 . i-M.C.L.UJ 122 (5JZ25) y j j - r j i . U-M.C.UJ.L (5.2.24) are implied by linear homogeneity in prices, while (5.2.25) are implied by symmetry of the hessian matrix. By definition of quality, P|_=F^/Q, where is the price aggregator for sawlogs, is the average sawlog price (i.e. sawlog expenditure divided by volume), and Q is wood quality. This relationship can be substituted into (5.2.21) with advantages for the testing procedure to be discussed below. Restrictions (5.2.25) were also substituted into equation (5.2.23). Hotelling's lemma applied to the above equation yields share equations for the variable outputs and inputs: (5226) S M - <*M • I 4 r M ilnPj * Z 35 M 8lnX 8 (5227) Sc - a c • zVCilnP, • I3*CemH8 (5228) -SL - «»L • Z4rLJlnPi * Z^lnXg (5229) " S U J ~ * U J * ^ uiilnPj • Z 3 ^ ^ where for example =(P^-M)/n. Input shares in profits are assigned negative numbers. The profit function (5223), the share equations (5.2.26) - (5229) and the restrictions (5224) constitute the empirical model. The profit function should exhibit the following additional properties: non-decreasing in output prices, non-increasing in input prices, convex in prices and non-decreasing in capital, wood quality and time. Convexity in prices is a result of the optimizing behaviour of producers. It implies that supply functions slope up and demand functions slope down and it is equivalent to the condition that the hessian (symmetric matrix of second order 123 partial derivatives) of the profit function with respect to prices be positive semidef inite. Positive semidef initeness implies that all the eigenvalues of the hessian must be nonnegative. This hessian for the above equation is: (5.2.30) H = | h„ h | 2 h J 3 h 1 4 j j h J 2 h 2 2 h 2 3 h 2 4 | I h13h23 h33 h34 I I h14 n24 h34 h44 I h t j = m/p^-trj/SjtSj-D) The monotonicity condition ensures that quantities demanded or supplied are greater than or equal to zero. In the translog case, this implies that the predicted shares will be positive for outputs (S^.SQ) and negative for inputs (S|_,Syy). The monotonicity condition with respect to the fixed factors is included because of its economic meaning. It implies that the production function is non-decreasing in capital, wood quality and time. With respect to time this implies that the industry exhibits a positive rate of technical progress. Several studies reviewed in the Introduction have found technical recess in sawmilling, but this result does not make economic sense if the time trend is viewed as a "proxy" for the "state of knowledge" in the industry. There is no reason for technical efficiency to decline if "knowledge" increases. These properties will be checked at each observation, because it is unclear how they might otherwise be imposed in the model. Monotonicity with respect to the fixed factors implies that the share of capital, elasticity of profits with respect to wood quality and the rate of technical progress are positive. These are obtained by differentiating the profit function with respect to the fixed factors: 124 (5.2.31) s K = pK • iXtnP, * X^glnXg (5.2.32) S Q = p Q • Z4*iQlnPi • I 3 e Q 8lnX 8 (5.2.33) TFP = (1/t).(f3t • Z43JtLnPj + S3et8lnXg] Although there are no a priori conditions concerning the curvature properties of the profit function with respect to capital or wood quality, it is of interest to analyze such relationships. If the profit function is concave in capital, this will have substantial economic meaning. Concavity with respect to capital implies that the production function is concave in all factors, and that there are decreasing returns to scale. Decreasing returns to scale are sometimes justified in resource industries on the basis that an increase in the size of the operation usually involves the exploitation of a lower quality resource. Note, however, that quality is being held fixed in this model, so concavity in capital is not implied. Concavity in capital also implies that even when capital is allowed to vary, there will be a long-run profit maximizing solution. It rationalizes the computation of long-run elasticities, i.e., elasticities of demands and supplies after the capital stock adjusts to its optimum level. Concavity of the profit function with respect to capital is checked through the following formula; (5.2.34) <5n2/r5zK = (n/K 2).[eK K+sK[s k-i)) Some studies have derived empirical, engineering type of relationships between product recovery or unit value of output and sawlog characteristics (e.g. Dobie el aj., 1975; Willinston, 1981). These relationships are based on mill studies, and the technology is fixed, although it is unclear in some of the studies if the labour input and the wood volume are held fixed. They can be interpreted as incomplete production or revenue functions, relating output or gross revenue to wood characteristics. Important characteristics analyzed are for example log diameter and decay, and the evidence suggests that mill level production functions 125 are concave in these two characteristics and increasing with average diameter. Examples of these relationships are depicted in Figures 5.1 and 5.2. It is of interest to check if the aggregate model in this research can replicate the results of mill studies, by showing concavity of the profit function with respect to the aggregate quality measure. Note that concavity is not implied by the model because several of the inputs are variable (labour, wood) 2. But one could argue that as log sizes increase, maximum machine capacity will be approached, and that there are diminishing returns to quality. This can be checked through the following formula: (5.2.35) 8T\2/dZQ={U/^U6m*SfX(SfX-m The properties discussed above are summarized in Table 5.1. In addition to these, several tests on the regional profit functions will be carried out. These are summarized in Table 5.2 and discussed below. It is of special importance for the objectives of this research to test the role of the wood quality variable in the model. The first and stronger hypothesis is that wood quality does not belong in the model. This would justify the approach of using average prices (value per unit of volume) and volume as measures of the sawlog price or log input, which has been the one explicitly or implicitly used in every study of sawmilling reviewed. Such a test involves the following restrictions: (5.2.36) p Q + c*L = 0 <5jQ*7iL = 0 .i-MX.LJU 8SQ * 5 8L = °- 8 = K . t eQlT 2 ,*LQ**LL" 0 A weaker hypothesis is that wood quality belongs in the model, but that the elasticities of demand and supply with respect to price or quality of wood are equal and of opposite signs, in this case it would suffice to include quality F I G U R E 5 . 1 Average Gross Lumber Recovery Factor for Various S m a l l - L o g F e e d - w o r k s and Headrig Combinat ions, 16—ft 4 .88m Straight Logs, Random Length Dimension 2 in. 50 m m Only SOURCE: Willinston,1981 FIGURE 5.2 Lumber and Chip Values per Cunit Related To Tree DBH for Risk Group 1 Trees SOURCE: Dobie et al, 1975 Table 5.1- Summary of the Properties of the Profit Function Imposed and Checked. Property Relationship Expected Justification Result Symmetry of the Hessian Tjj^Tji V.j=M.C,L,W Homogeneity of Zaj = 1, i=M,C,L,W degree one in prices Non-decreasing in prices 27 15 .=0. j=M,CJ-,W _=0, p=p,Q,t !M-.SC-Non-decreasing S^, SQ, TFP in fixed factors Convexity in prices Concave in capital Concave in wood quality Hessian (eigenvalues) an2/32k an2/32Q Imposed Theory Imposed Theory >0 <0 ^0 >0 Theory Theory Theory <0 Engineering Table 5.2- Summary of Tests on the Characteristics of the Prof i t Function. Property Null hypothesis Number of Restrict ions No wood quality a L = 0 8 6 i Q " 7 i L - 0 , i -= M , C , L , W 6SQ " 6 s L " °' s = =K,t 6QQ " 2 5 L Q + ^LL = 0 Quality = 0 adjusted prices 6 i Q = 0 , i = M , C , L 8 6sQ = 0 , S=K,Q,t 8 Homogeneity of aK = 1 degree one in K 6 i K = 0, i=M,C,L,W 8 Q P K = 0, p=K.Q,t No technical a T = 0 progress 5 i T = 0, i=M,C,L,W 8 Q P T = 0, p=K,Q,t Al l the second order regional 28 coeff ic ients are equal Across region A l l the first and second order regional 35 restrictions coeff ic ients are equal A l l the regional coeff ic ients are equal 36 129 in the model by utilizing quality adjusted prices (P^=F^-Q~ ) or volumes (L=V-Q), i.e., the price or quantity indices on which the wood quality measure is based. This hypothesis implies the following restrictions: (5.2.37) p Q»0 eQg-o.s-KAt Two additional tests of interest are those of homogeneity of degree one in capital and no technical progress. Homogeneity of degree one of the profit function in capital implies that if capital is increased by 1% all inputs and outputs are also increased by 1% (Lau, 1978) and so that there are constant returns to scale. This is consistent with the following restricitons; (5J2.38) <kK = 1 9 8 K-0,S-KAt No technical progress involves restricting all the coefficients on the time trend to be zero; (5.2.39) ftt = 0 «J j t = 0.i=M,C,L.W e 8 t = o ^ K A t All the above tests will be carried out for each of the regions separately and for the two regions taken together. The last set of tests, mentioned in Table 5.2, involves comparing the two regional industries. The three hypotheses to be tested are first, that the regional profit functions only differ on the intercept and first order terms, second that they only differ on the intercept, and third that they are equal. 130 Of special interest for policy analysis are own and cross price elasticities of output supply and factor demand. These elasticities measure the percentage increase in supply or demand when the price of a variable output or input is increased by one percent, and after all the variable quantities are allowed to readjust to their optimum levels. However, they are constrained by the fixed capital and wood quality, and so the measured responses are short-run and for a constant wood quality. They measure the total effects of a price change, and incorporate substitution and output effects. For the translog case they can be calculated as (Weaver, 1983; Gordon, 1984): (5.2.40) e,j - cHnX/cHnPj = V V ¥ - •-M.C.L.UJ eMM a n c* eCC s n o u ' c ' n a v e positive signs so that supplies slope up and e^_ and eWW s n o u ' c ' ha y e negative signs so that demands slope down. One can also define supply and demand elasticities with respect to changes in capital and in wood quality. Again, these measure the response to a 1% increase in the fixed input, after all the variable quantities are allowed to readjust to their optimum levels: (5-2.42) e|8 = dlnX/dlnXg - V V s s > 1-M.C.UU, s=«.Q Of considerable interest for this research, are elasticities of input ratios, output ratios and input/output ratios with respect to prices and fixed factors. These are calculated as (5.2.43) e j / j g = ejg -e j g IJ.M.C.L,!!!, s=M,C.LUUXQ The effects of time on input, output and input/output ratios are measured in a similar way, but rather than in elasticity form, the following measure is 131 usually employed: (52.44) byjjt - d\jM/d\ -*lnXj/dt = *Jt/(Sj.t) - * J t/[ S ,t] Such a measure has been called in the profit function literature the bias of technical progress with respect to inputs i and j (Weaver, 1983). For example, if i is wood and j is labour and bj/j t is greater than zero, then the technology is said to exhibit a wood using and a labour saving bias with respect to technical progress. This means that with the passage of time, and beyond the effects of other variables in the model, the amount of wood per unit of labour has been increasing. In more complete models, these biases are themselves postulated to be a function of expected changes in relative prices (Stevenson, 1980), but here they are assumed exogenous. In order to better characterize sawmilling, it is important to obtain information on the shape of the isoquants for wood and labour and transformation frontier for lumber and pulpchips. Because the above elasticities measure the total effects, and so model not only movements along isoquants but also movements from one isoquant to another, they are not useful for this purpose. Constant input supply elasticities and constant output demand elasticities are required. These could be obtained from a revenue or cost function respectively. Revenue and cost functions are special cases of profit functions in which all inputs, in the first case, or all outputs, in the second case, are held fixed. According to the results of Lau (1976) and Lopez (1982), these elasticities can also be obtained from profit functions. Profit maximization implies both cost minimization for fixed outputs and revenue maximization for fixed inputs. These two later problems are restricted versions of the profit maximization problem. Lau (1976) has derived the relationships between the hessians of the restricted and 132 unrestricted problems: C5-2-45) AppTKPAK) - Appn(P.UJ,K) - A.pi l Jn(P,UJ,K). (A^nlP^.K))"1 AujpnfP.UJ.K] where n(P,W,K) is the less restricted (first) profit maximizing problem, K are the restrictions common to both problems, W are the prices of those commodities which are assumed fixed in the more restricted (second) profit maximizing problem, and P the prices of those commodities which are variable in both problems; II(P,R,K) is the more restricted (second) profit maximizing problem, and R the new quantities being held fixed; AppII(P,R,K) is the matrix of second partial derivatives of the second problem with respect to prices (P) of variable quantities, and the other gradient matrices are defined in a similar manner. More explicitly, the matrix of constant output factor demand effects is obtained as follows; f5-2-46) | 6V*P L *u L / f fpW | =-| mL/9Pl 3xL/spW I • |#ji l l /*p L*p u /5P u , | |*v*pL*V*pU,l • I 5 X M / 5 P L 5 X C / 5 P L j . j 5 X M / 5 P M 5 X M / 5 P C j " 1 j SHt^/SP{iiSXc/6PUi | | S^/SP* SHC/SPC | | SX^/8Pl dXM/SPm | | «5Xc/tfPL tfXr/ffpW | where Mj,i=L,W denotes a constant output demand and Xj.i =M,C,L,W denotes variable output demand. The matrix of constant input supply effects is identical, except that the role of inputs and outputs, as well as signs, are reversed. All the elements of the matrices on the right hand side of the equation are available from the hessian of the translog profit function discussed above. 133 As an example, after converting the above effects to elasticity form, the total cross price elasticity of sawlog demand with respect to a change in the wage rate can be decomposed as follows: (5 .^47) e l p m = T i L > P l l j + € L M e M , P U J + ^L,C e C , P l i l where e[_ pyy measures the total effect and pw measures the substitution effect, i.e., the percentual change in sawlog demand when the wage rate increases by 1% holding the lumber and pulpchip outputs constant. f|_ ^  and ^ measure the change in sawlog demand due to the change in the lumber and pulpchip production, i.e., the change resulting from the movement from one isoquant to another one. e|\/| pw a n o " e c PW m e a s u r e t n e changes in lumber and pulpchip production due to the change in the wage rate, i.e., the changes in the output levels due to the shifts in the marginal cost schedules. Gould and Ferguson (1980) call e|_|\/| o r e L L t n e o u t P u t effect and eM pw o r eL PW t n e profit-maximizing effect. An identical decomposition can be used for the other own and cross price elasticities. The total effect of a change in a fixed factor can be decomposed in an identical way. For example, the total effect of a change in wood quality on pulpchip supply is, (52.48) * C j Q = n c < Q + e c > L ^ Q ^ c . u , where VQQ is the change in pulpchips when both the sawlog and labour inputs are held fixed, and e^yy- the change in pulpchip supply due to changes in the sawlog and labour input levels and e L Q and e ^ Q the change in the input levels induced by a change in quality. The constant input own price elasticities of lumber and pulpchip supply should be positive, so that constant input supplies slope up and the constant 134 output own price elasticities of wood and labour demand should be negative, so that constant output demands slope down. Furthermore, given that there are only two variable outputs and two variable inputs, the constant input cross price elasticity of lumber supply with respect to pulpchip price should be negative and the constant output cross price elasticity of sawlog demand with respect to labour price should be positive. This ensures that the two outputs and the two inputs are substitutes, or in other words, that the two output transformation frontier is concave to the origin and that the two input isoquant is convex to the origin. The other terms of equation (52.47) can also be signed following Nagatani (1978). The expected signs for some of the relationships are shown in Table 5.3. Except for the relationships signed above on the basis of economic theory, the other relationships were signed a priori on the basis of the characteristics of the industry and information available from engineering and technical studies. Given the dominant importance of lumber in the output mix and wood in the input mix, the hypothesized low substitution possibilities, and the fact that sawmilling is a low value added industry, it is expected that an increase in sawlog price will contract the industry and result in a smaller lumber output. An increase in lumber price, for the same reasons, would lead to an increased wood consumption. An increase in lumber price would lead to a decline in lumber recoveries because marginal producers would start operating. An increase in wood price would result in recovery gains because marginal producers would stop operating. An increase in the pulpchip price would increase the pulpchip proportion in output because first, more wood would be diverted to chipping, and second, more chipping mills would start operating. For the opposite reasons, an increase in lumber price would increase the proportion of lumber in output. Table 5.3: Expected Signs for Some of the Relationships. Relationship Variables Notation Expect Justification Result Own price elasticities Cross price elasticities Constant input or output own price elasticities Constant input or output cross price elasticities Elasticities of input and output ratios lumber pulpchips sawlogs labour lumber, sawlog sawlog, lumber lumber pulpchips sawlogs labour lumber, chips sawlogs, labour lumber recov., lumber lumber recov., chip lumber/chip, lumber lumber/chip, chip lumber/chip; quality lumber recov., quality MM eCC eLL 5 WW ML eLM ^MM ^CC "LL % W ^LC ^LW M/L,M eM/L,L eM/C,L eM/C,C eM/C,Q eM/S,Q + + + + + + + + + + theory theory theory theory engineering engineering theory theory theory theory theory theory engineering engineering engineering engineering engineering engineering 136 An increase in wood quality would lead to an increase in the lumber/chip ratio and in lumber recovery. This is because of the shape of sawlogs, and the nature of sawmilling: cutting lumber boards from truncated cones. An increase in log size or decline in defects, which are two of the most important quality characteristics, would permit a higher proportion of lumber recovered, and for the same reason a decline in the proportion of pulpchips produced. 5.4 THE STATISTICAL MODEL The sample data is described in Chapter 2 and Appendix I. It comprises yearly observations from' "1957 through 1981. For estimation, a normalized version of the model discussed in the previous Section is utilized. This procedure reduces the number of variables in the statistical model as well as the number of restrictions. The price of lumber was chosen as the norm. Stochastic disturbances e.( are added to the regional profit functions and share equations. These are interpreted as random errors in optimization. It is assumed that, (1) the errors are normally distributed with zero mean and a positive semi-definite variance covariance matrix, (2) the errors are contemporaneously correlated across equations and across regions, (3) the errors are not temporally correlated in each equation or across equations or regions. These assumptions can be summarized as follows: (52.49) € j ~N[0>Z) E<€int-€jmt) " ^injm where ij are counters for the equations within each region, n,m are counters for the regions and t,s are counters for time. In the above model, all coefficients are allowed to vary across regions but for each region they are assumed constant overtime. The error terms are assumed contemporaneously correlated across 137 regions due to common unmeasurable or omitted variables. This procedure also facilitates the imposition of across region restrictions. The above statistical model is discussed by Judge et aj. (1985). Because the profit shares add up to one, the error terms will add up to zero, this implying a singular variance covariance matrix. To avoid singularity, the lumber share equations are dropped from the system. All the parameters of this equation can be retrieved through the restrictions discussed previously. The system of eight equations: BC profit function, BC pulpchip share, BC sawlog share, BC labour" share, PNW profit function, PNW pulpchip share, PNW sawlog share and PNW labour share, with all the restrictions implied by symmery of the Hessian imposed is treated as a system of seemingly unrelated equations. Note that the restrictions due to homogeneity in prices are not required because of normalization, but are utilized to retrieve the lumber share parameters. The technique developed by Zellner (1962) permits a more efficient estimation of the above system because it takes the across equation and region correlation between residuals into account. The coefficients are iterated until convergence and the restrictions imposed at each iteration, this ensuring that the estimates are asymptotically maximum likelihood, and that they are invariant to which equation is dropped. 138 Footnotes The relationships between wood quality and milling technology have been analyzed in mill level engineering studies. Lau (1976) discusses the relationships between the curvature properties of production and restricted profit functions under alternative sets of assumptions. 139 6. EMPIRICAL RESULTS 6.1 INTRODUCTION In this Chapter, the results for the regional translog profit functions are reported and interpreted. In Section 2, some initial experiments, preliminary results obtained, and problems found in the statistical estimation are very briefly described. Section 3 presents parameter estimates, summary statistics, properties of the profit function for the initial and four more restricted specifications, and test results. In Section 4, elasticities and other economic relationships are reported and interpreted. Section 5 provides an evaluation of the regional models and a test of the research hypotheses. 62 EXPERIMENTS A preliminary assessment of the suitability of the theoretical model introduced in the previous Chapter was obtained for BC utilizing a much simplified data set and a Cobb-Douglas profit function. Cobb-Douglas profit functions are discussed by Lau and Yotopoulos (1971 and 1972), Yotopoulos and Lau (1973) and Gordon (1984). Own price elasticities of supply and demand had the right signs but were abnormally high, and profits were declining in capital and in wood quality. In spite of these problems it was decided to try a translog profit function. The overall results were considered better, due to the smaller magnitudes of the elasticities at the mean of the data, and so the translog functional form was kept. These preliminary results are reported in Constantino (1985a). Once the final data set was built, initial estimates for BC and the PNW were obtained by including only the share equations in the system of equations. The inclusion of the profit functions led to lower and, apparently, more realistic 140 elasticity estimates. The profit function parameters not present in the share equations are required for the study of some of the relationships of interest to this project. In these preliminary runs the regional systems of equations were estimated separately, i.e., no correlation between residuals across regions was assumed. Inclusion of the profit functions in the systems of equations required the elimination of three terms so that the variance-covariance matrix of the error terms would invert. This is a problem o f the algorithm utilized for estimation. The same problem was reported by Denny and Fuss (1982) and Martinello (1985a). Because there was no a priori information on which to base the choice of the three coefficients to be restricted to zero a number of runs were produced with alternative sets of three coefficients on the second order terms of the fixed factors that do not appear in share equations set to zero. The conclusions were that most parameters which also appeared in the lumber, sawlog and labour share equations, from which elasticities are derived, were robust to changes in coefficients dropped, but that the parameters of the pulpchip share equations and the derivatives of the profit function with respect to the fixed factors were not robust. Changes in the set of three coefficients restricted to zero affected in a very minor way the log of the likelihood function. Given the lack of a priori information on which to base the choice of coefficients to be restricted to zero, it was arbitrarily chosen to eliminate the interaction terms between the time trend and capital, the time trend and wood quality and the time trend squared, by adding the following three restrictions to the system of equations: (6-2-1) « 8 t = u\s=K,Q,t 141 From these preliminary experiments it was obvious that capital and the time trend were highly colinear, and that the data did not permit the independent analysis of the two variables in the model, so very little information appears to have been lost with the above restrictions. With the above restrictions, convergence was also attained after a reasonable number of iterations. The initial runs with the final PNW data produced very poor results. In particular all supplies sloped down and demands sloped up at the mean of the data. A casual analysis of the residuals indicated that 1982 was an outlier and the error term very large. In 1982, profits in the PNW were close to zero, and probably negative if the ignored minor factors of production such as energy and non-wood materials were accounted for. In spite of this, output and input levels were large, leading to very large shares in profits. It was decided to drop the 1982 observation in the PNW, after which results improved considerably. In order to keep the symmetry and identical number of observations in the two regions, 1982 was also dropped from the BC sample. Note, however, that 1982 was not an outlier in BC. The data appears to indicate that in 1982, the PNW industry was not behaving in a profit-maximizing manner. No attempts were made to explain the 1982 observation by trying an alternative model specification. It was mentioned in Chapter 2 that two alternative series on prices, volumes and expenditures with sawlogs were developed, because there was no certainty about the most suitable data, and in order to test the sensitivity of results to changes in the data. For BC, Vancouver log market prices (Series A) and Statistics Canada prices (Series B) were tried, and for the PNW, log market prices (Series A) and estimated delivered wood unit costs (Series B) were tried. It was found that for BC, the Statistics Canada data produced slightly better results. First, the log market data led to a wrong sign of the own price elasticity of lumber supply for eight observations as opposed to three with Statistics 142 Canada data. Second, two of the eigenvalues of the hessian were negative at the mean of the data as opposed to one negative, but very close to zero, with the Statistics Canada data. Poorer results were also obtained when delivered wood costs were utilized in the PNW. Given these results, it was decided to use the Statistics Canada sawlog data in BC, and the market sawlog data in the PNW. Elasticity estimates based on the log market data in BC were about half of those based on Statistics Canada data, but because it was found that elasticities were very unstable across the sample, this difference did not appear too serious. In the PNW, the log market data produced also lower elasticity estimates, but the differences were not as large as in BC. Although it was argued before that price taking behaviour at the firm level in the markets for variable inputs and outputs was not a very unrealistic assumption, exogeneity of prices at the industry level cannot be as easily justified. Several of the independent variables in the model are likely to be endogenous at the industry level. Because in such cases, these variables will be correlated with the error terms, biased estimates will result (Varian, 1978). The use of instrumental variables has been suggested to deal with this situation (Berndt and Wood, 1975). In the model utilized, endogeneity problems appeared to be more serious in the case of sawlog and pulpchip prices and wood quality, and it was decided to replace these variables by instruments obtained by regressing the variables on a set of exogenous variables. In order to identify such set of variables, the regional industry models were specified as part of an equilibrium model, and a sawlog supply equation, a pulpchip demand equation and a wood quality supply equation were formulated for the regions. The postulated exogenous shifters of demands and supplies of these three factors were utilized as regressors. Several of these shifters are also endogenous, due to the integrated nature of the 143 industry, and in these cases they were lagged one time period. Because the R2 from the wood quality regression was very low, it was decided not to use instruments for this variable. The exogenous shifters utilized for the sawlog price in BC were lagged logging cost, lagged stumpage, Annual Allowable Cut, lagged Annual Allowable Cut, lagged harvest, lagged sawlog price, lagged lumber price and lagged lumber output. An R2 of 0.73 was obtained. In the PNW, lagged bid stumpage and harvest sold were utilized instead of the Annual Allowable Cut variables, yielding an R2 of 0.94. The exogenous shifters for the pulpchip price were the same in both regions: lagged pulpchip price, price of electricity, lagged wage in pulp and paper mills, paper price, pulp price, Canadian and US GNP and Canadian and US population. The R2 were 0.83 for BC and 0.97 for the PNW. The model runs utilizing instruments yielded considerably worse results. In particular in both regions the own price elasticities had the wrong signs for a considerable number of observations, and convexity of the hessian was more violated, in the sense that a larger number of eigenvalues were negative. Although a different set of exogenous regressors might have led to improved results, it was decided not to pursue with this approach, and instruments were not utilized. It was chosen to trade endogeneity bias for theoretical consistency of the model. 6.3 PARAMETER ESTIMATES,. SUMMARY STATISTICS, PROFIT FUNCTION PROPERTIES AND TEST RESULTS In this Section, parameter estimates, summary statistics, profit function properties and test results are reported for the initial model, in which homogeneity in prices and symmetry are maintained hypothesis and the restrictions (6.2.1) were imposed. Following this, four alternative more restricted models are estimated and their porperties reported and compared with those of 144 the initial model. Parameter estimates and asymptotic t-ratios for the regional initial models are reported in Tables 6.1 and 6.2. In both regions, 62% of the second order coefficients are significant at the 99% level (assuming a large sample). All own price coefficients are significant in both regions. Of all the price coefficients, only those for sawlogs and labour in the BC pulpchip equation, and the one for labour in the PNW pulpchip equation were not significant. In BC, 33% of the second order coefficients of quality were' significant, and 66% of the second order coefficients of capital were significant. In the PNW, these percentages were respectively 50% and 16%. The R3's for individual equations were generally higher in BC than in the PNW, with the exception of the pulpchip share equation. It should be mentioned that low R2 are frequently obtained with share equations. This point is discussed by Deaton and Muellbauer (1980) and Spady and Friedlaender (1978). The statistical model utilized does not minimize the sum of square errors for individual equations, and so the individual RJ's are not a very important statistic. The Durbin-Watson statistics for individual equations are also higher in BC. Only for the BC lumber and sawlog shares can the hypothesis of autocorrelation be rejected. For all the other equations, the d test statistic lies in the inconclusive region. Because estimated first order p's were small, and in order not to complicate the statistical model further, no correction for autocorrelation was undertaken. In order to evaluate the theoretical consistency of the model, the properties reported in Table 5.1 were checked. These properties are: non-decreasing in output prices, non-increasing in input prices, non-decreasing in fixed factors and convexity in prices. Concavity in capital and wood quality were Table 6.1; Initial Model - British Columbia Parameter Estimates and Summary Statistics PRICES FIXED FACTORS Equation Lumber Pulpchips Sawlogs Labour Capital Quality Time Constant R ! DW Lumber -12.42 -1.40 9.52 4.29 (-17.80) (-6.21) (15.11) (20.52) Pulpchips -1.40 0.98 0.30 0.12 (-6.2 1) (7.84) (1.26) (1.46) Sawlogs 9.52 0.30 -7.42 -2.40 (15.1 1) (1.26) (-1 1.80) (-12.60) Labour 4.29 0.12 -2.40 -2.01 (20.52) (1.46) (-12.60) (-20.05) Capital 0.64 0.68 -0.70 -0.61 (1.00) (4.91) (-1.41) (-2.78) Quality 2.61 0.25 -1.64 -1.23 (1.01) (0.42) (-0.81) (-1.34) Time -1.14 -0.02 0.64 0.52 (-4.59) (-0.37) (3.27) (6.04) Profit Function 0.64 (1.00) 2.61 (1.01) -1.14 (-4.59) 32.41 (10.02) 0.58 2.12 0.68 (4.91) 0.25 (0.42) -0.02 (-0.37) 0.98 (7.84) 0.84 1.78 -0.70 (-1.41) -1.64 (-0.81) 0.64 (3.2 7) -22.15 (-7.88) 0.63 2.18 -0.61 (-2.78) -1.23 (-1.34) 0.52 (6.04) -10.24 (-8.85) 0.72 1.97 2.91 (3.81) -7.03 (-4.90) 0.00 -18.69 (-3.81) - -0.52 (6.04) -10.24 (-8.85) 0.00 31.04 (2.53) - -0.00 0.00 0.00 3.70 (5.25) 1 1.13 (0.73) 0.53 1.52 (1) Asymptotic t-ratios in parenthesis ; critical values for a large sample are t = 1.960 and t = 2.576 Table 6.2; Initial Model - Pacific Northwest Parameter Estimates and Summary Statistics Equation Lumber PRICES Pulpchips Sawlogs Labour FIXED Capital FACTORS Quality Time Constant R' DW Lumber -3.82 (-4.98) -1.1 1 (-6.12) 2.93 (4.68) 2.01 (7.53) 1.17 (0.86) -2.24 (-0.95) -1.12 . (-374) 9.40 (1.02) 0.34 1.45 Pulpchips -1.1 1 (-6.12) 0.46 (6.96) 0.68 (4.55) -0.029 (-0.38) 0.22 (0.87) -2.64 (-6.33) -0.094 (-1,81) 1.82 (0.98) 0.88 1.79 Sawlogs 2.93 (4.68) 0.68 (4.55) -2.24 (-4.03) -1.38 (-6.14) -1.17 (-1.08) 2.46 (1.36) 0.73 (3.19) -4.32 (-0.58) 0.28 1.47 Labour 2.01 (7.53) -0.029 (-0.38) -1.38 (-6.14) -0.61 (-4.47) -0.22 (-0.47) 2.43 (3.06) 0.48 (4.76) -5.91 (-1.85) 0.62 1.48 Capital 1.17 (0.86) 0.22 (0.87) -1.17 (-1.08) -0.22 (-0.47) -3.97 (-1.66) -10.85 (-4.43) o.bo 27.14 (1.49) - -Quality -2.24 (-0.95) -2.64 (-6.33) 2.46 (1.36) 2.43 (3.06) -10.85 (-4.43) 0.73 (0.12) 0.00 81.30 (371) - -Time -1.12 (-3.74) -0.094 (-1.81) 0.73 (3.19) 0.48 (4.76) 0.00 0.00 orjo 3.41 (4.14) - -Profit Function - - - - - - - -1 14.79 (-1.68) 0.51 1.46 (1) Asymptotic t-ratios in paranthesis; critical values for a large sample : 1.960 and ^ .005 = 2.576 147 also checked. Note, however, that these properties are not implied by the model. The properties checked are summarized in Table 6.3. In both regions, profits are increasing in output prices and decreasing in input prices. This property holds at every data point. At the mean of the BC data, profits were decreasing in capital and . wood quality, but increasing in time. Thus a positive rate of technical progress was found. At the mean of the PNW data, profits were decreasing in capital, but increasing in quality and time. The violation of the monotonicity conditions with respect to some of the fixed factors is the major" theoretical inconsistency of the model. This is probably due to statistical problems. It was mentioned previously that the capital stock and the time trend were highly colinear in both regions. Thus the model cannot do a good job of separating the effects of the two variables. Fuss (1983) discusses a similar multicolinearity problem between output and time in the estimation of cost functions in telecommunications. The same problems appear to have occurred with the estimation of non-homothetic, non-neutral technical progress, cost functions in the wood products (Rao and Preston, 1983) and the pulp and paper (Martinello, 1985a) industries. In these studies, either abnormally high returns to scale, or abnormally low rates of technical progress have been estimated. Abt (1984) also found that capital and technical progress effects could not be easily differentiated in US regional restricted cost functions of the sawmilling industry. There are two possible ways of dealing with this problem: (1) treat the effects of time and capital together, and not attempt to separate them, and (2) restrict the model, for example by imposing no technical progress, or by imposing homogeneity of degree one in capital. The second approach will be tried below. Tab le 6.3: Initial M o d e l - V io la t ions of Proper t ies of the Regional Prof i t Funct ions . B C P N W Proper ty Test A t the Number A t the Number M e a n of , o f M e a n of of the Data V i o l a t i o n s the Data V io la t ions N o n - d e c r e a s i n g s K > o True 0 True 0 in pr ices S c > o True 0 True 0 s L > o True 0 True 0 s w > o True 0 True 0 N o n - d e c r e a s i n g s K > o False 19/25 Fa lse 11/25 in f ixed fac to rs S Q > 0 s T > o Fa lse 15/25 True 7/25 True 0 True 0 C o n v e x i t y in pr ices Four e igenvalues >0 False (True) 21 /25 (10 /25) 1 True 7/25 (3 /25) 1 C o n c a v e in capital 9 n 2 / 3 2 K < 0 Fa lse 25 True 1/25 C o n c a v e in quality 9n 2/9 2 Q<0 Fa lse 25 Fa lse 25 (1) The number in parenthesis re fers to the result o f the test when very smal l e igenvalues were a s s u m e d equal to zero (at least the f irst 4 d igi ts were zero). In general one eigenvalue w a s a lways very smal l and the other three very large. 149 In the PNW, the monotonicity condition with respect to the quality variable is only violated at seven observations, but in BC this occurs in fifteen out of twenty^five observations. According to the results of Chapter 3, quality changed very little in BC from 1957 through 1981, while in the PNW quality fluctuations were much more important. It was then hypothesized that this could be due to the old growth first cut constraint, which only exists in BC. Violation of the monotonicity condition with respect to quality could then result from the low variability of the wood quality data, which would render the estimates of the quality parameters difficult, and it is reassuring that in the PNW model the wood quality variable performed as expected. One of the theoretical properties which is more prone to fail with flexible functional forms are the curvature conditions (Diewert and Wales, 1984). In the profit function case, convexity in prices is implied by the profit maximizing behaviour of producers, and if this property fails, this can be viewed as an indication that producers are not behaving in a profit maximizing manner. Convexity was violated at a considerable number of observations in BC. Usually one eigenvalue was negative. But it was also found that the magnitude of this eigenvalue was usually very small (at least the first four digits were zero) when compared with the other ones (at least three positive digits). Also, estimations with alternative sets of three second order coefficients involving only fixed factors restricted to zero (restrictions (62.1)), would yield different results with respect to the sign of the small eigenvalue. Although statistical tests of convexity were not carried out, the evidence suggests that this eigenvalue is not statistically different from zero, and in this case the performance of the BC model with respect to the curvature condition becomes more satisfactory. The profit function was concave in capital in the PNW suggesting decreasing returns to scale and convex in BC, suggesting increasing returns to 150 scale. Convexity in wood quality was found in both regions, and so the model is not reproducing the empirical output versus diameter curves observed in mill studies and discussed in the previous Chapter (Figures 5.1 and 5.2). Note that concavity of the profit function in quality implies concavity of the production function in quality but that the converse is not true. Violations of the expected signs of the relationships are summarized in Table 6.4. With respect to the expected signs of own price, cross price, compensated own price and compensated cross price elasticities, both regional models performed very satisfactorily.. In three observations, BC lumber supply sloped down and the BC sawlog and labour demands sloped up. In the PNW, all the relationships exhibited the right signs at every data point. Wrong signs for the elasticities of lumber recovery with respect to lumber price and wood quality were found in BC, contradicting common sense evidence. However, as will be discussed in the next section, in BC elasticity estimates were very unstable across the sample and for several observations the right signs were obtained. As mentioned above, the inferior performance of the quality variable in BC is likely to result from the lack of sample variability of this variable. The overall results indicated satisfactory performance of the models. As a rule, the PNW model performed better than the BC one, showing a smaller number of theoretical inconsistencies and no violations of expected signs of the elasticities. The main weakness in both regional models is the negative sign of the derivative of the profit function with respect to capital, which indicates that profits are decreasing with capital. Such a result contradicts both theory and common sense evidence. It is probably a result of the high multicolinearity between capital and the time trend, which renders difficult the separation of the effects of the two variables difficult. Table 6.4 : Initial Model - Violations of Expected Signs of Economic Relationships. BC PNW Relationship Variables Expected Result At the Mean ot Number of At the Mean of Number of the Data Violations the Data Violations lumber eMM + True 3/25 True 0 Own price pulpchips ecc + True 0 True 0 elasticities sawlogs eLL " True 3/25 True 0 labour *ww - True 3/2fe True 0 Cross price lumber, sawlog e ^ + True 3/25 True 0 elasticities sawlog, lumber "LM + True 3/25 True 0 Compensated lumber MM + True True own price pulpchips CC + True Not. True Not elasticities sawlogs LL " True Checked True Checked labour WW True True Compensated lumber, pulpchips LC " True Not True Not cross price sawlogs, labour LW + True checked True checked elasticities lumber- recov., lumber *M/L,M True True lumber recov, sawlogs •M/LJL + True True Elasticities of lumber /chips, lumber *M/C,L + False Not True Not input and lumber/chip, chip "M/C,Q True checked True checked output ratios lumber/chip, quality eM/C,0. + True True lumber recov, quality eM/S.Q + False True 152 Following this analysis of the theoretical consistency of the regional profit functions, the tests summarized in Table 5.2 of the previous Chapter are carried out. These are nested tests, because each model tested can be obtained from the unrestricted model through the imposition of a set of restrictions on the coefficients. The test statistic -2(lnL0 - InLj), where L 0 and Ll are, respectively, the logs of the likelihood functions of the restricted and unrestricted models, has asymptotically a chi-square distribution with r degrees of freedom, where r are the number of restrictions. The test results are reported in. Tables 6.5 through 6.7. Note first that the number of restrictions is smaller than in Table 5.2 because a normalized version of the model was estimated. The objective of the first series of tests, reported in Table 6.5, was to text for the statistical importance of the wood quality variable in the model.The hypothesis that wood quality did not belong to the model was rejected for both regions taken together and for each region separately, both at the 0.05 and 0.01 levels of confidence. An alternative hypothesis was that wood quality should be in the model but in a restricted way, i.e., it was sufficient to use quality adjusted prices (P*"), defined as p'~='P"^ /Q, where "P*" is the average price and Q the quality index. This restriction constrains the supply and demand elasticities with respect to the sawlog price and quality to be equal and of opposite signs. This hypothesis was also rejected in both regions taken together and for each region separately at both levels of confidence. The second series tested the hypothesis of homogeneity of degree one in capital of the profit function (Table 6.6). This implies that if the capital stock is increased by 1%, all inputs and outputs are increased also by 1% and that there are constant returns to scale. Homogeneity of degree one in capital was rejected in both regions taken together and in BC, but was accepted at the 0.01 level of Table 6.5; Results of Tests on the Characteristics of Regional Profit Functions - Wood Quality. Test Null Hypothesis Number of Restrictions ) \ ^(2(0.05) Decision ^( 2(0.01) Decision No wood quality in both regions 12 56.94 21.03 Reject 26.22 Reject No wood quality in BC* 2) 41.88 12.59, Reject 16.81 Reject No wood quality in the PNW* 2) 42.28 12.59 Reject 16.81 Reject Quality adjusted prices in BC* 2) 32.54 12.59 Reject 16.81 Reject Quality adjusted prices in the PNW* 2) 34.82 12.59 ' Reject 16.81 Reject (1) \ = -2(lnL0 - InL.) ' (2) For these tests the statistical model was modified, and no correlation between residuals across regions was assumed. Table 6.6: Results of Tests on the Characteristics of Regional Profit Functions - Homogeneity and Technical Progress. Test Null Hypothesis Number of Restrictions X 9( 2(0-05) Decision 2(0.01) Decision Homogeneity one in K in regions of degree both 12 53.32 21.03 Reject 26.22 Reject Homogeneity one in K in of degree BC* 2 * • 6 35.78 12.59 Reject 16.81 Reject Homogeneity one in K in of degree the PNW* 2) 6 14.76 12.59 . Reject 16.81 Accept No technical both regions progress in 8 63.14 15.51 "Reject 20.09 Reject No technical BC<2> progress in 4 40.98 9.49 Reject 13.28 Reject No technical the PNW* * progress in 4 35.96 9.49 Reject 13.28 Reject (1) \ = -2(lnL„ - InL,) (2) For these tests, the statistical model was modified, and no correlation between residuals across regions was assumed. Table 6.7; Results of Tests on the Characteristics of Regional Profit Funcitons - Regional Differences. Test Null Hypothesis Number of Restrictions h 9( 2(0.05) Decision 7( 2(0.01) Decision All the second order regional coefficients are equal 15 76.22 " 25.00 Reject 30.58 Reject Across region restrictions All the regional coefficients of fixed factors in share equations are equal 6 13.04 12.59 Reject 16.81 Accept All the first order regional coefficients of fixed factors are equal 3 6.56 7.81 . Accept 1 1.34 Accept (1) \ = -2(lnL0 - InL,) 156 confidence in the PNW. This is an important result for this research, because by imposing homogeneity, one forces the profit function to be increasing in capital, thus resolving the main theoretical inconsistency of the model. Martinello (1984b, 1985a) also rejected constant returns to scale in BC and in Canada and found increasing returns, while Abt (1984) did not reject constant returns to scale in the US West. These two authors specified an unrestricted and a capital restricted translog cost function, respectively. The third series tested for the existence of technical progress (Table 6.6). The hypothesis of no technical progress was rejected in the two regions taken together and in each region separately both at the 0.05 and 0.01 levels of confidence. The last series of tests attempted to check if the regional profit functions had common elements. The hypothesis that all the second order regional coefficients are equal was rejected both at the 0.05 and 0.01 levels of significance, and this implies that the other two null hypothesis described in Table 5.2 would also be rejected. In addition to the tests reported in Table 5.2, it was decided to test also the hypothesis that (1) all the regional coefficients of fixed factors in share equations are equal, and (2) all the first order regional coefficients of fixed factors are equal. The first hypothesis above was accepted at the 0.01 level of confidence, while the second hypothesis was accepted both at the 0.05 and 0.01 levels of confidence. Following these results, four more restricted models were specified: (1) no wood quality; (2) across region restrictions on the wood quality and time trend parameters which also appear in share equations; (3) homogeneity of degree one in capital; and (4) no technical progress. The first objective in specifying a model omitting the wood quality variable was to observe if very different demand and 157 supply elasticities resulted, this giving support to the hypothesis of this research that wood quality is an important variable in lumber industry modelling. The second objective was to compare the technical progress estimates with the estimates from the full model. It is another hypothesis of this research that the rate of technical progress is higher when wood quality is included in the model. The model with across region restrictions on the wood quality and time trend parameters which also appear in share equations was specified in an attempt to solve two of the theoretical inconsistencies found in the BC initial model: profits decreasing with wood quality and a negative elasticity of lumber recovery with respect to quality. Such restrictions would allow the BC model to benefit from the richer sample variability of the quality variable in the PNW. Furthermore, it was hoped that such restrictions would aleviate the multicolinearity problems between the time trend and capital. Note that the hypothesis that the above across region restrictions were true was not rejected at the 0.01 level of confidence, in the test reported in Table 6.7. The models with homogeneity of degree one in capital and no technical progress imposed were also specified in an attempt to aleviate the multicolinearity problems between the time trend and the capital stock and make the profit function increasing in capital. The hypothesis of homogeneity in capital was not rejected at the 0.01 level of confidence in the PNW model, according to the test results of Table 6.6. When estimating the above four models, there was also some interest in checking the sensitivity of elasticity estimates to changes in model specification. Parameter estimates and summary statistics for the above four models are reported in Tables A.2.1 through A.2.8 of Appendix II. With the exception of the model with across region restrictions, which exhibited a higher percentage of 158 statistically significant coefficients, all the other models performed statistically worse than the initial model, with a smaller percentage of significant second order coefficients and lower individual RJ. The d statistics of the BC model with no technical progress were very low, evidencing autocorrelation between residuals. The violations of the properties of the profit function and expected signs of relationships for the alternative specifications are reported in Tables 6.8 through 6.11. The BC model, omitting the wood quality variable (Ml), is still decreasing in capital at the mean of the data and at a larger number of observations than the initial model, and convexity in prices is more violated. At the mean of the data and 15 observations, the pulpchip supply slopes down, but in the initial model it had the right sign at every data point. The signs of the other own and cross price elasticities also exhibit a larger number of violations. It is therefore considered that the BC model including wood quality, outperformed the BC model omitting wood quality in terms of theoretical consistency. The PNW model omitting wood quality was increasing in capital at every data point, but showed three violations of the sign of the own price elasticity of labour demand. The BC model with across region restrictions (M2) yielded the right sign for the elasticity of lumber recovery with respect to quality, and was increasing in quality at a slightly larger number of observations than the initial model. With respect to the other properties and expected signs, both the BC and the PNW model performed identically to the initial one. The main advantage of the homogeneous model (M3) is that it is increasing in capital, thus suiting itself for long-run simulations in which the capital stock is allowed to change. On the other hand, it is decreasing in quality and so it is not appropriate for studying the impacts of wood quality changes in the industry. Both the elasticities of the lumber/chip ratio and lumber recovery Table 6.8: Alternative Model Specifications - Violations of Properties of the BC Profit 0) Functionv '. PROPERTY TEST M1 At the Mean of the Data M2 M3 M4 M1 M2 Number of Violations M3 M4 v° True True True True 0 0 0 0 Non-decreasing sc>o True True True True Q 0 0 0 in prices sL<o True True True True 0 0 0 0 v° True True True True 0 0 0 0 Non-decreasing False False True True 25/25 25/25 0 8/25 in fixed factors v-° - False False False .13/25 25/25 22/25 sT>o True True True - 0 0 0 -Convexity in prices Four eigenvalues>0 False (Two<0) False (One<0) False (One<0) False (One<0) Not checked Concave in capital False False - False 7/25 25/25 - 25/25 Concave in quality - False False False - 25/25 25/25 25/25 (1) M1 - No wood quality; M2 - Across region restrictions on wood quality and time trend; M3 - Homogeneous of degree one in capital; M4 - No technical progress Table 6.9: Alternative Model Specifications - Violations of Properties of PNW Profit Function. PROPERTY TEST Ml At the Mean M2 of the Data M3 M4 Ml M2 Number of Violations M3 M4 S M * ° True True true True 0 0 0 0 Non-decreasing sc>o True True True True 0 0 0 0 in prices sL<o True True True True 0' 0 0 0 s w * ° True True True True 0 0 0 0 Non-decreasing True False True True 0 16/25 0 8/25 in fixed factors S Q - ° , - True False False -'' 8/25 25/25 23/25 sT>o True True True - 0 0 0 -Convexity in prices Four eigenvalues^ True True True True Not checked Concave in capital True True - True 7/25 3/25 - 1/25 Concave in quality - False False False - 25/25 25/25 25/25 (1) M1 - No wood quality; M2 - Across region restrictions on wood quality and time trend; M3 - Homogeneous of degree one in capital; M4 - No technical progress Table 6.10; Alternative Model Specifications - Violations of Expected Signs of the BC Profit Functions.*^ At the Mean of the Data Number of Violations Relationship Variables Expected Result M1 M2 M3 M4 Ml M2 M3 M4 lumber 6 MM + True True True True 5/25 6/25 1/25 7/25 own price pulpchips e cc + False True True i True 15/25 0 0 0 elasticities sawlogs V " True- True True • True 7/25 6/25 2/25 6/25 labour e w w ~ True True True True 3/25 5/25 1/25 4/25 cross price lumber, sawlogs 6ML " True True True True 7/25 7/25 2/25 6/25 elasticities sawlogs, lumber 6 LM + True True True ; True . 7/25 7/25 2/25 6/25 lumber recov., lumber eM/l_,M True True True True elasticities lumber recov., sawlogs 6M/L,L + True True True True of input lumber/chips, lumber 6 M/C,C + True False False False Not checked and output lumber/chips, chips CM/C,C False True True True ratios lumber/chips, quality lumber recov., quality 6 M/C,Q +  6 M/S,Q + -True True False False True False (1) Ml - No wood quality; M2 - Across region restrictions on wood quality and time trend; M3 - Homogeneous of degree one in capital; M4 - No technical progress Table 6.11: Alternative Model Specifications - Violations of Expected Signs of the PNW Profit Function At the Mean of the Data Number of Violations Relationship Variables Expected Result Ml M2 M3 M4 Ml M2 M3 M4 lumber e MM + True True True True 0 0 0 0 own price pulpchips e c c + True True True , True 0 0 0 0 elasticities sawlogs 8 LL - True True True 'True 0 0 0 0 labour e w w - True True True True 3/25 2/25 2/25 0 cross price lumber, sawlogs 6ML - True True True True 0 0 0 0 elasticities sawlogs, lumber e LM - True True True True 0 0 0 0 lumber recov., lumber 6M/L,M - True True True True elasticities lumber recov, sawlogs CM/L,L + True True True True of input lumber/chips, lumber 6 M/C,C + True True True True Not checked and output lumber/chips, chips CM/C,C - True True True True ratios lumber/chips, quality 6M/C,Q + - True True True lumber recov., quality 6 M/S,Q + - True False False (1) M1 - No wood quality; M2 - cross region restrictions on wood quality and time trend; M3 - Homogeneous of degree one in capital; M4 - No technical progress. 163 with respect to wood quality exhibit wrong signs at the mean of the data in BC and the latter in the PNW. The model with no technical progress was increasing in capital at a considerable number of observations, but decreasing in quality. The elasticity of lumber recovery with respect to quality had the wrong sign in both regions and the BC model showed a larger number of violations of the signs of own price elasticities than the initial model. 6.4 ELASTICITIES AND RATES OF TECHNICAL PROGRESS Price supply and demand elasticities and elasticities with respect to changes in the capital stock and wood quality are reported in Table 6.12. These elasticities were estimated at the mean of the data. Lumber supply is elastic in both regions. A 1% increase in the lumber price has the following effects: (1) lumber supply increases by 1.1% in BC and 1.4% in the PNW; (2) pulpchip supply increases by 2.0% in BC and by 0.7% in the PNW; (3) sawlog demand increases by 1.5% in BC and by 2.0% in the PNW; and (4) employment increases by 1.4% in both regions. The BC elasticities of pulpchip supply with respect to the lumber price is high, and the PNW elasticity appears to be more realistic. A 1% increase in the pulpchip price increases lumber supply slightly in both regions, and it increases the pulpchip supply by 1.4% in BC and by 0.6% in the PNW. Sawlog demand was also found to be elastic in both regions. An increase in sawlog price causes a decline in all supplies and demands, and the same happens with an increase in the wage rate. The elasticities of supplies and demands with respect to the capital stock show the wrong signs in BC. In the PNW, a 1% increase in the capital stock leads to an increase of less than 1% in all variable outputs and inputs. A 1% Table 6.12: Initial Model - Demand and Supply Elasticites ( 1 ) . ( 2 ) PRICES FIXED FACTORS QUANTITIES TIME*3) Lumber Chips Logs Labour Capital Quality Lumber 1.11 0.22 -0.93 -0.39 -0.48 1.19 0.044 1.44 0.07 -1.13 -0.38 0.28 3.00 0.033 Pulpchips 2.00 1.43 -2.36 -1.07 0.70 -0.30 0.059 0.67 0.57 -0.21 -1.03 0.52 -2.21 0.039 Sawlogs 1.50 0.41 -1.43 -0.48 -0.38 1.70 0.046 2.03 0.04 -1.08 -0.25 0.54 2.70 0.029 Labour 1.42 0.42 -1.10 -0.74 -0.14 1.42 0.031 1.41 0.42 -0.52 -1.32 0.18 1.70 0.018 (1) These elasticities were computed at the mean of the data. (2) The top number refers to BC and the bottom number to the PNW. (3) These values give the percentage change per year. 165 increase in wood quality leads, in both regions, to a greater than 1% increase in lumber supply and sawlog and labour demand, but to a decline in pulpchip production, this result being consistent with a priori expectations. The responses of input and output ratios to changes in prices and in fixed factors are shown in Table 6.13. In both regions lumber recovery responds negatively to an increase in lumber price and positively to an increase in the sawlog price. This is because with market downturns the marginal more inefficient producers stop operating. The elasticity of the "lumber to chip ratio with respect to the lumber price exhibits a negative sign in BC, indicating that when the lumber price increases relatively to the pulpchip price, the proportion of lumber in output declines. This result was not expected and it was corrected in the model with across region restrictions on wood quality and time. In the PNW, an increase in the lumber price increases the lumber proportion in output, and in both regions an increase in the pulpchip price has the reverse effect. The response of labour productivity (i.e., lumber output per unit of labour), is different in both regions. For example, a 1% increase in the sawlog price leads to a 0.2% increase in labour productivity in BC and to a 0.6% decline in the PNW. The amount of wood utilized per unit of labour responds positively to increases in the labour and lumber prices and negatively to increases in the pulpchip and sawlog prices. In the PNW, a 1% increase in wood quality increases lumber recovery by 0.3%, the lumber to chip ratio by 0.8%, labour productivity by 02%, and the sawlog to labour ratio by 1.0%. In the BC initial model, lumber recovery responded negatively to an increase in wood quality, but this inconsistency was corrected in the model with across region restrictions (see Table 6.17). In BC, a Table 6.13: Initial ^ J 0 ^ 1 ~ Elasticities of Selected Input and Output PRICES FIXED FACTORS QUANTITIES TIME Lumber Chips Logs Labour Capital Quality Lumber -0.39 -0.19 0.50 ' 0.09 -0.10 -0.51 -0.002 Recovery -0.59 0.03 0.69 -0.13 -0.26 0.30 0.004 Lumber/Chips -0.89 : -1.11 1 A3 0.68 -.1.18 0.89 -0.015 0.77 -0.50 -0.90 0.65 -0.24 0.79 -0.006 Lumber/Labour -0.30 -0.10 0.17 0.09 -0.34 -0.23 -0.002 (Labour 0.03 -0.35 -0.61 0.20 1.30 0.19 0.004 productivity) Logs/Labour 0.08 -0.01 -0.33 0.26 -0.24 0.28 0.015 0.52 -0.38 -1.30 1.07 0.26 1.00 0.021 (1) Elasticities were computed at the mean of the data. (2) The top number refers to BC and the bottom number to the PNW. (3) These values give the percentage change in ratios per year. 167 1% increase in wood quality increases the lumber to chip ratio by 0.9% and increases the sawlog to labour ratio by 0.3%. In BC, an increase in the capital stock leads to a decline in lumber recovery, in the proportion of lumber in the output, labour productivity and in the proportion of wood in the input. These results are not reasonable, in particular the one involving labour productivity, because it contradicts the known phenomenon of substitution of capital for labour discussed in Chapter 2. However, they are probably a consequence of the high multicolinearity problems between capital and the time trend, and so they do not deserve confidence. In the PNW, labour productivity and the proportion of wood in the intput, increase with an increase in the capital stock, while lumber recovery and the proportion of lumber in output declines. In this region, an increase in the capital stock reduces the marginal profitability of wood quality, thus suggesting that capital is a substitute for wood quality. In BC, the reverse effect was obtained. However, the same warning concerning the relationships involving the capital stock parameters mentioned above apply here. The estimated rate of technical progress at the mean of the data in BC was 0.062% per year, and in the PNW it was . 0.057% per year. Thus, the BC industry exhibits better technological performance than the PNW industry. In both regions technical progress has been increasing the proportion of wood in input, suggesting a wood using, labour saving bias (Table 6.13). This result should be contrasted with the bias due to changes in capital stock: wood saving, labour using in BC and wood using, labour saving in the PNW. Technical progress has been increasing the proportion of pulpchips in output in both regions. Given the model specification utilized, in which capital is a fixed factor, and the multicolinearity problems between the time trend and capital, the separation of the effects of capital and technical progress is arbitrary and does not inspire 168 confidence. Al! the elasticities presented so far measure the response to a change in prices or fixed factors, after all the variable quantities are allowed to readjust to their optimum levels. As discussed previously, they include both substitution, and output or input effects due to the contraction or expansion of the industry, and are particularly useful for short-run policy analysis. However, due to the multitude of effects that they capture, they do not provide insights into the structure of sawmilling technology. It is, therefore, useful to decompose these elasticities into substitution and expansion effects, using the procedures described in Chapter 5. In Table 6.14, constant output demand elasticities are shown. These elasticities could be directly obtained by estimating a restricted cost function. In this case, the assumed producers' problem would be that of minimizing the costs of producing a fixed amount of lumber and pulpchips by optimally adjusting wood consumption and employment, subject to the capital stock, wood quality and "state of knowledge". They describe the shape of the isoquants, and how these isoquants shift with changes in fixed outputs and fixed factors. The constant output elasticity of labour demand with respect to sawlog price in the PNW (0.36) compares favourably with the one estimated by Abt (1984) (Table 1.3) for the US West utilizing a restricted capital cost function (0.39), and the same is true of the own elasticity of sawlog demand (-0.18 versus -020). The constant output elasticity of labour demand with respect to sawlog price in BC (0.19) is lower than the one estimated by Martinello (1984b) (Table 1.3) for BC utilizing an unrestricted (long-run) cost function (0.27), and this result is consistent with the theory, because short-run elasticities should be smaller in absolute value than long-run elasticities (Diewert, 1974; Lau, 1976). The same happened with the own elasticity of sawlog demand (-0.08 versus -0.12). Table 6.14: Constant Output Demand Elasticities*^ 2). PRICES FIXED OUTPUTS FIXED FACTORS QUANTITIES TIME* ) Logs Labour Lumber Chips Capital Quality Logs -0.08 0.08 1.15 0.11 0.09 0.36 -0.011 -0.18 0.19 1.47 -0.12 0.19 -2.04 -0.015 Labour 0.19 -0.19 1.03 0.14 0.25 0.23 -0.022 0.36 -0.39 0.68 0.65 -0.35 1.10 -0.029 (1) Elasticities were computed at the mean of the data. (2) The top number refers to BC and the bottom number to the PNW. (3) These values give the percentual change per year. 170 These elasticities can be put together with those of Table 6.12 to provide a description of total industry responses. For example, how does BC employment respond to an increase in sawlog price? First there is a substitution effect (^^^=0.19, Table 6.14), which in this case is very small, and which leads to an increase in employment due to the substitution of labour for wood. Second there is a change in the profit maximizing output levels of lumber (e|\/|L =—0.93, Table 6.12) and pulpchips (eLL=-2.36, Table 6.12), due to the shift in the marginal cost schedules, which, in this case, causes production to occur on a lower isoquant. Third, the declines in lumber ( e W M = 1.03, Table 6.14) and pulpchip (e W£=0.14, Table 6.14) production cause a decrease in employment because production is occurring on a lower isoquant. The total net effect is a reduction in employment (evy^=-1.1, Table 6.12). The relationships can be better seen in the following equation: (6.4.1) emi - T | m L • Cuj M e M L + Zmc <?CL BC: -1.10 - 019 + 1.03-(-0.93) + 0.14.(-2.36) PNUJ: -0 52 = 0.36 • 0.6B-H 13) • 0.65-(-O.Z1) The same analysis could be carried out with the other relationships, including those involving fixed factors. In order not to overextend this analysis, only some of the more interesting aspects are described. First, it is noted that the substitution possibilities between wood and labour are considerably limited in both regions, but more so in BC than in the PNW. As exemplified in equation (6.4.1) the industry responses are characterized by large output effects and small substitution effects. A 1% increase in lumber output will increase sawlog consumption more than employment in both regions, so that the amount of wood per unit of labour will increase. Furthermore, because the BC responses are elastic, both lumber 171 recovery and labour productivity (i.e. lumber/labour) will decline. In the PNW, lumber recovery declines but labour productivity increases. A 1% increase in the pulpchip output moves the industry to a more labour less wood intensive region of the input space in both regions (quality is held fixed). In the PNW, wood is an inferior good with respect to the pulpchip output. Both lumber recovery and labour productivity decline in BC with an increase in pulpchip production, while in the PNW lumber recovery increases and labour productivity declines. A decline in wood quality will move the BC industry to a more labour intensive region of the input space, this explaining why lumber recovery increases. As mentioned before, an unexpected sign was obtained in the initial model for the elasticity of lumber recovery with respect to the wood quality variable but this was corrected in the specification with across region restrictions on wood quality and time. A decline in wood quality will move the PNW industry to a more wood intensive region of the input space, and it will result in a decline in lumber recovery but will increase labour productivity. An increase in the capital stock saves wood per unit of labour in BC and increases wood consumption per unit of labour in the PNW, besides decreasing lumber recovery and increasing labour productivity. Technical progress has been wood using, labour saving by aproximately the same ammount in both regions. In both regions lumber recovery has been declining and labour productivity increasing due to technical progress. Given the superior performance of the PNW industry with respect to lumber recoveries, noted in Chapter 2, these results are somewhat unexpected. However, it is noted that the substitution possibilities between wood and labour are higher in the PNW than in BC, and, also, that in the PNW wood prices have increased relative to wages, while in BC the opposite has happened. The recovery gains in the PNW are, therefore, mostly explained through the substitution phenomenon due to price changes, rather than through exogenous 172 capital stock and technical progress ef fects. An equivalent analysis to the one described above can be carried out on the output side. In Table 6.15, constant input supply elast ici t ies are shown. These elast ici t ies could be obtained directly by estimating a revenue function. The assumed producers problem would be that of maximizing gross revenues (value of sales) by optimally adjusting lumber and pulpchip outputs, but holding all inputs f ixed, including wood and labour. They describe the shape of the transformation frontiers and how these transformation frontiers shift with changes in the input levels. A decomposit ion similar to the one done on the input side can be carried out with output. For example, how does BC pulpchip production change with an increase in the lumber price? First there is a substitution effect (VQM =-0.67, Table 6.15), which is relatively large, and which leads to a decline in pulpchip production because more lumber is produced (inputs and quality are constant). Second, there is an increase in the profit maximizing input levels of wood ( e L M = 1.50, Table 6.12) and labour ( e W M = 1.42, Table 6.12), due to the upward shift in the value of the marginal product schedules, which causes a movement to an upper transformation frontier. Third, the increases in the wood (eQ^ = 1.09, Table 6.15) and labour ( e £ W = 0 . 7 3 , Table 6.15) inputs cause an increase in pulpchip production, because of the movement to the new transformation frontier. The total net effect is an increase in pulpchip production (eQ|_=2.00, Table 6.12). The relationships can be better seen in the fo l lowing equation: (6.4.2) eC M = ^ • e C L . eL M 4 e C U J . e u i M BC: 2 00 = -067 • 1.09-1.50 • 0.73-1.42 PNUJ: 0.67 = -0.23 + (-0.1D-Z.03 • 0.79-1.41 Table 6.15: Constant Input Supply Elasticities^ 1^ 2). PRICES FIXED FACTORS TIME* ' Lumber Chips Logs Labour Capital Quality Lumber 0.01 -0.01 0.50 0.20 -0.26 0.06 0.015 0.03 -0.03 0.57 0.18 -0.06 1.15 0.016 Chips -0.67 0.67 1.09 0.73 1.21 -3.18 -0.014 -0.23 023 -0.11 0.79 0.44 -3.25 0.028 (1) Elasticities were computed at the mean of the data. (2) The top number refers to BC and the bottom number to the PNW. (3) These values give the percentual change per year. 174 From the above equation one can see that the considerable different elasticities of pulpchip supply with respect to an increase in lumber price in BC and in the PNW are due to the term e ^ . While in BC an increase in the sawlog input increases pulpchip production considerably, in the PNW the response is closer to zero and may be negative. A 1% increase in the wood input will increase lumber production by about half percent in both regions, and increase pulpchip production by 1.1% in BC and reduce it by 0.1% in the PNW. The proportion of pulpchips in the output will increase in BC and decline in the PNW. Because the lumber responses are inelastic, lumber recovery and labour productivity (lumber/labour) will decline in both regions. A 1% increase in the labour input moves both industries to a more pulpchip intensive region of the output space. Labour productivity declines because the lumber response is inelastic and lumber recovery increases because more lumber is produced with the same amount of wood. A decline in wood quality will increase considerably the proportion of pulpchips in the outputs of both regions, and reduce lumber recovery and labour productivity substantially more in the PNW than in BC. An increase in capital increases the proportion of pulpchips in the output in both regions and reducess lumber recovery and labour productivity. Technical progress has been increasing the share of pulpchips in output in the PNW and reducing it in BC. Given the above results, it was of interest to test the stability of elasticity estimates across the sample and across model specifications. All the total elasticities of Table 6.12 were also computed at each data point, and it was found that in BC, elasticity estimates were very unstable. In the PNW the instability was not serious. No explanation can be advanced for this phenomenon, but an important implication is that the BC elasticities at means, derived in this 175 study, do not inspire much confidence for policy analysis. Sample instability of elasticity estimates obtained with flexible functional forms is briefly discussed by Elbadawi et al (1983) and Diewert and Wales (1984). Own elasticities of lumber supply and sawlog demand for the two regions are plotted in Figures 6.1 and 6.2. This instability analysis was not carried out with the constant output demand and constant input supply elasticities. In Table 6.16, own price elasticities at the mean of the data for the initial model and the other four more restricted' specifications are compared. Detailed elasticity results for the alternative models are presented in Appendix II in Tables A.2.9 through A.2.12. Compared with the initial specification, the model omitting wood quality (Ml) yielded the wrong sign at the mean of the data for the own elasticity of pulpchip supply in BC. Given this result, wood quality appears to be an important variable to take into account when modelling residue supply. This model also yielded a substantially lower own elasticity of sawlog demand in BC, and a substantially lower own elasticity of labour demand in the PNW. The model with across region restrictions on wood quality and time (M2) produced the best results for both regions. In particular, the BC elasticity of pulpchip supply exhibited a lower and more realistic magnitude than in the initial model. The other elasticities were similar to those of the initial model. The models with homogeneity imposed (M3) and with no technical progress (M4) also produced elasticity estimates comparable to those of the other models. The only exception is the own elasticity of pulpchip supply which was considerably lower in the PNW in the homogeneous model. The elasticities with respect to changes in the capital stock or in wood quality were more unstable, as was expected, because the restrictions were imposed on the parameters of fixed factors. The results are compared in Table 176 FIGURE 6.1 Own Elasticities of Lumber Supply C O "c a> o i_ a> Q. BC C o a s t PNW West 1955 1960 1965 1970 1975 1980 1985 FIGURE 6.2 Own Elastcities of Sawlog Demand BC C o a s t PNW West 1955 1960 1965 1970 1975 1980 1985 Table 6.16: Comparison Between Initial and Alternative Model Specifications - Own Elasticities of Demand and Supply.*1 ) , ( 2 ) Initial M1 M2 M3 M4 Lumber Supply 1.11 1.03 0.92 1.56 1.14 1.44- 1.31 1.53 1.67 1.53 Pulpchip Supply 1.43 -0.05 0.58 0.32 0.69 0.57 0.25 0.41 0.08 0.42 Sawlog Demand -1.43 -0.80 -1.04 -1.57 -1.01 -1.82 -1.67 -1.78 -2.13 -1.93 Labour Demand -0.74 -0.68 -0.57 -0.89 -0.85 -1.32 -0.59 -0.91 -0.95 -1.59 (1) Elasticities were computed at the mean of the data. (2) The top number refers to BC and the bottom number to the PNW. 178 6.17. The model with across region restrictions (M2) produced considerably different estimates for the elasticities with respect to changes in quality, but the results are considered more reasonable than for the initial model. In this model, a 1% increase in wood quality in BC will lead to a 0.10% increase in lumber recovery, the sign of this relationship being consistent with common sense evidence. It is also noted that the homogeneous and no technical progress models produced elasticity estimates of input and output ratios with respect to quality changes which are not consistent with a priori expectations. 6.5 GLOBAL ASSESSMENT OF ECONOMETRIC MODEL AND TEST OF RESEARCH HYPOTHESES It is appropriate to discuss the suitability of the econometric models developed in this thesis for policy analysis. Although the overall results were considered satisfactory - because most of the model properties and signs of relationships were consistent with economic theory and conformed to a priori expectations, and the magnitudes of elasticities appeared to be reasonable - there are problems that may limit the usefulness of the models. The model with across region restrictions (M2) is appropriate for analyzing the impacts of wood quality changes in the industry. In order to carry out such analysis, it would be useful to have forecasts of wood quality. It is difficult to provide forecasts for the quality, index derived in this thesis, and the problem of replacing the quality variable by wood characteristics data which could then provide links with inventory models is suggested in Chapter 7 as an area for further research. It should be emphasized that all the elasticities discussed in the previous Section are short-run, i.e., the capital stock is held fixed. Although such relationships are useful for the analysis of many problems, a complete description Table 6.17: Comparison Between Initial and Alternative Model Specifications - Elasticities with Respect to Capital and Wood Quality* 1^ 2). Initial M1 M2 M3 M4 Lumber Supply, Capital -0.48 -0.36 -0.60 1.00 0.55 0.28 1.40 0.06 1.00 1.50 Pulpchip Supply, Capital 0.70 -0.01 0.64 1.00 1.85 0.52 .0.74 0.69 1.00 1.14 Sawlog Demand, Capital -0.38 -0.39 -0.47 1.00 0.65 0.54- 1.20 0.20 1.00 1.65 Labour Demand, Capital -0.14 -0.04 -0.26 1.00 0.62 0.18 1.35 0.59 1.00 0.48 Lumber Supply, Quality 1.19 _ 0.16 -4.04 -2.69 3.00 - 0.59 -0.66 -0.35 Pulpchip Supply, Quality -0.30 _ -3.15 -3.48 -4.41 -2.21 - -3.73 -4.43 -5.48 Sawlog Demand, Quality 1.70 _ -0.06 -3.44 -2.32 2.70 - 0.44 -0.01 -0.32 Labour Demand, Quality 1.42 _ -0.33 -2.99 -2.31 1.70 - -0.40 -1.49 -0.91 (1) Elasticities were computed at the mean of the data. (2) The top number refers to BC and the bottom number to the PNW. 180 of the industry responses to wood scarcity will not be possible until long-run relationships are also estimated. For example, it was shown above that a decline in quality will move the industry to a more labour intensive region of the input space, possibly because lower quality wood requires more handling, for a given technology. But through the introduction of new machinery capable of dealing with small log sizes and increasing throughputs, the long-run effect may lead to an increase in wood consumption and decline in the labour input. It would be of considerable interest to measure such relationships. In the initial model, it was found that the marginal profitability of wood quality responded positively to an increase in the capital stock in BC, indicating complementarity, and negatively in the PNW, indicating substitutability, but the BC result inspires less confidence than the PNW one. However, neither the initial model nor the model with across region restrictions can be utilized in a dynamic setting because profits were decreasing with capital and in BC some of the elasticities with respect to this input had the wrong sign. On the other hand, either the homogeneous (M3) or no technical progress (M4) models can be used in long-run simulations of the industry after an ad-hoc rule for changing the capital stock is chosen, but they cannot be used to model wood quality changes. Given the strong correlation between the BC real capital stock and the Annual Allowable Cut (RJ=0.98), such a relationship may provide a good starting point. for predicting industry investment, until more research in this area is carried out. Given that increasing returns were found in BC and constant returns could not be rejected in the PNW, and that these results are supported by previous research (Martinello, 1984b; Abt, 1984), it is important to note that the optimum long-run capital stock level may be infinite or undetermined. When modelling investment behaviour, it may be important to impose suitable bounds on 181 investment in sawmilling, such as adjustment costs, expected raw material supply or expected output. A cost function is likely to be a more adequate specification for analyzing the long-run relationships. An important weakness of the results is the instability of the elasticity estimates across the sample in BC which makes the computed elasticities less useful tools for policy analysis. In spite of the above problems, it is useful to make use of the signs and relative magnitudes of the relationships derived in the previous Chapter to make a rough prediction of the direction in which the regional industries will move under the scenario described in the quotation on page one of this thesis. First, it should be noted that contrary to what the quotation implies, the quality of the harvest in BC did not change very much during the last thirty years and that during the last decade it actually increased. This contrasts with what has been happening in one of BC's most important competitors, the PNW, where the quality of the harvest (as measured through the quality of wood traded) declined considerably. Second, it is noted that although the sawlog price increased slightly relatively to the lumber price in BC, the increase in relative wood costs was much sharper in the PNW. BC has been gaining in its competitive advantage both in terms of wood prices and wood quality relatively to the PNW. However, nothing implies .that these historical trends will be maintained in the future, and as Pearse et al. (1984) suggested, there are reasons to believe that wood quality will decline in BC, due to the shift to more marginal stands and second growth timber, and real wood costs will rise, in comparison to competing regions. Supposing that, (1) wood quality declines and wood costs increase in BC; (2) wood quality and wood costs remain stable in the PNW; and (3) the 182 sawmilling capital stock, lumber, pulpchip and labour prices, and technical efficiency remain constant in both regions under the conditions, the following predictions are possible; (1) the substitution possibilities between labour and wood are very small, and so the BC industry will contract and lose considerably in its lumber market share relative to the PNW; (2) pulpchip production may actually increase, if the quality decline is sufficiently large, and in this case a larger pulp and paper industry could be supported; (3) the proportion of pulpchips in output will increase; (4) the proportion of wood in input will decline, but in spite of the substitution of labour for wood there will be a considerable loss in employment due to the contraction of the industry;" (5) the response of lumber recovery will depend on the relative sizes of the quality decline or wood price increase. The remaining research hypotheses of this study (hypotheses 4 through 12) can be tested with the results of the econometric model. Hypothesis 6 is that the short-run competitive profit maximizing assumption is appropriate for modelling input and output producers choices both in BC and in the PNW, and this hypothesis is accepted. Although statistical tests of this hypothesis could be carried out by testing the properties of the profit function implied by the profit maximization assumption: homogeneity of degree one in prices, symmetry of the hessian and convexity in prices, some of these properties were imposed in the model. But a less rigorous test is still possible by analyzing in an informal way the model performance, the plausibility of the results obtained, and their theoretical consistency with the profit-maximizing hypothesis. The initial model produced the right signs for the own price elasticities of demand and supply in both regions. The hessian was positive semidefinite at the mean of the PNW data, and had one negative, but very small eigenvalue at the 183 mean of the BC data. Elasticity estimates were plausible, and so short-run competitive profit maximization appears to be an appropriate assumption for modelling demands and supplies in sawmilling. On the other hand it is noted that the wrong signs of the own elasticities of lumber supply and sawlog and labour demand were obtained for three observations in BC, and that the 1982 observation in the PNW was inconsistent with profit maximization behaviour. Convexity of the profit function was violated at a larger number of observations in BC (40%) than in the PNW (12%). This appears to indicate that the profit maximizing behaviour did not occur uniformly throughout the period, and that for the historical period utilized for estimation it" is a more appropriate assumption for the PNW industry than for the BC one. An additional theoretical inconsistency of the initial model was that profits decrease with capital and quality for a considerable number of observations in BC (75%, 60%), and decrease with capital for a considerable number of observations in the PNW (44%). However, this was considered to be a statistical problem due to the high multicolinearity between the terms involving fixed factors, and not a consequence of the inadequacy of the profit maximizing hypothesis. The model with across region restrictions on quality and time made profits increase with wood quality in BC for a considerable number of observations, while for the homogeneous (M3) and no technical progress (M4) models profits increase with capital at a large number of data points. Hypothesis 4, that wood quality is an important variable in lumber industry modelling, is accepted. The statistical null hypothesis, that wood quality did not belong in any of the regional models, was rejected. In the BC model, the omission of wood quality affected in a definite way the elasticities of pulpchip supply, producing the wrong sign for the own price elasticity at a considerable number of observations, and at the mean of the data, and also led to more 184 violations of the expected signs of the other relationships. In the PNW, the omission of wood quality led to the violation of the expected sign for the elasticity of labour demand at three observations as opposed to zero in the initial model. It is, therefore, considered that wood quality belongs in the model and that it is a particularly important variable for modelling residue supply. Although the other elasticities were affected by the omission of wood quality, the variations did not appear to be too large given the instability of the estimates. These results are of course contingent on the assumed empirical model and data base utilized. The consequences of ommiting wood quality on estimates of technical progress were evaluated in Chapter 4 but it is important to retest hypothesis 5 with the results of the econometric model. This hypothesis states that wood quality changes have a significant impact on measures of technical progress in the sawmilling industry. The rates of technical progress at the mean of the data for the initial specification and for .the model omitting wood quality are compared in Table 6.18. Inclusion of wood quality in the model results in higher technical progress estimates in both regions. In the PNW, where wood quality declined considerably, the rate of technical progess increased three times when wood quality was taken into account. The same conclusion holds when rates of technical progress are compared at each data point. In BC, the rate of technical progress increases slightly, in spJte of quality having increased a little during the historical period (0.01% per year) and this result contradicts the results for the residual measure of technical progress developed in Chapter 4. Given the results for the PNW, it is decided to accept hypothesis 5. Hypothesis 7, that the rate of technical progress is higher in the PNW, is rejected. The rate of technical progress was found to be higher in BC, and this contradicts the results of Chapter 4. However, the estimated rates of technical Table 6.18; Comparison of Technical Progress Estimates of the Models With and Without Wood Quality™ RATE OF TECHNICAL PROGRESS MODEL BC PNW With Wood Quality - Initial Model Without Wood Quality - Ml 0.062%/Year 0.057%/Year 0.057%/Year 0.018%/Year (1) Rates of technical progress were computed at the mean of the data. 186 progress are fairly close, and given the statistical nature of the model, and random nature of the technical progress estimates, this appears to indicate that neiter of the regions dominate in terms of efficiency performance over time. Hypothesis 8, that technical progress showed a wood using labour saving bias in BC, and a labour using wood saving bias in the PNW, is also rejected. In both regions, the bias of technical progress with respect to the input mix is wood using and labour saving. However, given the model utilized in which capital is a fixed factor, the multicolinearity problems between capital and the time trend and the measurement errors in the capital stock, the separation of the effects of capital and technical progress in the technology is arbitrary, and this result does not inspire much confidence. Hypothesis 9, that a decline in wood quality leads to an increase in the amount of wood utilized per unit of labour, is also rejected. In both regions, a decline in wood quality will move the industry to a more labour intensive region of the input space. A reasonable explanation for this fact is that for a fixed technology, lower quality wood requires considerably more handling per unit of volume than higher quality wood. The long-run relationship, i.e., after capital is allowed to readjust to its optimum level, between the wood/labour ratio and wood quality, is likely to be of different sign, because low wood quality technology which increases lineal throughputs can then be introduced. It is interesting to use the decomposed elasticities to observe that the reason behind this latter phenomenon is different in the two regions. In BC, a decline in quality decreases the proportion of wood in the input through the substitution effect, the lumber output effect reinforces this relationship and the pulpchip output effect is negligible. In the PNW, a decline in quality increases the proportion of wood in input through the substitution effect, but lumber and 187 pulpchip output effects work in the opposite direction, more than compensating the substitution effect. Hypothesis 10, that in both regions the pulpchip to lumber ratio will respond positively to increases in the pulpchip to lumber relative price, is accepted. The assumptions usually made in sawmilling econometric models that pulpchips and lumber are produced in fixed proportions or that pulpchips are a residue without market value that does not respond to market conditions, are,therefore,not very appropriate. Hypothesis 11, thar the proportion of pulpchips in output responds positively to a decline in wood quality, is also accepted. This result held in both regions and it is consistent with what could be expected from the engineering characteristics of the industry. Hypothesis 12, that there are few substitution possibilities between wood and labour, and that output effects are comparatively very large, is also accepted. The constant output elasticities of labour demand with respect to changes in wood price were very small, while the variable output elasticities were very large. Thus, industry responses to changes in market conditions are characterized by small substitution effects and very large output effects. This conclusion is important for practical modelling purposes, because it makes more defensible the assumption that in the short-run sawmilling inputs vary in fixed proportions. 7. EXTENSIONS OF THE RESEARCH 188 7.1 INTRODUCTION The objective of this Chapter is to briefly show how the results of the econometric model might be used to analyze some important policy and other issues relevant to BC lumber producers and to suggest areas for further research. Due to the instability of elasticity estimates in the BC model and the wrong signs obtained for some of the relationship's involving fixed factors, the following analysis is crude and should be viewed as a first attempt to provide evidence of industry responses to market and policy shocks. The main purpose of this analysis is to demonstrate the usefulness of the results- of econometric models, such as the one derived in this research, to the study of industry problems. In Section 2, the model results are utilized to look for explanations for the BC's currently increasing lumber production relative to the PNW. In Section 3, explanations are advanced for the superior lumber recovery performance of the PNW industry noted in Chapter 2. In Section 4, the impacts of changing wood quality on log utilization patterns, returns to capital and unit production costs, are evaluated through some simple simulations. Following this, the importance of declining wood quality as one dimension of wood scarcity is assessed through the historical trend in the marginal profitability of wood quality for a subset of the PNW data. In Section 5, the contribution of the model to the analysis of the economic impacts of log export restrictions in BC is described. In Section 6, the modelling of the impacts of a tariff on Canadian lumber exports to the US is discussed. In Section 7 the potential contribution of the modelling approach utilized in this research to the problem of measuring the size of the BC economic timber inventory is assessed. Finally, in Section 8, some areas for further research are mentioned. 189 72 DETERMINANTS OF TRENDS IN RELATIVE REGIONAL LUMBER OUTPUTS The question posed in this Section is, what are the causes underlying BC's increasing share of total lumber output compared to the PNW. The lumber supply equation specified in Chapter 5 was: (72.1) M . MtPM,PC.PL.PUJ.K,CLt) where M is lumber supply, P the lumber price index, P the pulpchip average L W price, P the quality adjusted sawlog price, P the wage index, K the capital stock, Q the index of sawlog quality and t is time. Differentiating the above equation with respect to time, dividing by lumber output and multiplying and dividing each of the terms on the right hand side by the level of the independent variables, yields: C7-2-3) (*M/*t]-(1/M] - E(*M/<5P,).(Pi/M).(c!P(/r5tHl/Pl) • • Z(«5M/«HJ]4xJ/M).(r5><-i/5t].(l/HJ] • • (»M/<5tHl/M) where p',i=M,CL,W are prices and XJj=K,Q are quantities. Denoting growth rates with a dot over a variable, noting that for example, (3M/9Pj)(Pj/M) is the elasticity of lumber supply with respect to price i, and using the fact that supplies are homogeneous of degree zero in prices to normalize by lumber price, yields: (7-2-4) M - e M C.(P c-^) • e^pL-f^ 1) • eMur|Pu4>M) • *eMK-K+eMQ'Q+bMt By substracting the PNW growth rate in lumber supply from the BC growth rate in lumber supply, one obtains a measure of the growth rate of the BC/PNW relative production and its decomposition into several sources: price effects and 190 capital, wood quality and technical progress effects, plus a residual which measures the change in relative supplies not predicted by the model. In a different context, this type of analysis has also been used by Kako (1980), Berndt and Watkins (1981) and Abt (1984). The above decomposition can be used to test the hypothesis that BC has been capturing part of the PNW market share, due to its superior technological performance (i.e., the combined effects of capital, quality and technical progress), and not because of changes in relative prices. It was noted in Chapter 2 that wood costs increased in the PNW relatively to BC but that the relative wage rate declined. The results are shown in Table 7.1. The elasticities from the homogeneous model (M3) were utilized (Table A.2.11, Appendix II). This is because growth in the capital stock was important during the period, but the elasticities of lumber supply with respect to capital in the other BC models were unreliable and often had the wrong signs. The quality elasticities in this model had the wrong sign, but this is not critical because quality changed little compared with other variables. Given the difficulties in separating the effects of capital, quality and time, these should be analyzed together. The observed growth rate of relative regional production was 1.4%, while the model predicts a growth rate of 3.4%. The single most important contributor was the effect of increases in the normalized sawlog price. Not only did the sawlog price increase at a faster rate and the lumber price at a slower rate in the PNW, but also lumber supply is more responsive to changes in sawlog price in this region. The increase in the nomalized wage rate put the BC industry at a disadvantage but this was not sufficient to offset the gains due to the relative wood prices. The faster decline in the normalized pulpchip price in BC also Table 7.1: Determinants of Trends in Relative Regional Lumber Outputs. Effect Definition BC PNW BC/PNW Observed - . : . M -Pulchip price e M r (P C - P M ) *l *iVI Sawlog price e M [_ (P L - PIVI) Wage > w ( P W - P M ) Technological e M | <K + e M Q Q + b M J Total Residual R 2.0 0.6 1.4 -0.3 -0.0 -0.3 -0.5 -3.0 2.5 -0.4 -0.1 -0.3 3.9 2.4 1.5 2.7 -0.7 3.4 -0.7 1.3 -2.0 192 decreased relative production in this region, but very slightly. This is because lumber is more responsive to pulpchip price changes in BC than in the PNW. The second most important contribution came from the technological variables (1.5%), mostly due to to increases in capital stock, which reflect the relatively increasing capacity in BC. The time and quality effects are negligible and the latter has the wrong sign. The above results confirm the hypothesis that the losses in the PNW market share relative to BC were mainly due to the greater scarcity of wood in that region. It is noted that growth in the PNW prices can be further decomposed into growth in the Canadian/US exchange rate plus the growth in the price in US dollars. Given that BC supplies mostly in the US market, the growth rate in exchange rate would make the PNW wood and labour inputs more expensive relative to the BC ones (and the pulpchip output more valuable). The exchange rate contribution to the sawlog price effect of 2.5% per year on growth of the BC relative production was approximately 0.5%. The exchange rate contribution to the total BC gain of 3.4% was slightly less than one sixth (0.6%). 7.3 DETERMINANTS OF TRENDS IN RELATIVE REGIONAL LUMBER RECOVERIES AND CHIP/LUMBER PROPORTION In Chapter 2, it was observed that lumber recoveries had increased considerably in the PNW, while they remained constant in BC. It is interesting to use an analysis similar to the previous one to look for explanations for this fact. The objective is to test whether the recovery gains in the PNW were brought about by exogenous technological factors or by price induced substitution and output effects. 193 The results are reported in Table 7.2. BC lost in lumber recovery relative to the PNW at an average rate of 0.9% per year, although the model predicts a loss of 0.6% per year. The increase in normalized sawlog price in the PNW was the single most important contributor to the recovery gains in this region. The substitution of labour for wood contributed about one fourth (0.4% per year) to the total effect of wood price increases (1.5% per year). In the PNW, the other prices did not affect lumber recoveries. In BC, all the price effects worked in the same direction to increase lumber recoveries. There was some substitution of wood for labour due to the increase in the normalized wage, but this was more than offset by the output effects, maTnly because the induced decline in labour input led to a considerable decline in pulpchip production. The technological effects were less important than the price effects. The growth in the capital stock contributed to recovery losses by approximately the same amount in both regions, possibly due to the introduction of equipment which increases lineal throughput. Wood quality did not affect lumber recoveries in BC because quality changed very little, but it led to a decline in lumber recovery in the PNW. In summary, the price effects, of which the main one was due to the rising wood prices in the PNW, led to a recovery gain of this region relative to BC of 0.9% per year, of which 0.5% per year was due to substitution effects. The technological effects worked in the opposite direction, leading to a relative recovery loss of 0.3% in. the PNW (02% due to the quality decline), for a total net gain of 0.6% per year. It is also of interest to look at the causes behind the increasing proportion of pulpchips in the output mix in both regions. Detailed results are not shown in order not to overextend this thesis. In BC, both the growth in capital stock and technical progress increased the chip/lumber ratio, while all the other variables worked in the opposite direction. There was considerable substitution of Table 7.2: Determinants of Trends in Relatvie Regional Lumber Recoveries. Effect Definition BC Total Substitution (1) PNW Total Substitution BC/PNW Total Substitution Observed Pulchip price Sawlog price Wage M/L o.o 0.3 0.2 0.1 0.0 0.0 -0.2 0.9 0.0 1.5 0.0 0.0 0.4 -0.1 -0.9 0.3 -1.3 0.1 0.0 -0.4 -0.1 Price Effects 0.6 -0.2 1.5 0.3 -0.9 -0.5 Capital Quality Time eM/L,K K  eM/L,Q ° bM/L,t -0.4 0.0 0.0 -0.5 -0.2 0.0 0.1 0.2 Techological effects -0.4 -0.7 0.3 TOTAL Residual 0.2 -0.2 0.8 -0.1 -0.6 -0.3 (1) The substitution effects were calculated using the constant output demand and constant input supply elasticities of Tables 6.14 and 6.15; for example, the substitution effect due to the change in the pulpchip normalized price is ft., (P - P ) where rv is the constant input • C ' *• • M ' » elasticity of lumber supply with respect to pulpchip price, P is the growth rate in the pulpchip price and P is the growth rate in the lumber price. 195 lumber for pulpchips because the lumber price rose at a faster rate than the pulpchip price, but the capital stock effect dominated all the other ones. In the PNW, the increases in the chip/lumber ratio were due to the growth in the sawlog normalized price, capital stock, decline in wood quality and technical progress. The effects due to the decline in wood quality were the most important. Similarly to BC, lumber was substituted for pulpchips, but this effect was dominated by the other ones. The proportion of pulpchips in output grew at a faster rate in the PNW than in BC, and the results suggest that this was mostly due to the considerable wood quality decline in the PNW. 7.4 IMPACTS OF QUALITY CHANGE ON UNIT PRODUCTION COSTS, RETURNS TO SCALE AND LOG UTILIZATION PATTERNS In this Section the importance of wood quality change in sawmilling is further assessed through some simple simulations of its impacts on production costs, returns to capital and log utilization patterns during the sample period. Historical unit production costs were simulated by keeping all the exogenous variables in the econometric model (lumber, pulpchips, wage and sawlog prices, capital stock and time trend) at their 1957 levels, but allowing wood quality to change following its historical trend. Unit costs are defined as total costs per unit of lumber output, and the pulpchip output was ignored. This is the definition of unit costs usually utilized by the industry. Unit costs change due to the adjustments in lumber output, sawlog consumption and employment brought about by the changes in wood quality. The simulation results are shown in Figure 7.1 for both regions. In BC, unit production costs varied very little because quality change was almost negligible. In the PNW, unit production costs were more noticeably affected showing an increasing trend until 1971, while quality declined considerably, and then remaining 196 FIGURE 7.1 Impacts of Wood Quality on Unit Lumber Production Costs 70 T — ~ E 65H a> C L V) 3. 60-o Q c o T> O c o O 55-BC PNW 50-1955 1960 1965 1970 1975 1980 1985 FIGURE 7.2 Impacts of Wood Quality on Returns to Capital 30 -i 197 more or less constant, on average, when quality increased slightly. Historical returns to capital were simulated in an identical way, but in this case pulpchips were included in the profit calculation. The simulation results are shown in Figure 72 for both regions. As with unit production costs, returns to capital varied considerably more in the PNW than in BC due to the sharper quality changes. Returns to capital changed due to the adjustments in lumber and pulpchip outputs, sawlog consumption and employment brought about by the changes in wood quality. In the PNW, the wood quality decline led to a decrease in returns to capital from 25% in 1957 to 7% in 1971. Of course, the absolute magnitudes are meaningless, due to the effects of scaling in the data, and only the changes should be considered. The end uses of a sawlog can be grouped into three main categories; lumber, chips and residues. It is of interest to analyze if changes in wood quality had a major impact on log utilization patterns, and in particular if the quality declines led to increased production of the valueless residues, such as sawdust. The simulation procedure was identical to the above ones. In this case, crude conversion factors were utilized to convert lumber and pulpchip quantities to roundwood equivalents, so that proportions might be computed. Because of this, only trends are important and the magnitude of the proportions meaningless. The trends in log utilization patterns, if all the variables were held at their 1957 levels and only the lumber and pulpchip outputs and the sawlog consumption and employment were allowed to vary due to the historical change in quality, are shown in Figures 7.3 and 7.4. In BC, wood quality changed very little, and so log utilization patterns were not affected by this variable. In the PNW, on the other hand, the decline in wood quality led to a decrease in the proportion of the log going to lumber and to an increase in the proportion of FIGURE 7 . 3 Impacts of Wood Quality on Log Utilization Patterns British Columbia 198 100 a) a> o ~c o <D 1955 1960 1965 1970 1975 1980 1985 FIGURE 7 . 4 Impacts of Wood Quality on Log Utilization Patterns Pacific Northwest 100 a> _o "c a> o i-a> 1955 1960 1965 1970 1975 1980 1985 199 the log going to pulpchips. The increase in the pulpchip proportion more than compensated, in volume terms, for the decline in lumber proportion, so the proportion of nonmarketable residues actually declined. The above results indicate that in the PNW, wood quality declines clearly affected the output mix of the industry, as well as its cost efficiency and profitability. However, because relative prices changed considerably, the capital stock increased and there was technical progress, these results do not show how well the industry has been coping with this dimension of wood scarcity. All of the above factors could have worked .lo mitigate the effects of declining wood quality. In Figure 7.5, an index of the marginal profitability of wood quality, as predicted by the PNW initial model for a subset of the data, is plotted. The marginal profitability of wood quality measures the increase in profits if quality is increased infinitesimally. It measures the worth of one marginal unit of quality to the industry, i.e., its shadow price. It was computed using equation (5221) of Chapter 5. Only the period 1957 through 1974 was utilized for this analysis because during this period quality declined drastically in the PNW, but after 1975 it showed an erratic behaviour and the marginal profitability often had the wrong sign. An equivalent analysis is not shown for BC because quality changed very little and profits were decreasing in quality at a considerable number of observations. The marginal profitabilty of wood quality shown in Figure 7.5 was rebased to 1957 = 100.0. The clear increasing trend indicates that during the period, the industry was not coping very satisfactorily with this dimension of wood scarcity. The value of a marginal unit of quality to the industry increased considerably from 1957 through 1974, and at a faster rate than the prices of any of the other FIGURE 7.5 Trends in the Marginal Profitability of Wood Quality in the Pacific Northwest During the Period 1957-1974 Logarithmic Scale 200 1000 o d o m CD V in O CO 100-70-1955 1960 1965 1970 1975 FIGURE 7.6 Simulation of PNW Production Costs Under BC Economic Conditions 1.6-201 factors of production or outputs. Although not too much weight can be given to this result due to the problems in the econometric model mentioned above, it is preliminary evidence that wood quality is an input of increasing value to sawmilling. It lends support to the forest policy of allocating investment funds to intensive management practices such as pruning, which increase wood quality, as opposed to the policy of concentrating investment only in volume production. It is also pertinent to ask what are the main causes behind the increase in the marginal profitability of wood quality verified during the period. An analysis identical to the ones carried out for .lumber supply and lumber recovery could provide answers to this question, through the decomposition of its growth rate into several sources. Because some of the elasticities of the marginal profitability of wood quality with respect to changes in the exogenous variables did not inspire much confidence, such decomposition was not attempted. A final and crude evaluation of the importance of wood quality for the relative performance of the two regions is given in Figure 7.6. The PNW industry was compared with the BC industry during the historical period under two scenarios: (1) BC prices, capital stock and BC wood quality; and, (2) BC prices, capital stock, and PNW wood quality. When the PNW industry was utilizing the BC wood quality, the two regions performed identically in terms of unit production costs. BC was the most efficient of the two regions until 1978, year in which it lost its efficiency advantage. In Chapter 4 the turning point was estimated to have occurred in 1981. However, if the PNW industry were operating with the PNW quality, its unit production costs would be substantially lower. This again confirms the results of Chapter 4 and suggests that wood quality is an important determinant of cost competitiveness. 202 7.5 LOG EXPORT RESTRICTIONS In BC, there are log export restrictions in effect that make the domestic log price lower than the international price. The welfare implications of these restrictions have been discussed by various authors (e.g. Pearse, 1976; Davies, 1977), and it is actually a policy issue whether the Province would not be better off if these restrictions were lifted and replaced by export taxes. The BC supply and demand elasticities estimated in the previous Chapter were utilized by Margolick .et al (1985), together with a sawlog supply elasticity estimated by Heaps (1985), a Pacific Rim sawlog demand elasticity and a US West sawlog export supply elasticity estimated by Flora and Vlosky (1984), to build a small equilibrium model of the Pacific Rim sawlog market, and solve for the domestic and international equilibrium prices with alternative values of the export tax. The relationships between sawlog price and lumber supply and labour demand derived in the previous Chapter were used in this model to research the welfare and rent distribution effects of lifting log export restrictions and imposing different export taxes. Important conclusions of the study were that lifting log export restrictions has a large impact on the international price, results in losses to the BC processing sector and in a considerable decline in production and employment, and in gains to the harvesting sector. Gains compensate losses, so that there will be an overall welfare improvement. Furthermore, the log export tax generates considerable government revenues and it is an effective policy tool permitting the control of the rent distribution between the extracting and processing sectors. Although elasticities at means similar to the ones derived in the previous Chapter were utilized, and the sample instability of the BC elasticities make these 203 estimates very unreliable, the conclusions of the study were not sensitive to changes in elasticities. In this case, the instability was not a serious problem. The results of the above study are detailed in Margolick et aj (1985) and Margolick and Uhler (1986). 7.6 TARIFFS ON CANADIAN LUMBER EXPORTS TO THE US Among the several bills concerning international trade actually being discussed in the US Congress, there are several which would impose tariffs on Canadian lumber exports to the US. This movement towards lumber trade restrictions has its origin in the Canada's increasing share of the US market during the past decade. Given the elastic relationship between lumber supply and lumber prices estimated in the previous Chapter, one could expect a tariff on lumber imports entering the US to result in a large decline in BC lumber production, leading to a considerable contraction of the industry. However, because all Canadian producers would be affected, and they supply over 30% of the US market, such a tariff would lead to increases in the US lumber price. The magnitude of these increases would depend on the elasticities of US lumber demand and lumber supply, and can only be evaluated through a market equilibrium analysis which falls outside the range of this research. Assuming such tariff would result in a fall in the BC lumber price and in an increase in the PNW lumber price, it is possible to predict that the industries would move in the following directions: (1) production would decline in BC and increase in the PNW, and given the magnitude of the elasticities, the BC share would decline considerably relative to the PNW one; (2) pulpchip production would 204 also decline in BC and increase in the PNW, this having implications for the pulp and paper industry; (3) the proportion of pulpchips in output would decline in both regions; (4) both sawlog consumption and employment would decrease in BC and increase in the PNW; (6) labour productivity would increase in both regions; (7) the amount of wood utilized per unit of labour would decline in BC and increase in the PNW. 7.7 ONE AREA FOR FURTHER RESEARCH: MEASURING THE SIZE OF THE BC ECONOMIC TIMBER INVENTORY One of the most challenging research areas in forest economics, both in BC and other regions, is the problem of measuring the economic size of the timber inventory. Although forestry has an advantage over other natural resources in that the physical size and growth rate of the inventory is, or can be, known with a certain degree of certainty, not all this inventory can be economically recovered. This is very important information for policy purposes. In many of the forest producing regions of the world, the rate of harvest is regulated, with the objective of not allowing the depletion of -the stock and ensuring in the future a sustained yield. Such a harvest constraint, the Annual Allowable Cut (AAC) is computed in BC as a function of physical growth, the volume of overmature timber, rotation age and assumed utilization standards. However, because of the physical nature of the AAC calculation, two main problems occur; (1) the volume of overmature timber that can be economically recovered may be considerably smaller than the physical volume, and so the harvest will be biased towards the present; (2) the economic (value) growth rate of the stock may be larger or smaller than the physical growth rate. An alternative to current policies would be the planning of current and future 205 harvests by bringing such economic information into the calculations. In order to obtain such planning tool, two types of information are required: (1) an assessment of the current and future costs of recovering the inventory, and (2) an assessment of the current and future value of the inventory, i.e., how much the processing industry is willing to pay for timber. A considerable research effort has been done in the first area in BC (Berndt et a\, 1979; Cooney, 1981; Cooney and Haley, 1982; Williams and Morrison, 1985). The last two authors are developing a classification of the full BC inventory in terms of the unit costs of wood delivered to the mill. However, current and future information on the market price firms are willing to pay for the wood is still required, in order to measure the proportion of the stock that can be economically recovered. A sawlog demand equation, such as the one derived in this research, could be put together with a log supply equation such as the one recently developed by Heaps (1985), providing a system for solving for the equilibrium sawlog price. Such a price would be a function of sawlog demand shifters, like lumber and pulpchip price and wage rate, capital stock and technical progress, and of exogenous supply shifters such as the AAC and other variables relevant to the logging sector. The equilibrium price could be used to compute the economic size of the inventory and generate an equilibrium economic AAC through an iterative procedure. Furthermore, forecasts of the exogenous variables could be used to assess the growth rate of the economic inventory, from which a dynamic AAC could be computed. Such a modelling tool would allow the research of interesting issues such as: (1) what would be the impacts of moving from a physical calculation of the AAC to an economic one on lumber and pulpchip supply and employment in 206 sawmilling? (2) how does technical progress in sawmilling contribute to an increase in the size of the economic inventory? Furthermore, the economic AAC computed in such a way would respond to short-run market conditions, and this response could be used in building more rational limits on the allowed deviations of the harvest in the AAC. In order to make models such as the one developed in this research useful for the above purposes, information on the investment behaviour of lumber producers is still required. This is likely to be a complex problem and it is suggested in the next Section as aru area for further research. A preliminary ad-hoc investment rule could be developed by regressing investment on AAC changes and some additional relevant market information. It was mentioned in Chapter 5 that during the historical period analyzed in this research, increases in the AAC appeared to be a good predictor of investment in sawmilling. 7.8 OTHER AREAS FOR FURTHER RESEARCH A problem with the quality variable utilized in this research is that it is not explicitly linked with wood characteristics. It is an important area of research to develop such links, because information on the characteristics of the inventory is usually available. This could be accomplished by either utilizing wood characteristics variables in the industry model, or by developing an empirical relationship between the quality -index derived in this research and average wood characteristics. Such a study could produce two useful results: (1) forecasts of supplies and demands when the average characteristics of the harvest are changing, and (3) derivation of the shadow value of characteristics and the value of the inventory. It would also be of considerable interest to extend the above characteristics model to the logging sector. Log supply equations could then be specified from a profit maximization model as a function of market conditions, 207 regulations and timber and terrain characteristics such as hauling distances and slopes. In this research, variations in the quality of the lumber output were not adequately accounted for. There is extensive information on prices and characteristics of lumber traded. The estimation of a hedonics price equation with such data would allow the derivation of prices and price trends in the implicit values of characteristics. That information would be useful to the industry. Furthermore, the hedonics price equation could be utilized in deriving a measure of lumber quality, which could then be_ used to research the interactions between lumber and wood quality and other inputs and outputs, utilizing a modelling framework similar to the one in this research. Another important area for research is the modelling of the investment behaviour of sawmilling producers. In addition to price expectations and adjustment costs, such a model should consider BC industry specific variables, such as Annual Allowable Cut and tenure characteristics. It would be a research area of considerable interest for forest policy, and it would also contribute important information for the development of forest sector models. If mill data could be obtained, another interesting research effort would be the testing of the profit maximizing hypothesis at the plant level. The measurement of wood quality -and other variables with a greater degree of accuracy would increase the confidence in the parameters and test results. Such a model would also be suitable for the inclusion of plant-specific technological parameters, for the analysis of the relative efficiencies of specific technologies and degree of returns to scale at the plant level. One interesting observation made while visiting sawmills during the course of this study, was that input substitution appeared to occur at different rates and in different directions in 208 different points in the sawmill. For example, labour saving techniques were sometimes being introduced in the small log line headrig and in the back end of the sawmill, but wood saving innovations were being introduced in the large log line headrig. It would be of interest to model the sawmill as a set of cost minimizing decision points. The model developed from this research could be extended to other Canadian provinces, with the objective of generating a planning tool for the entire Canadian sawmilling sector. However, in other regions, such as the BC Interior, the assumption that firms behave competitively with respect to the sawlog input may not be as appropriate as on the BC Coast, because log trading is negligible. It would be of interest to formally test such hypothesis. 8. SUMMARY AND CONCLUSIONS 209 In this Chapter, the methods and results of the research are summarized. The results of the tests of the main research hypotheses are summarized in Table 8.1. The main goal of this research was to develop a modelling methodology for the analysis of the impacts of sawlog scarcity revealed in the rising wood prices and declining wood quality, on the sawmilling industries of the BC Coast and in one of its most important competitors, the Pacific Northwest. The existing literature dealt with this problem by providing measures of the substitution possibilities between wood and other inputs and of the rates of technical progress. High substitution and technical progress could mitigate the impacts of wood scarcity. However, some important information was still missing from the literature. First, no study had yet analyzed the quality dimension of wood scarcity, and tested whether wood quality has been declining. Second, most studies found technical recess in sawmilling or showed that the industry ranked close to last with respect to this measure of efficiency when compared with other sectors of the economy, but did not advance explanations for this fact. A plausible explanation could be the declining quality of wood which would bias downwards the measures of technical progress. Third, no study had yet analyzed the relationships between wood quality and other inputs and outputs in sawmilling, nor provided predictions of industry responses to wood quality changes. Fourth, no study had yet analyzed sawmilling as a multi-output industry by including pulpchips as an output. Fifth, most studies concentrated on long-run relationships and assumed the capital stock could be instantaneously adjusted to its optimum Table 8.1: Summary of Tests of Main Research Hypotheses. HYPOTHESIS DESCRIPTION RESULT 7 8 9 10 1 1 12 Wood quality has declined both in BC and in the PNW. Wood quality has declined at a faster rate in BC than in the PNW. Wood quality is higher on average in the PNW than in BC. , Wood quality is an important variable in lumber industry modelling. Wood quality changes have a significant impact on measures of technical progress in the sawmilling industry. Short-run, competitive profit maximization is an appropriate assumption for modelling input and output choices of sawmilling producers. The PNW industry exhibits a higher rate of technical progress than the BC industry. Technical progress has been wood using, labour saving in BC and wood saving, labour using in the PNW. In the short-run, a decline in wood quality will increase the ammount of wood utilized per unit of labour. The proportion of pulpchips in output responds positively to an increase in the pulpchip/lumber relative price. The proportion of pulpchips in output increases with a decline in wood quality. Input demands are characterized by large expansion effects and small substitution effects. 0) (2) Accept Reject Accept Accept Accept Accept Inconclusive Reject ( 3 ) Reject Accept Accept Accept (1) During the last decade, quality increased on average in both regions. (2) Wood quality only is clearly important for modelling pulpchip supply and technical progress. (3) Due to the statistical problems mentioned in Chapter 6 this result is weak. 211 level. In addition to this assumption being questionable, information on the total short-run responses of the industry was missing in the literature. Sixth, some studies provided measures of substitution, returns to scale and homotheticity, but did not produce measures of output responses to wood scarcity which are important for policy analysis. This thesis attempted to extend the information currently available in the literature through the investigation of the above issues. Three major research objectives were: (1) to test whether wood "quality has declined over time in BC and in the PNW; (2) to test whether the omission of wood quality from the regional industry models resulted in significantly different estimates of technical progress; and (3) to characterize sawmilling producers as short-run competitive profit maximizers producing two outputs: lumber and pulpchips, model the industry responses to wood quality changes, and provide measures of the total short-run effects as well as input and output substitution effects due to changes in relative prices and fixed factors. In Chapter 2, the regional lumber industries were briefly described and compared. It was noted that both lumber and chip recoveries had been increasing in the PNW relative to BC, so that the PNW industry was saving on the wood input at a faster rate than the BC one. The average lumber recovery level was also considerably higher in the PNW than in BC. The BC industry outperformed the PNW industry in terms of the growth rate of labour productivity. The BC industry increased its wood input per unit of labour while the reverse occurred in the PNW. Because the wage rate increased relative to the wood price in BC, but declined in the PNW, the industries appeared to be behaving according to the theory, by becoming more wood intensive in BC, and more labour intensive in the PNW. An analysis of trends in innovations suggested that the BC industry favoured labour saving innovations while in the PNW the demand for innovations 212 which save on wood input was stronger. In Chapter 3, the problem of measuring wood quality change was addressed. It was suggested that declining quality over time is consistent with the predictions of standard deterministic models of resource depletion, although short-run quality fluctuations could also be expected. The two main approaches for deriving quality indices described in the literature, the hedonics and the index number approaches, were briefly described. Given the data available, the index number approach was chosen, implying the assumption that the regional industries are behaving competitively in the choice of the sawlog grade mix. Quality was defined as the ratio of an aggregate measure of the wood input to the wood volume. Quality change was decomposed into two effects: a species effect and a grade effect. The species effect measures the change in the species composition while the grade effect is an aggregate of the changes in the grade mixes of the various species. It was shown that the wood quality measure depended on the units of measurement of the wood volume, i.e., board feet or cubic meters. The quality index was applied to data on the volumes and prices of the several wood grades harvested in the Vancouver Forest Region from 1925 through 1980, traded in the Vancouver Log Market from 1925 through 1982 and traded in six log markets in the Pacific Northwest from 1957 through 1982. It was established that wood quality shows a declining trend overtime in the several time series. In BC, both the deterioration of the species and grade mixes contributed to the quality decline, while in the PNW, all the decline arose from the deterioration of the grade mix. From 1957 through 1982, quality changed very little on average in BC, and during the last decade, it showed an increasing trend in both regions. From 1957 through 1982, quality declined at a considerably faster rate in the PNW than in BC. It was hypothesized that the different patterns of quality change in the two regions could result from the old-growth- first cut 213 constraint in BC, which results in cutting at the extensive margin, as opposed to the increasing cut of second growth timber in the PNW. When average quality levels were compared in both regions, it was found that wood quality was considerably higher in the PNW, although the quality gap is diminishing. The regional quality indices were utilized to convert wood prices to a constant quality level, the results indicating that higher quality more than explained the higher wood prices in the PNW. After such adjustment, the BC industry showed a wood price disadvantage for most observations. This result gave support to the argument advanced by BC lumber producers, in the context of the issue of tariffs on Canadian lumber imports to the US, that wood price differences between the two regions resulted mostly from quality differences. In Chapter 4, a measure of technical progress popular in the literature was presented. Technical progress, or growth in total factor productivity, was defined as the sum of the growth rates of the lumber and pulpchip outputs weighted by their respective revenue shares, minus the sum of the growth rates of the wood volume, labour input and capital ' stock weighted by their respective cost shares, minus the growth rate in wood quality weighted by the wood cost share. The same framework was utilized to measure regional differences in average efficiency levels. Due to its residual nature, such a measure incorporates the effects of omitted variables such as wood quality, both in intertemporal and interregional technical efficiency comparisons. The quality corrected average rate of technical progress for the period 1957-1982 in BC was slightly lower than the uncorrected one because wood quality increased a little during the period. The quality corrected average rate of technical progress for the period 1957-1982 in the PNW was higher than the uncorrected one because quality declined during the period. The PNW outperformed 214 the BC industry in terms of technical progress, and the poor performance of the BC industry would be considerably underestimated if wood quality variations in both regions were not accounted for. The PNW industry exhibited a higher efficiency level, on average, if wood quality was not accounted for, but the higher efficiency could be completely explained away by the higher wood quality level in the PNW. Accounting for wood quality differences changed the ranking of the regions and caused BC to become the more efficient of the two. However, the efficiency advantage of the BC industry has been deteriorating and, according to average growth rates, was lost in 1981. In Chapter 5, a theoretical short-run, competitive, profit maximizing model of sawmilling was introduced. Producers were assumed to maximize short-run profits by optimally adjusting lumber and pulpchip outputs and wood and labour inputs in response to changes in exogenous input and output prices, but were constrained by the capital stock, wood quality and "state of knowledge" as measured through a time trend. A restricted profit function was specified accordingly. The main innovative feature of the model was in the way the wood quality variable was incorporated. The approach was a generalization of existing models because wood input and wood quality were allowed to interact independently with other inputs and outputs and the wood quality variable was not assumed separable in the model. The rationale for the several behavioural assumptions made was discussed. A translog functional form was utilized in the empirical model, and so the second order relationships between the variables were not constrained. Homogeneity of degree one in prices and symmetry of the hessian were maintained hypotheses, while the other properties of the profit function were 215 checked. Several statistical tests were formulated and comparative statics carried out for the translog case. In particular, the short-run elasticities were decomposed into substitution and input or output effects. Several of the relationships were signed a priori in accordance with the theory and what could be expected from the engineering characteristics of the industry. The empirical model was estimated as a system of seemingly unrelated equations, including the profit function and share equations, and allowing for contemporaneous correlation between residuals across equations and regions. The 1957-1981 sample period for BC and the PNW was utilized for estimation. The statistical performances of both regional models were satisfactory. The profit functions were increasing in output prices and decreasing in input prices at every data point. The PNW model was convex in prices at the mean of the data and at a considerable number of observations. The hessian of the BC model had one negative eigenvalue at the mean of the data, but given that its magnitude was very small and its sign was unstable, it probably was not statistically different from zero. Both models were decreasing in capital and the BC model decreasing in quality at a considerable number of observations, these being the main theoretical inconsistencies of the models. However, it was considered that the results were due to high colinearity between fixed factors and small variations of the quality variable in the BC sample, and not from the inadequacy of the theoretical model. The PNW model reproduced all the expected signs for elasticities which were implied by the theory and the engineering characteristics of the industry. In the BC model, lumber recovery did not respond positively to increases in wood quality, but all the other relationships produced the expected signs at the mean of the data. In BC^ in three observations out of twenty-five, lumber supply 216 sloped down and sawlog and labour demands sloped up. The overall assessment was that in spite of these problems, the models were useful and could be utilized for the testing of most the research hypotheses. Statistical tests showed that wood quality belonged in both regional models and that it was not sufficient to include it through a simple quality adjustment of the price or volume of the wood input. This result held for both regions. Constant returns to scale were rejected in BC but were accepted at the 99% level of confidence in the PNW. Profits were' convex in capital in BC suggesting increasing returns to scale. The hypothesis of no technical progress was rejected in both regions. The hypothesis that the regional profit functions were equal in both regions was rejected, but the hypothesis that some of the coefficients on fixed factors were equal across regions could not be rejected. Four more restricted models were specified in order to test some of the research hypotheses and remove some of the theoretical inconsistencies of the initial models. The omission of wood quality resulted in substantially lower estimates of the rate of technical progress in the PNW, and led to the wrong sign for the own elasticity of pulpchip supply in BC for a considerable number of observations. The model with wood quality outperformed the model without wood quality in terms of theoretical consistency, and given the results of the statistical tests it was considered that wood quality was an important variable in lumber industry modelling. The imposition of across region restrictions on wood quality and time parameters improved the performance of the BC model with respect to the quality variable and, in particular, lumber recoveries were increasing in quality. However, the models were still decreasing in capital. A constant returns to scale model and a no technical progress model were estimated, producing the right sign of 217 the derivative of the profit function with respect to capital, but in both of these models, the wood quality variable performed poorly. All supplies and demands increased with increases in the prices of outputs, and all supplies and demands decreased with increases in the prices of inputs. Lumber supply and sawlog demand were elastic in both regions, while pulpchip supply was elastic in BC. An increase in wood quality increased lumber supply and sawlog and labour demand and decreased pulpchip supply in both regions. An increase in wood prices increased lumber recovery and decreased the amount of wood utilized per unit of labour. An increase in wood quality increased the proportion of lumber in output and the proportion of wood in input. Constant output demand elasticities and constant input supply elasticities were computed utilizing the relationships between the hessians of the more restricted and less restricted maximization problems. The constant output demand elasticities were low and conformed to the results available in the literature. Output effects were very large, indicating that an increase in wood prices would contract considerably the industry and result in negligible short-run substitution effects. A decline in wood quality would move the BC industry to a more wood intensive region and the PNW one to a more labour intensive region of the input space. Increases in lumber output would make both industries more wood intensive. In the PNW, sawlogs were an inferior good with respect to the pulpchip output. Increases in capital resulted in savings of wood input in BC and of labour input in the PNW, while technical progress has been wood saving in both regions. The constant input supply elasticities showed that the proportion of pulpchips in output is responsive to changes in relative output prices in both regions. An increase in wood quality would move the industry to a more lumber 218 intensive region of the output space. Both capital and technical progress increase the proportion of pulpchips in output in both regions. The estimated rates of technical progress were very close in the two regions and positive. The saving on the labour input due to technical progress occurred at a faster rate in BC than in the PNW. Estimated elasticities were found to be very unstable across the BC sample for all alternative model specifications, but instability was not serious in the PNW. The own and cross price elasticities of lumber supply and sawlog and labour demands were robust across model specification but the elasticities of pulpchip supply and those involving fixed factors were not. The sample instability of elasticities in BC and the violation of monotonicity conditions involving fixed factors, limited the usefulness of the models for policy analysis, but they could still be used to test the research hypotheses. The results of these tests are summarized in Table 8.1. In Chapter 7, the results of the econometric model were utilized for the analysis of some issues pertinent to BC lumber producers. Growth in regional lumber supplies was decomposed into several effects, and it was shown that the PNW has been loosing in its market share relative to BC, mostly due to more rapidly increasing wood prices reflecting higher wood scarcity. The greater rate of increase in wood prices in the PNW also explained that region's superior historical performance in terms of lumber recovery relative to BC. The faster decline in wood quality in the PNW was not sufficient to offset this effect. Simple simulations of the impacts of historical changes in wood quality showed that in the PNW, this variable clearly affected unit production costs and returns to capital as well as log utilization patterns, leading to a decline in the proportion of the log going to lumber and to valueless residues, and an increase 219 in the proportion going to pulpchips. Historical wood quality changes did not have important impacts on the BC industry. For the period in which wood quality declined considerably on average in the PNW (1957-1974), the marginal profitability of wood quality increased at a faster rate than the prices of any other inputs and outputs, indicating that the industry was not coping satisfactorily with this dimension of wood scarcity, and that it is an important one. The potential usefulness of the econometric model for analyzing the impacts of log export restrictions and of a tariff on Canadian lumber imports to the US was discussed, as well as its potential contribution to the problem of measuring the size of the BC economic timber inventory. Areas for further research were also suggested. Four important ones were the utilization of log characteristics variables in the industry models, the modelling of lumber quality, the modelling of the logging industry utilizing quality variables, and the investigation of the investment behaviour of lumber producers in BC. 220 BIBLIOGRAPHY Abt, R. 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The PNW data were not available in the form and regional and industrial disaggregation level required. A considerable amount of work had to be done in order to build the final series from the raw data, and the several procedures utilized may have introduced errors. Thus the PNW data set appears to be of inferior quality than the BC one. In Section 4 the capital stock and user cost data are described for both regions. In Section 5 a critique of the data is presented. In Section 6 the data for the main variables including those of the econometric model, are listed. 2. BRITISH COLUMBIA COAST 2.1 LUMBER AND SHINGLES PRICE INDEX (Table A.1.1) The lumber and shingles price index is a Tornqvist price index (Diewert, 1976) in which the price components are the average implicit prices of lumber of Douglas-fir, hemlock, red cedar, spruce, other species and shingles. The lumber and shingle price index was rebased so that 1971 would equal the average lumber price in that year. These prices were obtained from Statistics Canada, catalogue 35-204 (Statistics Canada, 1957-1982). The price of Douglas-fir is the value of 239 shipments of Douglas-fir lumber divided by the volume of shipments of Douglas-fir lumber in Mfbm. An identical procedure was used for hemlock, red cedar and spruce. For 1957-1960 value and volume of production were used, instead of shipments. The 1964 and 1982 data for spruce were missing. The 1964 observation was estimated by subtracting BC Interior figures from BC total. The 1982 observation was estimated by applying the 1981 Coast and Interior volume shares in total BC to the 1982 data for total BC. Other species data were computed by subtracting Douglas-fir, hemlock, red cedar and spruce from total hardwoods and- softwoods for the BC Coast. The 1975 and 1976 data for total hardwoods and softwoods" "were missing. Figures for total softwoods were used for these years. Other species include white pine, yellow cypress, balsam fir, other softwoods and hardwoods. Because balsam fir and hemlock are marketed together, it is likely that hemlock includes a considerable component of balsam fir. The shingles price was obtained by dividing value of shipments of shingles without further processing by their respective volume. The Tornqvist price index utilizes revenue shares as weights. Lumber revenues with the several species are the values of shipments (or production for 1957-1960) discussed above. Shingle revenue is the value of shipments of goods of own manufacture in the shingle mill industry. For 1957 through 1960 shingle mills were together with sawmills. Ratios of total value of shipments to value of shipments of shingles without further processing were computed for 1961-1963. The average of these ratios (1.7676) was applied to the 1957-1960 value of shingle shipments without further processing to estimate total value of shipments by shingle mills. Shingle revenue includes revenues with shingles, shakes and any by-products produced by the shingle industry. These revenues were used in constructing the weights for the Tornqvist price index. Because shingle mill data is not disaggregated by BC Coast and Interior, it was assumed that all shingle 240 mills were operating on the Coast. This is not exact, but it probably is a good enough approximation. It should be mentioned that more disaggregated data was available for BC, but because this was not the case for the PNW, it was chosen to use an identical definition for the price index in both regions. From 1957 through 1961, the sawmill data excluded planing mills, while after 1962 these were included. This discontinuity in the data base was ignored. This is not a very serious problem, since it also affects the other variables. 22 LUMBER AND SHINGLE" REVENUE AND IMPLICIT VOLUME (Table A.1.1) Total revenue with lumber and shingles was computed by subtracting revenue with pulpchips from value of shipments of goods of own manufacture of sawmills, planing mills and shingle mills. This revenue is higher than the one utilized above and includes secondary products manufactured by the industry, such as railroad ties and residues other than pulpchips. This procedure was preferred in order to maintain the comparability between the BC and PNW data sets. The measurement of revenue with residues is described below. A quantity measure of lumber and shingle output was derived by deflating lumber and shingle revenue by the lumber and shingle price index. 2.3 PULPCHIP PRICE (Table A.1.1) Pulpchip data was also obtained from Statistics Canada catalogue 35-204 (Statistics Canada, 1957-1982). Other residues were ignored due to unavailability of data. For 1966-1982 the pulpchip price was computed by dividing value of pulpchip shipments by the respective quantity in oven dry tons. For 1957-1965 data were only available for total BC. The 1966 ratio of the BC Coast price to BC total price was applied to the 1957-1965 average price, in order to estimate 241 the 1957-1965 Coast price. Coastal and Interior prices differ mostly due to the different structures of the chip market in the two regions. The pulpchip price is considerably higher on the BC Coast, probably due to lower transportation costs and a smaller degree of oligopsony. 2.4 PULPCHIP REVENUE AND IMPLICIT VOLUME (Table A.1.1) Pulpchip revenue for 1966-1982 is the value of shipments with pulpchips. For 1957-1965 these data had to be estimated, because no disaggregation in terms of Coast and Interior was available. First shipments of railroad ties were computed by applying the Coast and Interior proportions to BC shipments of railroad ties from all industries. The estimated BC Coast shipments of ties were multiplied by the BC average price of ties and the value of BC Coast tie shipments was computed. The same procedure was used for the BC Interior. The BC Coast value of tie shipments was added to the BC Coast value of lumber shipments computed as the sum of species. Value of the shipments in the BC Interior was added to value of lumber shipments in the BC Interior, computed identically to the Coast. The value of shipments of lumber and ties was subtracted from value of shipments of goods of own manufacture. This yielded a residual income for both BC Coast and Interior. The Coast and Interior proportions on this residual income were applied to total BC pulpchip shipments. This yielded Coast and Interior income with pulpchips. For 1957 value and volume of chip shipments for total BC was missing. It was assumed that it was equal to the 1958-1959 average. In order to test the accuracy of this procedure, it was also applied to the 1966-1982 period, for which regional pulpchip data was available. The difference between the two pulpchip revenue series was negligible. The pulpchip implicit volume was computed by dividing pulpchip revenue by the pulpchip average price. 242 2.5 SAWLOG PRICE (Table A.l.2) Two alternative data series for sawlog prices were constructed, in order to check the sensitivity of results to changes in the data. The first series was obtained from Statistics Canada catalogue 35-204 (Statistics Canada, 1957-1982). It is the implicit price obtained by dividing the value of total logs purchased or transferred by their respective volume. Where required, these prices were converted to cubic meters with the conversion factors derived in Chapter 3. The second series is the average Vancouver log market price of sawlog grades. It is assumed that this price reflects the opportunity cost of wood to sawmills, and that sawlog quality in the log market is a good proxy of the quality of logs going to sawmills (up to a scaling factor). The price is expressed in $/m3. The conversion factors discussed in Chapter 3 were utilized to convert the average price per Mfbm (BC Board Foot Log Scale) to cubic meters, where required. The data were obtained from the Council of Forest Industries of BC (1957-1982). 2.6 SAWLOG VOLUME AND EXPENDITURES WITH WOOD (Table A.12) Two alternative data series for sawlog expenditure corresponding to the two sawlog prices were also developed. For the first series, total sawmill expenditure with sawlogs was initially computed as total expenditure with materials, minus operating, maintenance and repairs expenditures available in Statistics Canada catalogue 35-204 (Statistics Canada, 1957-1982). Because data for operating, maintenance and repairs was only available for large establishments, it was scaled up by the ratio of total materials expenditures in large establishments to total materials expenditures in small establishments. Small establishments constitute a very small proportion of the industry. These calculations were carried out for sawmills. For shingle mills, expenditure with 243 wood is defined as cost of materials and supplies, and so maintenance and repair expenditures were not subtracted. Such data were not disaggregated for BC. For 1961-1982 this shingle mill expenditure data were added to the sawmill expenditure data. For 1957-1960 the sawmill data already included shingle mills, and adjustments were not required. An estimate of total wood consumed by sawmills and shingle mills was subsequently obtained by dividing the expenditure data by the implicit sawlog price. The latter was derived by dividing total expenditure with softwood and hardwood sawlogs and chippers, by their respective volume. The second data series on expenditures with wood was constructed by multiplying the implicit wood volume in sawmills and shingle mills obtained through the procedure discussed above, by the average log market sawlog price discussed in Section 2.5. 2.7 LABOUR WAGE INDEX (Table A.1.3) The wage index is a Tornqvist index (Diewert, 1976) of wages per hour paid of production and nonproduction workers. This index was rebased so that 1971 would equal the average wage per man hour of production and nonproduction workers for that year. All the required data were obtained from Statistics Canada (1957-1982). For production workers, wages were computed by dividing total wages by man hours paid in sawmills. Data on hours worked were only available for recent years, and so this information was not used. For nonproduction workers, total wages were computed by subtracting production workers wages from total wages. Nonproduction workers were assumed to work 2000 hours per year, and this figure was multiplied by the number of nonproduction workers to obtain an estimate of total hours paid to nonproduction workers. Wage per hour of nonproduction worker was obtained by dividing wages 244 by hours paid. Hours paid times wages were used in constructing the expenditure share weights for the index. For 1957-1961 disaggregated data for production and nonproduction workers were not available. The shares of production and nonproduction workers for 1957-1961 were assumed to be equal to the 1962 shares, and these shares were applied to total workers. The same amount of hours per worker were assumed to have been paid for these years, as in 1962. Wages of production and nonproduction workers for 1957-1961 were assumed to have followed the same trend than average wage per worker for the period. The shingle mill wage index was assumed to be the same than the sawmill wage index. 2.8 EXPENDITURES WITH LABOUR AND IMPLICIT LABOUR INPUT (Table A.1.3) Expenditure with labour was obtained directly from Statistics Canada (1957-1982). For 1961 through 1982 the shingle mill expenditure with labour was added to the sawmill expenditure with labour. For 1957 through 1960 the two industries were already aggregated. A measure of the labour input in sawmills and shingle mills was derived by dividing total expenditure with labour by the wage index discussed in the previous section. 3. PACIFIC NORTHWEST WESTSIDE . 3.1 LUMBER AND SHINGLES PRICE INDEX (Table A.1.4) The lumber and shingle price index is a Tornqvist price index (Diewert, 1976) in which the price components are the average implicit prices of lumber of Douglas-fir, hemlock, red cedar, spruce, other species and shingles. This price index was linked with the BC one through the 1971 cross-section.1 245 For 1964 through 1982, the Douglas-fir lumber average price (green and dry) was obtained from the Western Wood Products Association (1964-1982a). In order to extend this price series back to 1957, it was regressed on the Douglas-fir price for the PNW Westside available for 1950-1976 from Adams et a|. (1979). This latter price is for Dimension Lumber, Standard and Better, 2*4, Random Length, Kiln Dried. For 1967 through 1982 the hem-fir lumber average price (green and dry) was also obtained from the Western Wood' Products Association (1964-1982a). In order to extend this price series back .to 1957, it was regressed on the hemlock dimension lumber price index from the US Department of Labour (1957-1981b), and on the BC Coast hemlock average price, discussed in Section 2.1. For 1967 through 1982, the red-cedar lumber average price was obtained from the Western Wood Products Association (1967-1982b). This series was extended back to 1957 by regressing this price on the BC Coast cedar average price, discussed in Section 2.1. The 1957-1982 spruce lumber price in the PNW is assumed to be equal to the BC Coast one. The price for other species for 1967 through 1982 was also obtained from the Western Wood Products Association (1964-1982a). The 1957-1966 price was predicted by regressing this price on the Ponderosa pine price and the average realization price. The Ponderosa pine price was obtained from the Western Wood Products Association (1967-1982b). 1957-1966 was predicted by regressing this price on the Ponderosa pine price available in Adams et aj. (1979). The average mill realization price is a weighted average of the prices of all the other species. Although there is a minor proportion of Ponderosa pine produced in the PNW West, but none on the BC Coast, its importance is almost negligible, so the comparability of the two price indices is maintained. 246 The 1964-1982 shingle price was obtained from Random Lengths (1964-1982). Although prices for several grades were available, Random Lengths suggested the use of the price for shingles 5X, #1, Red Cedar Dry, because it was the most representative grade in the PNW West. 1957-1963 was predicted by regressing this price on the BC Coast shingle price. All prices were expressed in US dollars per Mfbm of lumber. These were converted to Canadian dollars using the yearly average noon spot exchange rate, which was obtained from the Bank of Canada Statistical Summary (1957-1960) and from the Bank of Canada Review (1961r 1982). In order to derive the weights for the price index, estimates of revenue for each species were required. Estimates of lumber production for each species were obtained from the Western Wood Products Association (1957-1982), and these multiplied by the prices mentioned above. Estimates of shingle revenue were obtained from the US Department of Commerce (1957-1982a). These estimates were available for 1967, 1969, 1970, 1971, 1977 and 1978. First, all shingle mills in the states of Washington and Oregon were assumed to operate on the Westside. According to Larsen et al. (1983), in 1982 in Washington 0.4% of the state shingle and shake capacity was located in the PNW Eastside, while according to Howard (1984), for the same year in Oregon, 6.3% of the state shingle and shake capacity was located in the PNW Eastside. Shingle revenue is defined as value of shipments by the shingle industry. The ratio of shingle revenue to total lumber and shingle revenue (value of shipments) for the states of Washington and Oregon was computed for the years available. It was verified that this ratio was extremely stable. The 1957-1966 ratio was assumed equal to the 1967 one, the 1979-1982 equal to the 1978 one, and the 1968 and 1972-1976 ratios were computed by linear 247 interpolation of the ratios. Subsequently these ratios were multiplied by the total value of lumber and shingle shipments (see following section for a description of how these were calculated), and an estimate of yearly revenues with shingles obtained. All revenues were expressed in Canadian dollars. 32 LUMBER AND SHINGLE REVENUE AND IMPLICIT VOLUME (Table A.1.4) Several data series of lumber and shingle revenue were available. Following Abt (1984), it was decided to use the US Department of Commerce (1957-I982a) series, because it was the only one that permitted the consistent measurement of lumber revenue and sawlog expenditure. There were two problems with this series: first, there were missing observations and second, the series was available for the states of Washington and Oregon, and so procedures had to be used to allocate the data between West and Eastside. The first step was to complete the value of shipments data for the states of Washington and Oregon. For Washington, data for the 3—digit level industry was missing for 1957-1963, 1968, 1972-1976 and 1979-1981. For Oregon, data for the 3—digit level industry was missing for 1957-1963, 1968 and 1979-1981. The procedure utilized by Abt (1984) to complete the series for the period 1964-1978 was also used here for all the missing observations in the same period.' This procedure amounts to computing the ratios of value of shipments at the 3—digit level industry to the 2—digit level industry. These ratios are very stable. Ratios for the missing years between 1964 and 1978 were computed by linear interpolation, and subsequently multiplied by the 3—digit level value of shipments data, which was available for every year from 1964 through 1978. This yields computed value of shipments for 1968 in Washington and Oregon, and 1972-1976 in Washington. The data for the two states were added together, yielding total value of shipments in the lumber and shingle industry in the PNW for 1964-1978 248 and 1982. The 1957-1963 value of shipments data were computed by means of an alternative data set. Revenue with lumber in the PNW West and Eastside were computed by multiplying the average lumber price by lumber production in both regions, utilizing data supplied by Adams (1985). The PNW West and Eastside lumber revenue series were added to yield total lumber revenue in the PNW. The revenue with pulpchips to be discussed in Section 3.4 and the revenue with shingles were added to lumber revenue, ' to yield an alternative measure of revenue with lumber, shingles and pulpchips. The revenue with shingles utilized in this procedure is not the same as the one discussed in Section 3.1, but it is very similar. It was calculated by multiplying the ratio of shingle value of shipments to lumber and pulpchip value of shipments by the sum of value of lumber shipments from Adams (1985) and value of pulpchip shipments (see Section 3.4). This was necessary because the shingle revenue series utilized in Section 3.1, which is consistent with the ASM data, could only be derived after the Annual Survey of Manufacturers (ASM) data series were extended from 1957 to 1982. The ratio of the ASM revenue series to the calculated revenue series was computed for 1957-1963. This ratio was quite stable for 1964-1969 and unstable from 1970 on. The average of the 1963-1964 ratios was multiplied by the calculated revenue series. This yielded an estimate of value of shipments consistent with the ASM series for 1964-1978. Due to the instability of the ratio after 1970, it was decided not to use this procedure to generate the missing observations in the ASM series for 1979-1981. In order to allocate value of shipments between West and Eastsides the following procedures were utilized. First, shingle and pulpchip revenues were V 249 subtracted from the ASM value of shipments, yielding an estimate of value of lumber shipments. Proportions of PNW West and Eastside value of lumber production were computed from the data obtained from Adams (1985). These proportions were utilized to allocate the ASM value of lumber shipments between West and Eastside. The value of shingle shipments was subsequently added to the PNW West value of lumber shipments to yield an estimate of revenue with lumber and shingles in the PNW West for 1957-1978 and 1982. To extend the PNW West lumber and shingle revenue series to 1979-1981, the revenue computed above was regressed on the sum of revenues with lumber from the various species discussed in Section 3.1 and shingle revenue described in the previous paragraph. This yielded a lumber and shingle revenue series for 1957-1982 in the PNW West consistent with the ASM data series. All revenues were converted to Canadian dollars using the exchange rate described in Section 3.1. 3.3 PULPCHIP PRICE (Table A.1.4) The pulpchip price was obtained by dividing calculated pulpchip revenue by calculated pulpchip volume of shipments, which are discussed in Section 3.4. 3.4 PULPCHIP REVENUE AND VOLUME (Table A.1.4) The series for pulpchip revenue and volume2 for the entire PNW were derived from the following equation: PNW PULPCHIP SHIPMENTS = PNW PULPMILL CHIP CONSUMPTION + PNW BOARD MILL CHIP CONSUMPTION - CHIP IMPORTS FROM CANADA - CHIP IMPORTS FROM IDAHO - CHIP IMPORTS FROM CALIFORNIA + CHIP EXPORTS FROM WASHINGTON + CHIP EXPORTS FROM OREGON This yields total pulpchip shipments by the lumber, plywood and shingles and shake industries in the PNW. Minor industries such as pole, post and piling and 250 hardwood were ignored. This calculation also ignores pulpchip exports from Oregon and Washington to the rest of the US. The volume and value of pulpchips consumed by pulpmills were obtained from the Northwest Pulp and Paper Association (1972, 1977) for 1957-1976 and from Ruderman (1979) for 1977-1978. This series includes pulpchips, shavings and sawdust, and unfortunately it was impossible to separate the pulpchip component from total residues consumed. Residues other than pulpchips were estimated to be the following proportions of total residues consumed: 26% in 1982 in Oregon (Howard, 1984), and 6% in 1982 in Washington (Larsen et al., 1983). The two series gave volume and value of pulpchips (residues) consumed by pulpmills in the PNW from 1957 through 1978. An alternative series for the volume of residues consumed was constructed using data from the American Pulpwood Association (1976-1982) for 1976-1982. First the proportion of residues to total pulpwood receipts in the US West for the month of December were computed. These proportions were assumed to hold throughout the year. These proportions were multiplied by the pulpwood used (roundwood and residues) in the US West to yield an estimate of residues used. The volume share of the PNW in the US West pulpwood consumed was computed and multiplied by the volume of residues used in the US West to yield an estimate of residues consumed in the PNW for 1976-1982. These estimates for 1977 and 1978 were very close -to the ones discussed in the previous paragraph, but the 1976 one was considerably different, probably due to different sample sizes in that year. This procedure yielded an estimate of residue consumption by pulpmills for 1979-1982 in the PNW. The volume of pulpchips consumed by particleboard mills in the PNW was estimated in the following way. First, data on particleboard production in the US West were obtained for 1957-1966 from Wright and Phelps (1967) and for 1971 251 and 1976 from Dickerhoof and Mckeever (1979). According to McKeever (1979), hardboard and insulation board plants use woodpulp as a raw material, not sawmill residues, and so these were ignored. Data on particleboard production in the US West and in Oregon for 1971-1976 were obtained from the US Department of Commerce (1971-1976). According to Larsen et a\. (1983), no board mills operated in Washington in 1982, and according to Bergval et a_[. (1979), only one particleboard mill operated in Washington in 1978, so it was decided to ignore pulpchip consumption by the board industry in Washington. From the US Department of Commerce data, the ratio of Oregon particleboard production to the US West production was " computed. This ratio was very stable and so it was assumed to be equal to 0.71 for 1957-1970 and to 0.70 for 1977-1982. This ratio was multiplied by the US West particleboard production to obtain an estimate of particleboard production in Oregon for 1957-1966 and 1971-1976. Particleboard production data for 1967-1970 were obtained by linear interpolation and for 1977-1982 it was assumed to be approximately equal to the 1976 level and equated to 1000 million square feet of particleboard. A more correct series on particleboard production was later obtained from the National Particleboard Association (1972-1982), but because it was verified that the series derived above was fairly accurate when compared with the later one, and that pulpchip consumption by board mills is a very minor proportion of total raw materials consumed, it was decided not to alter the above calculations. Wood raw material requirements per 1,000 sq. feet of board produced were obtained from Maloney (1981 ).3 Because the distribution of the several types of particleboards produced was not obtained, an average conversion factor of 1.5 OJD. tons/1,000 sq. ft (3/4 in. basis), based on national average, was utilized (Wright and Phelps, 1967). This conversion factor was multiplied by particleboard production in Oregon to obtain an estimate of wood raw material consumed. 252 From Dickerhoof and McKeever (1979), the proportions of the several types of wood raw materials used by the particleboard industry in the US West in 1973 were obtained. It was verified that the single two most important categories were planer shavings and sawdust, and that pulpchips amounted only to 2% of total wood raw materials consumed (in volume). This proportion was assumed to hold in Oregon and throughout the period, and it was multiplied by total wood raw material consumed to yield an estimate of pulpchips consumed by the board industry in the PNW for 1957-1982. This estimate was added to the volume of pulpchips consumed by the- pulp industry. Pulpchip imports from Canada into Washington were obtained for 1961-1982 from Ruderman (1979). The ratio of pulpchip imports from Canada in 1961 and 1962 to pulpchips consumed by pulpmills was stable in those years and equal to 0.15. This ratio was used to derive the 1957-1960 data on chip imports from the pulpmill chip consumption series. The volume of pulpchip imports was subsequently subtracted from the pulp and board mill pulpchip consumption. The proportions of pulpmill chip consumption which were imported from Idaho and California into Oregon for 1972, 1976 and 1982 and from Idaho into Washington in 1974, 1978 and 1982 were obtained respectively from Shuldt and Howard (1974), Howard and Hiserote (1978), Howard (1984). Bergval et aj. (1975, 1979), and Larsen et a\. (1983). From these an average proportion of imports from Idaho (4%) and California (1%) in pulpchip consumption by pulp and board mills from sources other than Canada was computed. From these proportions estimates of pulpchip imports from Idaho and California were obtained. Pulpchip imports from Idaho and California that were either reexported or utilized by industries other than Pulp and Paper were ignored. 253 Data on pulpchip exports from Washington for 1968-1982 and from Oregon for 1965-1982 were obtained from Ruderman (1979). The plotting of the Oregon data indicated that chip exports rose from zero in some year prior to 1965 to a peak. Because chip exports prior to 1966 appeared negligible, the 1964 figure was set equal to half the 1965 one, and the 1957-1963 figures were set to zero. Although the same pattern was evident in the Washington chip export data, it was unclear for which years chip exports could be assumed to be zero. Thus the Washington chip export data was regressed on chip exports from Oregon and time. The 1964-1967 observations are predicted values and the 1957-1963 observations were set to" zero. This completed the calculations required to estimate pulpchip shipments in the PNW by the sawmilling, shingle and plywood industries. It remained to allocate shipments between the several industries and West and Eastsides. In order to do this, estimates of the theoretical chip production in the two regions and industries were obtained. Theoretical chip production here is interpreted as the volume produced based on average chip recovery factors obtained from mill studies. It was assumed that all pulpchips were produced from coarse residues; slabs, edgings and trim in sawmills; spur trim, roundup and veneer clip in plywood mills. All veneer cores were assumed to go to sawmills. Recovery factors for these residues in sawmills and plywood mills in Washington and Oregon, West and Eastside were obtained from Bergval and Gedney (1970), Bergval and Ormrod (1974), Bergval et aj. (1975), Bergval et al. (1977), Bergval et aj. (1979), Larsen and Gee (1981), Shuldt and Howard (1970,1974), Howard and Hiserote (1976) and Howard (1984). These recovery factors were multiplied by lumber production in Oregon West and East and Washington West and East obtained from the Western Wood Products Association (1957-1982c), and by plywood production in the PNW West and Eastside, obtained from Adams et 254 al. (1985). Pulpchip production by shingle mills was ignored. This procedure yielded an estimate of theoretical pulpchip production by region and industry. To make this production series consistent with the shipment series, estimates of the proportion of pulpchips produced that were utilized were also obtained from the same sources than pulpchip recovery factors. These were multiplied by the theoretical pulpchip production. From these data, the proportion of theoretical pulpchip production in sawmills and plywood mills in the PNW West and Eastside were obtained, and multiplied by the calculated PNW pulpchip shipments, to yield an estimate of volume of pulpchip shipments by sawmills in the PNW West. The calculation of pulpchip revenues followed a similar procedure. First the average price of pulpchips exported from Oregon for 1957-1964 were obtained by regressing the average price for 1965-1982 (Ruderman, 1979) on the average price of pulpchips consumed by pulpmills (Northwest Pulp and Paper Association, 1972 and 1977; Ruderman, 1979). The average price of pulpchips exported from Washington was predicted for 1957-1967 by regressing the 1968-1982 price (Ruderman, 1979), on the Oregon export price obtained above. The 1957-1960 average price of pulpchips imported from Canada was predicted by regressing it on the average price of pulpchips consumed mentioned above. The 1979-1982 average price of pulpchips consumed was predicted by regressing this series on all the prices derived above, as well as the BC Coast pulpchip average price. These prices were subsequently multiplied by the several pulpchip volumes calculated, to yield pulpchip revenues and expenditures. The same procedure than for volume was utilized to derive an estimate of value of pulpchip shipments by sawmills in the PNW West. 255 3.5 SAWLOG PRICE (Table A.1.5) As for the BC Coast, two alternative data series for sawlog prices were constructed. The first series is an estimated delivered wood cost obtained by adding the average price of stumpage cut in the PNW West to the average logging costs in that region. Both series were obtained from Adams (1985). This price was converted to Canadian dollars per cubic meter with the exchange rates mentioned previously and the average conversion factors derived in Chapter 3. The second series-is: the average log market price of sawlog grades in the PNW, converted to Canadian dollars per cubic meter, as the one above. The data for this series were obtained from the Industrial Forestry Association (1957-1962 and 1963-1982). This second series is more defensible as a measure of the opportunity cost of sawlogs, but the two were built in order to test the sensitivity of results to changes in the data. 3.6 SAWLOG VOLUME AND EXPENDITURES WITH WOOD (Table A.l.6) An estimate of total cost of materials in sawmills and shingle mills in the PNW was obtained for 1957-1978 and 1982 by subtracting value added from value of lumber, shingle and pulpchip shipments. The value added series was obtained from the US Department of Commerce (1957-1982a). Missing observations in this series were dealt with as for" value of shipments (Section 3.2). In order to separate wood costs in total materials expenditure, the ratios developed and justified by Abt (1984) were also used here. Abt (1984) estimated that nonwood materials amount to 17% of total materials costs, and that this proportion is stable. This correction is important in order to maintain the comparability between the PNW and BC data sets. This yielded estimated cost of wood in the PNW for 1957-1978 and 1982. 256 This cost was subsequently allocated between West and Eastside through the proportions of theoretical cost of wood in the West and Eastside in total costs of wood, but assuming that all shingle mills operated on the Westside. The theoretical cost of wood was estimated by multiplying estimates of the theoretical wood consumption in sawmills by the sawlog price based on National Forest timber sales and logging costs. The theoretical wood consumption was derived by multiplying yearly average overrun factors by lumber production. These overrun factors are based on individual mill studies in the PNW West. All the data were obtained from Adams (1985). This yielded estimated cost of wood in sawmills in the PNW West. The shingle mill cost of wood was derived through the use of ratios of the shingle to the lumber and shingle cost of wood, obtained for selected years. The shingle mill cost of wood was subsequently added to the sawmill cost of wood. The two series for sawlog volume consumed by sawmills and shingle mills in the PNW West were obtained by dividing the cost of wood series by the National Forest based sawlog price and by the average log market sawlog price. 3.7 LABOUR WAGE INDEX (Table A.1.6) The wage index is a Tornqvist index (Diewert, 1976) of wages per hour paid of production and nonproduction workers. This index was linked with the BC one through the 1971 cross-section.4 Average hourly earnings per man hour paid in Washington were obtained from the US Department of Labour (1957-1981). Earnings include overtime, holidays, vacations and sick leave, but exclude bonuses. An alternative data series was obtained from the Western Wood Products Association (1959-1979). This later series includes overtime, vacation, holiday, bonuses, workmen's compensation, social security, unemployment compensation, health, welfare and pensions. A comparison of the two series with the BC Coast 257 data and wages reported in several studies of costs in the industry, indicated that the earnings reported by the Western Wood Products Association were abnormally high, and so the Department of Labour series was preferred. Nonproduction workers were assumed to work 2000 hours per year. Estimates of earnings per hour paid both to production and nonproduction workers were derived for 1958-1967, 1969-1978 and 1982 from the US Department of Commerce, Annual Census of Manufacturers data discussed previously. The ratio of earnings per hour of nonproduction worker to earnings per hour of production worker was multiplied by the US Department of Labour series. Ratios for missing years were computed by linear interpolation. This yielded wages per hour paid of production and nonproduction workers. In order to build the wage index, shares of production and nonproduction workers in total expenditures with labour were required. Average weekly hours paid per year to production workers were also obtained from the US Department of Labour data for Washington, and these multiplied by 52 to yield yearly hours paid per worker. The Oregon figures were assumed to be equal to the Washington ones. The US Department of Commerce data were used to obtain estimates of the number of production and nonproduction workers in sawmills and shingle mills for the entire PNW. These were multiplied by the yearly earnings per worker to yield an estimate of expenditures with production and nonproduction workers. 3.8 EXPENDITURES WITH LABOUR AND IMPLICIT LABOUR INPUT (Table A.1.6) Data on the average annual employment in sawmills and planing mills (SIC 2421) in Washington and Oregon West and Eastside were obtained for 1957-1971 from Wall and Oswald (1975) and for 1972-1982 from Wall (1985). From these, annual employment in the PNW West was computed. Average annual employment in shingle mills was calculated by first computing the ratio of employment in 258 shingle mills to employment in sawmills, similarly to the computations for value of shipments (Section 3.2). This ratio was multiplied by total PNW sawmilling employment and the result was added to the PNW West sawmilling employment series. The quantity shares of production and nonproduction workers obtained from the US Department of Commerce data were multiplied by this series to yield PNW West production and nonproduction workers. These were multiplied by the average yearly wages, and added, to yield total labour costs in sawmills and shingle mills in the PNW West. An implicit index of total hours paid per year to production and nonproduction workers in sawmills and shingle mills in the PNW West was obtained by dividing the labour expenditure series by the wage index. 4. CAPITAL STOCK 4.1 REAL CAPITAL STOCK IN BC AND IN THE PNW Capital stock is a Tornqvist quantity index (Diewert, 1976) of the stocks of equipment and stuctures. The treatment of capital stock as a quasi-fixed input in sawmilling was justified in the thesis, and this contradicts the optimizing behaviour assumption with respect to the capital input implicit in the aggregation procedure. Aggregation of quasi-fixed factors has been discussed by Epstein (1981). The use of two separate -capital stocks for structures and equipment would make the econometric model of Chapter 5 unmangeable, and the simple adding of the two stocks implies assuming that they are the same good. It was considered that an aggregation procedure identical to the one utilized for variable factors was perhaps the least bad. In order to build the quantity index, estimates of real capital stocks and user costs of capital were required. Estimates of real net capital stock for 259 equipment and structures for sawmills and shingle mills in BC were obtained from Statistics Canada (1984). This series was built using the perpetual inventory method, and assuming straight line depreciation and service lives of 30 years for structures and 26 years for machinery. Statistics Canada could not provide the raw investment data utilized in the development of the capital stock series. This was unfortunate because the straight line depreciation and the long service lives assumed are perhaps not very appropriate in sawmilling. Coen (1975) developed a model that allows the identification of depreciation patterns and service lives from the investment behaviour of producers. According to his results, the US wood products capital is best characterized with straight line depreciation and 12 years service lives for equipment and with straight line depreciation and 20 years service lives for structures. In a more recent study (Coen, 1980), straight line depreciation and 8 years service lives for equipment and finite geometric depreciation and 50 years service lives for structures were obtained. Merrifield (1985) applied Coen's model to the US 3—digit level industry and found a geometric declining depreciation and 9 years service lives for equipment and an inverse geometric declining and 37 years service lives for structures. The US Department of Labour (1979), utilizes a hyperbolic depreciation pattern and assumes that discards follow a normal distribution around the mean service lives. Harper (1982) mentions that there is little evidence for choosing among alternative depreciation patterns. Given the lack of knowledge and disparity of results concerning depreciation patterns in the wood products industries, straight line depreciation may be a compromise as good as any other one. But the scarce evidence suggests that the Statistics Canada assumed lives for equipment are too long. Given that the raw investment data for BC could not be obtained, it was decided to use the Statistics Canada capital stock estimate (described in Statistics Canada, 260 catalogue 13-522) and construct the PNW capital stock accordingly. Unpublished data on gross investment for the US sawmill and shingle mill industry (SIC 242) were obtained from the US Department of Commerce (1985). This data covered the periods 1890-1981 for structures and 1921-1981 for equipment. Data on gross investment for Washington and Oregon sawmill and shingle mill industry were obtained from the US Department of Commerce (1957-1982a). This series covered the years 1954, 1958-1967, 1969-1978 and 1982 (SIC 2421) for Oregon and the years 1954^  1958-1967, 1969-1971, 1977-1978 and 1982 for Washington. Missing observations were calculated by first computing the ratio of gross investment in sawmills and shingle mills to gross investment in the wood products industry (SIC 24). The SIC 242/SIC 24 ratio was computed for the missing years by linear interpolation and used to calculate the SIC 242 investment expenditures in both states. For the 1979-1981 missing observations the average of 1977 and 1978 ratios of Washington plus Oregon investment in sawmills and shingle mills to total US investment were used instead. This yielded a gross investment series for sawmills and shingle mills in the PNW. From this series, the ratio of PNW gross investment to US gross investment in sawmills and shingle mills was computed for 1954-1982. This ratio was surprisingly stable. The average of the 1954-1955 ratio was multiplied by the US gross investment series for years prior to 1954, to yield estimated capital expenditures in structures and equipment in the PNW sawmill and shingle mill industry. The above gross investment series was converted to real dollars using the structures (1890-1981) and equipment (1921-1981) implicit price deflators (1972 = 100.) for US sawmills and shingle mills (SIC 242), obtained also from the US Department of Commerce (1985). The 1982 observation was estimated using the GNP implicit price deflator for Nonresidential Gross Private Fixed Investment from the US National Income and Product Accounts (US Department of Commerce, 261 1984). Utilizing 30 year service lives for structures and 26 year for equipment and assuming straight line depreciation, the perpetual inventory method was used in obtaining an estimate of real capital stock in constant 1972 US dollars for structures and equipment in the PNW sawmill and shingle mill industry. This series was converted to constant 1971 Canadian dollars by rebasing and using the 1971 average noon spot exchange rate. 42 USER COST OF CAPITAL IN BC AND IN THE PNW (Tables A.1.3 and A.1.6) The model developed by Hall and Jorgenson (1967) to derive the cost of capital services was also "used here. The original equation was slightly modified to take into account the assumed straigt line depreciation (Coen, 1975) and the Canadian and the US corporate tax structures. The equation utilized is, (A.4.1) C = q(i(1-u))/(1-f) * (1-k-uz+mkuz)/(1-u) where c - user cost of capital q - price of capital goods (structures and equipment) i - nominal interest rate u - effective rate of corporate income tax k - effective rate of investment tax credit z - present value of the depreciation deduction on one dollar's investment m - the proportion of the investment credit that must be deducted from the depreciable base of assets on which the credit is claimed F - present value of the stream of capacity (efficiency) depreciation on a unit of capital (Coen, 1975); for straight line depreciation this formula is 262 (AA2) F = (1-e- i n)/i-where i is the nominal interest rate and n is the assumed service life of the asset (Merrifield, 1985). With geometric depreciation this formula reduces to the ones derived by Hall and Jorgenson (1967) and Boadway (1980). For BC, Z was calculated as in Boadway et aj. (1984): where a is the declining balance rate for the capital cost allowance. For the PNW, Z was calculated using" the sum-of-the-years digits depreciation schedule, where t is the life of the asset for tax purposes. This formula was obtained from Hall and Jorgenson (1967) and Merrifield (1985). At least three depreciation formulae for tax purposes have been allowed in the US. The one that yields the highest present value of the depreciation deduction was chosen. For BC, q are the price indices for structures and equipment (1971=100.0) obtained from Statistics Canada (1983). i is the McLeod, Young, Weir, 10 industrials corporate bond yield average for 1957-1977 (Statistics Canada, 1983) and the McLeod, Young, Weir, .weighted long term corporate bond yields for 1978-1982 (Bank of Canada Review, December issues, 1968-1982). u is the effective corporate income tax for sawmills and shingle mills in Canada for 1957-1983 (Department of National Revenue, 1957-1964; Statistics Canada, catalogue #61-208, 1965-1981). The 1970-1971 effective tax rates for sawmills and shingle mills were assumed equal to the ones for the wood products industries. K is the effective rate of investment tax credit (1975-1982), obtained (A.4.3) Z B C = a/(a + i) (A .4.4) ZPNW = (Z/it)-(1-(1/it>(1-e jt)) 263 from Statistics Canada, catalogue #61-208, 1975-1981). Prior to 1975 the investment tax credit was not in effect in Canada, a for 1957-1982 was taken from Boadway et a|. (1984). Also, following these authors, m was set to one for 1957-1982, because in Canada, the investment tax credit k reduces the subsequent base for capital cost allowance by the amount of the credit. For the PNW, q is the implicit investment deflator for structures and equipment for sawmills and shingle mills (SIC 242), obtained from the US Department of Commerce (1985) for 1967-1981, rebased to 1971 = 100. and converted to Canadian dollars. It was extended to 1982 using the GNP implicit price deflators for gross private fixed investment (nonresidential) for structures and equipment (US Department of Commerce, 1984). i is the corporate bond yield industrial average (Moody's, 40 bonds) for 1968-1982. This series was extended back to 1957 by using the corporate bonds yield industrial average (Moody's AAA) and linking them based on the average ratio of the two series for 1968-1970 and 1973-1982. Both series were obtained from the US Department of Commerce (1975 and 1984). u is the effective corporate income tax for logging, sawmills and shingle mills in the US for 1957-1960 and 1963-1981 obtained from the US Department of Treasury (1957-1981). 1961-1962 and 1982 were calculated using the ratios of effective income tax in logging, sawmills and shingle mills to the effective income tax for total corporations. This latter series was obtained from the US Department of Commerce (1975 and 1984). The effective rate of investment tax credit k was obtained from the US Department of Treasury (1963-1981). K in 1957-1962 was set to zero and in 1982 was assumed equal to 1981. m is zero for every year, except 1962-1963 in which it was set to one (Coen, 1975; Merrifield, 1985). It is customary the introduction of a measure of expected capital gains in the user cost formula, usually set equal to Aq/At. This was experimented, as well 264 as several moving averages for Aq/At, but it was verified that in some years and for some capital goods, rental prices were negative, and that rental prices had a very erratic behaviour. Because of this reason the above formulation was preferred. Thus static expectations about the price of investment goods are assumed (Hall and Jorgenson, 1968). 4.3 AGGREGATE CAPITAL STOCK IN THE BC COAST AND PNW WEST (Tables A.1.3 and A.1.6) Rental prices were multiplied by capital stock to derive estimates of costs of services of structures and equipment. These were utilized in building an aggregate index of capital stock. Total costs were subsequently deflated by aggregate capital stock and an implicit rental price obtained, for BC and for the PNW. The problem of allocating this capital stock between BC Coast and Interior and PNW West and Eastside remained. Investment data on a subprovincial or substate basis is not available, and so different procedures were tried to carry out this allocation: (1) the ratio of regional capital stocks is equal to the ratio of regional profits; (2) the ratio of regional capital stocks is equal to the ratio of regional physical production; (3) the ratio of regional capital stocks is equal to the ratio of regional capacities; (4) the ratio of regional capital stocks is equal to the ratio of energy - consumption at full capacity. First all criteria produced comparable results in terms of long-run capital stock trends. Criterion (1) was not used because it implies equal average rates of return on capital in both regions, and this did not appear to be theoretically sound. Criteria (2) and (4) yielded results similar to (3) but the capital stock series when plotted evidenced unrealistic short-run fluctutions. Also criterion (4) could not be used in the PNW, because energy consumption data were only available for selected 265 years. Criterion (3) was therefore chosen. It probably overestimates capital stock on the BC Coast, because mills in this region are considerably less capital intensive than in the BC Interior. Capacity was estimated for the sawmill and shingle mill industries and of the BC Coast and Interior using the trend-through-peaks approach. The results compared favourably with capacity estimates by Nillson (1985) for BC. For the PNW capacity data were obtained from Adams (1985). It is not probably this procedure that causes the series to do a bad job in depicting the historical evolution of the capital stock, as well, as the capital stock differences between the BC Coast and PNW West. If this happens, it is likely to be due to the assumed long service lives for equipment. 5. A CRITIQUE OF THE DATA The main weakness of the data utilized is by far the capital stock measurement. Problems in measuring capital stock are not only empirical, due to lack of data, but also theoretical. In addition to this, the procedures that had to be used to allocate the BC and PNW capital stocks by region were perhaps not optimal. In both regions, changes in inventories were ignored, and value of shipments utilized as a proxy for value of production. This was done because for the BC data set, the inventory data are not consistent with the shipment data, and for the PNW the inventory data set is rather incomplete. The plots of volume of shipments on the PNW against production data from other sources. (Western Wood Products Association, 1957-1982c; US Department of Commerce, 1957-1982; Adams, 1985), indicated discrepancies in 1970 and 1973 and these could be due to variations in inventories. In BC, inventories in 1980 were 266 considerably above the average and in 1982 below the average. Another possible source of bias is the failure to measure the labour input in hours worked, instead of hours paid. Data on hours worked for 1977-1982 on the BC Coast obtained from Statistics Canada (1985) showed that the two series were considerably different. Unfortunately, data on hours worked for 1957-1976 were only available for selected years from Forest Industries Relations (1984), and this data set was not consistent with the Statistics Canada one. Martinello (1984a), who researched the BC labour market thoroughly, also defined labour input in terms of man hours paid in later studies. Several sources of biases may have been introduced in the PNW data, due to the several procedures that had to be utilized to reconcile data from different sources, generate missing observations and to regionalize the data. But with the exception of pulpchips, it should be mentioned that for the PNW there was no lack of data, but excess of data. Most of the procedures were carried out to reconcile and make alternative data series consistent with one another, or to allocate the data regionally, and in all cases the results compared favourably with the alternative sources, this increasing the confidence in the data generated. The calculation of pulpchip volumes is weak, first, because residues other than pulpchips could not be excluded from the pulpmill residue consumption, second because there may be several pulpchip inventory buffers between the sawmill and the pulpmill not accounted for, and third because the flow of pulpchips between the PNW East and Westside which may be important had to be ignored. On the other hand, the reasonable results obtained in Chapter 5 for the pulpchip variable could be used to justify the procedures. 267 6 . DATA LISTINGS In the f o l l o w i n g eight tab les , the f inal data for the several var iab les ut i l ized in the research are l is ted . Due to the very large number of o b s e r v a t i o n s and var iables in the raw data , these c o u l d not be l is ted because of s p a c e and resource l imi ta t ions . For the s a m e r e a s o n , not all qual i ty indices der ived in Chapter 3 are p resen ted . 268 Footnotes 1. The logarithmic difference between the two indices was computed for 1971, and e *99.89 was calculated (P is the price index). AlnP = Z0.5(SjpfvjVY + Sjg^)-AlnP., where P. is the price of component i of the index, SiPNW revenue snare in the PNW and S J B Q the revenue share in BC. This value gives the value of the price index in the PNW in 1971 utilizing the BC 1971 value (=CD$99.89) as a basis. The remainder of the PNW series was scaled accordingly. 2. Where required, volumes in cords were converted to bone dry tons by using a conversion factor of 1.00 bone dry ton per cord. 3. Underlayment Particleboard - 1.60 O.D. tons/1,000 sq. feet of 44 Pcf (3/4in.) board; Industrial Particleboard - 2.00 O.D. tons/1,000 sq. feet of ss Pcf (3/4in.) board; Flakeboard - .846 - .815 tons green/1,000 sq. feet (3/8 in. basis); Medium Density Fiberboatd 1.60 O.D. tons/1,000 sq. feet (3/4 in. basis). 4. The logarithmic difference (AlnP71) between the two indices was computed for 1971 and e n 71*4.359 was calculated (P is the wage index). This value gives the value of the price index in the PNW in 1971 utilizing the BC 1971 value (=CD$4.359) as a basis. The remainder of the PNW series was scaled accordingly. See footnote 1 for an explanation of how AlnP,, was calculated. Table A.1.1: BC Coast - Lumber and Shingle Price Index, Implicit Quantity Index and Revenue; Pulpchip Price, Volume and Revenue. Year Lumber Lumber Lumber Pulpchip Pulpchip Pulpchip and and and Average Volume Revenue Shingle Shingle Shingle Price Price Implicit Revenue Index Quantity Base: Index BC 1971 = CD$'000 CD$/O.D.Ton '000 CD$'000 CD $99.89/ O.D.Ton Mfbm 1957 68.85 2702. 186032. 13.25 1102. 14598. 1958 67.77 2900. 196545. 13.41 989. 13252. 1959 68.82 2732. 188013. 13.08 1016. 13293. 1960 67.12 3190. 214125. 13.49 1316. 17751. 1961 63.60 3545. 225462. 15.84 1517. 24028. 1962 69.06 3479. 240277. 13.55 1386. 18774. 1963 72.28 4079. 294867. 13.71 986. 13524. 1964 77.37 3967. 306923. 15.71 1821. 28601. 1965 76.87 ' 4107. 315739. 18.36 2171. 39853. 1966 78.64 3796. 298479. 18.11 2796. 50144. 1967 81.19 4353. 353441. 17.17 2884. 49515. 1968 98.45 4597. 452576. 18.73 3088. 57835. 1969 108.76 4185. 455179. 19.64 2969. 58320. 1970 95.44 4113. 392562 19.07 2892. 55150. 1971 99.89 4710. 470435. 19.21 3095. 59458. 1972 122.79 4746. 582802. 18.56 3022. 56091. 1973 175.04 4887. 855447. 23.34 3534. 82485. 1974 180.79 4029. 728409. 33.56 3306. 110961. 1975 169.30 3194. 540710. 40.20 2778. 111657. 1976 199.67 4520. 902469. 37.86 3338. 126360. 1977 235.45 4956; 1166798. 34.09 3301. 112540. 1978 276.88 5445. 1507631. 29.04 3515. 120076. 1979 361.73 4886. 1767390. 36.59 3269. 119605. 1980 341.04 4518. 1540757. 51.81 4273. 221365. 1981 302.31 4111. 1242757. 66.23 3196. 211690. 1982 306.94 3572. 1096269. 65.66 2867. 188280. Table A.1.2: BC Coast - Average Sawlog Price, Sawlog Volume, Sawlog Expenditure and m3/Mfbm BC Board Foot Log Scale Conversion Factor. Year Statistics Vancouver Statistics Statistics Sawlog Log Market Canada Log Market Canada Canada Expenditure Implicit Average Average Implicit Sawlog Based on Conversion Sawlog Sawlog Sawlog ExpenditureLog Market Factor Price Price Volume Price CD$/m3 CD$/m3 '000 m3 CD$'000 CD$'000 m3/Mfbm (BC Board . ..... Foot Log Scale) 1957 9.45 9.33 11427. 108023. 106614. 5.0073 1958 8.78 8.90 12113. 106402. 107806. 4.9804 1959 8.93 9.32 11094. 99092. 103396. 4.9986 1960 9.62 9.16 13390. 128829. 122920. 4.9937 1961 9.68 8.92 14460. 139990. 128983. 4.9871 1962 10.40 9.20 13458. 139940. 123814. 5.0154 1963 10.63 9.90 15371. 163397. 152173. 5.0123 1964 12.25 12.08 16006. 196010. 193352. 5.0063 1965 12.54 12.25 16762. 210261. 205335. 5.0190 1966 12.65 11.27 16486. 208478. 185797. 5.0346 1967 12.98 11.09 16922. 219730. 187665. 5.0231 1968 14.26 13.01 19163. 273336. 249311. 5.0359 1969 16.30 15.14 17668. 287935. 267494. 5.0389 1970 14.57 13.27 17698. 257941. 234852. 5.0418 1971 15.66 13.38 19045. 298324. 254822. 5.0587 1972 19.14 16.90 18338. 351046. 309912 5.0344 1973 23.50 24.02 21355. 501758. 512947. 5.0377 1974 27.42 23.99 16623. 455789. 398786. 5.0110 1975 26.92 22.40 13237. 356334. 296509. 5.0229 1976 31.08 27.85 18594. 577893. 517843. 5.0454 1977 33.74 32.05' 20541. 693044. 658339. 5.0535 1978 39.82 41.04 21363. 850676. .876738. 5.0327 1979 54.92 56.13 20303. 1115047. 1139607. 5.0265 1980 55.07 49.81 18915. 1041640. 942156. 5.0434 1981 51.30 44.35 16529. 847920. 733061. 5.0346 1982 52.43 44.65 14215. 745314. 634700. 4.9976 Table A.1 .3: BC C o a s t - Wage Index, I nplicit Index of M a n - hours Paid and Expenditures with Labour ; Index of the User C o s t o f Capital , Index of Real Capital Stock ; and Expendi tures with Capital Year W a g e I mpl ic i t Expenditure Index of Index of Expenditure Index Index of with User C o s t Real wi th B a s e : Man Hours Labour of Capital Capita l Capi ta l BC 1971 Paid Base B C 1971 Stock in B C 1971 CD$4.359 / '000 CD$'000 CD$0.1317/ CD$'000 CD$'000 Man hour . . . . $1 paid C A P I T A L 1957 2.005 28223. 56601. 0.0766 155120. 11886. 1958 2.124 28238. 59977. 0.0765 151177. 11569. 1959 2.112 26525. 56020. 0.0795 150226. 11945. 1960 2.275 28072. 63869. 0.0815 151900. 12377. 1961 2.370 29298. 69427. 0.0816 156488. 12773. 1962 2.396 27831. 66688. 0.0843 160800. 13550. 1963 2.509 29655. 74418. 0.0811 164757. 13355. 1964 2.649 29712. 78696. 0.0839 170468. 14301. 1965 2.828 30044. 84961. 0.0881 178527. 15733. 1966 3.037 29168. 88587. 0.0974 187859. 18297. 1967 3.286 29911. 98288. 0.1101 192586. 21206. 1968 3.524 31006. 109271. 0.1134 196523. 22284. 1969 3.760 29473. 110825. 0.1221 215818. 26358. 1970 4.022 29527. 118765. 0.1296 237091. 30736. 1971 4.359 31989. 139430. 0.1317 255247. 33607. 1972 4.796 32220. 154526. 0.1352 266687. 36069. 1973 5.366 35865. 192442. 0.1375 277865. 38195. 1974 6.291 31483. 198071. 0.1705 292818. 49930. 1975 7.264 24650. 179068. 0.1936 297847. 57661. 1976 8.283 31804. 263441. 0.1977 298053. 58919. 1977 9.189 33933.' 311823. 0.2026 301065. 60984. 1978 9.909 36314. 359839. 02243 317474. 71196. 1979 11.057 36781. 406691. 02616 331720. 86780. 1980 12.586 34516. 434419. 0.3085 351993 108594. 1981 14.010 29112. 407873. 0.3921 345561. 135495. 1982 16.033 23880. 382880. 0.4294 317453. 136305. Table A.1.4: PNW West - Lumber and Shingle Price Index, Implicit quantity Index and Revenue; Pulpchip Price, Volume and Revenue. Year Lumber Lumber Lumber Pulpchip Pulpchip Pulpchip and and and Average Volume Revenue Shingle Shingle Shingle Price Price Index Implicit Revenue Base : Quantity BC 1971 Index CD$99.89/ CD$'000 CD$/O.D. '000 O.D. CD$'000 Mfbm - - : - Ton Tons 1957 68.72 8716 598987. 17.57 1346 ' 23654. 1958 69.24 9016 624275. 17.52 1471 25767. 1959 74.92 10117 757973. 16.17 1541 24915. 1960 70.98 9386 666270. 16.66 1628 27120. 1961 70.83 8871 628353. 15.79 1820 28718. 1962 75.54 9412 710980 16.88 1948 32870. 1963 77.74 9739 757145 18.97 1957 37121. 1964 79.56 10350 823378 19.31 2244 43325. 1965 79.16 10427 825392 16.27 3083 50158. 1966 81.83 9628 787887. 15.95 3635 57994. 1967 84.00 9245 776535. 18.66 3789 70687. 1968 101.37 9555 968578. 19.60 4292 84101. 1969 112.14 8561 960000. 18.67 5399 100824. 1970 89.59 9584 858653. 19.27 5737 110555. 1971 108.37 9748 1056432. 21.62 5186 112096. 1972 127.20 11934 1517937. 21.24 6275 133281. 1973 170.39 11530 1964563. 21.23 7024 149178. 1974 154.21 10847 1672653. 29.40 7345 215929. 1975 15126 9899 1497281. 45.65 5726. 261340. 1976 184.96 10133 1874281. 44.38 6481 287654. 1977 230.54 11640 2682416. 44.11 6205 273696. 1978 280.58 11732 ' 3291698. 48.28 5166 249355. 1979 329.05 11571 3807598. 50.42 5186 261452. 1980 299.35 9298 2783424. 96.34 6316 608500. 1981 274.86 8477 2329999. 106.88 5329 569520. 1982 245.37 8085 1983717. 110.18 4395 484271. Table A.1.5: PNW West - Average Sawlog Price, Sawlog Volume, Sawlog Expenditure and mVMfbm Scribner Log Scale Conversion Factor. Year National PNW Log National PNW Log Sawlog Log Market Forest Markets Forest Market Expenditure Implicit Sales Average Price Based Conversion Based Sawlog Based Implicit Factor Sawlog Price Implicit Sawlog Price Sawlog Volume Volume CD$/m3 Cp$/m3 CD$'000 mVMfbm Scribner 1957 9.24 11.19 31093. 25696. 287445. 4.7338 1958 8.91 10.70 35266. 29364. 314091. 4.8011 1959 9.26 11.45 41146. 33278. 381073. 4.7024 1960 9.77 11.31 38848. 33556. 379435. 4.7775 1961 9.58 11.11 35618. 30688. 341059. 4.8346 1962 9.93 11.60 38783. 33199. 385196. 4.8468 1963 10.18 12.91 37125. 29280. 378007. 4.7175 1964 10.30 12.42 32217. 26716. 331686. 5.0650 1965 11.39 13.08 38767. 33744. 441476. 4.9356 1966 12.31 12.63 34204. 33318. 420891. 5.0861 1967 12.98 12.62 32709. 33643. 424557. 4.9680 1968 13.73 15.06 36664. 33410. 503273. 5.3162 1969 15.51 18.07 33448. 28704. 518751. 5.3171 1970 14.02 13.74 34175. 34855. 479038. 5.4693 1971 15.06 15.41 35427. 34624. 533677. 5.4147 1972 18.18 18.80 42206. 40818. 767260. 5.2178 1973 19.75 26.27 45201. 33989. 892736. 5.2458 1974 22.75 28.30 40462. 32547. 921240. 5.2893 1975 26.30 29.74 37209. 32901. 978620. 5.2684 1976 31.11 37.52 35868. 29743. 1115993. 5.1990 1977 39.89 48.76 39027. 31929. 1556893. 5.2617 1978 47.54 56.85 39692. 33198. 1887150. 5.3467 1979 55.34 71.16 36325. 28247. 2010142. 5.1223 1980 58.74 74.09 27275. 21625. 1602076. 4.9343 1981 59.91 64.87 26455. 24432. 1584951. 5.2901 1982 68.51 56.96 23343. 28075 1599305. 5.2423 274 Table A.1.6: PNW West - Wage Index, Implicit Index of Man-hours Paid and Expenditures with Labour; Index of the User Cost of Capital; Index of Real Capital Stock and Expenditures with Capital. Year Wage Implicit Expenditure Index of Index of Expenditure Index Index of with User Cost Real with Base: Man hours Labour of Capital Capital Capital BC 1971 Paid Base: BC 1971 Stock in BC 1971 CD$4.359/ '000 CD$'000 CD$0.1317/ CD$'000 CD$'000 Man-hour S1CAPITAL paid 1957 2.276 " 84131. 191478. 0.0652 543590. 35435. 1958 2.288 75725. 173227. 0.0671 546087. 36661. 1959 2.435 81063. 197356. 0.0692 553007. 38261. 1960 2.453 74603. 182970. 0.0708 570059. 40367. 1961 2.601 65117. 169339. 0.0742 586736. 43525. 1962 2.779 67212. 186794. 0.0768 593520. 45592. 1963 2.932 64898. 190303. 0.0783 586490. 45908. 1964 3.072 66664. 204814. 0.0800 582599. 46605. 1965 3.128 65506. 204907. 0.0809 597087. 48309. 1966 3.293 64116. 211155. 0.0884 608521. 53792. 1967 3.612 59922. 216462. 0.0939 608423. 57126. 1968 3.836 62075. 238115. 0.1034 610251. 63070. 1969 4.079 59216. 241568. 0.1152 623293. 71817. 1970 4.259 57366. 244350. 0.1305 630545. 82284. 1971 4.396 62481. 274696. 0.1225 628951. 77074. 1972 4.651 67512. 313993. 0.1226 638856. 78352. 1973 5.048 722213. 364506. 0.1333 667645. 88981. 1974 5.299 70362. 372873. 0.1572 706176. 110980. 1975 6.005 64976. 390192. 0.1750 750634. 131366. 1976 6.578 73193. 481479. 0.1807 775861. 140210. 1977 7.988 79487. 634920. 0.2011 797781. 160452. 1978 9.648 79032. 762484. 02495 832554. 207747. 1979 10.639 75887. 807347. 0.2977 866895. 258079. 1980 11.683 69283. 809443. 0.3649 890252. 324816. 1981 13.334 64554. 860755. 0.4674 .896597. 419074. 1982 14.362 56455. 810809. 0.4903 875141. 429050.' 275 Table A.1.7: Wood Quality Indices (one-stage) - Vancouver Forest Region, Vancouver Log Market and PNW Log Market. Year Vancouver Vancouver Vancouver Forest Log MarketLog Market Region (Stat. (Stat. (All Grades, BC Grades, BC grades, BC log scale) log scale) log scale) VLM VLM VLM 1925 = 100. 1925 = 100. 1925=.1J00. PNW Log Vancouver PNW Log Market Log Market Market (All (Sawlogs, (Sawlogs, grades, cubic cubic Scribner meters) meters) log scale) PNW VLM VLM 1957 = 100. 1947 = 100. 1947 = 100. 1925 98.79 100.00 100.00 - - -1926 97.22 96.05 96.05 - - -1927 97.28 96.31 96.31 - — — 1928 95.08 92.07 92.07 - - -1929 92.89 91.40 91.40 - - -1930 92.07 89.04 89.04 - - -1931 91.17 86.11 86.11 - - — 1932 91.61 86.74 86.74 - - — 1933 91.15 86.00 86.00 — - — 1934 89.26 85.56 85.56 - - -1935 89.21 89.13 89.13 - - — 1936 89.38 87.15 87.15 - - — 1937 87.50 86.98 86.98 - - -1938 88.02 85.93 85.93 - - -1939 86.90 85.45 85.45 - - -1940 85.48 86.10 86.10 - - — 1941 86.19 84.47 84.47 - - — 1942 8627 85.30 85.30 - . - -1943 85.85 84.23 84.23 - - -1944 84.41 83.11 82.54 - - -1945 84.98 84.46 85.16 - — -1946 84.96 83.20 • 84.47 - - -1947 84.39 84.02 85.42 - 100.00 — 1948 84.03 84.17 85.31 - 98.31 -1949 84.75 84.02 85.15 - 98.40 -1950 84.49 83.34 83.94 - 97.00 -276 Table A.1.7 Continued. Year Vancouver Vancouver Vancouver PNW Log Vancouver PNW Log Forest Log MarketLog Market Market Log Market Market Region (Stat. Stat. (All (All (Sawlogs, (Sawlogs, grades, BC grades, BC grades, BC grades, cubic cubic log scale) log scale) log scale) Scribner log scale) meters) meters) VLM VLM VLM PNW VLM VLM 1925 = 100. 1925 = 100. 1925 = 100. 1957 = 100. 1947 = 100. 1947 = 100. 1951 83.48 82.62 82.44 97.92 1952 83.59 82.45 82.32 - 99.29 -1953 81.88 80.88 80.64 - 95.63 -1954 80.44 79.19 78.74 - 92.57 -1955 81.24 80.77 80.67 - 94.27 -1956 81.05 79.88 80.79 - 93.68 -1957 80.84 79.99 80.69 100.00 94.15 151.94 1958 81.31 81.74 82.27 95.41 96.49 144.01 1959 79.92 78.59 79.50 92.91 93.06 147.29 1960 79.75 80.81 81.55 91.38 95.80 143.37 1961 78.61 80.71 81.39 87.25 95.67 137.06 1962 78.28 78.90 80.19 87.99 91.98 136.64 1963 77.16 79.92 82.16 91.18 91.87 144.61 1964 77.52 79.49 81.46 88.76 92.26 132.73 1965 77.13 7927 81.32 88.80 90.80 136.30 1966 77.05 78.21 80.48 87.17 89.72 129.83 1967 76.98 77.57 79.66 85.89 89.35 131.78 1968 76.76 76.48 78.73 88.69 88.95 126.18 1969 76.61 77.48 80.00 88.03 90.48 125.11 1970 75.75 76.94 79.36 86.30 89.18 120.24 1971 75.47 75.57 77.03 86.71 88.20 119.06 1972 75.58 75.19 76.59 86.07 90.17 127.16 1973 75.36 76.00 77.74 85.31 89.78 125.00 1974 74.32 77.16 78.30 85.29 93.34 124.79 1975 72.97 76.38 78.41 85.35 91.75 126.59 1976 74.35 77.28 79.25 88.63 92.85 135.54 1977 74.69 77.83 80.68 88.64 93.41 134.25 1978 75.25 81.56 83.97 86.37 98.86 130.38 1979 76.45 82.74 85.08 86.52 99.83 131.12 1980 75.13 80.92 81.39 86.69 97.73 136.42 1981 — 78.68 79.62 82.40 96.40 120.68 1982 - 83.15 84.36 82.47 100.79 120.03 APPENDIX II - RESULTS OF ALTERNATIVE SPECIFICATIONS OF THE ECONOMETRIC MODEL Table A.2.1: No Wood Quality - British Columbia Parameter Estimates and Summary Statistics PRICES FIXED FACTORS Equation Lumber Pulpchips Sawlogs Labour Capital Quality Time Constant R1 DW Lumber -12.8 (-13.2) -2.34 (-9.90) 10.6 (13.0) 4.53 (147) 0.617 (0.916) 0.00 -1.42 (-5.56) 35.7 (9.03) 0.53 2.01 Pulpchips -2.34 (-9.90) 0.22 (2.07) 1.58 (6.62) 0.54 (6.33) 0.26 (1.78) 0.00 -0.08 (-1.51) 4.50 (4.63) 0.75 1.69 Sawlogs 10.6 (13.0) '1.58 (6.62) -9.19 (-12.40) -2.97 (-1 1.40) -0.29 (-0.53) 0.00 0.87 (4.24) -27.96 (-8.38) 0.53 2.13 Labour 4.53 (14.7) 0.54 • (6.33) -2.97 (-11.40) -2.10 (-16.70) -0.59 (-2.42) 0.00 1 0.63 (6.88) -1 1.26 (-8.08) 0.63 1.77 Capital 0.617 0.916 0.26 (1.78) -0.29 (-0.53) -0.59 (-2.42) -0.38 (-0.65) 0.00 0.00 -0.45 (-0.10) - -Quality 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - -Time -1.42 (-5.56) -0.08 (-1.51) 0.87 (4.24) 0.63 (6.88) 0.00 0.00 0.00 4.32 (6.04) - -Profit Function - - - - - - - -42.47 (-2.85) 0.65 1.68 (1) Asymptotic t-ratios in parenthesis ; critical values for a large sample are t n n 9 1 - = 1.960 and t = 2.576 Co Table A.2.2; No Wood Quality - Pacific Northwest Parameter Estimates and Summary Statistics PRICES FIXED FACTORS Equation Lumber Pulpchips Sawlogs Labour Capital Quality Time Constant R ! DW Lumber -4.81 -1.33 3.71 2.43 -0.284 0.00 -0.807 19.8 0.33 1.54 (-4.65) (-4.75) 4.36) (5.91) (-0.198) (-3.68) t (1.83) Pulpchips -1.33 0.36 0.72 0.259 -0.30 0.00 0,.1 23 4.67 0.75 1.1 1 (-4.75) (2.99) (3.06) (1.93) (-0.91) (2.40) (1.81) Sawlogs 3.7 1 0.72 -2.95 -1.48 0.50 0.00 0.36 -15.0 0.25 1.58 (4.36) (3.06) (-4.06) (-4.39) (0.43) (2.09) (-1.70) Labour 2.43 0.26 -1.48 -1.22 0.09 0.00 0^ 32 -8.45 0.56 1.54 (5.91) (7.53) (-0.38) (-6.14) (-4.47) (-0.47) (3.06) (476) (-1.85) Capital -0.284 -0.30 0.50 0.09 -4.32 0.00 0.00 30.2 _ (-0.198) (-0.91) (0.43) (0.17) (-1.40) (1.33) Quality 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -Time -0.807 0.12 0.36 0.32 0.00 0.00 0.00 2.09 _ (-3.68) 2.40 (2.09) (4.15) (3.47) Profit Function _ _ _ _ _ _ -123. 0.36 1.36 (-1.48) (1) Asymptotic t-ratios in paranthesis; critical values for a large sample 3 r e V 0 2 5 = 1.960 and *0.005 = 2.576 Table A.2.3; Across Region Restrictions on Wood Quality and Time - British Columbia Parameter Estimates and Summary Statistics PRICES FIXED FACTORS Equation Lumber Pulpchips Sawlogs Labour Capital Quality Time Constant R ! DW Lumber -13.1 -1.66 10.4 4.66 0.685 -8.23 -1.19 35.4 0.33 1.18 (-20.9) (-8.19) (19.7) (22.4) (1.08)' (-4.32) (-5.62) (9.74) Pulpchips -1.66 0.55 0.95 0.36 0.72 -2.43 -0.12 0.77 0.73 1.24 (-8.19) (4.84) (4.73) (4.95) (5.77) (-6.12) (-3.11) (0.88) Sawlogs 10.4 6.95 -8.47 -2.77 -0.82 7.78 0.75 -23.7 0.41 1.23 (19.7) (4.73) (-17.0) (-15.2) (-1.67) (5.23) (4.69) (-8.04) Labour 4.66 0.36 -2.77 -2.22 -0.64 2.82 0''.56 3.81 0.48 1.06 (22.4) (4.95) (-15.2) (-22.1) (-2.79) (4.14) (7,17) (6.31) Capital 0.685 0.72 -0.82 -0.64 2.03 -7.48 0.00 -14.3 _ _ (1.08) (5.77) (-1.67) (-2.79) (2.50) (-5.00) (-2.87) Quality -8.23 -2.43 7.78 2.82 -6.44 108. 0.00 64.5 _ (-4.32) (6.12) (5.23) (4.14) (-3.74) (5.04) (5.78) Time -1.19 -0.12 0.75 0.56 0.00 0.00 0.00 3.81 _ (-5.62) (-3.11) (4.69) (7.17) (6.31) Profit Function _ _ _ _ _ _ -2.1 1 0.74 1.00 (-0.13) (1) Asymptotic t-ratios in parenthesis ; critical values for a large sample = 1.960 a n d W s : = 2.576 Table A.2.4; Across Region Restrictions on Wood Quality and Time - Pacific Northwest Parameter Estimates and Summary Statistics PRICES FIXED FACTORS Equation Lumber Pulpchips Sawlogs Labour Capital Quality Time Constant R ! DW Lumber -3.34 -1.19 2.71 1.81 (-4.32) (-7.93) (4.23) (6.90) Pulpchips -1.19 0.40 0.67 0.14 (-7.93) (6.59) (4.61) (2.02) Sawlogs 2.71 0.67 -2.35 -1.06 (4.23) (4.61) (-3.93) (-5.12) Labour 1.81 0.14 -1.06 -0.92 (6.90) (2.02) (-5.12) (-7.18) Capital 1.88 0.44 -1.27 -0.94 (1.56) (1.93) (-1.28) (-2.28) Quality -0.585 -2.15 1.65 1.51 (-0.291) (-6.38) (1.08) (2.25) Time -1.19 ' -0.12 0.75 0.56 (-5.62) (-3.11) (4.69) (7.17) Profit Function 1.88 (1.56) -0.585 (-0.291) -1.19 (-5.62) 3.20 (0.365) 0.29 1.42 0.44 (1.93) -2.15 (-6.38) ^0.12 (-3.11) 0.74 (0.43) 0.87 1.43 -1.27 (-1.28) 1.65 (1.08) 0.75 (4.69) -2.64 (-0.36) 0.21 1.45 -0.94 (-2.28) 1.51 (2.25) Q.56 (7.17) -1.30 (-0.45) 0.59 1.35 -2.21 (-0.97) -9.82 (-4.65) 0.00 12.8 (0.74) - --9.82 (4.65) 1.06 (0.20) 0.00 70.1 (3.78) - -0.00 0.00 0.00 3.70 (6.25) -56.9 (-0.87) 0.74 1.38 (1) Asymptotic t-ratios in paranthesis; critical values for a large sample are t = 1.960 and t = 2.576 Table A.2.5; Homogeneity of Degree One in Capital - British Columbia Parameter Estimates and Summary Statistics PRICES FIXED FACTORS Equation Lumber Pulpchips Sawlogs Labour Capital Quality Time Constant R' DW Lumber -10 .5 (-8.46) -1 .72 (-6.57) 8.45 (8.03) 3.80 (11.0) 0.00 5.16 (2.10) - 0 . 8 8 5 (-6.50) 32.5 (10.5) 0.57 1.99 Pulpchips -1 .72 (-6.57) 0.43 (3.64) 1.00 (3.72) 0.29 (3.39) 0.00 0.91 (1.38) 6,.io (2.46) 3.90 (5.71) 0.71 1.41 Sawlogs 8.45 (8.03) 1 .do (3.72) -7 .28 (-7.70) -2 .19 (-7.42) 0.00 -3 .09 (-1.51) 0.47 (3.91) -23.1 (-8.91) 0.58 2.00 Labour 3.80 (11.0) 0.29 (3.39) -2 .19 (-7.42) -1 .90 (-16.4) 0.00 -3 .00 (-3.43) 0(.32 (7,24) . -12.1 (-13.8) 0.68 1.84 Capital 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 - -Quality 5.16 (2.10) 0.91 (1.38) -3 .09 (-1.51) -3 .00 (-3.43) 0.00 1 1.27 (0.46) 0.00 -17 .8 (-2.72) - -Time - 0 . 885 (-6.50) . 0.10 (2.46) 0.46 (3.91) 0.32 (7.24) 0.00 0.00 0.00 2.31 (6.51) - -Profit Function _ _ _ _ _ _ -45 .0 0.76 1.10 (-11.6) (1) Asymptotic t-ratios in parenthesis ; critical values for a large sample are t = 1.960 and t n = 2.576 Table A.2.6: Homogeneity of Degree One in Capital - Pacific Northwest Parameter Estimates and Summary Statistics*^. PRICES FIXED FACTORS Equation Lumber Pulpchips Sawlogs Labour Capital Quality Time Constant R2 DW Lumber -3.76 (-6.63) -1.40 (-9.97) 2.81 (6.38) 2.35 (10.6) 0.00 5.03 (3.14) -0.360 (-2.41) 13.2 (7.73) 0.15 1.58 Pulpchips -1.40 (-9.97) 0.28 (3.68) 0.82 (7.10) 0.30 (3.27) 0.00 -1.50 (-4.24) -0.012 (-0.36) 3.73 (7.96) 0.85 1.23 Sawlogs 2.81 (6.38) 0.82 (7.10) -2.04 (-5.69) -1.59 (-9.77) 0.00 -3.82 (-2.98) 0.04 (0.38) 8.32 (-6.27) 0.09 1.56 Labour 2.35 (10.6) 0.30 (3.27) -1.59 (-9.77) -1.05 (-6.63) 0.00 0.28 (0.53) 6.33 (6.16) -7.60 (-10.0) 0.52 1.44 Capital 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - -Quality 5.03 (3.14) -1.50 (-4.24) -3.82 (-2.92) 0.28 (0.53) 0.00 0.93 (0.17) 0.00 -8.67 (-1.92) - -Time -0.360 (-2.41) -0.012 (-0.36) 0.04 (0.38) 0.33 (6.16) 0.00 0.00 0.00 1.35 (3.47) - -Profit Function _ _ _ _ _ _ -18.8 0.74 1.39 (-6.42) (1) Asymptotic t-ratios in paranthesis; critical values for a large sample are t = 1.960 and t n = 2.576 Table A.2.7; No Technical Progress - British Columbia Parameter Estimates and Summary Statistics PRICES FIXED FACTORS Equation Lumber Pulpchips Sawlogs Labour Capital Quality Time Constant R> DW Lumber -13.7 -1.99 1 1.1 4.60 -1.33 1.70 0.00 44.6 0.23 0.73 (-17.3) (-8.88) (14.9) (21.4) (-3.62) (0.676) t (13.4) Pulpchips -1.99 0.62 1.16 0.21 0.56 -0.69 0.00 1.47 0.78 1.25 (-8.88) (5.63) (4.81) (3.22) (6.02) (-1.35) (159) Sawlogs 1 1.1 1 .i 6 -9.49 -2.72 0.50 0.35 0.00 -30.6 0.38 0.88 (14.9) (4.81) (-12.8) (-14.0) (1.64) (0.18) (-10.1) 1 Labour 4.60 0.2 1 -2.72 -2.09 0.27 -1.34 6.oo -14.5 0.27 0.60 (21.4) (3.22) (14.0) (-23.7) (2.03) (-1.41) (-13.7) Capital -1.33 0.56 0.50 0.27 4.25 -7.54 0.00 -19.4 (-3.62) (6.02) (1.64) (2.03) (7.32) (-6.74) (-5.55) Quality 1.70 -0.69 0.35 -1.34 -7.54 36.1 . 0.00 34.4 _ _ (0.676) (-1.35) (0.18) (-1.41) (-6.74) (2.47) (3.06) Time 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - -Profit Function _ _ _ _ _ 2.02 0.37 0.42 (0.17) (1) Asymptotic t-ratios in parenthesis ; critical values for a large sample are t = 1.960 and t = 2.576 Table A.2.8: No Technical Progress - Pacific Northwest Parameter Estimates and Summary Statistics PRICES FIXED FACTORS Equation Lumber Pulpchips Sawlogs Labour Capital Quality Time Constant R' DW Lumber -4.7?. -1.53 3.52 2.69 -2.45 2.84 0.00 31.3 0.04 1.25 (-5.5 7) (-7.72) (4.99) (9.07) (-2.21) (1.47) t (3.49) Pulpchips -1.53 0.43 1.08 -0.019 -0.44 -2.60 O'.OO 6.61 0.87 1.59 (-772) (5.95) (6.30) (-0.26) (-2.15) (-8.79) (3.75) Sawlogs 3.52 1.08 -2.50 -2.10 1.06 -1.1 1 0.00 -18.1 (4.99) (6.30) (-3.95) (-8.20) (1.16) (-0.76) (-2.44) 0.05 1.24 Labour 2.69 -0.019 -2.10 -0.57 1.83 0.87' o'.oo -18.7 0.38 1.19 (9.07) (-0.26) (-8.20) (-4.14) (4.54) (1.27) (-5.83) Capital -2.45 -0.44 1.06 1.83 -5.14 -2.70 0.00 43.70 - -(-2.21) (-2.15) (1.16) (4.54) (-2.26) (-1.20) (2.54) Quality 2.84 -2.60 -1.1 1 0.87 -2.70 -6.61 0.00 1 7.1 _ -( M 7 ) (-8.79) (-0.76) (1.27) (-1.20) (-1.13) (0.87) Time 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - -Profit Function _ _ • _ _ _ -188. 0.75 1.21 (-2.85) (1) Asymptotic t-ratios in paranthesis; critical values for a large sample are t = 1.960 and t = 2.576 Tab A2.9: No Wood Quality - Demand and Supply Elasticites*1)'*2) PRICES FIXED FACTORS QUANTITIES TIME*3) Lumber Chips Logs Labour Capital Quality Lumber 1.03 0.05 -0.74 -0.34 -0.36 0.034 1.31 0.07 -1.07 -0.32 1.40 0.001 Pulpchips 0.40 -0.05 -0.05 -0.30 -0.01 0.045 0.58 0.25 -0.44 -0.39 0.74 0.040 Sawlogs 1.17 0.01 -0.80 -0.30 -0.39 0.035 1.87 0.09 -1.67 -0.28 1.20 0.005 Labour 1.24 0.13 -0.68 -0.68 -0.04 0.020 1.16 0.17 -0.59 -0.75 1.35 -0.007 (1) These elasticities were computed at the mean of the data. (2) The top number refers to BC and the bottom number to the PNW. (3) These values give the percentage change per year. Tab A2.10;Across Region Restrictions on Wood Quality and Time -Demand and Supply Elasticites' ' PRICES FIXED FACTORS QUANTITIES TIME* ) Lumber Chips Logs Labour Capital Quality Lumber 0.92 0.13 -0.74 -0.30 -0.60 0.16 0.040 1.53 0.04 -1.18._ -0.39 0.06 0.59 0.035 Pulpchips 1.13 0.58 -1.11 -0.60 0.64 -3.15 0.042 0.39 0.41 -0.25 -0.55 0.69 -3.73 0.038 Sawlogs 1.19 0.20 -1.04 -0.34 -0.47 -0.06 0.040 2.11 0.05 -1.78 -0.37 0.20 0.44 0.032 Labour 1.11 0.24 -0.78 -0.57 -0.26 -0.33 0.026 1.48 0.23 -0.81 -0.91 0.59 -0.40 0.014 (1) These elasticities were computed at the mean of the data. (2) The top number refers to BC and the bottom number to the PNW. (3) These values give the percentage change per year. Tab A2.11 :Homogeneous of Degree One in Capital - Demand and Supply Elasticites*1'-* ' PRICES FIXED FACTORS QUANTITIES TIME*3) Lumber Chips Logs Labour Capital Quality Lumber 1.56 0.20 -122 -0.53 1.00 -4.04 0.002 1.67 0.04 -1.34 -0.37 1.00 -0.66 0.009 Pulpchips 1.69 0.32 -1.20 -0.81 1.00 -3.48 0.029 0.33 0.08 -0.14 -0.28 1.00 -4.43 0.015 Sawlogs 1.95 0.22 -1.57 -0.60 1.00 -3.44 -0.014 2.35 0.03 -2.13 -0.25 1.00 -0.01 -0.061 Labour 1.90 0.34 -1.35 -0.89 1.00 -2.99 -0.008 1.35 0.12 -0.52 -0.95 1.00 -1.49 0.008 (1) These elasticities were computed at the mean of the data. (2) The top number refers to BC and the bottom number to the PNW. (3) These values give the percentage change per year. Tab A2.12:No Technical Progress - Demand and Supply Elasticites^ 1)'^ PRICES FIXED FACTORS QUANTITIES TIME*3' Lumber C