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Investigation of methods to determine economic recoverability of timber inventories on a regional basis Cooney, Timothy Martin 1981

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INVESTIGATION OF METHODS TO DETERMINE ECONOMIC RECOVERABILITY OF TIMBER INVENTORIES ON A REGIONAL BASIS by TIMOTHY MARTIN COONEY B . S c , Michigan State U n i v e r s i t y , 1976 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF FORESTRY in THE FACULTY OF GRADUATE STUDIES ( F a c u l t y of F o r e s t r y , U n i v e r s i t y Of B r i t i s h Columbia) We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l 1981 © Timothy M a r t i n Cooney, 1981 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of 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 c o p y i n g 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 . Department of Forestry  The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 DF-6 (2/791 i i ABSTRACT Information on the economic reco v e r a b i l i t y of timber inventories becomes increasingly important as timber harvesting approaches the extensive margin. In B r i t i s h Columbia, as elsewhere in North America, concern for e f f i c i e n t temporal a l l o c a t i o n of timber supplies requires a greater understanding of the economic dimensions of timber inventories now and in future years. There are two general categories of problems encountered when attempting to estimate the economic re c o v e r a b i l i t y of inventory. F i r s t , there has been a general confusion or misunderstanding of the meaning and measure of economic timber supply. Second, the d i f f i c u l t i e s associated with measuring inventory recoverability have either discouraged further action or resulted in f a i r l y subjective measures being developed for large regions. In t h i s study, two broad concepts of economic timber supply are discussed; flow, or true economic, supply and stock supply. From this discussion i t is shown that a stock-flow supply measure i s most suited to forest management needs. That i s , periodic stocks of recoverable timber which are adjusted for inflows and outflows that occur between periods as a result of both b i o l o g i c a l and socio-economic forces. Various uses of stock-flow supply modeling and inventory estimates in forest management are then presented. i i i Next, three alternative means of estimating stock-flow timber supplies are discussed, with reference to previous studies using each a l t e r n a t i v e : (a) experienced estimates, (b) engineering studies, and (c) s t a t i s t i c a l models. Reasons are enumerated for further developing the s t a t i s t i c a l approach, re l a t i n g the operability of logging to the s i t e , stand and tree c h a r a c t e r i s t i c s that describes the physical timber inventory. Using data collected from logging operations in coastal B r i t i s h Columbia over the period 1977 to 1979, i t i s shown that s i g n i f i c a n t relationships can be developed for predicting logging o p e r a b i l i t y , using only those c h a r a c t e r i s t i c s that are or could be included in inventory records. S p e c i f i c a l l y , equations are estimated for determining (a) the length of roads required for logging an area, (b) f a l l i n g and bucking productivity, (c) yarding productivity, (d) scaled volume of logs harvested, and (e) the p r o b a b i l i t y of choosing a s p e c i f i c harvesting system. These equations are then combined with others already developed for stumpage appraisals to i l l u s t r a t e how recoverable stock timber supplies could be estimated. Using current factor costs in B r i t i s h Columbia and log prices on the Vancouver Log Market, an estimate of the 1980 economic inventory was developed for the University of B r i t i s h Columbia Research Forest. Trends in logging costs and log prices in B r i t i s h Columbia were developed, and inventory rec o v e r a b i l i t y on the Research Forest was projected through the year 2000 to XV i l l u s t r a t e how stock estimates can then be adjusted for temporal flows. It has been concluded that new developments in inventory recording and c o l l a t i n g f a c i l i t i e s being implemented by the B r i t i s h Columbia Forest Service enhance the f e a s i b i l i t y of following simlar procedures on Timber' Supply Areas in the province. V TABLE OF CONTENTS T i t l e Page i Abstract i i Table Of Contents .... v L i s t Of Tables ix L i s t Of Figures x Acknowledgement xi Glossary x i i i 1 INTRODUCTION - 1 1.1 TIMBER INVENTORIES AND ECONOMIC RECOVERABILITY ... 1 1.2 RESEARCH OBJECTIVE 4 1.3 SCOPE OF RESEARCH AND PROCEDURAL OUTLINE 5 1.4 ORGANIZATION 10 2 EONOMIC TIMBER SUPPLY -- CONCEPTS AND USES 12 2.1 CONCEPTS OF ECONOMIC TIMBER SUPPLY 12 2.11 Flow Supplies 12 2.12 Stock Supplies 23 2.2 APPLICATIONS OF STOCK-FLOW SUPPLY MODELS 30 2.21 Multiple-use Planning 32 2.22 Access Planning 33 2.23 Logging Planning 34 2.24 S i l v i c u l t u r a l Planning 35 2.25 Determining Optimum Rotation Periods 36 2.26 Yi e l d Planning ; 37 2.3 SUMMARY 39 v i 3 ALTERNATIVE METHODS FOR ESTIMATING ECONOMIC TIMBER SUPPLY 41 3.1 INTRODUCTION 41 3.2 EXPERIENCED ESTIMATES 42 3.3 ENGINEERING STUDIES 45 3.4 STATISTICAL STUDIES 47 3.5 STUDY APPROACH 53 4 RESOURCE CHARACTERISTICS AND LOGGING OPERABILITY IN COASTAL BRITISH COLUMBIA ' 55 4.1 INTRODUCTION 55 4.2 PROCEDURAL CONCEPTS 56 4.21 Revenues And Costs 56 4.22 Cost vs. Time Studies 57 4.221 Cost Center Problems 58 4.222 Dual Vector Of Temporal Cost Changes 60 4.223 Industry Reluctance 60 4.224 Accounting Differences 60 4.23 Estimation by Phase of Logging 61 4.3 RESOURCE FACTORS AFFECTING LOGGING COSTS -DESCRIPTION 64 4.31 Harvesting System Choice 64 4.32 Access Development 70 4.33 F a l l i n g And Bucking 72 4.34 Yarding 74 4.4 INPUT DEMANDS AND PRODUCTIVITY OF LOGGING IN COASTAL BRITISH COLUMBIA 7 6 4.41 Objective 76 v i i 4.42 Scope 78 4.43 Variables Sampled And Measurement Procedures . 80 4.44 Regression Hypotheses And Procedures 82 4.45 Qualitative Analysis 84 4.46 Regression Analysis 91 4.461 Road Length (RL) ; 93 4.462 F a l l i n g And Bucking Productivity (F&BP) .. 97 4.463 Yarding Productivity (YP) 101 4.464 Volume Harvested (Q) 107 4.465 System P r o b a b i l i t i e s 109 4.5 SUMMARY 113 5 ECONOMIC TIMBER SUPPLY OF THE U.B.C. RESEARCH FOREST .. 117 5.1 INTRODUCTION 117 5.2 DESCRIPTION OF THE RESEARCH FOREST 119 5.3 PROCEDURES 124 5.31 Data C o l l e c t i o n , Preparation And Co l l a t i n g ... 124 5.32 Logging Production Simulation 132 5.33 Costs 139 5.34 Revenues 143 5.35 P r o f i t And Risk 150 5.36 Harvesting P r i o r i t i e s 152 5.37 Stand Growth 153 5.38 Cost And Price Trends 156 5.4 RECOVERABLE TIMBER SUPPLIES ON THE U.B.C. RESEARCH FOREST: 1980-2000 164 5.41 Marginal Recovery Costs And Values 178 5.42 Comparative Inventory Characteristics 181 v i i i 6 CONCLUSIONS AND RECOMMENDATIONS 184 6.1 CURRENT APPLICABILITY 184 6 . 2 SUMMARY . 185 6.3 RECOMMENDATIONS 188 Bibliography 192 Appendix 1. Correlation Matrices and Histograms of Variables used in Logging Productivity, Production and • System Probability Regression Analyses 202 Appendix 2. L i s t i n g of Computer Program (ETS) Developed for Determining Recoverable Timber Stocks Supplies and Simulating Periodic Flow Adjustments .... 221 Appendix 3. U.B.C. Research Forest Economic Inventory Data 262 Appendix 4. Coefficents of Height (HGT), Diameter (DBH) and Stand Density (SPH) Decadal Growth Equations 274 Appendix 5. Annual Reports of Economic Timber Supplies on the University Of B r i t i s h Columbia Research Forest: 1982-2000 276 ix LIST OF TABLES T a b l e Page 1. P o s s i b l e C o m b i n a t i o n s of F a c t o r C o s t s and P r o d u c t i v i t y i n D e t e r m i n i n g D i r e c t i o n of U n i t L o g g i n g Cost Changes 61 2. Resource F a c t o r s and I d e n t i f i e d V a r i a b l e s . 81 3. V a r i a b l e S t a t i s t i c s : Mean, S t a n d a r d D e v i a t i o n , Minimum and Maximum 86 4. Beta C o e f f i c i e n t s f o r F a l l i n g and 3 u c k i n g P r o d u c t i v i t y E q u a t i o n 99 5. Beta C o e f f i c i e n t s f o r Y a r d i n g P r o d u c t i v i t y E q u a t i o n ' „ .. .. 102 6. Beta C o e f f i c i e n t s f o r L o g g i n g System L i n e a r P r o b a b i l i t y E q u a t i o n s 109 7. L o g g i n g C o s t s By Component 141 8. Log P r i c e s Used i n Revenue C a l c u l a t i o n s -- By S p e c i e s , Diameter L i m i t s And Grade C a t e g o r i e s 147? 9. R e a l Wage R a t e s , P r i c e I n d i c e s , Annual P r o d u c t i o n , and F a c t o r C o s t s : 1980-2000 161 10. 1980 S t o c k S u p p l y of E c o n o m i c a l l y A c c e s s i b l e Timber 167 11. R e p o r t of P r o j e c t e d L o g g i n g f o r 1981 172 12. Summary Report Of Economic Timber S u p p l i e s On The U n i v e r s i t y Of B r i t i s h C olumbia R e s e a r c h F o r e s t 1980 To 2000 174 X LIST OF FIGURES Figure Page l a . Hypothetical Total Revenue and Cost Curves 14 lb . Hypothetical Net Revenue Curve 14 l c . Hypothetical Marginal Revenue and Cost Curves 14 2. Gross Physical and Recoverable Stock Timber Supplies on a Hypothetical Management Unit 26 3a. Change in Recoverable Stock Over Time ( t ) , Under Conditions of Increasing Productivity ( a l l Else Constant) 29 3b. Change in Recoverable Stock Over Time ( t ) , Under Conditions of Increasing Factor Costs, Log Prices and Productivity . 29 4. Road Length (A = lha) 95 5. Economic Timber Supply Modeling Procedures 118 6. U.B.C. Research Forest Primary Cover D i s t r i b u t i o n 121 7. I l l u s t r a t i o n Of Hauling Distance Concept 128 8. Average Grade Di s t r i b u t i o n of Annual Harvests on the Research Forest: 1968-1979 147 9. Projected Real Log Prices And Logging Costs In B r i t i s h Columbia: 1980 - 2000 163 10. Stocks Of Timber In Physical And Economic Inventories On The University Of B r i t i s h Columbia Research Forest: 1980 - 2000 175 11a. 1980 ' Total Cost and Revenue Curves Logging on the U.B.C. Research Forest 180 l i b . 1980 Marginal Cost and Revenue Curves Logging on the U.B.C. Research Forest 180 12. Recoverable vs. Non-recoverable Inventory Characteristics on the U.B.C. Research Forest 183 XX ACKNOWLEDGEMENT I would l i k e to gra t e f u l l y acknowledge the assistance provided by my thesis advisor, Dr. David Haley. In addition to suggesting an area of research, Dr. Haley has provided continuous d i r e c t i o n and advice, as well as the enthusiasm, friendship and f i n a n c i a l support necessary to complete this thesis. The review and advice of Dr. P. C o t t e l l and Dr. D. Williams was also greatly appreciated. For their cooperation in obtaining data on coast logging operations, I would l i k e to thank Mr. G. Boothroyd ( B r i t i s h Columbia Forest Products Limited), Mr. S. Chester (Canadian Forest Products Limited), Mr. H. K. Williams (MacMillan Bloedel Limited), Mr. B. Devitt (Pac i f i c Logging Company Limited), Mr. D. Gyton (Rayonier Canada (B.C.) Limited), and, Mr. D. Thompson (Weldwood of Canada Limited). I would also l i k e to acknowledge the assistance of their management and staff at the div i s i o n s from which data was c o l l e c t e d . The assistance and cooperation of Mr. G. Nagy ( B r i t i s h Columbia Forest Service) during data c o l l e c t i o n , was also greatly appreciated. Mr. P. Sanders provided both helpful comments and assistance during the c o l l e c t i o n of inventory data on the University of B r i t i s h Columbia Research Forest. Financial assistance for t h i s research was provided by the National' Sciences and Engineering Research Council, Canada; and Canadian Forestry Service Graduate Research Assi stantships. xix F i n a l l y , the assistance and unending support of my wife, Beverly, made i t possible to carry this project through to i t s completion. Timothy M. Cooney Vancouver, B.C. A p r i l , 1981 x i i i GLOSSARY General AAC allowable annual cut AR average revenue ATC (AC) average t o t a l cost AVC average variable cost cm cent imeters c . u. Close u t i l i z a t i o n standards cunit 100 cubic feet (CCF) dbh diameter at breast height DW Durbin-Watson "d" s t a t i s t i c test) (autocorrelation G gross physical stock of timber point in time at a discrete ha hectare(s) m meters MC marginal cost MR marginal revenue m3 , cu.m. cubic meters NR net revenue P product price Q to t a l production for a discrete point in time Q economically optimal rate of production over a Q/t given period (economic supply) periodic rate of production R recoverable stock of timber at in time (economic inventory) a discrete point SEE standard error of the estimate t time TC to t a l cost TFC to t a l fixed cost TVC t o t a l variable cost TR tot a l revenue Operabi1i ty Study Regression Variables A area in hectares ALV log volume (actual) for 10 m log, in m3 B brush density index C c u l l (decay, waste and breakage %) D diameter at breast height in centimeters E elevation in meters EX exposed bedrock index F&BP f a l l i n g and bucking productivity (m3/hour) F&BT f a l l i n g and bucking time in man-hours GY grapple yarding H stand average height (merchantable) in meters HL highlead yarding LR long-reach yarding 0 obstacles index x i v Q volume harvested in m3 (net) RL road length in meters S ground slope in % SD s o i l depth in meters SM s o i l moisture index SPH stems per hectare ST s o i l type index T terrain index V t o t a l standing timber volume in m3 VPH volume per hectare YP yarding productivity (m3/hour) YT yarding time in machine-hours Z dummy variable for yarding system i Species Abbreviations B balsam f i r (Abies balsamea(L.)Mi11.) C western red cedar (Thuja "plicata Donn) Cy cypress (Chamaecypar i s nootkatensis (D-.Don) Spach) D deciduous species (in this study): A red alder (Alnus rubra Bong.) Cot black cottonwood (Populus trichocarpa Torr. and Gray) Mb broadleaf maple (Acer macrophyllum Pursh) F Douglas f i r (Pseudotsuga menziesii(Mirb.)Franco) H western hemlock! (Tsuga heterophylla (Raf . ) Sarg.) Pw western white pine' (PTnus roonticola Dougl.) Ss sitka spruce (Picea sitchensis(Bong.)Carr) 1 CHAPTER 1 INTRODUCTION 1.1 TIMBER INVENTORIES AND ECONOMIC RECOVERABILITY Determination of the '.economic recoverabi 1 it y of current and future timber inventories has been an increasing concern of forest managers. This concern is precipitated mainly by longstanding expectations of timber shortages (Clawson, 1978; Jackson, 1980); expectations which can only be f u l f i l l e d in terms of economic rather than physical scarcity (Hair, 1978). To f u l l y understand the effect world demands for timber products w i l l have on recoverable timber supplies, and s i m i l a r l y for supply on r e l a t i v e prices, i t is clear that we must redefine our measures of resource stocks. Currently, timber supply estimates (inventories) are a simple accounting of physical assets. As noted by Zivnuska (1967) in his assessment of U.S. Timber Resources in a World Economy: "From the standpoint of economic and s o c i a l inquiry . . . such a concept is inadequate, since i t f a i l s to consider the questions of why and to whom such a stock or flow is a resource. There must be . . . the a b i l i t y to use t h i s stock or flow to the s a t i s f a c t i o n of human wants and desires." (p. 8). Thus, the true, or economic, stock supply of timber is the volume that can be supplied to an economy at a given point in time, and result in a potential increase in s o c i a l welfare (Stewart, 1975). The accessible l i m i t of t h i s supply is 2 defined by the point at which harvesting additional timber volumes result in no change in s o c i a l welfare. Measuring so c i a l welfare in pecuniary terms, the economically recoverable portion of forest resource inventories consists of timber with market values s u f f i c i e n t to provide a return, at least equal to opportunity costs, to a l l factors of production employed in harvesting, transporting, manufacturing and marketing the desired products. This assumes either a perfect market ( i . e . no e x t e r n a l i t i e s ) , or, that the lands being considered earn their highest use in timber production and any external economies or diseconomies w i l l be included in the analysis of net value. Current timber inventories redefined in terms of their economic recoverability w i l l provide the measure of supply necessary to forecast the occurrance and/or extent of an ". . . economic ' f a l l down'. . ." (Gayle, 1977. p. 44) in future timber supplies. This information is of primary importance to the determination of harvest rates on regulated lands. Inaccurate supply estimates, via their influence on harvest rates, could adversely af f e c t income generation, employment and the general economic development of current and future generations, p a r t i c u l a r l y in economies dependent on the forest sector (Pearse, 1976). Accurate measures of recoverable timber supplies are very important in B r i t i s h Columbia, where 94.1 percent (Pearse, 1976. p. 26) of forest lands are p u b l i c l y owned and regulated. Consequently, the need to include s o c i a l and economic 3 variables in the assessment of current inventory data was e x p l i c i t l y recognized in the 1976 Report of the Royal Commission on Forest Resources in B r i t i s h Columbia; in which Commissioner Pearse recommended " . . . modifications to the inventory to recognize forest lands that w i l l probably not be operable, at least with present technology and under prevailing economic conditions, r e l a t i v e to recoverable values, unacceptable environmental damage, or s i l v i c u l t u r a l d i f f i c u l t i e s . " (Pearse, 1976. p. 236). This recommendation was subsequently incorporated into p r o v i n c i a l forest planning guidelines (Province of B r i t i s h Columbia,' 1978a. sect. 1.01), which formed the basis for a recently completed analysis of resources in B r i t i s h Columbia (Province of B r i t i s h Columbia , 1980a-1980d). In this analysis, however, a c c e s s i b i l i t y is defined primarily by physical c r i t e r i a that w i l l not, under a l l circumstances, r e f l e c t the true economic relationship between resource c h a r a c t e r i s t i c s and r e c o v e r a b i l i t y . This approach was a necessary ' f i r s t step' due to the lack of information on s i t e -s p e c i f i c harvesting costs and resource values. It is imperative that recoverablity estimates now be improved, with timber inventories more c r i t i c a l l y defined by the socio-economic forces that t r u l y a l t e r the status of recoverable timber supplies. 4 1.2 RESEARCH OBJECTIVE The f i n a l result of any research into quantifying economic timber supply is simply a statement of q u a l i f i e d physical supplies: the volume of raw input which, when combined with other productive factors, can be economically converted into market products. Therefore, the primary objective of my research is to develop and demonstrate a method of estimating economic timber supply for a management unit, using the s i t e , stand and tree c h a r a c t e r i s t i c s that define the location, quality and o p e r a b i l i t y of physical timber inventories. In achieving this objective, i t w i l l be necessary to develop s i t e - s p e c i f i c relationships that define the productivity of input factors used in timber harvesting. No new concepts of supply theory w i l l be, or need be, developed. However, i t w i l l be necessary to c l a r i f y economic supply theory in terms of the uses for timber supply estimates. Too often in the forestry l i t e r a t u r e the term 'supply' is loosely used to delineate physical stocks of timber. This is c l e a r l y not a d e f i n i t i o n of supply in an economic sense: which is the quantity supplied to a market per unit of time, over varying levels of product price. Therefore, prerequisite to meeting my outlined objective i s the need to e x p l i c i t l y identify the differences and a p p l i c a b i l i t y of stock and flow supply estimates in forest management planning. 5 1.3 SCOPE OF RESEARCH AND PROCEDURAL OUTLINE There are three levels of timber 'supplies' that could be inventoried on a management unit: (a) t o t a l physical, (b) technologically recoverable, and, (c) economically recoverable. At any given point in time these are fixed stocks. The physical stocks are the most obvious as they consist of the measurable standing volumes. Technological stocks are the volumes of physical stocks as constrained by our current physical e f f i c i e n c y in recovering these stocks. This l e v e l of inventory is synonymous with statements of "merchantable timber" commonly referred to in forestry l i t e r a t u r e . The economically recoverable stock i s the volume of technological stock as constrained by current values and costs of forest resource use. Assuming, r e a l i s t i c a l l y , that the f r o n t i e r s of technology in any production process precede economic f e a s i b i l i t y , and technological advances w i l l increase future intensive and extensive margins of r e c o v e r a b i l i t y , then, the stock of timber w i l l decrease from the physical to economic l e v e l . Economically recoverable stocks can be further categorized into two sub-levels. The f i r s t comprises volumes which are recoverable i f only market costs and revenue of harvesting are considered. The second category is the volume in accessible stocks when a l l costs and benefits, tangible and intangible, of harvesting are considered ( i . e . the impact of harvesting on the production of public and quasi-public goods and services i s internalized to the harvesting decision 6 process) . Given the stated objective of my research, the analysis is focused on the t h i r d l e v e l of timber stocks -- the economically recoverable volume. Within this framework, only market costs and revenues w i l l be considered in the discussion of supply theory and development of the proposed methodology. Once the a c c e s s i b i l i t y of timber supplies has been described under perfect conditions, market imperfections can be considered, and the impact on s o c i a l welfare of alternative strategies for corrective action can be analyzed. This approach is the f i r s t step, common to economic analysis, necessary to c l a r i f y supply theory in terms of timber production (Jackson, 1980). There are numerous uses to which estimates of economically recoverable timber supplies could be applied. The intended use w i l l , to some extent, define the form, calcu l a t i o n and required precision of such estimates. Some of the primary uses are i n : (a) harvest scheduling, (b) s i l v i c u l t u r a l investment planning, (c) stumpage appraisal, (d) ca l c u l a t i n g rotation lengths, and , (e) regulation of harvest rates (Berndt and others, 1979). The f i r s t two are part of the t a c t i c a l or operational planning that result in the year to year a c t i v i t i e s associated with forest management. For these, the amount of information and precision required w i l l be r e l a t i v e l y high, to ensure a proper ranking of opportunities and thus e f f i c i e n t a l l o c a t i o n of resources. Stumpage appraisal requires the greatest amount of information 7 and p r e c i s i o n to ensure t h a t a l l p r o d u c t i v e r e s o u r c e s earn t h e i r f a i r v a l u e . T h i s i s p a r t i c u l a r l y t r u e i n B r i t i s h Columbia due to the l a c k of market c o m p e t i t i o n f o r t i m b e r . The i m p l i c a t i o n i s t h a t t h e r e i s no means of j u d g i n g whether a p p r a i s e d p r i c e s r e f l e c t t r u e market v a l u e s ( H a l e y , 1980). The f i n a l two uses mentioned, r o t a t i o n l e n g t h d e t e r m i n a t i o n and h a r v e s t r e g u l a t i o n , r e q u i r e the l e a s t i n terms of i n f o r m a t i o n and p r e c i s i o n due t o t h e i r s t r a t e g i c n a t u r e . The l o n g - t e r m p l a n n i n g (or r o t a t i o n ) p e r i o d i n most f o r e s t s t y p i c a l of N o r t h America can range up t o a c e n t u r y or more. Thus, t h e r e e x i s t s a c e r t a i n amount of f l e x i b i l i t y i n d e t e r m i n i n g the optimum r o t a t i o n l e n g t h and h a r v e s t r a t e t h a t w i l l b e n e f i t s o c i e t y the most. C o n t i n u o u s a d j u s t m e n t s can be made t o r e c o v e r a b l e t i m b e r s u p p l y e s t i m a t e s as b i o l o g i c a l , t e c h n o l o g i c a l and socio-economic c o n d i t i o n s change, and as more i n f o r m a t i o n becomes a v a i l a b l e . The approach taken i n t h i s s tudy i s t o d e v e l o p e s t i m a t e s of economic a c c e s s i b i l i t y f o r use i n s t r a t e g i c y i e l d p l a n n i n g . The p r i m a r y reason f o r c o n c e n t r a t i n g i n t h i s a r e a i s because of the a f f e c t t h a t i n a c c u r a t e s u p p l y e s t i m a t e s can have on h a r v e s t r a t e d e t e r m i n a t i o n , and t h u s the w e l f a r e of s o c i e t y , as noted e a r l i e r . In f a c t , t h e r e a r e those who b e l i e v e t h a t , i n terms of community s t a b i l i t y , we have a l r e a d y reached the stage where pa s t e r r o r s i n h a r v e s t r a t e c a l c u l a t i o n s may soon r e s u l t i n economic h a r d s h i p f o r some ar e a s (Reed, 1979). A d d i t i o n a l l y , y i e l d r e g u l a t i o n p o l i c i e s are l i k e l y the most debated i s s u e i n f o r e s t management a t p r e s e n t ( P e a r s e , 1976), 8 thus i t i s urgent that current research in forest policy and economics be directed towards improving our a b i l i t y to analyse regulation p o l i c i e s . Since y i e l d planning requires estimates of supplies over time, the analysis w i l l show how point estimates of the recoverable inventory can be adjusted to r e f l e c t expected changes in forest structure ( i . e . b i o l o g i c a l growth and mortality), harvesting technology and r e l a t i v e scarcity among productive resources. The analysis w i l l be carr i e d out in three stages. In the f i r s t stage, concepts of economic timber supply are c l a r i f i e d ; both in i s o l a t i o n and in reference to desired uses of supply measures. Second', alternative methods of determining economic timber supplies are reviewed. These f i r s t two stages are supported primarily by the results of past studies as reported in the forestry and economics l i t e r a t u r e . The f i n a l stage, and focus of this analysis, concerns the development and application of a methodology for estimating economically recoverable timber supplies from currently available inventory data. In th i s stage, the scope is narrowed to consider development and application of the estimation process in the context of coastal B r i t i s h Columbia only. Here, the inter r e l a t i o n s h i p s between resource c h a r a c t e r i s t i c s and logging productivity w i l l be both t h e o r e t i c a l l y and quantitatively defined. S p e c i f i c a l l y , the objectives of this stage are as follows: 9 (a) Identify s i t e , stand and tree c h a r a c t e r i s t i c s which would seem a p r i o r i to have an influence on productivity of logging in coastal B r i t i s h Columbia. (b) Estimate the relationship between logging road development needs and the s i t e , stand and tree c h a r a c t e r i s t i c s i d e n t i f i e d above. (c) Estimate the relationships between productivity and the s i t e stand and tree c h a r a c t e r i s t i c s i d e n t i f i e d in (a), for; (i) labor in f a l l i n g and bucking, and ( i i ) c a p i t a l in yarding, of major logging system(s) currently in use. If unique relationships can 'be i d e n t i f i e d for more than one system, id e n t i f y the c r i t e r i a that determine the choice of system to be used on a logging operation. (d) Estimate the relationships between logging output (scaled volume of logs) and timber input (cruised volume of timber) as influenced by the p r o d u c t i v i t i e s experienced. (e) I l l u s t r a t e how the relationships determined above, when combined with information on market prices, factor costs and other productivity relationships, can be applied to inventory data on a coastal management unit in B r i t i s h Columbia to estimate the recoverable stock of timber. Objective (a) is completed primarily through a search of the available l i t e r a t u r e on logging productivity. The relationships in objectives (b) to (d) are estimated from sample data c o l l e c t e d on 64 logging operations in the coast region of B r i t i s h Columbia, from July 1979 to A p r i l 1980. The University of B r i t i s h Columbia Research Forest (Maple Ridge, B.C.) was used as the sample management unit for i l l u s t r a t i n g application of the model in f u l f i l l i n g objective (e). This area was chosen primarily because of the perceived a v a i l a b i l i t y of s u f f i c i e n t resource data to expedite sample appl i c a t i o n . F i n a l l y , the model is made dynamic with consideration given to the effects of expected trends in stand growth, factor, costs and resource values, on rec o v e r a b i l i t y of 10 the inventory. Although the s p e c i f i c relationships used in the f i n a l stage are applicable only to other management units in the coastal region, the basic procedures followed can be si m i l a r l y developed for the i n t e r i o r region of B r i t i s h Columbia, and in general, for other regulated forests in North Amer i c a . 1.4 ORGANIZATION Chapter Two begins with a discussion of the theoreti c a l concepts of supply. The difference between flow supplies (supply in the true economic sense) and stock supplies (inventories) is developed in the framework of forest management. Some applications of economic timber supply estimates and relationships w i l l close the chapter. Chapter Three presents alternative means of estimating economic timber supplies. The alternatives are grouped into three categories: (a) experienced estimates, (b) engineering studies, and (c) mathematical and s t a t i s t i c a l models. Supported by past studies, the basic methodology, advantages and disadvantages of each are discussed. Chapter Four begins with a discussion of procedural concepts basic to the methodology I am proposing. Next, the effect of resource c h a r a c t e r i s t i c s on logging o p e r a b i l i t y is hypothesized by phase of logging, based upon information from the forestry l i t e r a t u r e . The remainder of this chapter presents the results of regression analyses on logging data 11 for coastal B r i t i s h Columbia including both a q u a l i t a t i v e and quantitative description of sample c h a r a c t e r i s t i c s and estimated equations. Chapter Five i l l u s t r a t e s application of the productivity relationships for estimating economic recoverability of timber inventories. Using inventory data available on the University of B r i t i s h Columbia Research Forest, current labor and machine costs in B r i t i s h Columbia and current log prices on the Vancouver Log Market, an estimate of recoverable timber supply in 1980 is derived. Reviewing trends in log prices and factor costs, recoverability estimates are developed for the period 1981 - 2000, to i l l u s t r a t e adjustments for temporal flows in timber supplies. A brief statement on the current a p p l i c a b i l i t y of similar procedures on timber supply areas in B r i t i s h Columbia is given in Chapter Six. This i s followed by the conclusion and recommendations for further research needed to implement economic supply modeling in the province. 12 CHAPTER 2 EONOMIC TIMBER SUPPLY ~ CONCEPTS AND USES 2.1 CONCEPTS OF ECONOMIC TIMBER SUPPLY The purpose of this chapter is to set the foundation for selecting the method of estimating economically recoverable timber supplies. Although this section b r i e f l y covers well known neo-classical theories of production and supply, i t is necessary to set these theories in the context of timber production in order to c l a r i f y the measure of supply necessary for y i e l d planning. It is also necessary that the basic d e f i n i t i o n of the term "supply" used in this paper be set forth, so as to avoid semantic confusion. This confusion i s evidenced by studies of forest resource "supply" that are actually statements of inventories (Callahan, 1979). 2.11 Flow Supplies The economic timber supply in a flow, or true economic, sense is the volume of timber that w i l l be made available to primary product (log) markets over a given period of time for a given level of timber (stumpage) price. The relationship between supply and stumpage price ( i . e . timber supply schedule) expresses the volumes that w i l l be made available, per unit.of time, over a range of possible prices. Deriving a timber supply schedule and periodic estimates of volume supplied i s , t h e o r e t i c a l l y , quite straight forward. However, 13 i t w i l l be shown later that numerous problems can arise in empirical applications of the theory. The following discussion is presented under the basic condition that perfect competition exists in both product . and factor markets. Thus, no single producer controls the price i t receives for i t s products ( i . e . a l l firms are "price-takers"), nor does any single firm have input demands s u f f i c i e n t to,influence market prices of inputs. In the short run, 1 given the objective of a firm is to maximize p r o f i t s , (Awh, 1976; I n t r i 1 i g a t o r ; 1971) the output decision becomes primarily a problem of minimizing costs with respect to given input prices and the current production function of the firm. The firms' supply of products to the market over a given period i s the output l e v e l where the difference between t o t a l revenue (TR) and t o t a l costs (TC) of production i s the greatest ( i . e . where net revenue i s maximized). At t h i s point the marginal cost (MC) of production is equal to the marginal revenue (MR) earned by the last unit of output. 2 This l e v e l of output the economic supply of the firm. Graphically, hypothetical costs and revenues as described above are shown in Figures la to l c . 1Period of time over which at least one productive input i s fixed in quantity. 2Since product price (P) is constant for the firm, price = marginal revenue = average revenue. Thus, the firm's economic supply is that output where MC = P. It is also necessary to note that for p r o f i t maximization to be ensured using marginal analysis, two " s u f f i c i e n t conditions" must be met. The f i r s t order condition is for MC = P. The second order condition is for MC to be increasing (Awh, 1976). Figure l c . Hypothetical Marginal Revenue and Cost Curves 15 The firm's supply curve is c l e a r l y represented by that portion of i t s MC curve (heavily shaded in Fi g . l c ) that l i e s above the minimum average variable cost (AVC) of production. As long as price remains greater than or equal to AVC the firm can continue to produce since i t can cover operational costs. Should price f a l l below AVC the firm must close as continued operation increases the size of losses. If AVC < P < ATC (average t o t a l cost), the firm continues operation so as to minimize the losses to fixed costs that i t would otherwise incur (Awh, 1976). Assuming industry-wide changes in production levels w i l l not a f f e c t factor prices, the industry supply curve is simply the summation of individual firm supplies at a l l price l e v e l s . If industry-wide changes in production result in factor price increases, each firm operates on a higher cost and thus supply curve. The industry supply curve is then the summation of the set of points connecting each firm's new supply curve at the higher output l e v e l s . (Awh, 1976). Analysis of production in the long run, when a l l inputs can be freely varied, is similar to that for short-run production, the main difference being that a l l costs are variable. Also, the long-run i s e s s e n t i a l l y a planning concept since a l l inputs can be varied only in a discrete sense. Changing the quantities of fixed inputs moves the firm immediately into a new short-run cost structure. 16 Jackson (1980) has investigated the theory of timber production and supply in the context of neo-classical economic production theory as described above. Jackson's production function related mean annual increment (MAI, i.e. the flow or rate of production), to time and the l e v e l of inputs used to establish a growing stock after harvesting. Under stated conditions of perfect competition, i t was assumed the firm would maximize present wealth ( p r o f i t s ) . S p e c i f i c a l l y , i t was assumed that a firm w i l l attempt to maximize the net present value of harvests; that i s , revenue at harvest (net stumpage price x vol./acre harvested), less the compounded costs of establishment (unit cost of establishment inputs x quantity of inputs used), discounted to the present. Holding the supply of land, unit establishment cost and net stumpage price constant, i t was shown that a firm's market rate of harvest was a function of both quantity available at rotation age and the "frequency" of harvests. (Jackson, 1980. pp. 22-23). Allowing timber price to increase he determined that, due to increased investment in establishment inputs, the production (yield) function would s h i f t to higher levels of output over a l l time periods. However, marginal value growth of the timber stand would approach marginal cost of production at an e a r l i e r rotation age, thus increasing the frequency but reducing the volume of harvests. As long as the mean annual increment at the new production l e v e l i s greater than the l e v e l prior to the price increase, i t was shown that marginal costs of timber 17 production w i l l increase with increasing production l e v e l s . Hence, supply w i l l increase (as expected) with increasing timber prices (Jackson, 1980. pp. 24-25). He went on to demonstrate that industry aggregate supply could be determined by summing the supply of each firm at various timber prices, with the analysis also considering the impact of increasing unit establishment costs and land supply on the e l a s t i c i t y of aggregate timber supplies. Jackson's work is a s i g n i f i c a n t contribution to the understanding of timber production economics. It also helps to point out some of the problems associated with estimating economic timber supply based on a neo-classical approach. F i r s t , Jackson's analysis assumed the non-existence of old growth inventories, thereby ignoring the problems of determining their rate of harvest. This approach is quite appropriate in a production study since old growth inventories are e s s e n t i a l l y the product of past production. Depletion of these inventories occurs at a rate dependent on present and expected future net timber prices, d u r a b i l i t y of the inventory ( i . e . rate of decay and mortality), and the private (or social) opportunity cost of c a p i t a l . However, in an analysis of timber reco v e r a b i l i t y the volume in mature old-growth inventories cannot be ignored where i t comprises the bulk of harvested timber, as in western North America. Hence, in determining annual timber supplies i t w i l l be necessary to know the reco v e r a b i l i t y of old-growth stocks, as well as that of current growing stocks. 18 A second problem, and p o s s i b l y the most p e r v a s i v e i n a p p l i e d timber p r o d u c t i o n economics, c o n c e r n s the d e t e r m i n a t i o n and a p p l i c a b i l i t y of aggregate r e l a t i o n s h i p s . A p r o d u c t i o n f u n c t i o n r e p r e s e n t s the maximum q u a n t i t y of homogeneous output t h a t can be produced u s i n g g i v e n q u a n t i t i e s of homogeneous i n p u t s . In h i s a n a l y s i s of t i m b e r p r o d u c t i o n , J a c k s o n assumed each f i r m would be o p e r a t i n g on l a n d s of homogeneous p r o d u c t i v e c a p a c i t y , w i t h homogeneous species-c h a r a c t e r i s t i c s and homogeneous i n p u t s t o e s t a b l i s h m e n t . A l t h o u g h he c o n s i d e r e d the impact of r i s i n g f a c t o r p r i c e s and l i m i t e d s u p p l i e s of l a n d on aggregate i n d u s t r y s u p p l y , no c o n s i d e r a t i o n was g i v e n t o problems of a g g r e g a t i o n w i t h i n an i n d i v i d u a l f i r m . R e c o g n i z i n g t h a t f o r e s t s a r e heterogeneous w i t h r e s p e c t t o p r o d u c t i v e c a p a c i t i e s , a c c e s s i b i l i t y , and s p e c i e s , i t would be a r e a l i s t i c assumption t h a t a g g r e g a t i o n problems would a r i s e . For example, i f s u p p l i e s were e s t i m a t e d i n i s o l a t i o n by i d e n t i f i a b l e c a t e g o r i e s of s i t e p r o d u c t i v i t y , a g g r e g a t i o n over a l l c a t e g o r i e s may p r o v i d e a m i s l e a d i n g e s t i m a t e of the t o t a l , s i n c e f a c t o r s o t h e r than s i t e q u a l i t y w i l l i n f l u e n c e r e c o v e r a b i l i t y . 3 3 A l t h o u g h annual growth on sta n d s f o r the same s i t e q u a l i t y ( f o r a g i v e n s p e c i e ) w i l l be s i m i l a r once the s t a n d i s e s t a b l i s h e d , the i n p u t s r e q u i r e d f o r e s t a b l i s h m e n t w i l l d i f f e r a c c o r d i n g t o s t a n d a c c e s s i b i l i t y . Thus, J a c k s o n s ' a n a l y s i s i s v a l i d o n l y under f u r t h e r assumptions of homogeneity of l a n d i n terms of s l o p e , t e r r a i n , e l e v a t i o n , e t c . , as w e l l as r e q u i r i n g t h a t p r o d u c t i o n i n p u t s be c e n t r a l l y l o c a t e d t o a l l s i t e s . 19 An extension of aggregation problems within a single firm is the problem of i n d u s t r i a l aggregation. With an industry being defined " . . . as a set of firms producing close substitutes. . ." (Awh, 1976. p. 264), i t must be assumed that a l l firms enjoy the same species types and timber size d i s t r i b u t i o n s , and that increasing stumpage prices are equally d i s t r i b u t e d among a l l species. Without this assumption, determining industry supplies would require additional adjustments for r e l a t i v e changes among firms within the industry over time. The d i f f i c u l t i e s of applied aggregation in production and cost studies led Walters (1963) to conclude that: "The variety of competitive and technological conditions we find in modern econonomies suggests that we can not approximate the basic requirements of sensible aggregation except, perhaps, over firms in the same industry or for narrow sections of the economy." (p. 11; emphasis added). In the context of timber production, I feel the sensible range may be smaller; including only aggregation within the firm, or, over narrow sections of the industry (e.g. sawtimber, pulpwood, et c . ) . A t h i r d area of d i f f i c u l t y is in our current i n a b i l i t y to accurately' estimate the c o e f f i c i e n t s of timber production functions over the range of production inputs. If we define, as Jackson (1980) has, our l e v e l of establishment input to be a measure of "management intensity", then, increasing levels of input w i l l result in higher yields on lands of any given productive capacity. At present we have r e l i a b l e measures of 20 natural growth (production) functions. These measures are usually in the form of s p e c i e s - s i t e - s p e c i f i c volume/age relationships developed from inventory data on natural stands. However, i n s u f f i c i e n t information exists on the response of stands to "basic" (Province of B r i t i s h Columbia, 1980c) or "intensive" s i l v i c u l t u r a l p r a c t i c e s . 4 Information which does exis t , p a r t i c u l a r l y in areas with a preponderance of old-growth timber, allows development of managed-stand production functions for only a few species within narrow ranges of s i t e productivity. Projections for other species and/or outside the range of sampled productivity must rely on estimates of percentage increases in y i e l d s , generally based upon ". . . 'best guesses' . . ." (Smith, 1977; p. 10). Thus, attempts at determining aggregate timber supplies in the context of neo-classical production theory, cannot be made on a sound basis u n t i l accurate responses to establishment and management input levels can be predicted, over a substantial portion of the range in production p o s s i b i l i t i e s on a given area. 4 E s s e n t i a l l y , basic practices represent those a c t i v i t i e s c a r r i e d out to ensure regeneration of lands denuded due to logging, w i l d f i r e , diseases and pests. This can be a program of planting, seeding or planned natural reforestation, that include the necessary s i t e preparation, brushing or weeding a c t i v i t i e s . This also includes basic protection a c t i v i t i e s . Intensive s i l v i c u l t u r a l a c t i v i t i e s are basic practices plus j u s t i f i a b l e investments in such a c t i v i t i e s as f e r t i l i z a t i o n , commercial thinning, species conversion, genetic improvement, shorter rotations, etc. (Province of B r i t i s h Columbia, 1980c; Smith, 1977). 21 F i n a l l y , assuming the relevant production functions could be i d e n t i f i e d for a l l ownerships, that aggregation within individual firms and across industry would y i e l d "sensible" results, and the recov e r a b i l i t y and desired market rate of old-growth harvest could be estimated, then, the predictive c a p a b i l i t i e s of a neo-classical production model of timber supply would s t i l l be in doubt, due to the assumption of p r o f i t maximization as the primary objective (Marty, 1969). The inappropriateness of p r o f i t maximization as an objective function in the public sector of timber production is apparent in forest management practices and p o l i c i e s on public lands. Alternative objectives, some intangible or with non-pecuniary values, ensure a downward bias in neo-classical economic supply estimates from the true volume of recoverable timber supply. The same conclusions could be drawn for large corporate forest land owners. The existence of returns to c a p i t a l invested in forest lands that are lower than the minimum rate achievable in alternative private investments, suggests these owners have objectives that override p r o f i t maximization (Gregory, 1972). As a result, the true supply of timber in the private sector w i l l also be greater than estimates provided through a neo-classical production study. 5 5The same could be said of small private landowners, corporate and non-corporate, although p r o f i t maximization may be more r e a l i s t i c in these instances. 22 Having spent considerable time on the disadvantages of a neo-classical approach to timber supply estimation, I would l i k e to b r i e f l y restate the importance of such models to forest management. The study by Jackson (1980) has reasserted the v a l i d i t y of the basic economic premise that timber supply is an increasing function of stumpage prices in the private sector. This tenet provides a strong foundation for rational analysis of government p o l i c i e s intended to stimulate timber production. Neo-classical models of production and supply, in addition to providing t h e o r e t i c a l structure for rational policy analysis, can be useful as tools in applied planning and analysis in forest management. In general, such models are useful where p a r t i a l analysis of response to management inputs is j u s t i f i e d , and a l l variables are /r e l a t i v e l y homogeneous. Given that there are a number of objectives in forest management, i t is evident that ". . . a new decision model is needed that i s adapted to multi-goal analysis. . ." (Marty, 1969. p. 91), based upon " . . . new multiresource inventory concepts' and procedures." (McClure, 1979. p. 67). Towards thi s end, the development of stock measures of economically recoverable supplies of timber should greatly improve the current status of information on the quality of timber in inventories. This information could then be used to measure the costs of foregoing net value maximization in order to achieve any number of other objectives that may be e x p l i c i t 23 considerations of the landowners. Concepts of stock supplies and the basic procedures necessary to measure stocks of accessible timber, as well as adjust for flows over time, are presented in the' following section. 2.12 Stock Supplies Stock supplies are an accounting of the quantity of a good.or service available at a single point in time. There is no inter-temporal dimension to stock estimates. That i s , the estimated supply is a measure of t o t a l quantities, not periodic production. Stock a v a i l a b i l i t y in later periods is determined by remeasuring the supply in the future period, or, by adjusting i n i t i a l estimates for inflows and outflows. If the good is in no way perishable then the flow adjustments r e f l e c t periodic consumption (outflows) and production (inflows). Perishable stocks must also be adjusted for additional outflows as measured by the rate of decay (or natural l o s s ) . In forest management, timber inventories are the most commonly encountered form of stock supply models. The extensive amount of l i t e r a t u r e on forest mensuration attests to our a b i l i t i e s to estimate current stocks, as well as adjust for temporal flows in resource stock supplies. However, the current inventories and flow-adjustments are concerned only with the physical attributes of the forest; l i t t l e or no information is collected that allow us to define supplies in relation to the values society places on the goods and services provided by the forest. Focusing on a subset of the 2 4 goods a forest can produce, manufactured wood products, the economic stock supply of timber is the quantity that can be converted to the desired products and result in a net gain in s o c i a l welfare. That i s , product sales revenues equal or exceed a l l costs incurred in bringing the products to market. Hence, information on the quantity of goods producible from the standing timber, market prices of the f i n a l products, and costs of manufacturing from stump to product, is necessary to enable economic c l a s s i f i c a t i o n of present inventories. The process of producing f i n a l consumer goods from timber can be characterized by a chain of four inte r r e l a t e d 'sub-markets' known as the stumpage, primary product (e.g. log), secondary product (e.g. lumber, chips, plywood, etc.) and f i n a l product (e.g. furniture) markets (Manthy, 1978). Assuming each of these markets is characterized by perfect competition, the economic stock supply of timber could be estimated at any point along the production chain. This supply is the volume of timber with cumulative costs of production less .than or equal to the price of the product in the market to which supplies are assessed. The product price in one market is an input cost to the succeeding market, thus, production costs need only be assessed for the market in which supply is estimated. Because of the v a r i a b i l i t y in product recovery factors ( our technological a b i l i t y to f u l l y u t i l i z e raw material inputs), supply estimates derived at the stumpage market should prove to be the most r e l i a b l e . However, there are two situations in which th i s w i l l not hold true. F i r s t , 25 i f the owner has multiple-objectives, then the costs of producing a given volume of timber for log production may understate the true value of the resource to the owner. Where these costs are intangible and/or non-pecuniary, the economic stock supply w i l l be less than the volume determined from market e q u i l i b r i a . Second, i f the market for stumpage is non-competitive, there is no assurance that stumpage prices r e f l e c t true timber values. Thus,, the v a l i d i t y of economic timber supply estimates would be in doubt. Both situations are c h a r a c t e r i s t i c of B r i t i s h Columbia's stumpage market. Thus, r e l i a b l e supply estimates depend on the analysis of production, costs and prices at primary product (log) markets in the Coast Region, and for lack of a log market, secondary product (lumber and chip) markets in the I n t e r i o r . If the analysis is to be carried out in a market other than stumpage, the assumption of p r o f i t maximization may be more acceptable. Since product prices ( i m p l i c i t in an integrated firm) are determined competitively, producers w i l l attempt - to minimize production costs thereby maximizing p r o f i t s to logging, m i l l i n g or manufacturing. That i s , once the decision to harvest timber has been made, the primary objective w i l l most l i k e l y be to maximize economic e f f i c i e n c y , as measured by p r o f i t s . Under this assumption a stock timber supply schedule can be developed as shown in figure 2. Given market prices at a single point in time, log producers would choose to log those stands of timber that for reasons of proximity to log markets, slope, te r r a i n and timber 26 c h a r a c t e r i s t i c s , can be harvested at the least cost. To increase the volume of harvest, producers w i l l have to log successively higher cost stands. Assuming that a l l inputs to logging (labor, c a p i t a l equipment, supplies, e t c . ) , except for land or timber, could be continuously increased, at some l e v e l of harvest the cost of logging the next succeeding volume (MC) would exceed the a d d i t i o n a l revenue (MR) earned. This l e v e l (R in F i g . 2) i s then a measure of the gross recoverable or economic stock supply of timber. Unless the management unit i s r e l a t i v e l y small with homogeneous s i t e , stand and timber c h a r a c t e r i s t i c s representing the easiest operating conditions and highest timber q u a l i t y , then, t h i s recoverable volume can be'expected to be less than the gross physical stock of timber (G*in F i g . 2). * * R G Figure 2. Gross Physical and Recoverable Stock Timber Supplies on a Hypothetical Management Unit 27 The costs considered in deriving the MC of logging include (temporary) road, f a l l i n g and bucking, primary transport (yarding or skidding), loading, hauling, unloading, sorting, scaling, booming, t e r t i a r y transport ( i f any), normal p r o f i t allowance, and stumpage cos t s . 6 Marginal revenue (MR) in figure 2 has been i l l u s t r a t e d as a decreasing function of timber volume due to a presumed declining tree quality with increasing d i f f i c u l t y . Although the function w i l l exhibit s i g n i f i c a n t variance, the more inaccessible s i t e s (especially in mountainous terrain) are hypothesized, in general, to have poorer quality and/or smaller timber than the most accessible areas. It must be emphasized at t h i s point that the recoverable stock as determined above is not a periodic (or annual) rate of harvest. Rather, i t i s the t o t a l volume from which producers can select timber to meet production quotas ( i . e . f u l f i l l supply requirements). The associated marginal cost curve is neither a short run or long-run phenomenon, since i t does not represent a production rate. Producer cost curves (in the true microeconomic sense) w i l l l i e somewhere along the MC curve shown, depending on the op e r a b i l i t y of remaining physical timber supplies. Actual costs w i l l r i s e much more rapidly in any one production period due to diminishing marginal returns to a l l inputs, including timber. 6In B r i t i s h Columbia, although stumpage prices may not r e f l e c t true timber values, they are an accurate measure of true timber input costs to log producers. 28 It was assumed that costs would ri s e over increasing volumes due to logging the easiest (lowest cost) s i t e s f i r s t . If an increasing cost function is to be j u s t i f i e d we must determine what factors influence the l e v e l of d i f f i c u l t y and define their impact on the costs of logging. The general approach taken for defining accessible forests in the past has been to exclude a l l timber that does not meet some physical c r i t e r i o n of r e c o v e r a b i l i t y (Zivnuska, 1967). The c r i t e r i a are often so broad as to exclude s i g n i f i c a n t volumes of recoverable timber. S i m i l a r l y , the "recoverable" timber may also include s i g n i f i c a n t volumes that meet the subjective standard(s) but for other reasons are uneconomic. Hence, there is a need to quantify the actual relationship between logging d i f f i c u l t y and the s i t e , stand and tree c h a r a c t e r i s t i c s of timber inventories. Assuming technological advances w i l l increase future p r o d u c t i v i t i e s , while a l l else remains constant, then marginal costs'of logging w i l l decline over time and the recoverable stock (Rt) w i l l approach the t o t a l growing stock (G*) as shown in figure 3a. Under more r e a l i s t i c assumptions of increasing real factor costs, increasing real log prices and changing t o t a l growing stock i t is not clear, without empirical investigation, as to the direction of change in recoverable stocks. Also, i f there are real increases in factor p r o d u c t i v i t i e s , the magnitude and d i r e c t i o n of change in logging costs w i l l be unknown because of increasing factor cost e f f e c t s . This situation is shown in figure 3b, where 29 MC^  / rt+1 / / Jt+n / / i /1 m -7 / f i . _ — — — • • ( R. 't+l... t+n F i g u r e 3a. Change i n R e c o v e r a b l e Stock Over Time ( t ) , Under C o n d i t i o n s of I n c r e a s i n g P r o d u c t i v i t y ( a l l E l s e C o n s t a n t ) Fj___re 3b. Change i n R e c o v e r a b l e Stock Over Time ( t ) , Under C o n d i t i o n s of I n c r e a s i n g F a c t o r C o s t s , Log P r i c e s and P r o d u c t i v i t y • 30 Factor cost increases are expected to more than offset increases in productivity, y i e l d i n g net annual increases in real logging costs. The preceding discussion has concentrated on log markets for derivation of stock timber supply estimates and the flow adjustment process. The same procedure could be followed i f estimation were to occur in a later market ( i . e . m i l l i n g or manufacturing). However, as noted e a r l i e r , the r e l i a b i l i t y of estimates declines as one moves along the market chain. The most desirable market for estimation of timber supplies is the f i r s t possible market in which competition exists for the market products. To r e i t e r a t e , in B r i t i s h Columbia t h i s i s the primary product or log market, and the secondary product or lumber and chip market in the Coastal and Interior regions, respect i v e l y . 2.2 APPLICATIONS OF STOCK-FLOW SUPPLY MODELS Economic assessments of timber inventories have been neglected for several reasons. I n i t i a l l y , a seemingly endless supply of accessible timber obscured the need for such an assessment. Although this b e l i e f is no longer prevalent, s u p e r f i c i a l reviews of inventory s t a t i s t i c s could give the impression that adequate timber supplies exist (Reed, 1979). Second, there is the be l i e f that we need not be concerned with the r e c o v e r a b i l i t y of the inventory or possible timber shortages, since market forces w i l l maintain supply-demand e q u i l i b r i a in forest products. Although this i s true, we must 31 ask ourselves what degree of sc a r c i t y , rate of r e l a t i v e price increase and i n s t a b i l i t y are we w i l l i n g to accept. Also, the very existence of harvest regulations p o l i c i e s and, in B r i t i s h Columbia, stumpage rates that do not r e f l e c t timber s c a r c i t y , indicate the market is not operating f r e e l y . The spectre of impending timber shortages has prompted Reed (1979) to declare that "The issue facing us today is one of stimulating supply, s p e c i f i c a l l y . . . There is a genuine urgency to intensify forestry in Canada,. . ." (p. 219). There is no question that some le v e l of i n t e n s i f i e d forest management is warranted on most economically operable forest lands in North America today. However, increasing supply levels in general w i l l not necessarily a l t e r the conditions for economic shortages. Marty (1969) has elaborated on our r e s p o n s i b i l i t y in meeting s o c i a l demands for timber supplies: "More timber w i l l not in i t s e l f generate more wages, p r o f i t s and wealth. Additional supplies of timber must find a use and f i l l a need in order to have economic value. Although foresters do not control the demand for forest products and services, they have a r e s p o n s i b i l i t y to. . . determine (1) whether or not the condition of the timber resource i s (or is l i k e l y to be) a l i m i t i n g condition and (2) the actions that would be required to remove or ameliorate this l i m i t a t i o n , and the economic cost of these actions." (p. 88). The stock-flow supply modeling procedures discussed in the previous section can help us to meet our f i r s t r e s p o n s i b i l i t y by providing estimates of resource supplies over time on a l o c a l , regional and/or national basis. If the 32 associated demands exceed expected supplies, then s p a t i a l and temporal resource lim i t a t i o n s to growth are indicated. The model also provides us a tool through which alternative corrective strategies can be tested to determine the most e f f i c i e n t course of action. This section presents a brief description of the uses to which economic timber supply estimates and the modeling process i t s e l f can be applied. One f i n a l reason economic assessment of timber inventories has been neglected i s due to technical d i f f i c u l t i e s . That i s , changing technology, e r r a t i c market demands, in f l a t i o n a r y pressures and the nature of the resource i t s e l f impart an elusive quality to the margin of economic reco v e r a b i l i t y , f r u s t r a t i n g attempts to define economic timber supplies (Pearse, 1976. vol.1; Berndt and others, 1979; Reed, 1979). Owing to the consequences of poor planning resulting from inaccurate supply estimates, these a n a l y t i c a l d i f f i c u l t i e s can no longer be used as j u s t i f i c a t i o n for ignoring the problem. The means for overcoming these d i f f i c u l t i e s , in this study, are discussed in chapters 3, 4 and 5. 2.21 Multiple-use Planning Stock-flow analysis of timber supplies would provide estimates of regional and sub-regional timber re c o v e r a b i l i t y , exclusive of the value of forests in other uses. Since multiple-use forest management can be expected to gain in importance with increasing demands for non-timber uses, forest 3 3 managers must become increasingly adept at planning forest development so as to maximize the value of the forest in a l l i t s uses. Two major d i f f i c u l t i e s preventing e x p l i c i t consideration of other uses in supply models are: (a) the lack of market values for non-timber forest uses, and (b) i n s u f f i c i e n t information on the technical trade-offs between timber and non-timber uses (Kimmins, 1976; Pearse, 1976. vol.1). One possible approach for determining forest development p r i o r i t i e s i s to compare opportunity costs of al t e r n a t i v e strategies, as measured by foregone timber values (Pearse, 1976. vol.1). The proposed stock-flow supply analysis provides the measure of timber value necessary for th i s approach. By conducting the supply analysis under various constraints (e.g. available land base), timber values in each alternative development option can be determined. The most e f f i c i e n t course of action w i l l depend on the willingness of the decision-maker to forego timber value to achieve other objectives. 2.22 Access Planning The costs developed for the supply analysis are net of primary transportation network costs. That i s , the analysis assumes the transportation infrastructure necessary also for other sectors of the economy already exists and i s s u f f i c i e n t to allow f u l l development of the forest resource. At the strategic l e v e l , budget requirements could be i d e n t i f i e d on a regional basis over time by comparing existing infrastructure with that needed to secure recoverable timber supplies. At a 34 more t a c t i c a l l e v e l , such as in Timber Supply Area planning in B r i t i s h Columbia, estimated net stand values could be used to prepare access development proposals. One method of achieving t h i s end is through the application of "integer programming" as suggested by Kirby (1972), for l i n k i n g road costs to harvest values of the various timber stands on a management un i t. 2.23 Logging Planning The proposed stock-flow supply model also provides s p a t i a l information on the accessible timber supply, as implied through the consideration of hauling costs (secondary transport phase; C o t t e l l , 1967b). These costs cover the true transportation distance, from product o r i g i n to the actual product market. In Coastal B r i t i s h Columbia t h i s implies that logs destined for " . . . a timber processing f a c i l i t y . . ." (Province of B r i t i s h Columbia, 1978b. p. 9) w i l l be assigned transport cost to that f a c i l i t y , not to the Vancouver Log Market on Howe Sound. Where more than one processing f a c i l i t y could possibly obtain the timber, that f a c i l i t y closest to the assessed timber, as constrained by input requirements, could be used as the product destination. Hence, the supply analysis would provide the i n d u s t r i a l log procurer with information on the future probable locations of accessible timber as well as estimates of t o t a l available supplies. 35 This information, in addition to the i d e n t i f i e d s i t e , stand and tree c h a r a c t e r i s t i c s of recoverable stands, would f a c i l i t a t e the development of operational plans (or working plans) as required by the B.C. Forest Service (Province of B r i t i s h Columbia, 1978a. sect. 5.0-5.5). In general, i t would also provide logging managers with the information necessary to project c a p i t a l and labor requirements, and trends in species and quality of logs recovered from future cut blocks. 2.24 S i l v i c u l t u r a l Planning Stock-flow supply analyses procedures would benefit s i l v i c u l t u r a l planning in two ways. F i r s t , net stand values provided by such analyses are essential, to determining the f i n a n c i a l f e a s i b i l i t y of alternative investments. Computer programs for investment analysis in forestry, such as those by Forster (1968), Chappelle (1969), and Goforth and M i l l s (1975), a l l require future revenue to be provided externally. By a l t e r i n g the growth and y i e l d functions of the supply analysis to r e f l e c t expected treatment response, investment revenues could be calculated. These revenues can then be compared with the i n i t i a l costs to determine f e a s i b i l i t y of the investment. Second, where ownership is characterized by multiple objectives and numerous feasible investment plans have been i d e n t i f i e d , ranking of investments w i l l depend on more than the r e l a t i v e p r o f i t a b i l i t i e s between alt e r n a t i v e s . For example, for a firm requiring a minimum l e v e l of log input to maintain continuous production in i t s processing f a c i l i t i e s , 36 the objective may be to maximize investment revenues subject to a minimum recoverable timber supply in any one period. In the public sector, in order to maintain employment levels, the objective may be to maximize net s o c i a l benefits subject to providing necessary log inputs to a l l manufacturing f a c i l i t i e s , via maintenance or growth of recoverable timber supplies. Here the t o t a l estimated recoverable supplies under the various investment alternatives becomes an important input to the decision process. Supply analyses, under various assumed s i l v i c u l t u r a l investment le v e l s , w i l l also be useful in comparing the costs of intensive vs. extensive methods of increasing future recoverable timber supplies. Where the "supply cost" of logging an additional unit of timber on more remote and d i f f i c u l t t e r r a i n in the future, exceeds the cost of supplying that same volume through intensive s i l v i c u l t u r a l a c t i v i t i e s on less d i f f i c u l t s i t e s , then a reallocation of funds from the extensive to intensive investments is necessary to ensure economic e f f i c i e n c y . 2.25 Determining Optimum Rotation Periods On ownerships where the c a p i t a l costs of holding timber and land (in timber production) are considered, the value information generated by a stock-flow supply analysis would be useful for determining rotation ages of f i n a n c i a l maturity. The optimum rotation length, in an economic sense, is generally recognized as the period of time that maximizes the net value (discounted) of a stand. If more than one rotation 3 7 i s to be considered, i t is the rotation length that maximizes the net present value of the stream of costs and revenues of successively i d e n t i c a l rotations taken into perpetuity. Normally, stands of similar s i t e productivity and species c h a r a c t e r i s t i c s would be assigned the same rotation periods. Realizing that such stands could command d i f f e r i n g market values due to location and ope r a b i l i t y c h a r a c t e r i s t i c s , i t is • evident that their respective growth in value may also d i f f e r . Thus, the stand-specific net values provided by stock supply cost and revenue equations, could be used to calculate rotation periods that maximize f i n a n c i a l maturity on a stand by stand basis i f desired. 2.26 Yi e l d Planning One of the p r i n c i p a l reasons for developing estimates of accessible timber supplies i s to improve harvest scheduling e f f o r t s on regulated lands. The importance of the economic rec o v e r a b i l i t y of inventories in determining harvest rates i s conceptually simple. If harvest rates are optimized or scheduled based on stocks which include timber that is not, or w i l l not become, a part of usable resource supplies, then, at some time in the future (and over succeeding periods) i n s u f f i c i e n t recoverable timber w i l l be available to meet planned harvests. Harvest scheduling models have a l l been developed on the premise that users w i l l know the recov e r a b i l i t y of their supply, or, the cost and revenue relationships defining 38 recoverable supplies. Timber RAM 7 (Navon, 1971) develops harvest scheduling plans based ". . .on the assumptions a l l stands are currently accessible." (p. 7). If a l l areas are not accessible, then the manager must supply estimates of the percent of area accessible now, and percent expected to be accessible in future periods. The current "Two-Phase Method" (Smith, 1978), employed by the B.C. Forest Service, determines a short-term • (20 year) rate of harvest which optimizes timber a l l o c a t i o n from Timber Supply Areas to manufacturing f a c i l i t i e s , and then projects the impact of t h i s rate on long term timber supply l e v e l s . The supply used in the analysis is " . . . an inventory of accessible usable timber. . ." (Smith, 1978. p. 77). In the long-term analysis, using Timber RAM, a c c e s s i b i l i t y constraints are relaxed to include currently inaccessible areas. A new y i e l d planning model, FORPLAN (Johnson and others, 1980), being developed in the United States, s t i l l requires basic user input on the periodic proportions of accessible area in the planning unit. Although s p e c i f i c harvesting cost (by timber type) information can be input to the model, their purpose is in value calculations that are not used to i n t e r n a l l y adjust estimates of recoverable timber supplies. 7Acronym for Resources Allocation Method. 39 As discussed e a r l i e r , accessible (recoverable) supplies are usually defined in terms of physical c r i t e r i a that may or may not r e f l e c t true constraints on o p e r a b i l i t y . Hence, estimated supplies w i l l l i k e l y overstate the true volume of economically recoverable timber. Adjusting these estimates for future a c c e s s i b i l i t y must also rely on judgemental decisions concerning the influence of future prices, costs and technology, on the remaining inaccessible supplies. Therefore, stock economic timber supplies determined from empirical relationships of costs and revenues to physical supplies would provide more r e l i a b l e estimates of true timber supplies for the harvest scheduling models discussed above. S i m i l a r l y , flow adjustments that e x p l i c i t l y consider changing product prices, factor costs and productivity, w i l l better indicate future changes in a c c e s s i b i l i t y than subjective decision c r i t e r i a can provide. 2.3 SUMMARY In th i s chapter I have presented the basic concepts of neo-classical and stock flow approaches to estimating economic timber supplies. Supply in the true economic sense i s the quantity of goods or services provided to a s p e c i f i c market, at a given price l e v e l , over a specified period of time. Stock-flow supplies are measures of t o t a l quantities or inventories of goods available at discrete points in time under s p e c i f i c price, cost and technological conditions. 40 The neo-classical approach was rejected in favor of a stock-flow timber supply model because: (a) stumpage markets are characterized by resource owners with multiple objectives, (b) i n s u f f i c i e n t information exists on managed timber production functions, (c) the heterogeneous nature of the resource and v a r i a b i l i t y among ownerships make i t d i f f i c u l t to derive "sensible" aggregate supply estimates, and (d) neo-classical supply models provide no means for determining the r e c o v e r a b i l i t y of old-growth timber inventories. In contrast, stock-flow supplies do not provide a measure of the optimal rate of harvest (production) as provided through neo-classical supply modeling. However, estimates of recoverable timber stocks derived from stock-flow supply modeling can be used in available harvest scheduling models to test alternative harvest rates. The information provided by stock-flow timber supply analysis was also shown to be useful in applications other than y i e l d planning. Throughout the remainder of t h i s thesis references to "supply", "economic timber supply", "accessible timber supply", etc., are defined as describing the stock or inventory of timber economically recoverable ( i . e . value exceeds cost) at a single point in time. They are not re f e r r i n g to supply in the neo-classical or true economic sense. 41 CHAPTER 3 ALTERNATIVE METHODS FOR ESTIMATING ECONOMIC TIMBER SUPPLY 3.1 INTRODUCTION Determining the economic re c o v e r a b i l i t y of a timber inventory requires an assessment of the interaction between net timber values and various physical c h a r a c t e r i s t i c s of the resource that influence a c c e s s i b i l i t y . The interactions may be undefined as in supply analyses where recov e r a b i l i t y is based upon the experienced estimates of supply region producers. In such cases, expected costs and revenues are i m p l i c i t considerations of the estimates provided. In contrast are operability studies that e x p l i c i t l y define the relationships between resource c h a r a c t e r i s t i c s and the costs, revenues or net values of harvesting. These interactions may be modeled upon engineering p r i n c i p l e s or s t a t i s t i c a l analyses of observed interactions. The following sections present further descriptions of these three approaches to modeling inventory r e c o v e r a b i l i t y . The descriptions are supported by references to previous studies of a similar nature. Advantages and disadvantages are given for each approach. 42 3.2 EXPERIENCED ESTIMATES In general, studies in this category determine inventory a c c e s s i b i l i t y using broad physical c r i t e r i a based on judgements provided by timber owners, managers and processors. In short, estimates are the best-guesses of informed observers. Examples in Canada over the previous two decades include: Wood Products - the Supply of Timber from Canadian  Forests (Wilson, 1966), Canada's Reserve Timber Supply (Reed, 1974) , Terrace-Hazelton Regional Forest Resource Study (Province of B r i t i s h Columbia, 1976), Forest Management in  Canada (Reed, 1978. v o l . I ) , and Canada's Forest Inventory - 1976 (Bowen, 1978). Although none of these studies had economic supply modeling as a primary objective, a l l had to develop a c c e s s i b i l i t y estimates to reduce the inaccuracies imposed by physical inventory data. Such analyses usually begin with a disaggregation of the study area into regions, zones or management units that represent some broad measure of homogeneity. Excluding the study by Bowen (1978), an allowable annual cut (AAC) is then determined for each supply area from inventory records. These estimates are then reduced to account for inaccessible timber volumes. Although the exact methods and s p e c i f i c factors used to develop recoverability estimates d i f f e r e d among these studies, they were a l l based on subjective judgements using similar c r i t e r i a . In general, as noted by Reed (1978. vol.1, p. 6): 4 3 "Economic a c c e s s i b i l i t y estimates are based upon c r i t e r i a such as location r e l a t i v e to infrastructure, timber quality, t e r r a i n and delivered wood costs.". The study by Bowen (1978) was completed by surveying a l l p r o v i n c i a l and federal forestry agencies in Canada. Each respondent was responsible for separately i d e n t i f y i n g the accessible and inaccessible portions of their timber inventory. The estimates were most l i k e l y based upon subjective c r i t e r i a , since the study by Reed (1978) covered the same area, during a similar time period and had to rely upon such judgements as the only current means for developing a c c e s s i b i l i t y estimates in each province. Of the studies mentioned above, the regional analysis by the Province of B r i t i s h Columbia (1976) went the furthest in conceptualizing relationships between resource c h a r a c t e r i s t i c s and timber a c c e s s i b i l i t y . Operability classes were developed that represented levels of risk or p r o f i t a b i l i t y in logging. To apply the c l a s s i f i c a t i o n system i t was shown how expected costs and revenues of logging could be projected for sub-units within the region to determine the acreages within each op e r a b i l i t y c l a s s . None of the studies addressed the procedures for adjusting estimates for flows over time. The present system of inventory analysis for strategic y i e l d planning in B r i t i s h Columbia f a l l s into t h i s category. At the Provincial and Regional l e v e l , calculations of the accessible timber supply p a r a l l e l s the studies described. Generally, physical o p e r a b i l i t y c r i t e r i a are defined which 4 4 constrain the inventoried supply of timber. In the recent resource analysis (Province of B r i t i s h Columbia, 1980a-1980d) such constraints were spe c i f i e d by minimum cutting ages, s i t e types, minimum harvestable volumes (per hectare), species types and general a c c e s s i b i l i t y judgements provided by regional assessments. Clearly these c r i t e r i a are relevant, but, their general application in determining harvest rates leaves a margin of error that . may impose substantial unnecessary costs on present and future generations. Hence, the p r i n c i p a l disadvantage of these approaches is their reliance on broad physical c r i t e r i a . The precision of the estimates may be s a t i s f a c t o r y for reviews of national or p r o v i n c i a l p o l i c i e s , but not for regulating the rate of harvest on a regional or sub-regional basis. A second disadvantage is their i n a b i l i t y to readily evaluate the impacts of new technology, changing product prices, factor costs and government p o l i c i e s . Flow adjustments cannot be modeled for simulation of assumed future conditions, thus, updates require periodic reassessment of the entire process. The p r i n c i p a l advantage of this approach is the low l e v e l of information, manpower and time necessary to develop estimates. This i s important when accuracy is not c r i t i c a l , the supply region is large and costs must be kept to a minimum. 4 5 3.3 ENGINEERING STUDIES To my knowledge no major studies have attempted to model the economic a c c e s s i b i l i t y of a timber inventory using an engineering approach. The basic procedures, however, would be similar to those used in long-run cost analysis in manufacturing industries, and system cost comparisons in the logging sector. Where necessary, the analysis would begin by designing the optimal location of transportation infrastructure for timber development. Next, proposed cutting blocks would be designated based on inventory and landform c h a r a c t e r i s t i c s . For each block an optimal logging system would be determined and access roads designed. Base p r o d u c t i v i t i e s by phase of logging (access development through f i n a l transportation) could be developed from l o c a l averages or equipment s p e c i f i c a t i o n s . These could then be adjusted to r e f l e c t the influence of physical factors on productivity, such as; slope, landing size, t e r r a i n , etc. . Current labor, c a p i t a l and supply costs could be applied to phase input requirements and pr o d u c t i v i t i e s , and summed for an estimate of t o t a l phase costs. This estimate could be increased to r e f l e c t overhead and administrative costs, and thus provide an estimate of t o t a l logging cost. Revenues could be determined using market log prices and information on species and log sizes, obtained from inventory records. Those blocks with a non-negative net value would be considered a part of the recoverable inventory. o 4 6 An example of a logging cost study using this approach is Coast Logging: Highlead Versus Long-Reach Alternatives (Sauder and Nagy, 1977). In this study, the costs of logging, using five a lternative yarding methods, were developed by "paper logging" a map area of representative conditions in coastal B r i t i s h Columbia. If developed, an engineering approach could substantially improve the accuracy of rec o v e r a b i l i t y estimates. Unlike the approach discussed in the previous section, developed costs and revenues would provide estimates of recoverable supplies that vary more r e a l i s t i c a l l y with resource c h a r a c t e r i s t i c s . Where the analysis is well disaggregated, p r o d u c t i v i t i e s could be more l o c a l i z e d to r e f l e c t intra and inter-regional differences in costs and thus timber a c c e s s i b i l i t y . Disadvantages of this approach are as follows. F i r s t , optimality in system choice, cutting block designation and road layouts are r e l a t i v e to the decision-maker. That i s , the v a r i a b i l i t y in entrepreneurial or management s k i l l s among operators within the supply region is not reflected in the harvest design. Also, given perfect knowledge of the optimal system or design, a manager may be constrained, for example, by equipment a v a i l a b i l i t y in the short-run and may have to operate sub-optimally. Thus, an engineering approach would estimate the least-cost solution to harvesting the region's timber supply, which is not a r e a l i s t i c representation of supply costs experienced on the area. Second, the adjustment of p r o d u c t i v i t i e s , input demands, etc., to r e f l e c t operating 47 conditions that vary from a pre-defined norm, must rely p r i n c i p a l l y on subjective c r i t e r i a developed by the analyst. Third, only a few variables w i l l l i k e l y be considered when adjusting production estimates, with omitted variables possibly contributing to s i g n i f i c a n t v a r i a t i o n in true logging costs. F i n a l l y , this approach requires a high 'level of information, manpower, time and s k i l l . 3.4 STATISTICAL STUDIES Models in this category are characterized by the use of s t a t i s t i c a l relationships to describe the interactions between resource c h a r a c t e r i s t i c s and a c c e s s i b i l i t y . However, because (a) i t would be extremely d i f f i c u l t to model the random c h a r a c t e r i s t i c s of an entire logging system, and (b) some of the randomness w i l l i n s i g n i f i c a n t l y influence a c c e s s i b i l i t y , then, s t a t i s t i c a l timber supply models w i l l also include deterministic elements ( C o t t e l l , 1967a). Ba s i c a l l y , there are two ways in which recoverability can be s t a t i s t i c a l l y modeled. Relationships can be separately i d e n t i f i e d for c a l c u l a t i n g logging costs and revenues, or, net value relationships can be d i r e c t l y estimated. If the cost-revenue approach i s chosen, relationships can be estimated d i r e c t l y between t o t a l logging costs and resource c h a r a c t e r i s t i c s , or, separately for each phase of logging. Estimation by phase permits further refinement i f the relationships define phase p r o d u c t i v i t i e s rather than phase costs. Phase costs could then be calculated using current 48 factor costs. For the phase approach there are numerous examples of productivity studies in yarding and loading. These include studies by Tennas and others (1955), Adams (1965), Binkley (1965) and Dykstra (1975). Each of these studies sampled yarding cycle times by cycle elements and regressed element times against variables describing yarder and/or resource c h a r a c t e r i s t i c s . Their samples c h a r a c t e r i s t i c a l l y covered a single cutting block or several units in close proximity to each other, and were conducted for one type of cable yarding system (e.g. highlead). Dykstra (1975) studied four cable yarding systems separately on five cutting units. Adams (1965) also analyzed loading productivity on the sampled units. Nelson (1980) sampled dai l y p r o d u c t i v i t i e s in highlead yarding and loading on sixteen cutting blocks over a period of two and one half years in Coastal B r i t i s h Columbia. He used the data to determine (a) whether block, s h i f t or machine variations could account for the greatest t o t a l v a r i a t i o n in productivity, and (b) the amount of block variation that could be explained by resource variables. For p r o d u c t i v i t i e s in a l l phases of logging, Dobie (1966) developed regressions for phase times or costs in f a l l i n g and bucking, yarding (highlead), loading, booming and towing, and road construction, as a function of log volume. Data for the study were developed from the l i t e r a t u r e or based upon l o c a l operator information. The B r i t i s h Columbia Forest Service conducts logging productivity studies for major "stump to 49 landing" and "log loading" systems to improve stumpage appraisals (Province of B r i t i s h Columbia, 1979). Productivity i s related to various tree, stand and s i t e c h a r a c t e r i s t i c s which are sampled during operational cruises. However, cross-sectional sampling of the regional logging industry is not undertaken in a manner that w i l l represent average expected p r o d u c t i v i t i e s or costs. As described by the B.C. Forest Service: "Productivity data used in an appraisal is not intended to represent the s t a t i s t i c a l averages of productivity throughout the industry. Instead, they are intended to represent p r o d u c t i v i t i e s that are reasonably attainable by an average e f f i c i e n t operator." (Province of B r i t i s h Columbia, 1979. p. 1). An example of the t o t a l cost (vs. phase) approach is provided by a recent study on the Estimation of Logging Costs  and Timber Supply Curves from Forest Inventory Data (Berndt and others, 1979). In this study, estimated unit costs of logging on 26 cutting blocks (one firm, highlead yarding) were related to resource c h a r a c t e r i s t i c s . The study i l l u s t r a t e d how timber supply curves could then be developed by applying forest inventory data to the estimated cost equation. It was noted that although the necessary input data were available, ". . . as is often the case, these sets of data are not c o l l a t e d in a form amenable to this kind of analysis." (Berndt and others, 1979. p. 8). 5 0 On the revenue side, l i t t l e attention has been given to developing relationships that can predict stand values, without a p r i o r i knowledge of s p e c i f i c log grade d i s t r i b u t i o n s , beyond using average prices by species. To increase the accuracy of revenue estimates i t w i l l be necessary to further develop models of log size and grade d i s t r i b u t i o n from future harvests. An example of the complete cost-revenue approach to estimating inventory rec o v e r a b i l i t y is C o t t e l l ' s (1967a) study of economic a c c e s s i b i l i t y on • the University of B r i t i s h Columbia Research Forest. Costs by stand were estimated by phase: (a) road construction costs per unit road length were developed for three land classes, by four slope and five s o i l type categories, (b) yarding times (per cunit) were calculated using a production equation developed by a l o c a l firm, (c) road and landing construction costs, and yarding (including road changing) costs were optimized using a series of mathematical models obtained from the l i t e r a t u r e , and (d) a l l other phase costs were calculated using data developed by Dobie (1966). Revenues by stand were calculated from inventory data on species d i s t r i b u t i o n and stand area, and Vancouver Log Market average prices by species. C o t t e l l ' s results showed that few stands had negative net values, thus timber recoverability was quite high on the Research Forest, under conditions at the time. 51 Jackson and McQuillan (1979) recently presented the results of research into net stand value prediction. S p e c i f i c a l l y , they estimated the c o e f f i c i e n t s of a linear equation that related stumpage price (bid value) to the logarithm of tree diameter, lumber s e l l i n g price index, logging method, regeneration method, average volume per acre harvested, and haul distance to market. Although the data and equation are s p e c i f i c to the area sampled (Lolo National Forest, Montana), the authors noted that the general s p e c i f i c a t i o n would be useful elsewhere, p a r t i c u l a r l y in models of timber inventory valuation. Dobie (1966) combined the cost equations and estimates discussed e a r l i e r with information on product recovery and value to determine estimated conversion return (net value) per tree. The estimated values were regressed against a number of tree and stand variables to develop a predictive equation for net value. The p r i n c i p a l advantage of s t a t i s t i c a l models, as with engineering studies, is that estimates of recoverable timber are more accurate and less prone to bias than those provided through e n t i r e l y subjective assessments. Likewise, l o c a l i z e d sampling can improve the quality of estimates for intra and inter-regional supply analysis. Unlike engineering studies the derived estimates do not represent optimal conditions; rather, recoverability r e f l e c t s the current economic c h a r a c t e r i s t i c s of the logging industry. This information would be valuable for simulating the effect of various 52 p o l i c i e s (e.g. taxation) on industry e f f i c i e n c y and subsequent impact on resource supplies. Also, since the estimates rely on fewer judgements by the analyst, more variables can be included to improve • model s p e c i f i c a t i o n of resource a c c e s s i b i l i t y interactions. F i n a l l y , once the i n i t i a l sampling and inventory data organization have been completed, periodic updates and analysis require less time than in an engineering approach. There are three primary disadvantages to the s t a t i s t i c a l • modeling approach. F i r s t , developing the relationships requires extensive operational sampling in each supply area. Second, technological changes over time reduce the v a l i d i t y of model estimates. Third, s t a t i s t i c a l relationships may not be strong enough to support acceptable confidence in the r e s u l t s . The f i r s t two disadvantages are less c r i t i c a l in B r i t i s h Columbia because of annual productivity studies c a r r i e d out through cooperative e f f o r t s of the Valuation and Engineering Divisions of the Forest Service. The t h i r d disadvantage has been s p e c i f i c a l l y noted for the results of yarding productivity studies ( C o t t e l l and others, 1976). The primary reason I believe such studies have not shown strong relationships is due to the measure of production used. In the studies discussed e a r l i e r , d a i l y productivity or cycle times were regressed against block or setting resource (and other) variables. Resource c h a r a c t e r i s t i c s on a single block or setting w i l l be r e l a t i v e l y homogeneous when compared to the range of possible conditions that could occur. Hence, 53 production v a r i a b i l i t y in yarding can be expected to show stronger correlation to the day to day va r i a t i o n in crew attitudes, weather, etc., as is suggested by Nelson's (1980) measure of s h i f t v a r i a t i o n . Therefore, sampling to develop productivity relationships for s t a t i s t i c a l models of timber re c o v e r a b i l i t y should cover the widest possible range of resource conditions, using block averages of both p r o d u c t i v i t i e s and resource variables. This i s supported by the findings of a study on skidding productivity in the Interior Region of B r i t i s h Columbia by Mcintosh and Johnson (1974). S p e c i f i c a l l y , i t was determined that, "Average tree size, stand and t e r r a i n c h a r a c t e r i s t i c s were main factors a f f e c t -ing productivity between forest types, while degree of d i f f i c u l t y of individual logging chances and the skidder operators s k i l l and motivation were determining factors within forest types." (Mcintosh and Johnson, 1974. abstract). Their "forest types " were based on a c l a s s i f i c a t i o n scheme that considered species, elevation, t e r r a i n , ground maneuverability and a subjective logging chance rating. 3.5 STUDY APPROACH In this study the s t a t i s t i c a l modeling approach w i l l be further developed. This approach was chosen primarily for the increased accuracy and o b j e c t i v i t y in developing supply estimates. In specifying and estimating the relationships, and designing the simulation model, I w i l l attempt to acheive the following objectives: (a) The estimates should r e f l e c t actual e f f i c i e n c i e s in the logging industry. That i s , the model should not determine recoverability under optimum conditions. (b) The model should consider the various logging systems commonly used on the supply area. (c) The variables used for prediction should be those available (or capable of being incorporated) in inventory records; avoiding variables requiring operator, crew or machine s p e c i f i c data. (d) Samples should cover a wide range of resource, system and operator c h a r a c t e r i s t i c s , to develop relationships f u l l y representative of the supply area. 5 5 CHAPTER 4 RESOURCE CHARACTERISTICS AND LOGGING OPERABILITY IN COASTAL BRITISH COLUMBIA 4.1 INTRODUCTION There are four major factors that together determine the portion of t o t a l physical timber supplies that are economically recoverable: (a) the b i o l o g i c a l c h a r a c t e r i s t i c s of the resource base, (b) the technological c a p a b i l i t y of the logging industry, (c) market demands for resource goods and supply of productive factors (other than timber), and (d) government p o l i c i e s towards resource development and a l l o c a t i o n . At any point in time we can calculate the economic supply, under current conditions of government policy and the state of technology, by assessing the interaction between physical resources and market conditions. Presently we have measures of these two factors in the form of physical timber inventories, and prices for goods and costs of producing factors. This chapter d e t a i l s procedures for modeling the interactive relationship using these measures in the process. In the previous chapter three alternative methods of modeling this interaction were presented. For reasons of short-term accuracy and long-term f l e x i b i l i t y , the s t a t i s t i c a l approach has been chosen for further development in this thesis. 56 S p e c i f i c a l l y , I w i l l present a method for s t a t i s t i c a l l y c a l c u l a t i n g operable volumes by developing relationships between resource c h a r a c t e r i s t i c s and the costs of timber harvest ing. In the next section I w i l l discuss some general concepts for procedural development. Section three deals with the assumed eff e c t of resource c h a r a c t e r i s t i c s on logging o p e r a b i l i t y . The f i n a l two sections, four and f i v e , d e t a i l s t a t i s t i c a l research ca r r i e d out in coastal B r i t i s h Columbia including a description of the scope and procedures followed during sampling, the relationships hypothesized for testing, sampled variable s t a t i s t i c s , and the resulting equations. 4.2 PROCEDURAL CONCEPTS 4.21 Revenues And Costs Market demand for forest products and the supply of productive factors interact with the resource base to determine economic timber supplies in two basic ways. F i r s t , equilibrium between market supply of and market demand for products, determine the value of standing timber by species and log qu a l i t y ( i . e . product type). Thus, the d i s t r i b u t i o n of t o t a l inventoried timber by homogeneous 'products' ( s p e c i f i c species-grade categories), combined with market prices provides the gross value of converting forests into marketable logs. As the markets for forest products are s u f f i c i e n t l y dispersed and free from producer control, the 5 7 prices are market determined and are constant, at a discrete point in time, for a l l producers supplying similar products regardless of resource location. Second, market demand and supply equilibrium for the factors of production determine the cost of employing productive factors in timber production (e.g. wages, interest, e t c . ) . However, unlike the prices received for timber produced, costs can not be d i r e c t l y assigned to product groups, since they can vary widely for any one species or grade produced. This variance in the costs of production is d i r e c t l y related to the amount of each factor employed in logging an area. In turn, factor demand w i l l vary for a given area or 'plant s i z e ' , even though operator e f f i c i e n c y is held constant, as the volume of timber available for harvesting, tree size, stand density, stand quality and t e r r a i n c h a r a c t e r i s t i c s vary. Therefore, defining the economic timber supply for an area becomes, e s s e n t i a l l y , a study of logging costs and the factors causing their var i a b i 1 i ty. 4.22 Cost vs. Time Studies There are two ways of measuring the relationships between logging costs and resource variables. The f i r s t - production time method - is to measure the dir e c t relationships that exist between the time i t takes to log an area and the c h a r a c t e r i s t i c s that define area o p e r a b i l i t y . Then wage and machine rates can be applied to time estimates to calculate the costs of production. A second, more indirect approach production cost method - is to estimate the relationships 58 between the costs of logging an area and the c h a r a c t e r i s t i c s that define area o p e r a b i l i t y . The f i r s t method i s considered a direct approach, even though a two-stage procedure, because resource c h a r a c t e r i s t i c s d i r e c t l y influence the times required to complete the entire harvesting process for a cutting block. | Costs, on the other hand, are influenced by other factors such as labor and c a p i t a l a v a i l a b i l i t y , i n f l a t i o n , etc., that are not affected by resource v a r i a b i l i t y . Two studies discussed in chapter three, by C o t t e l l (1967), and Berndt and others (1979), are examples of the production time and production cost methods respectively. Primarily for the reason of the dir e c t relationship between production times and logging d i f f i c u l t y , I favor the time study approach for determining logging costs in a supply analysis. Other reasons for avoiding the cost approach are: (a) cost center problems, (b) dual vector of cost changes over time, (c) industry reluctance, and (d) accounting differences. Each of these problems with the cost approach are discussed in turn below. 4.221 Cost Center Problems. To analyze the affect of resource c h a r a c t e r i s t i c s on logging costs, over a wide range of operating conditions, the smallest possible operational unit must be sampled for which there are i d e n t i f i a b l e production data and measures of resource variables. Operational cruises conducted for cutting permit applications in B r i t i s h Columbia provide measures of resource variables on s p e c i f i c cutting blocks proposed for harvesting. However, 59 estimates of production costs are most often available only at the d i v i s i o n a l level as combined into cost centers that can range from as small as a single machine (e.g. yarders, loaders, etc.) to entire phases in the harvesting process (e.g. f a l l i n g and bucking, scaling, sorting and booming, et c . ) . These costs can not be d i r e c t l y associated with any one operational cutting block, thus, they include the effects of resource v a r i a b i l i t y throughout the d i v i s i o n a l administrative area. 1 A sampling unit of thi s magnitude reduces the probability of obtaining samples that cover a wide range of operable conditions. It should be possible, however, to go back through da i l y time records that associate labor and machine data to s p e c i f i c cutting areas, and sum the t o t a l time required to log an area. These times would thus be area-specific and could be d i r e c t l y related to resource variables estimated from operational cruises and/or s i t e inspection. This approach would provide the range in resource v a r i a b i l i t y necessary to identify o p e r a b i l i t y relationships. *The need for operational area accounting has been noted by Wellburn (1976): " . . . planning and accounting should be on the same basis, cover the same area and t o t a l period of logging. We must consider each definable logging area as a project and keep track of a l l costs r e l a t i n g to the project or area." (pp. 115-116). 6 0 4.222 Dual Vector Of Temporal Cost Changes. Unit cost changes can occur as a result of changes in productivity, factor costs, or both. Increases in productivity (factor costs), other things being equal, y i e l d decreases (increases) in unit logging costs. The opposite occurs with decreases in productivity (factor costs). When one of the two vectors i s held constant the d i r e c t i o n of change in unit logging costs is d i r e c t l y related to action of the non-constant vector. If both act in the same dir e c t i o n then the effect on unit logging cost depends on the r e l a t i v e rate of change between productivity and factor costs. The range of p o s s i b i l i t i e s i s given in Table 1. Identifying and estimating each vector separately for future projections should improve the f i n a l estimates of unit logging costs. 4.223 Industry Reluctance. To keep i t s ' internal cost structure c o n f i d e n t i a l a company is often reluctant to open i t s books to external investigators. Thus, in a supply analysis using the cost study approach, problems arise over obtaining cooperation from the logging industry to conduct operational sampling. This can be extremely important when the supply unit size is extensive and the number of samples desired is subsequently large. 4.224 Accounting Differences. To develop relationships that are representative of the supply unit being analysed, samples of logging operations must necessarily be drawn from a number of d i f f e r e n t firms operating in the area. This raises 61 Table 1. Possible Combinations of Factor Costs and Productivity in Determining Direction of Unit Logging Cost Changes Direction of Chang e Relat ive Unit Logging Cost Factor Productivity Factor Costs Rate of Change I ncreasing T l TT T l Increasing Constant Decreasing T l Increasing II Constant Decreas ing FC 1 > P 2 * * FC < P Constant TT TT Increasing Constant Decreasing Increasing Constant Decreasing FC = P * FC = P Decreasing TT T l T l Increas ing T l Constant Decreasing Increasing Constant Decreasing TT FC < P * * FC > P FC = factor cost 2P = factor productivity * = irrelevant Problems of adjusting recorded costs between the companies, where necessary, to ensure comparability between samples. Time, on the other hand, is a standard measure, thus, records of production times between firms do not suffer from accounting discrepancies. Since the supply analysis is supposed to represent the expected production c a p a b i l i t y on the supply unit given current technology and standard wage and machine rates, precise knowledge of individual firms' cost structures i s not important. 4.23 Estimation by Phase of Logging Developing relationships between logging op e r a b i l i t y and resource conditions using a time study approach is not without 62 problems. If the cost study approach is used, the cost of the entire operation from stump to dump could be d i r e c t l y related to resource factors believed to cause cost v a r i a t i o n . This i s not possible, however, when production times rather than costs are used as the independent variable. Because a unit of time in logging i s not homogeneous with respect to value, the production process must be divided into phases to which single wage and machine rates can be applied. Commonly i d e n t i f i e d phases of the logging process are: (a) access development; 2 (b) f a l l i n g and bucking; (c) primary transport (e.g. cable yarding in coastal B.C.); (d) loading; (e) hauling; (f) unloading, sorting and booming; and, (h) re-hauling; or, some combination of these phases ( C o t t e l l , 1967b; Conway, 1976). The s k i l l and quantity of labor d i f f e r s between phases, thus, so w i l l the average wage rate applicable to each phase. The same applies to the equipment and materials used in each phase. Even within phases the average wage and machine rates can d i f f e r , as the part i c u l a r system or cap i t a l to labor combinations chosen to complete each phase w i l l vary with operating conditions. Therefore, to calculate the costs of logging, a l l phases combined, i t is necessary to estimate the relationships between production times and resource variables for each system commonly used within each phase of logging. 2Includes cutting block layout, c r u i s i n g , engineering and road construction. 63 Another reason for estimating production relationships by phase is due to the i n d i r e c t , weak association between production and resource v a r i a b i l i t y in some phases. Phases that are increasingly distant from the operating unit w i l l not show strong relationships to resource s p e c i f i c c h a r a c t e r i s t i c s . Estimates of t o t a l times or costs, with respect to tree, stand and s i t e c h a r a c t e r i s t i c s , are weakened by the embodied time or costs which are e s s e n t i a l l y free of resource influence. Thus, by concentrating on phases d i r e c t l y affected by operating conditions, stronger relationships can be developed. Costs for phases weakly correlated with resource v a r i a b i l i t y can be calculated based on deterministic equat ions. In logging, then, the v a r i a b i l i t y of production time in the f i r s t three phases, access development, f a l l i n g and bucking, and primary transport, can be shown to be d i r e c t l y affected by resource c h a r a c t e r i s t i c s on the operational unit. Loading productivity is determined by the landing size, volumes to be loaded, and most importantly, yarder productivity , which i n d i r e c t l y associates loader productivity to the resource c h a r a c t e r i s t i c s (Conway, 1976; Pearce and Stenzel, 1972; Sauder and Nagy, 1977; Province of B r i t i s h Columbia, 1979b). Hauling productivity is primarily a function of vehicle load c a p a b i l i t i e s , road conditions, and most importantly, hauling distance; although loader productivity can have considerable influence when pre-load t r a i l e r s are not employed (Conway, 1976). Scaling, unloading, 64 sorting and booming costs are primarily a function of the volume of logs handled as related to the type of scale, weigh or s t i c k , and type of sorting grounds, dryland or water (Province of B r i t i s h Columbia, 1979b). Thus, main considerations for developing costs in the l a s t four phases (loading to re-haul) are knowledge of area logging systems, expected p r o d u c t i v i t i e s in e a r l i e r phases and estimated production. 4.3 RESOURCE FACTORS AFFECTING LOGGING COSTS - DESCRIPTION In this section I w i l l describe the perceived effects of a number of resource factors on phase p r o d u c t i v i t i e s . The discussion is based upon hypothesized or proven interactions as reported by a number of sources (Dobie, 1966; Allan, 1969; Pearce and Stenzel, 1972; Conway, 1976 and 1978; Province of B r i t i s h Columbia, 1976, 1979b, and 1980e). For organizational purposes this section w i l l be divided into four sub-sections; describing the effects of tree, stand and s i t e factors on system choice and phase p r o d u c t i v i t i e s in access development, f a l l i n g and bucking, and yarding. 4.31 Harvesting System Choice There are two general categories of systems available for the phases of f a l l i n g and bucking, and yarding. In f a l l i n g and bucking the operator can choose between some form of mechanized system or manual operation. In the yarding phase the operator has a choice of several ground skidding or cable 65 yarding systems. The c r i t i c a l factor in each phase is ground slope of the s i t e . Skidding with track or wheeled vehicles, or f a l l i n g with mechanical cutters attached to either, is generally limited to adverse slopes less than 15 percent, and favorable slopes less than 35 percent (Studier and Binkley, 1974). A second l i m i t i n g factor, associated with the above, is the terr a i n v a r i a b i l i t y . Uniform t e r r a i n ( i . e . few and/or shallow g u l l i e s , ravines, etc.,) is more suitable for mechanized cutting and ground skidding operations. A t h i r d l i m i t i n g factor for mechanized cutting operations is tree diameter. Hydraulically operated shears, the most commonly used mechanized cutting device, are limited to tree diameters of 61 centimeters or less (Allan, 1969; Conway, 1976). In coastal B r i t i s h Columbia the steep slopes, variable te r r a i n and large timber sizes t y p i c a l of the region preclude the use of mechanized cutting operations. Smaller timber sizes of future second growth stands on lower elevation, uniform s i t e s may accommodate limited use of such systems presently an integral part of i n t e r i o r operations. However, even then the high c a p i t a l costs may l i m i t their coastal use unless s u f f i c i e n t volumes are available to j u s t i f y the investment. S i m i l a r l y , steep slopes and variable t e r r a i n have limited the extent of ground skidding operations in the coastal region. Ground skidders are used, but only occasionally and often only as minor support to the more commonly used cable systems. Since this thesis is concerned 66 with estimating economic timber supply in coastal B r i t i s h Columbia, the remainder of thi s section w i l l deal only with the effect of resource c h a r a c t e r i s t i c s on manual timber cutting and cable yarding operations. Because there are a number of d i f f e r e n t cable systems available for completing the primary transport phase, i t is necessary to know the eff e c t of resource variables on the choice of a pa r t i c u l a r cable system to employ on a given area. The conditions which aff e c t the choice of cable system w i l l be described with reference to 'normal' conditions; that i s , conditions which are t y p i c a l of highlead yarding operations. Resource conditions c h a r a c t e r i s t i c of highlead operations can be considered the norm because i t is the most widely used system in coastal B r i t i s h Columbia, due to c a p a b i l i t i e s for operating over an extensive range of conditions (Holmes, 1978; C o t t e l l 1980). Preferred yarding d i r e c t i o n is u p h i l l for highlead yarders with a maximum slope of 70 percent and maximum yarding distance of 1000 feet. Downhill yarding reduces l i f t c a p a b i l i t y , thus, maximum slope and yarding distance are reduced to 40 percent and 600 feet, respectively (Studier and Binkley, 1974). Other deterrents to downhill yarding are concentration of runoff via yarding roads, and increasing the danger to yarder operator and landing crew from runaway logs (Holmes, 1978). On gentle slopes where downhill yarding i s not extremely d i f f i c u l t , larger areas can be yarded from a single location. On increasingly steep slopes problems with 67 downhill yarding w i l l become proh i b i t i v e , requiring more yarder settings and construction of more roads. Similar increases in road development w i l l be necessary where the terr a i n is highly variable resulting in poorer deflection and payload c a p a b i l i t y , which must be offset by shorter yarding distances (both u p h i l l and downhill). The problem is compounded i f both steep slopes and broken t e r r a i n occur in combination. . Because of the higher road costs and increased risk of environmental damage resulting from highlead operations on steep, variable t e r r a i n with shallow s o i l s , a di f f e r e n t cable yarding system is l i k e l y to be employed under these conditions. To meet this need operators in the western coastal region of North America have increasingly used some form of long-reach yarding system. These are characterized by a "skyline" running the length of the setting, over which a carriage suspending the logs travels. Thus, in long-reach yarding the skyline provides the l i f t and a separate mainline provides the d i r e c t i o n a l p u l l , instead of the mainline providing both the v e r t i c a l and horizontal forces as in highlead yarding. Depending on the ground p r o f i l e of the setting, the skyline can be suspended from the yarding tower to a stump or backspar, and be supported along i t s length by one or more intermediate supports. Because of these c h a r a c t e r i s t i c s long-reach systems can be designed to log over favorable and adverse slopes of 100 percent or more (Studier and Binkley, 1974), and up to 68 distances of approximately 2800 meters (Conway, 1976). Hence, the longer yarding distances of these systems reduce the roads necessary to log an area, which can lower logging costs and reduce the risk of s o i l erosion. Depending on the slope, t e r r a i n , yarding distance and setting layout, i t is possible to transport the logs f u l l y suspended over the length of the skyline. This aspect further reduces the risk of damage to s o i l s and advance regeneration. However, because of longer yarding distances, higher c a p i t a l cost of yarders and larger crew sizes, yarding costs w i l l be greater than for highlead. Subsequently, more s k i l l in planning and operating a skyline operation is required to ensure the reduction in road costs i s not lost to excessive increases in yarding and timber cutting costs. 3 Long-reach systems receive less application than they should, over only the more d i f f i c u l t or sensitive s i t e s , due to a lack of experience with long-reach yarders, and the re l a t i v e s i m p l i c i t y of and extensive experience with highlead yarding systems. This may overstate the problem of high skyline costs as noted by Waelti (1976): "Operations should be planned on a drainage basis, so as to optimize the range and application of each system that w i l l be needed. So often the mistake is made that common systems and equipment are used to the l i m i t (or even beyond the li m i t ) of their c a p a b i l i t y , leaving only the toughest blocks for skylining. The decreasing road densities have been associated with decreasing productivity in f a l l i n g and bucking due to increased walking time (Sauder and Nagy, 1977). 69 consequence is that the applications for the uncommon system become very limited and costs abnormally high." (p. 173). In summary then, we can conclude that long-reach systems w i l l be generally used as a u x i l l i a r y support for high lead yarding, on steeper slopes with more variable t e r r a i n where road density has been reduced to offset high costs or environmental damage. On the other end of the spectrum, running skylines with a mechanical or remote controlled grapple are being used to yard shorter distances than conventional highlead. Although t y p i c a l of a skyline system and capable of yarding over distances up to approximately 365 meters (Conway, 1976), grapple yarders are preferably used over shorter distances of approximately 150 meters or less (Oakley, 1976). Reasons for shorter yarding distances concern a loss in productivity over longer distances due to (a) loss of de f l e c t i o n , (b) r e s t r i c t e d operator vision in placing the grapple, (c) one log per turn, (d) slower speeds of grapple yarders, and (e) increased l i n e p u l l (Oakley, 1976). Because of the shorter distances, grapple yarding requires a higher road density than highlead, thus increasing road costs. These higher costs can be offset by lower yarding costs due to smaller crew sizes. Since increased road development times and costs would become prohibitive on steeper, variable t e r r a i n s i t e s , grapple yarding w i l l tend to be used on the gentler more uniform • areas. ' Another factor a f f e c t i n g the productivity of grapple yarding is log s i z e . 7 0 Since only one log is yarded per turn, any change in log size w i l l proportionately a l t e r productivity. Other cable methods can o f f s e t decreases in log volumes by increasing the number of chokers, to some extent (Oakley, 1976). Thus, as with the long-reach systems, grapple yarding in coastal B.C. has been most commonly used as an a u x i l l i a r y system to conventional highlead. E f f i c i e n t l y located on a highlead operation the grapple yarder can substantially increase yarding productivity. 4.32 Access Development Categories in the development phase include: (a) timber c r u i s i n g , (b) engineering and planning of area boundaries, road locations, setting layout, etc., and (c) road construct ion. The time required to cruise an area is primarily a function of area size, timber density, and s k i l l of the crew. This time w i l l also be affected by c h a r a c t e r i s t i c s of the area that may impede crew mobility, such as dense brush, windfalls, rockbluffs, variable t e r r a i n , and others. However, for a given crew, over a f a i r l y wide range of conditions, strong correlations between area, timber density and crui s i n g times should develop (Province of B r i t i s h Columbia, 1980e). Engineering times w i l l also be primarily affected by area size.. However, in addition to factors that hamper f i e l d work, the logging system to be used on the area w i l l a f f e c t the time required for operational design. Thus, increased road requirements and s k i l l in planning w i l l increase engineering 71 times (costs). Road construction times and costs are related to area size, yarding distance, road cl a s s , and slope, t e r r a i n and s o i l c h a r a c t e r i s t i c s . Total road requirements increase -with increasing area. Yarding distance is determined by the yarding system employed, which is influenced by slope, terrain and timber size c h a r a c t e r i s t i c s as discussed e a r l i e r . As distances decrease,, road development (per unit area and in total) increases. For a given area and yarding system combination, road development costs w i l l vary depending on the type of roads constructed. On average, roads designed for long-term and/or heavy use w i l l involve more time and cost more than roads designed for a single short-term use. Thus, areas with a high proportion of mainline or permanent branchlines w i l l have higher road costs. However, as these roads w i l l be used to produce logs or services (e.g. recreation, forestry, etc.) from other areas, the f u l l cost should not be charged to any one s p e c i f i c logging operation. For the purposes of iden t i f y i n g timber supply costs on a s p e c i f i c area, analysis of road costs w i l l be concerned primarily with short-term access roads, thus, the relevant standard of road w i l l be f a i r l y constant. However, further variance in road costs can be expected for a s p e c i f i c area-system-road class combination as slope, te r r a i n and s o i l c h a r a c t e r i s t i c s a l t e r the time and materials required to build a unit of road. 72 Calculation of road costs for a supply analysis is e s s e n t i a l l y a two-stage process. F i r s t , the t o t a l road requirements are determined as a function of area size and yarding system used (or the s i t e , stand and tree c h a r a c t e r i s t i c s that affect system choice). Second, for a given road class the cost per unit of road must be adjusted to account for v a r i a b i l i t y in s o i l depth, type, slope, terrain and stems per hectare, to name a few (e.g. road cost calculations as determined by the B.C.F.S. (Province of B r i t i s h Columbia, 1980e) for stumpage appraisals). 4.33 F a l l i n g And Bucking There are two basic ways in which tree, stand and s i t e c h a r a c t e r i s t i c s of an area affect the time required to f a l l and buck standing timber. F i r s t , there are those factors which hamper crew mobility over an area, and second, there are those factors which increase the actual time cutting a given tree or area. In the f i r s t category such factors as brush density, windfalls, slope and t e r r a i n v a r i a b i l i t y w i l l affect the a b i l i t y of a crew to move throughout an area. An increase in any of these factors increases the time spent moving, rather than cutting, thus decreasing productivity These same factors may also increase actual cutting times. In dense brush the f a l l e r must f i r s t clear the brush from around the tree to be f e l l e d . Extra care must be taken when f a l l i n g trees around windfalls to avoid excessive breakage. For the same reason extra time must be taken on 73 highly variable or broken t e r r a i n . On steep slopes trees w i l l s l i d e or r o l l downhill, thus, requiring additional walking time to complete bucking and limbing. Other factors a f f e c t i n g timber cutting times are tree diameter, merchantable height, log or stem volume, defect, stems per hectare and volume per hectare. As diameter increases so w i l l f a l l i n g times, but, greatly increased volumes at larger diameters offset the increased time thus productivity increases. Subsequently, greater log or stem volumes also imply longer cutting times but increased productivity. Since tree height and diameter are p o s i t i v e l y correlated, increased tree height is also associated with longer f e l l i n g times. Additionally, more care must be taken when f a l l i n g t a l l e r trees to avoid excessive breakage. Bucking times also increase with larger diameter trees, and for trees of greater merchantable height which require more cuts to desired length. An increase in either the number of stems or volume per hectare, other things being equal, results in an increase in cutting times. However, more time is spent on cutting timber rather than walking, thus, productivity increases and unit costs decrease. Best conditions for productive f a l l i n g are stands with many stems of high volume per stem. However, since diameter (thus log and stem volume) decreases with increasing stem densities, the relationship between f a l l i n g times and stems or volume per hectare, as with other variables, is not clear and w i l l be affected by variations in a l l stand factors. An increasing amount of tree 7 4 or stand defect w i l l increase the time necessary to f a l l and buck an area, as well as decrease the net production from the s i t e . As a result, defect has a double impact on unit costs by increasing factor costs per unit and lowering productivity. Considering a l l variables i t can be seen that those factors increasing production times for a given area (e.g. tree diameter and height, stems per hectare, etc.,) w i l l increase productivity and decrease unit costs, while those factors increasing production times for a given volume (e.g. brush, slope, t e r r a i n , area, etc.) w i l l decrease productivity and increase unit costs. 4 . 3 4 Yarding Many of the same variables a f f e c t i n g productivity in f a l l i n g and bucking have an influence on yarding productivity also. However, the effects of these variables are mostly f e l t in an indirect manner. Once a yarder setting has been designed for a sp e c i f i c system, and the yarder has been placed into position, few resource variables w i l l have strong influence over yarder productivity. This has been discovered through production studies as discussed e a r l i e r and has been reinforced by statements of logging managers I have contacted. Weather and crew effects w i l l have greater influence over productivity variation at th i s stage. However, for any given yarding method variations in productivity w i l l occur between cutting blocks, under similar conditions of weather and crew experience, that should be traceable to s p e c i f i c resource c h a r a c t e r i s t i c s . It is these variations that must be 75 accounted for in a study of timber a c c e s s i b i l i t y , since over a given area, temporal variation in logging productivity w i l l be mainly affected by the interaction between resource c h a r a c t e r i s t i c s and production technology in each time period. With these considerations in mind then, yarding productivity w i l l also be affected by such variables as brush density, slope, t e r r a i n v a r i a b i l i t y , windfalls (and other obstacles), log volume, volume per hectare, stems per hectare, t o t a l volume, area size and defect. As with f a l l i n g and bucking productivity, brush density, slope, t e r r a i n and windfalls (non-recoverable) w i l l effect a decrease in productivity by hampering movement of the crew, in this case the choker setters. However, because choking is only a portion of t o t a l yarding time, the noticeable e f f e c t s of these variables may be r e l a t i v e l y minor over a f a i r l y wide range of conditions. 4 Increases in log volumes result in increases in yarding times since: (a) i t takes longer to choke larger logs, (b) depending on equipment c a p a b i l i t y , the number of chokers used per turn must be reduced, thus, increasing the number of turns, other things being equal, 5 and, (c) heavier weight of larger logs may increase inhaul times. In general, however, 4With regard to slope effect on the ground crew, Conway (1976, p. 216) feels that maximum production is possible up to slopes of 50 percent, with a loss of ". . .10 to 12 percent of normal production. . . for each 10 percent increase in slope. . . ". 5An increasing number of turns may not be r e a l i s t i c , since, increases in log volumes are generally associated with decreasing number of stems per hectare and thus fewer pieces to be yarded on an area. 76 the increased times are offset by the greater volume yarded per turn, thus, costs are reduced through greater productivity. Similarly, with increased volume per unit area, production times increase but unit costs of production decrease, as the increases in volume recovered should be greater than increases in yarding time. Therefore, increases in t o t a l volume or area to be yarded result in an increase in production times. However, the effect on productivity and costs d i f f e r between the two. Volume increases with a l l else constant imply productivity increases and cost decreases. The reverse i s true with area increases when a l l other factors remain constant. F i n a l l y , defect, as with f a l l i n g and bucking productivity, reduces the net scale yarded and thus decreases productivity and increases unit costs. This may be offset somewhat i f decay reduces log weights thereby decreasing inhaul times and increasing productivity. However, the loss of 'sound' wood is l i k e l y to have i t s greatest effect by decreasing productivity through net scale reductions in volumes yarded. 4.4 INPUT DEMANDS AND PRODUCTIVITY OF LOGGING IN COASTAL BRITISH COLUMBIA 4.41 Objective The objective in th i s stage of the analysis is to develop relationships between input demands, logging productivity and resource c h a r a c t e r i s t i c s , for phases of the logging process d i r e c t l y influenced by v a r i a b i l i t y in operating conditions. 77 Because of d i f f i c u l t i e s encountered in obtaining area-specific data on road construction times, the analysis concentrated on the phases of f a l l i n g and bucking, and primary transport (yarding). Additionally, relationships were analysed to provide estimates of the length of roads constructed, choice of yarding system, and actual volume cut, as determined by operational c h a r a c t e r i s t i c s . The relationships developed are intended to be used for predictive purposes. Using the equations, p r o d u c t i v i t i e s can be projected based on inventory c h a r a c t e r i s t i c s , and phase costs can be estimated. The equations are not to be misconstrued as representative of functional relationships in logging production. Interactions among the included and omitted variables preclude development of true structural relationships based only on resource c h a r a c t e r i s t i c s . But, i t is these very c h a r a c t e r i s t i c s that q u a l i f y the physical timber inventory and thus should be useful in predicting i t s economic re c o v e r a b i l i t y . Additionally, predictive equations can be useful for identifying the most s i g n i f i c a n t as well as a l l relevant variables which w i l l aid future e f f o r t s at production modeling. For these purposes the predictive approach seems most suited, as noted by Draper and Smith (1966): " . . . predictive models are very useful and under certain conditions can lead to real insight into the process or problem. . . (which) are usually referred to as 'problems with messy data' - that i s , data in which much in t e r c o r r e l a t i o n e x i s t s . . . " (p. 235). 7 8 4.42 Scope Sampling was c a r r i e d out in the coast region of B r i t i s h Columbia, which includes the combined areas of the Vancouver and Prince Rupert "Forest Analysis Regions" as designated by the Ministry of Forests (Province of B r i t i s h Columbia, 1980b). Although t h i s i s an extensive area, operational c h a r a c t e r i s t i c s are similar throughout. The sampling units were cutting blocks on which logging operations had been completed for a l l or part of the block. A l l samples were located on Tree Farm Licences (TFL), since the best combined records of area s p e c i f i c production and resource data are available on these tenures. Because logging operations may take several years between i n i t i a t i o n and completion, the period sampled ranged from 1977 to 1979. Most blocks had been completed prior to 1979. On cutting blocks where operations were s t i l l in progress, data were collected for the area completed. Block size ranged from one to many yarder settings, governed mainly by landform and/or•timber type. The majority of samples were located on Vancouver Island. Of a t o t a l 48 samples taken along coastal B.C., 37 were located on Vancouver Island, 7 on the southwestern lower mainland, and 4 on the Queen Charlotte Islands. 6 Even though the d i s t r i b u t i o n of samples on a regional basis i s narrow, I 'The exact location of samples w i l l not be shown so as to conform with requests by cooperating firms to conceal the source of production data. 79 believe the sample data are representative of the range in logging conditions on the coast; exhibiting c h a r a c t e r i s t i c s of the easiest to most d i f f i c u l t topography, and poor to good timber q u a l i t y . Also, I believe the companies sampled - six of the major integrated forest i n d u s t r i a l firms in B r i t i s h Columbia - are indicative of coastal logging management. These companies controlled approximately 71.9 percent of the coastal allowable annual cut (AAC) on TFL's in 1978. 7 Each sampled cutting block was i d e n t i f i e d by the type of cable yarding method used to log the area. On one-third of the blocks more than- one yarding method was employed. If the data could be i d e n t i f i e d separately for each method, then two or more samples were formed from the single block. If not, the sample was c l a s s i f i e d by the system most extensively used on the area. Since t h i s s i t u a t i o n occurred on only 3 of the sampled blocks, and the area logged by the lesser systems were small, the effect on the dominant system and f i n a l analysis w i l l be minor. As a result of this sample s p l i t t i n g by yarding system, t o t a l sample size increased to 64. Four methods of cable yarding were encountered: conventional highlead, grapple, tension skidder and s l a c k l i n e . Sample d i s t r i b u t i o n among the systems is 36, 15, 6 and 7 respectively. Because of small sample sizes and s i m i l a r i t i e s 7In turn, the AAC on coastal TFL's was about 55% of combined coastal AAC for PSYU's and TFL's. The most recent estimate of t o t a l control (Pearse, 1976. vol.1, p. 39) show these same companies to control approximately 65% of t o t a l committed AAC in 1974. 80 between tension skidder and s l a c k l i n e systems the two methods were combined into one sample group c l a s s i f i e d as long-reach systems 4.43 Variables Sampled And Measurement Procedures For each sample I recorded the length of roads constructed (meters), f a l l i n g and bucking times (man hours),, yarding times (machine hours), net volume harvested (cubic meters), and a number of variables describing the tree, stand and s i t e c h a r a c t e r i s t i c s of the area logged. Based on a review of the l i t e r a t u r e , as discussed in the previous section, seventeen variables describing seven resource factors «• were measured and recorded as shown in Table 2. Variables defining tree size, stand density, volume, quality and stand size were determined from records of operational cruises that had been completed prior to logging -. Site a c c e s s i b i l i t y variables (excluding elevation) were measured on-site during t r i p s to the sampled operations. The indices are d i r e c t l y based on those developed by the B r i t i s h Columbia Forest Service for stumpage appraisal productivity studies (Province of B r i t i s h Columbia, 1979a). Mean elevation as well as length of roads constructed were calculated from engineering maps of the sampled cutting blocks. Production times for f a l l i n g and bucking, and yarding were developed from da i l y time cards or monthly production summaries. Net volumes scaled were also determined from company records. 81 Table 2. Resource Factors and Identified Variables Factor Notation D e f i n i t i o n Tree Size Stand Density Stand Volume Stand Quality Stand Size Site A c c e s s i b i l i t y 2 S o i l C h aracteristics D H ALV VPH SPH V •c A S T B EX 0 E ST SM SD Stand average diameter at breast height (1.37m) in centimeters. Stand average height to close u t i l i z a t i o n standards : i n meters. Stand average log volume for a 10 meter log, in cubic meters, based on actual number of logs harvested and net harvested volume. Average volume per hectare to close u t i l i z a t i o n standards, in cubic meters Average number of stems per hectare to close u t i l i z a t i o n standards. Total cruised timber volume to close u t i l i z a t i o n standards in cubic meters. Estimated decay, waste and breakage, as a percent of t o t a l volume Area in hectares. Ground slope across contours in percent. Terrain v a r i a b i l i t y index; measure of v a r i a b i l i t y along contours: l=even, 2=rolling, 3=gullied, 4=broken. Brush density index: l = l i g h t , 2=medium, 3=heavy, 4=v. heavy. Exposed bedrock index; of area with exposed 1=1-10%, 2=11-30%, bl u f f s or c l i f f s . Obstacles index; measure of the size and extent of boulders, windfalls (<50% recoverable), stumps, etc. : sum of the number in each size category (0.25-0.5,0.51-1.0,1.1+ meters in height) times the low-end height value for the category. Mean stand elevation in meters. S o i l type index: 10=organic, 20=silt, 30=clay, 40=loam, 50=sand, 60=gravel, 70=cobble. Record major and minor types (e.g. 56=gravel/sand). S o i l moisture index: l=dry, 2=moist, 3=wet, 4=swampy. S o i l depth to hardpan in meters. measure of bedrock: 3=31%+, percent 0=none, 4=rock ^ l o s e u t i l i z a t i o n standards on the B r i t i s h Columbia coast consist of u t i l i z a t i o n of a l l volumes in trees with 22.5 cm+ DBH, between a 30 cm stump and 10 cm top d.i.b. 2 " S i t e A c c e s s i b i l i t y " and " S o i l C h a r a c t e r i s t i c s " indices and variables are d i r e c t l y based upon those developed for stumpage appraisal productivity studies (Province of B r i t i s h Columbia, 1979a). 82 4.44 Regression Hypotheses And Procedures Based on the presumed influence of resource variables on production times a set of hypotheses was formed equating the response variable with an unknown linear function of predictor variables. Seven hypotheses were set up to determine predictive equations for: length of roads constructed, f a l l i n g and bucking productivity, yarding productivity, volume harvested and yarding system choice. The hypothesized regressions were as follows: (4.1) RL = F(D,H,ALV,SPH,VPH,A,E,S,T,B,EX,0,ST,SM,SD,Z) (4.2) F&BP = F(D,H,ALV,SPH,VPH,C,A,S,T,B,EX,0,RPH) (4.3) YP = F(D,H,ALV,SPH,VPH,C,A,S,T,B,EX,0,Z) (4.4) Q = F(Vnet,F&BT,YT,Z) (4.5) Pi = F(D,H,ALV,SPH,VPH,V,C,A,E,S,T,B,EX,0,RPH) Where: RL = road length in meters. F&BP = f a l l i n g and bucking productivity in cubic meters per man hour. YP = yarding productivity in cubic meters per machine hour. Q = harvest volume, net scale in cubic meters. Pi = probability of choosing logging system i ; i=1,highlead; 2,grapple; 3,longreach. Z = vector of logging system dummy variables. RPH = road density in meters per hectare. F&BT = f a l l i n g and bucking phase time in manhours. YT = yarding phase time in machine hours. Vnet = t o t a l cruised timber volume net of estimated decay, waste and breakage (C), in cubic meters. (Other variables as given in Table 2) Equations were calculated using stepwise regression programs compiled at the University of B r i t i s h Columbia Computing Centre by White and Grieg (1979), and Le and Tenisci (1978). In addition to the o r i g i n a l variables l i s t e d in Table 83 2, polynomial and logarithmic transformations of potential independent variables were tested. A number of factors were considered in selecting the "best" equation. Because of the extensiveness of inte r r e l a t i o n s h i p s in the b i o t i c and edaphic communities comprising forests, and the r e l a t i v e l y small sample obtained, i t was taken that m u l t i c o l l i n e a r i t y in the explanatory variables would present problems in correct model s p e c i f i c a t i o n ( i . e . a l l relevant variables included). To attempt proper s p e c i f i c a t i o n , i n i t i a l estimations considered a subset of the variables hypothesized in each of the equations (4.1) to (4.5). Variables included in th i s stage were those most often, or strongly, indicated in the l i t e r a t u r e as important sources of variation in the response variable. Through the use of " p a r t i a l F-tests" (Draper and Smith, 1966), variables were added to, retained or excluded from the regression at each stage, i f their associated "F" value was s i g n i f i c a n t at the 95 percent confidence l e v e l . If at least 60 percent of t o t a l variation could not be explained, then the remaining hypothesized variables were considered for potential i n c l u s i o n . After tests of relevant transformations, i f explained variations remained less than .60 percent, then the pro b a b i l i t y l e v e l was reduced to 10 percent (90 percent confidence level) and regressions were recalculated. Equations selected for hypotheses (4.1) to (4.4) were analysed, using dummy variable covariance techniques (Johnston, 1972; Cunia, 1973), to determine i f a single 84 equation across a l l yarding systems was s u f f i c i e n t or whether an individual equation was necessary for each system. F i n a l l y , residuals of the selected regressions were examined and tested for heteroscedasticity and autocorrelation. In developing the li n e a r probablity model for predicting system choice, the above procedures were carried out for each system independently. From the selected equations variables were i d e n t i f i e d that proved,to be s i g n i f i c a n t in at least two of the equations. Regressions were recalculated using the same independent variables for each system. This approach was necessary to ensure that the sum of system p r o b a b i l i t i e s equal one (Pindyc.k and Rubinfeld, 1976), guarantying a unique solution. 4.45 Qualitative Analysis Variable means, c o e f f i c i e n t s of variati o n , minimum and maximum values, by individual yarding systems and across a l l systems, are given in Table 3. Simple correlations by system and across a l l systems .are given in Appendix 1, as are variable histograms for a l l systems combined. Because of i t s wide use and r e l a t i v e i n s e n s i t i v i t y to operating conditions, highlead yarding operations occurred on areas representing the f u l l range in nearly a l l variables sampled. This can be seen by comparing the minimums and maximums for each variable between highlead (HL) and a l l system (ALL) s t a t i s t i c s in Table 3. For this reason, i t w i l l be d i f f i c u l t to explain much of the va r i a t i o n in system choice. That i s , since highlead yarding was used over the 8 5 same conditions as were grapple and long-reach systems i t appears that equipment a v a i l a b i l i t y and management s k i l l s were the major factors in determining system choice, rather than resource v a r i a b i l i t y . However, by looking at those variables where highlead did not represent the extremes, and by comparing the r e l a t i v e dispersion of variables about their means between systems, i t should be possible to identif y some resource c h a r a c t e r i s t i c s that are l i k e l y to influence management choice, given the option of alternative yarding systems The lowest observed and lowest mean road density (RPH) was, as expected, on areas where long-reach yarding systems were used. This is a natural result of the longer yarding distances. Although the difference is i n s i g n i f i c a n t , minimum and mean road density was greater on grapple than highlead operations. This supports the assumption of shorter yarding distances on average for grapple yarding. The i n s i g n i f i c a n t difference between the two systems was expected since 13 of the 16 additional samples derived by " s p l i t t i n g " the sampled blocks, were grapple on highlead operations. For the samples obtained i t appears that grapple yarding was used to complement highlead yarding in a manner as described by Oakley (1976): Table 3. Variable S t a t i s t i c s : Mean, Standard Deviation, Minimum and Maximum. ( B r i t i s h Columbia — Coast Region) Means Co e f f i c i e n t of Variation Minimum Maximum Variable ALL 1 2 •a • A HL GV LR ALL HL GY LR ALL HL GY LR ALL HL GY LR RL (M) 1003.4 1268.9 875.4 540.7 95.9 83.8 105.7 103.4 29.4 148.6 205.0 29.4 3988.6 3988.6 3044.7 1884.9 RPH (RL/A) 37.52 41.67 42.39 25.55 60.5 63.5 31.5 57.0 2.1 16.8 24.1 2.1 153.3 153.3 61.9 44.0 F&BT (Man Hours) 1457.0 1607.4 1376.0 1134.0 68.9 69.0 68.2 60.9 127.4 163.6 127.4 310.8 4101.5 4101.5 3234.4 2830.8 F&BP (Q/F&BT) 12.93 13.76 11.18 12.66 39.3 46.8 14.7 18.4 6.52 6.52 6.87 10.69 44.47 44.47 13.20 20.23 YT (Mach. Hrs.) 765.54 879.4 689.9 537.4 79.2 78.6 77.5 59.8 48.0 130.6 48.0 142.0 2972.0 2972.0 1868.9 1282.2 YP (Q/YT) 25.07 24.73 24.20 27.0 27.4 28.5 32.7 18.8 14.48 14.48 14.98 16.32 45.46 44.36 45.46 36.95 Q (Cu. M.) 18511.0 21389.0 15172.0 14393.0 83.4 86.1 68.3 61.6 1276.0 2124.4 1276.0 3822.8 82206.0 82206.0 39454.0 34530.0 E (H) 454.04 484.5 362.5 475.45 46.6 48.3 42.6 38.7 91.4 91.4 121.9 182.9 1005.8 1005.8 701.0 792.5 S tt) 30.31 32.91 21.84 32.89 45.6 38.2 41.8 55.2 0.0 0i0 7.3 10.0 85.0 60.0 36.2 85.0 T 2.47 2.60 2.26 2.35 27.1 23.0 28.8 35.3 1.0 1.0 1.0 1.0 4.0 4.0 3.53 4.0 B 1.84 1.79 1.73 2.09 41.3 37.4 48.0 44.0 1.0 1.0 1.0 1.0 3.0 3.0 3.0 3.0 EX 0.98 0.96 0.71 1.34 95.9 101.0 104.2 73.1 0.0 0.0 0.0 0.0 4.0 4.0 2.11 3.0 0 1.01 1.20 0.87 0.65 87.1 85.0 51.7 110.8 0.0 0.0 . 0.19 0.0 5.75 5.75 1.81 2.25 SD (M) 0.52 0.57 0.60 0.29 105.8 119.3 66.7 41.4 0.11 0.12 0.11 0.12 4.10 • 4.10 1.00 0.50 ST 45.84 45.19 42.0 52.08 36.3 40.4 36.8 22.7 13.0 13.0 13.0 13.0 75.0 75.0 56.0 56.0 SM 2.29 2.37 2.32 2.00 17.9 18.6 19.0 0.0 2.0 2.0 2.0 2.0 3.0 3.0 3.0 3.0 H (M) 30.60 31.36 29.05 30.30 11.4 12.0 10.7 8.2 26.2 26.2 26.2 27.0 40.7 40.7 37.0 36.1 D (CM) 54.85 55.45 52.17 56.29 11.8 12.5 13.5 6.7 43.2 43.2 43.2 49.7 72.8 72.8 72.8 61.8 C (7.) 17.70 19.74 16.39 13.54 33.6 31.8 31.4 18.3 11.4 11.7 11.9 11.4 32.2 32.2 25.0 20.2 ALV (Cu. M.) 1.71 1.52 1.71 2.23 36.2 35.5 24.6 30.9 0.55 0.55 0.99 0.81 2.97 2.77 2.74 2.97 SPH 206.25 231.02 .172.8 176.3 34.5 31.4 20.5 42.3 108.2 114.70 114.70 108.2 391.6 391.6 231.6 335.5 VPH (V/A) 982.15 989.7 938.7 1011.3 21.5 21.8 23.4 19.1 539.9 539.9 556.8 573.1 1336.8 1336.8 1186.6 1301.4 V (Cu.M., C.U.) 27610.0 33751.0 21085.0 18135.0 83.0 79.2 69.4 89.9 1531.2 2737.4 1531.2 5914.4 103380.0 103380.0 42602.0 48136.0 A (HA) 28.38 34.16 23.34 18.19 76.1 71.0 71.2 70.6 1.5 2.4 1.5 6.0 89.0 89.0 51.0 53.7 VNET l 22230.0 26628.0 17401.0 15622.0 80.7 78.3 69.2 69.8 1286.2 2376.1 1286.2 5163.3 82396.0 82396.0 37532.0 42504.0 S t a t i s t i c s for A l l Systems Combined. N (Number of Observations) = 64 for A l l Variables Excluding RL and RPH Where N = 49. S t a t i s t i c s for Highlead Yarding. N " 36 for A l l Variables Excluding RL and RPH Where N = 27. S t a t i s t i c s for Grapple Yarding. N - 15 for A l l Variables Excluding RL and RPH Where N » 9. S t a t i s t i c s for Long-Reach Yarding. N • 13 for A l l Variables. CO 87 "To gain a l l the advantages of yarding distance, log size and def l e c t i o n , careful engineering layout is e s s e n t i a l . . . so that the maximum acres are logged with grapple yarding cranes without leaving an impossible situation for conventional yarding equipment. . . the usual practice is to yard f i r s t with the crane so that doubtful areas are t r i e d and maximum pr a c t i c a l volumes are yarded." (p. 30) Thus, cutting blocks engineered for highlead yarding with high road densities appear to provide greater opportunities for a u x i l l i a r y logging with grapple yarders. Many of the s i t e variables support the assumption that grapple yarding is generally used on more accessible areas. For example, measures of slope, t e r r a i n v a r i a b i l i t y , brush density and area in exposed bedrock had their lowest mean and maximum values on grapple yarding operations. Since these variables were measured separately on blocks with both highlead and grapple yarding, the values are indicative of the type of conditions a grapple yarder would operate on i f i t were the primary system used. The d i s t i n c t i o n i s not equally clear between highlead and long-reach logging operations. In contrast to assumed relationships, slope and te r r a i n variables had their highest mean value on highlead rather than long-reach cutting blocks. However, since slope means were nearly i d e n t i c a l between the two systems, and long-reach blocks had the highest minimum, maximum and var i a t i o n in observed values, i t i s l i k e l y that further sampling w i l l reveal a greater mean slope on long-reach cutting blocks. The s t a t i s t i c s may also indicate that conventional yarding equipment are being used beyond e f f i c i e n t l i m i t s on some 88 areas. Another p o s s i b i l i t y is that most of the long-reach samples were obtained from one company over an area that appears to have easier logging conditions and better timber quality, on average, than did areas sampled from other companies. It is probably for t h i s same reason that mean diameter, log volume and volume per hectare were greatest on long-reach sample blocks. Increased sampling of long-reach operations over a wider range of conditions and companies would be needed to further test t h i s assumption. Since sample log volumes were net of decay, part of the explanation for higher log volumes on long-reach cut blocks may also be due to lower decay values as expressed by the variable c u l l (C). It i s d i f f i c u l t to draw any inference about comparative height, diameter, c u l l , stems per hectare and volume per hectare between grapple and highlead samples, since cruise data could not be separately i d e n t i f i e d where they occurred together on a single cutting block. The greater log volumes yarded on grapple settings indicate that grapple yarders are located to take advantage of log size in maintaining productivity, as proposed e a r l i e r . In summary, since the sampled values for variables on highlead cutting blocks are representative of the range for nearly a l l variables, l i t t l e of the variation in the p r o b a b i l i t y for choosing a system can be possibly explained by resource c h a r a c t e r i s t i c s as w i l l be seen in the next section. However, analysis of the variables shows that increased sampling of individual grapple and long-reach logging 89 operations should strengthen some underlying trends in resource c h a r a c t e r i s t i c s and system choice. Simple correlations (Appendix 1) between pr o d u c t i v i t i e s in f a l l i n g and bucking, yarding, and variables representing s i t e , stand and tree c h a r a c t e r i s t i c s are as hypothesized, with a. few exceptions. As expected, f a l l i n g and bucking productivity is negatively correlated with slope, ter r a i n , brush and exposed rock, and p o s i t i v e l y correlated with height, diameter, volume per hectare, stems per hectare and road density. S i m i l a r l y , yarding productivity i s negatively correlated with slope, t e r r a i n , exposed rock and road density (because of an im p l i c i t increase in setting changes), and p o s i t i v e l y correlated with height, diameter, volume per hectare and log volume. Discrepancies in f a l l i n g and bucking are; (a) positive c o r r e l a t i o n with obstacles and c u l l (decay, waste and breakage), and (b) negative co r r e l a t i o n with log volume. Since values for both obstacle and c u l l variables are p o s i t i v e l y correlated with height and diameter, i t appears that greater tree volumes in old-growth stands offset the increased cutting times caused by loss of mobility and increasing decay percentages. Hence, these two measures are e s s e n t i a l l y indices of r e l a t i v e timber size. Usually, the relationship between f a l l i n g and bucking productivity and log volume is discussed in terms of a single tree. That i s , as tree diameter (log volume) increases cutting time w i l l increase, but, the change in volume is 90 greater than the change in time, thus productivity (per m3) increases (Conway, 1978). When measured on a stand average basis, as done here, log volumes w i l l be negatively correlated with stand height and stems per hectare ( i . e . as merchantable height increases more logs are recovered per tree (per block), reducing the tree (block) average log volume). Hence, with increasing log volumes more time w i l l be spent on non-productive moving between trees. Apparent exceptions to hypothesized yarding productivity relationships are: (a) positive correlations with brush density, obstacles and c u l l ; and (b) negative co r r e l a t i o n with stems per hectare. As with f a l l i n g and bucking productivity, tree size ( i . e . height and diameter), which is p o s i t i v e l y correlated with brush, obstacle and c u l l variables, appear to increase recovered volumes at a greater rate than is yarding time by increased d i f f i c u l t y . Since the number of stems per hectare i s negatively correlated with log volume, turn volumes w i l l decrease with increasing stems per hectare, with smaller r e l a t i v e changes in yarding time; which j u s t i f i e s the observed negative correlation between productivity and stems per hectare. In general the samples obtained are t y p i c a l of resource and logging c h a r a c t e r i s t i c s in old growth forests of B r i t i s h Columbia's coast region. In the future, however, logging w i l l occur increasingly in younger, second-growth stands. Therefore, to improve a c c e s s i b i l i t y modeling for long-term planning w i l l require sampling of second growth logging operations. Further, the variations in sample data 91 presented here can be reduced by increased sampling, with: (a) samples of resource variables more uniformly d i s t r i b u t e d throughout their range (Demaerschalk and Kozak, 1974); (b) sampling by logging systems more uniformly d i s t r i b u t e d across companies and their range of operating conditions; and (c) selection of samples to enable unique measurement of resource c h a r a c t e r i s t i c s for each logging system considered. 4.46 Regression Analysis The selected regressions are given in Equations (4.6) to (4.12). A l l c o e f f i c i e n t s are s i g n i f i c a n t at the 95 percent confidence l e v e l (0(=O.O5), for equations expressing road length (Eq. 4.6), f a l l i n g and bucking productivity (Eq. 4.7), yarding productivity (Eq. 4.8) and volume harvested (Eq. 4.9). Because of the r e s t r i c t i o n that a l l f i n a l probablity equations have the same•variables, some of their c o e f f i c i e n t s w i l l not be s i g n i f i c a n t even at the 80 percent confidence l e v e l (OC=0.20), which was the minimum c r i t e r i o n for acceptance in the o r i g i n a l equations by individual logging systems. The i n s i g n i f i c a n t c o e f f i c i e n t s w i l l be noted with a , + ' next to their respective standard errors (Equations 4.10 to 4.12). As can be seen in the probability equations, any one of the explanatory pr o b a b i l i t y variables w i l l be s i g n i f i c a n t in at least two of the system equations, excluding the intercept c o e f f i c i e n t , due to the manner in which variables were i d e n t i f i e d for f i n a l estimation (see section 4.44). 92 (4.6) RL = 0.1164 A*SPH + 6.070 A*ALV { 0 .0 1 6 7 ) ( 2 .1 6 8 ) R2 = 0.8198 SEE = 546.15 DW = 2.305 (54.4% of mean) (4.7) F&BP = 35.58 T - 4.566 0 - 0.1866 D - 0.052 VPH ( 3.9 2 6 ) { 1.6 0 ) ( 0 .0 7 9 1 ) ( 0 .0 1 0 3 ) + 1.762 T*0 - 0.9688 T*H - 0.00796 T*VPH ( 0 . 4 9 1 4 ) ( 0 .1 4 5 1 ) ( 0.0 0 1 8 6 ) + 0.0026 H*VPH ( 0.0 0 0 2 7 ) R2 = 0.9683 SEE = 2.64 DW = 1.829 (20.4% of mean) (4.8) YP = -0.1131 S + 1.501 0 + 0.6732 H - 1.118 B*EX ( 0.0 4 4 7 ) ( 0 .7 4 8 ) ( 0 .0 6 9 6 ) ( 0 .3 2 4 ) + 0.0565 B*H*(z +z ) + 0.1461 B*H*z ( 0.0 2 8 5 ) ( 0 .0 3 3 5 ) + 0.1354 C*ALV*z + 0.3072 C*ALV*z ( 0 .0 6 2 4 ) ( 0,0 7 5 7 ) R2 = 0 .9763 SEE = 4.277 DW = 1.561 (17.1% of mean) (4.9) Q = 11.273 YT + 0.4358 Vnet ( 1.7 3 8 ) ( 0 .0 6 2 6 1 ) R2 = 0.9623 SEE = 4804.1 DW = 1.713 (26.0% of mean) (4.10) P{HL} = -0.20044 - 0.000069 E + 0.0099 S - 0.1146 H ( 0, 5 6 8 4 ) + ( 0 . 0 0 0 3 0 ) + ( 0 . 0 0 4 6 ) ( 0 ,0 2 1 6 ) + • + 0.03375 C + 0.00314 RPH + 0.000006 Vnet ( 0.0 1 2 8 ) ( 0 .0 0 2 8 ) ( 0.0 0 0 0 0 3 4 ) R2 = 0.2778 SEE = 0.4467 (4.11) P{GY} = 1.5198 - 0.000290 E - 0.0093 S + 0.0306 H ( 0 .5 0 7 ) ( 0 .0 0 0 2 7 ) ( 0 .0 0 4 1 ) ( 0 ,0 1 9 ) + 0.00218 C + 0.00201 RPH - 0.000002 Vnet ( 0.0 1 1 4 ) + ( 0. 0 0 2 5 ) + ( 0 .0 0 0 0 0 3 ) + R2 = 0.2119 SEE = 0.3985 (4.12) P{LR] = -0.31936 + 0.000359 E - 0.0006 S + 0.0421 H ( 0.4 5 9 4 ) + ( 0.0 0 0 2 5 ) ( 0.0 0 3 7 ) + ( 0. 0 1 7 5 ) - 0.03593 C - 0.00515 RPH - 0.000004 Vnet ( 0.0 1 0 3 ) ( 0.0 0 2 3 ) I 0 .0 0 0 0 0 3 ) R2 = 0.2827 SEE = 0.3610 Where: A l l variables as defined in Table 3, and in Equations (4.1) to (4.5). Two adjacent variables with '*' between indicate a cross-product term. Coefficient standard errors in parantheses. P{xx} = prob a b i l i t y of system "xx"; HL=highlead, GY=grapple yard, LR=long-reach. Z] = dummy variable for system i ; i=l,highlead; 93 2,grapple; 3,long-reach. SEE = standard error of the estimate. DW = Durbin-Watson " d - s t a t i s t i c " autocorrelation test. R2 based on uncorrected sums of squares for Equations (4.6) to (4.9). 4.461 Road Length (RL). As expected, size of the cutting block or area (hectares) accounted for the greatest amount of variation in the t o t a l length of roads needed to log an area. None of the other independent variables could s i g n i f i c a n t l y account for additional variation in any form, as long as area remained in the model. To account for some of the variation in roads b u i l t between blocks of the same size, and s t i l l retain area in the model, interactions between area and other resource c h a r a c t e r i s t i c s were tested using the cross-products of area and a l l other independent variables. The f i n a l equation selected (Eq. 4.6) must be analysed with regard to the correlations between stems per hectare (SPH), log volume (ALV), road length and other resource variables (correlation matrices in Appendix 1). Interpretation of regression c o e f f i c i e n t s as measuring change in the dependent variable with a one unit change in the independent variable requires the assumption that remaining variables are held constant. Since area i s included in both terms th i s interpretation is no longer v a l i d . Also, a strong negative correlation between SPH and ALV implies that variation in one can not be observed without s i g n i f i c a n t (and opposite) variation in the other. To i l l u s t r a t e the rela t i o n s h i p of stand density and log volume on road length, 94 representative log volumes for various stand densities were extrapolated from the sample data. These values were used to calculate the expected road lengths for an area of one hectare (Figure 4 ) . It is readily seen that road length (and density since area is one hectare) increases with increasing number of stems per hectare (decreasing log volume). R e a l i s t i c a l l y , increasing stand density (as measured by stems per hectare) does not "cause" more roads to be b u i l t for a given area. However, stems per hectare (log volume) appears to provide a measure of area a c c e s s i b i l i t y as indicated by positive (negative) correlations with variables such as elevation, slope, t e r r a i n , and obstacles, which w i l l influence road layout and construction. Thus, SPH and ALV are e s s e n t i a l l y proxy measures of the underlying variation in a c c e s s i b i l i t y that cause variation in road construction for a cutting block of given size. It must be noted that the developed equation is only v a l i d on mature old-growth stands similar to those on which sampled logging operations occurred. On young second-growth the number of stems per hectare w i l l decline (log volume increases) as the stand ages, thus predicted road length would decrease with increasing stand age. Here the v a r i a t i o n in the independent variables is a function of both stand age and r e l a t i v e a c c e s s i b i l i t y . Figure 4 . Road Length (A = lha) 96 Examination of the residuals revealed the p o s s i b i l i t y of non-constant variance (heteroscedasticity) with respect to area. Using the "Goldfeld-Quandt test" (Pindyck and Rubinfeld, 1976) i t was found that the variance of regression errors increased s i g n i f i c a n t l y with cutting block area. As suggested by Johnston (1972), the residuals from ordinary least-square (OLS) estimation of road length were regressed on several functions of area to determine the best possible explanation of variance in the regression errors. The selected function 8 was then used to weight a l l variables at each observation, and c o e f f i c i e n t s were reestimated using OLS regression (Draper and Smith, 1966; Johnston, 1972; Pindyck and Rubinfeld, 1976). Co e f f i c i e n t s estimated by the "weighted least-squares" procedures are those given in Equation 4.6. I n i t i a l l y the model was sp e c i f i e d with an intercept term. Since the estimated c o e f f i c i e n t was not found to be s i g n i f i c a n t l y d i f f e r e n t from zero i t was dropped from the equation. This implies that road length w i l l be zero when observed area is zero (obviously), or, where both observed SPH and ALV are zero. 9 Since bare land could have existing roads i t would appear that an intercept term is j u s t i f i e d . However, the equation was specified to measure the length of road 8|RESIDUALi| = 17.98Ai-0.1344Ai 2, R2=0.459 (based on uncorrected sums of squares) 9A zero value for SPH is s u f f i c i e n t to guarantee a zero value for ALV. However, merchantable log volume could be zero under conditions of positive SPH. Since such a stand would have no marketable value under these conditions the cal c u l a t i o n of RL. is i r r e l e v a n t . 97 n e c e s s a r y t o l o g a g i v e n a r e a . I f no timber e x i s t s then the s o l u t i o n of RL i s unnecessary s i n c e the a r e a does not c o n t r i b u t e t o the t o t a l p h y s i c a l t i m b e r s t o c k from which r e c o v e r a b l e s t o c k s a r e b e i n g e s t i m a t e d . Because the e q u a t i o n has been e s t i m a t e d w i t h o u t an i n t e r c e p t term the sum of squares a re not c o r r e c t e d f o r the mean. For t h i s reason the c o e f f i c i e n t of m u l t i p l e d e t e r m i n a t i o n , or R 2 , i s a measure of the p r o p o r t i o n of t o t a l v a r i a t i o n i n observed RL e x p l a i n e d by the r e g r e s s i o n , r a t h e r than v a r i a t i o n about the mean e x p l a i n e d by the r e g r e s s i o n , as " r - s q u a r e s " a r e n o r m a l l y i n t e r p r e t e d . T h e r e f o r e , the R 2 g i v e n here w i l l appear t o be h i g h e r than e x p e c t e d , and i n f a c t . w i l l be g r e a t e r than f o r a s i m i l a r model w i t h i n t e r c e p t and sums of squares c o r r e c t e d f o r the mean. Any model w i t h o u t an i n t e r c e p t , t h a t a p p r o x i m a t e s the set of observe d v a l u e s can be expected t o e x p l a i n a s i g n i f i c a n t p r o p o r t i o n of t o t a l v a r i a t i o n . T h i s does not i n v a l i d a t e the use of the R 2 as a measure of the 'goodness of f i t ' ; i t o n l y r e q u i r e s t h a t comparisons be made t o models w i t h R 2 v a l u e s computed i n the same manner. 4.462 F a l l i n g And Buck i n g P r o d u c t i v i t y (F&BP). T o t a l time i n f a l l i n g and b u c k i n g i s as ex p e c t e d s t r o n g l y c o r r e l a t e d w i t h t o t a l s t a n d i n g t i m b e r volume. To account f o r v a r i a t i o n s i n time caused by f a c t o r s not r e l a t e d t o b l o c k s i z e , t o t a l f a l l i n g and b u c k i n g times were d i v i d e d by t o t a l p r o d u c t i o n f o r each b l o c k . T h i s measure of p r o d u c t i v i t y i n f a l l i n g and b u c k i n g was r e g r e s s e d a g a i n s t a l l o t h e r v a r i a b l e s , t r a n s f o r m e d and u n t r a n s f o r m e d . A l t h o u g h a l l c o e f f i c i e n t s i n the f i n a l 98 equation (Eq. 4.7) are s i g n i f i c a n t at the 95 percent confidence l e v e l (<X = 0.05), the additional variation explained by each independent variable, to the variation already explained by other included variables, is only s i g n i f i c a n t at the 90 percent confidence l e v e l (O(=0.10). By reducing the significance l e v e l for entry into the model, t o t a l explained variations adjusted for the number of variables (R2 adjusted) more than doubled, while the standard error of the estimate was reduced by approximately 50 percent. However, as a res u l t , correlations between included variables w i l l be greater, possibly masking the true influence of independent variables on the dependent variable (Johnston, 1972). In such cases where s i g n i f i c a n t linear dependence exists between independent variables ( m u l t i c o l l i n e a r i t y ) , Pindyck and Rubinfeld (1976) suggest that "... The model can be u t i l i z e d with a l l i t s variables, i f s u f f i c i e n t care is given to the interpretation of the regression r e s u l t s . " (p. 67). With this in. mind, and upon a quick review of simple correlations among sample data, i t can be seen that few of the included terms can be varied without concurrent variations in the others. Hence, both the magnitude and direction of influence each variable has on productivity must be assessed with reference to any linear dependence that may af f e c t i t s estimation. Additionally, with the c o e f f i c i e n t s expressed in the scale-free manner of "Beta C o e f f i c i e n t s " (Pindyck and Rubinfeld, 1976) comparisons of the r e l a t i v e importance of each independent variable can be d i r e c t l y made. These 99 c o e f f i c i e n t s for variables in the F&BP equation are given in Table 4. Table 4. Beta C o e f f i c i e n t s for F a l l i n g and Bucking Productivity Equation 1 Var iable Coefficient T 4.7114 T*H -4.5599 H*VPH 4.4099 VPH -2.1598 T*VPH -1.4078 T*0 1.1282 0 -0.7911 D -0.2400 1/§; = (dx, / O V , ), where: /Jj = Beta c o e f f i c i e n t ; fi\ = estimated c o e f f i c i e n t of variable i ; = estimated standard deviation of independent variable i , and; ffy= estimated standard deviation of the dependent variable. The simple correlations do not show any strong relationships between t e r r a i n and other dependent variables, with the possible exception of a positive association (0.37027) with o b s t a c l e s . 1 0 Holding a l l other variables constant at their sample means i t can be shown that productivity w i l l decline with increasing t e r r a i n d i f f i c u l t y , even though the beta c o e f f i c i e n t is strongest and positive for 1 0 T h i s does not preclude the p o s s i b i l i t y of other relationships since, as noted by Pindyck and Rubinfeld (1976), simple correlations alone may not give adequate indication of the degree of m u l t i c o l l i n e a r i t y , p a r t i c u l a r l y with more than two independent variables, because of more complex linear dependencies among variables. 100 t e r r a i n by i t s e l f . 1 1 It appears that the net negative effect on productivity of other cross-product terms that include ter r a i n have a stronger joint influence than t e r r a i n alone. If the measure of obstacles does consistently move in positive association with t e r r a i n d i f f i c u l t y , the net affect on productivity of increasing d i f f i c u l t y is hard to interpret from the results. This is p a r t i c u l a r l y true i f the positive c o r r e l a t i o n (0.27337) between obstacle and tree height is also cons i stent. If a l l variables other than volume per hectare are held constant at their sample means, productivity and volume per hectare w i l l move in the same d i r e c t i o n . However, changes in VPH w i l l most l i k e l y occur with positive changes in tree height (0.39862) and diameter (0.45221), which obscures the net af f e c t of VPH on predicted productivity. Because of their association with volume per hectare and the strong positive c o r r e l a t i o n between height and diameter (0.78025), i t is s i m i l a r l y d i f f i c u l t to assess the individual influence of either height or diameter by a simple review of their estimated c o e f f i c i e n t s . However, i f terrain and obstacles are held constant while diameter, height and volume per hectare increase, the r e l a t i v e l y minor reduction in productivity associated with the diameter c o e f f i c i e n t should be offset by greater increases in productivity associated with increases in height and volume per hectare. A review of the equation 11The decreased e f f i c i e n c y of the Beta c o e f f i c i e n t s as measures of r e l a t i v e importance is a further indication that the F&BP equation suffers from m u l t i c o l l i n e a r i t y , which is not readily discernable from an inspection of simple cor r e l a t i o n s . 101 s t a t i s t i c s r e v e a l s t h a t a s u b s t a n t i a l p r o p o r t i o n of the t o t a l v a r i a t i o n i n observed p r o d u c t i v i t i e s i s e x p l a i n e d , w i t h a r e l a t i v e l y s m a l l s t a n d a r d e r r o r (±20.4% of mean p r o d u c t i v i t y ) , and w i t h no i n d i c a t i o n of a u t o c o r r e l a t e d e r r o r s between o b s e r v a t i o n s . F u r t h e r e x a m i n a t i o n and a t e s t of the r e s i d u a l s s u p p o r t e d the assumption of c o n s t a n t v a r i a n c e ( h o m o s c e d a s t i c i t y ) . Hence,. a l t h o u g h the v a r i a b l e s and c o e f f i c i e n t s a re d i f f i c u l t t o i n t e r p r e t due t o i n t e r c o r r e l a t i o n s , the s e l e c t e d e q u a t i o n appears t o a c c e p t a b l y f i t o b s e r v e d p r o d u c t i v i t i e s . R i g o r o u s t e s t i n g of the c o n s i s t e n c y of the e q u a t i o n depends on enhancing c u r r e n t data w i t h a d d i t i o n a l samples. 4.463 Y a r d i n g P r o d u c t i v i t y ( Y P ) . As w i t h f a l l i n g and b u c k i n g , t o t a l y a r d i n g times were s t r o n g l y c o r r e l a t e d w i t h b l o c k s i z e as measured by a r e a or s t a n d i n g t i m b e r volume. A g a i n , t o account f o r some v a r i a t i o n caused by r e l a t i v e a c c e s s i b i l i t y , p r o d u c t i o n was d i v i d e d by phase time t o p r o v i d e a measure of y a r d i n g p r o d u c t i v i t y f o r use as the dependent v a r i a b l e . Beta c o e f f i c i e n t s f o r the independent v a r i a b l e s a re g i v e n i n T a b l e 5 below. 102 Table 5. Beta Coefficients for Yarding Productivity Equation Highlead Grapple Long-Reach Variable C o e f f i c i e n t Variable Coefficient Variable C o e f f i c i e n t H 0.34075 B*H 0.52852 C*ALV 0.56281 B*EX -0.34005 H 0.34075 H 0.34075 C*ALV 0.31653 B*EX -0.34005 B*EX -0.34005 B*H 0.27.317 S -0.22732 B*H 0. 27317 S -0.22732 0 0.19185 S -0.22732 0 0.19185 0 0.19185 I n i t i a l l y the model was estimated across a l l systems. Using dummy variables for each system (Zi; i=l, highlead; 2, grapple; 3, long-reach), a general linear regression was estimated that allowed testing differences between systems (Johnston, 1972; Cunia, 1973). If there i s an i n s i g n i f i c a n t difference between the c o e f f i c i e n t s for any given variable, then a single c o e f f i c i e n t estimated across a l l systems i s s u f f i c i e n t to explain the variables' influence on productivity for a l l of the sampled yarding systems. S i g n i f i c a n t differences between two or a l l three of the c o e f f i c i e n t s for any one variable indicate i t s influence on yarder productivity i s dependent on the system, and thus separate c o e f f i c i e n t s are j u s t i f i e d . The general equation for yarding productivity (Eq. 4.8) shows that, based on sample data for this thesis, some of the variables do have s i g n i f i c a n t l y d i f f e r e n t influence on productivity, depending on the yarding method used. Disaggregating the equation by yarding system i t can be seen, through the use of the Beta c o e f f i c i e n t s in Table 5, that the r e l a t i v e importance of a given variable may also 103 d i f f e r between systems. Across a l l systems, slope has a negative (minor r e l a t i v e to other variables) impact on yarder productivity, holding a l l else constant. This w i l l l i k e l y be reinforced in highlead and grapple yarding i f the positive correlation 'of slope with exposed rock and negative correlations with height and c u l l are consistent. In long reach yarding, although a positive co r r e l a t i o n with exposed rock and negative c o r r e l a t i o n with log volume w i l l reinforce the reduction in productivity caused by increasing slope, a positive correlation between slope and height w i l l offset the reduction. Since the r e l a t i v e importance of the height variable is lower in long-reach yarding, i t is l i k e l y that the net influence of increasing slope w i l l be a reduction in yarding productivity. Since the obstacles index includes a measure of ". . . . windfalls (less than 50% sound wood content) uprooted trees and old stumps. . ." (Province of B r i t i s h Columbia, 1979a. p. 33) the index may account for additional variation in the model as caused by large old-growth timber, rather than s t r i c t l y that caused by a loss of mobility for the yarding crew. Hence, the positive impact on yarder productivity, while holding a l l else constant. However, since obstacles have positive correlations (>0.20) with slope, brush, exposed rock and height for a l l systems, the net impact on productivity is unclear. If obstacles increase with increasing slope and exposed rock while brush and height remain constant (or even decline), productivity w i l l decrease 104 because of the greater r e l a t i v e importance of S and EX in accounting for productivity variations. Here the index may actually be representative of decreasing a c c e s s i b i l i t y . I f , however, slope and exposed rock remain constant while brush density, tree height (and diameter), and obstacles increase, yarder productivity w i l l also increase. In such cases the obstacles index may be more a measure of timber size than area a c c e s s i b i l i t y . As hypothesized, tree height w i l l p o s i t i v e l y influence yarder productivity due to increasing the number of logs that can be yarded per setting ( a l l other variables remaining constant). Increases in productivity may be offset somewhat i f increases in brush density occur over increasing height as indicated by the posit i v e correlation between the two var iables. Contrary to the hypothesis that brush density w i l l decrease yarder productivity through i t s adverse effect on crew mobility, the equation and simple correlation between productivity and brush support the conclusion of a positive impact. Since brush density is p o s i t i v e l y correlated with obstacles, height and log volumes, and negatively correlated with exposed rock, movements in brush density w i l l occur with changes in the other variables which p o s i t i v e l y influence yarder productivity. The reason for the discrepancy with the hypothesized e f f e c t - l i e s with the l e v e l at which productivity i s measured. If a time study is carr i e d out for a single choker setter over varying brush densities, i t is l i k e l y that 105 increased d i f f i c u l t y in movement at higher densities w i l l reduce productivity ( a l l other variables being constant). However, i f productivity is measured at the cutting block l e v e l as done here, then greater brush density w i l l be associated with stands having greater average tree heights, diameter and log volume. Thus, the (positive) change in volume w i l l be greater than the (positive) change in yarding time caused by increased d i f f i c u l t y , and productivity w i l l increase. The sample data show a positive c o r r e l a t i o n between productivity and both c u l l and log volume. The correlation with c u l l is contrary to that hypothesized. However, since c u l l includes component measures of waste and breakage estimates, i t appears that an increase in the c u l l variable implies a decrease in the proportion of t o t a l volume harvested, hence, a concentration of yarding time on the higher quality proportion of the f e l l e d volumes. Since c u l l and actual log volume are negatively correlated, the net influence on productivity of the C*ALV cross product term in the developed equation is uncertain, for stands of a given timber size, since changes in one variable of the term imply opposite changes in the other. However, in comparing stands of d i f f e r e n t timber sizes i t can be shown that productivity w i l l increase with increases in the C*ALV term, since both c u l l and actual log volume w i l l be greater on larger old-growth than smaller second growth stands. 106 As with f a l l i n g and bucking, the equation s t a t i s t i c s show that a substantial „ proportion of the t o t a l variation in observed productivity is explained, with a r e l a t i v e l y small standard error of the estimate (±17.1% of mean yarding p r o d u c t i v i t y ) . However, for the yarding equation the Durbin-Watson "d" s t a t i s t i c (DW) f a l l s in the indeterminate range, thus we can not p o s i t i v e l y prove or disprove the hypothesis of autocorrelated residuals. In t h i s range i t is possible that the autocorrelation i s among independent variables rather than residuals (Pindyck and Rubinfeld, 1976). Autocorrelation among independant variables may indicate that there are variables omitted from the equation that are influencing the error term in a continuous pattern (Johnston, 1972). Since the yarding productivity equation w i l l have di f f e r e n t variables depending on the yarding system used, i t is possible that the prediction errors w i l l follow different patterns that are d i s t i n c t between systems. Thus i t is possible that no autocorrelation exists for the prediction on any one system, but, that the error term across a l l observations is correlated with the logging system on each observation. For this reason, the equation was accepted without further adjustment. F i n a l l y , examination and testing of the residuals supported the hypothesis of constant error variance (homoscedasticity). 107 4.464 Volume Harvested (Q). Hypothetically the volume harvested should equal standing timber volume net of decay, waste and breakage. However, since estimated volumes, decay, waste and breakage can be estimated in error, the volume in logs harvested w i l l most l i k e l y be dif f e r e n t than estimated volumes. Usually, as can be seen in the variable means given e a r l i e r , estimated volume stated in close u t i l i z a t i o n terms w i l l be greater than harvested volume. Knowledge of actual volume harvested i s necessary to determine how much of standing timber stocks must be removed to harvest volumes equal to allowable cuts; or, for unregulated lands, how much timber must be cut to meet log supply requirements. Also, in determining stand values, applying log prices to standing volumes would overestimate the t o t a l stand value. Estimates of harvest volume w i l l of course depend on estimated timber volume and the amounts of labor and c a p i t a l employed to harvest the timber. As inputs to a constant timber volume are increased, more of the timber w i l l be converted into marketable products ( i . e . logs). However, the additional volume gained by increasing inputs other than timber w i l l decline thus the productivity or recovery per unit of labor or c a p i t a l w i l l also decline and unit costs w i l l increase. To estimate this relationship for my sample data, production was specified as a function of f a l l i n g and bucking time, yarding time and net volume. The regression results are given in Equation 4.9. Since yarding time, and f a l l i n g and 108 bucking time were highly correlated, both could not be maintained as explanatory variables. The higher c o r r e l a t i o n between production and yarding time thus prevented the entry of the f a l l i n g and bucking time variable. As expected, production w i l l increase as either timber volume or yarding time increases. Yarding time can be considered a measure of the size of logging operation since i t is p o s i t i v e l y correlated with a l l other phases. The equation given for production is the result of weighted least squares regression, since residuals of the o r i g i n a l unweighted OLS regression revealed increasing variance with increasing net volume. Procedures were the same as followed in the road length regression. That i s , residuals were regressed on several functions of net volume to determine an equation for changing error variance, with the best function used to weight each observation. 1 2 Then, the production equation was reestimated using the transformed variables in an OLS regression. As shown in Equation 4.9, a high proportion of the t o t a l v a r i a t i o n in observed production has been explained by the selected equation, with a standard error of the estimate equal to approximately one-fourth of mean production. The Durbin-Watson s t a t i s t i c allows rejection of the hypothesis that errors in estimation are correlated between observations. 1 2|RESIDUALi| = 1511.8 + 0.00000181 Vnet 2, R2 = 0 .4431 1 0 9 4 . 4 6 5 System P r o b a b i l i t i e s . Because each system was forced by s p e c i f i c a t i o n to have the same variables as other system equations, not a l l of the c o e f f i c i e n t s in any equation w i l l be s t a t i s t i c a l l y s i g n i f i c a n t , as discussed e a r l i e r . However, those variables which were s i g n i f i c a n t in predicting each system separately are s i g n i f i c a n t in the equations presented, and w i l l be r e l a t i v e l y more important in determining variations in pr o b a b i l i t y as shown by their Beta c o e f f i c i e n t s given in Table 6. Those variables not in the o r i g i n a l equation for each system are indicated by a , + ' . Table 6. Beta Coe f f i c i e n t s for Logging System Linear Probability Equations Highlead Grapple Long-Reach  Var iable Coef f ic ient Variable Coefficient Variable Coefficient c 0 . 4 0 0 7 9 S - 0 . 3 0 0 1 6 C - 0 . 5 2 6 1 1 s 0 . 2 7 3 8 5 H -0 . 2 4 4 9 7 H 0 . 3 6 1 4 6 Vnet 0 . 2 1 3 4 6 E - 0 . 1 4 3 6 9 RPH - 0 . 2 5 5 4 7 RPH 0 . 1 2 6 4 4 RPH 0 . 0 9 4 5 7 E 0 . 1 8 7 2 6 H + - 0 . 0 7 9 8 7 Vnet + - 0 . 0 9 2 3 1 Vnet - 0 . 1 6 6 0 1 E + - 0 . 0 2 9 1 8 C + 0 . 0 3 0 3 2 S + - 0 . 0 2 1 6 3 Most of the c o e f f i c i e n t s are d i r e c t i o n a l l y oriented as would be hypothesized. Increasing road density and c u l l (as a general index of timber size) increases the pr o b a b i l i t y of highlead and grapple yarding while decreasing that of long-reach yarding. Because of the common use of highlead yarding systems and more specialized conditions necessary for grapple or long-reach systems, larger cutting blocks (as expressed by net volume), with a wide range in operating c h a r a c t e r i s t i c s , w i l l increase the pr o b a b i l i t y of highlead yarding, with subsequent decreases for grapple and long-reach. 110 Considering that stands at higher elevations w i l l be increasingly inaccessible (sample correlations show positive relationships between elevation and slope, t e r r a i n , exposed rock and obstacles), and/or more sensitive to logging, the p r o b a b i l i t y of long-reach yarding w i l l understandably increase while that for highlead and grapple yarding decreases. S i m i l a r l y , since log volumes are negatively correlated with height and elevation, then increasing average stand heights (decreasing log volumes) reduces the pr o b a b i l i t y of highlead and grapple yarding while increasing the pr o b a b i l i t y of long-reach yarding. The increase (decrease) in the p r o b a b i l i t y of highlead (grapple) yarding associated with increasing slope is expected. However, long-reach yarding p r o b a b i l i t y is shown to decrease with increasing slope contrary to the positive relationship hypothesized. The discrepancy may be due to several factors, such as: (a) samples that are not representative of t y p i c a l long-reach operations ( i . e . only the lower end of the range was observed), or (b) because some of the sampled long-reach operations were undertaken to avoid stream damage, average slopes were low and not c r i t i c a l to the choice of system. Since the r e l a t i v e importance of slope is minor in determining long-reach probability the equation was accepted with the negative slope c o e f f i c i e n t . The R-squares of the pr o b a b i l i t y equations are based on the corrected sums of squares (due to s p e c i f i c a t i o n of an intercept term) and are unadjusted for the degrees of freedom I l l (since a l l equations have the same number of explanatory variables). Although in r e l a t i v e terms i t can be seen that the long-reach equation w i l l provide better predictions of long-reach p r o b a b i l i t i e s than w i l l the other two equations for highlead and grapple yarding, no d e f i n i t e conclusion can be made about the individual "goodness of f i t " of each equation. Normally, R2 values w i l l range from zero to one with higher values indicating a better f i t . However, in a linear probability model the maximum value an R2 can assume may be much less than one, thus a low R2 may actually be high r e l a t i v e to the maximum possible (Pindyck and Rubinfeld, 1 9 7 6 ) . I n t u i t i v e l y , because of the wide d i s t r i b u t i o n of sampled variables on highlead operations, the R2 for highlead p r o b a b i l i t i e s most l i k e l y indicates a lower explanation of observed variations than that for grapple or long-reach. Due to the s p e c i f i c a t i o n of a linear probability model, i t can be shown that the error term w i l l be heteroscedastic with increasing variance as p r o b a b i l i t y approaches 0.50 (Kmenta, 1 9 7 1 ; Pindyck and Rubinfeld, 1 9 7 6 ) . Therefore, weighted least-squares estimation would seem appropriate. However, i t has been suggested that for r e l a t i v e l y small samples weighted least-squares may lead to greater i n e f f i c i e n c i e s in linear probability estimation, and thus i t may be better to retain ordinary least-squares estimates (Pindyck and Rubinfeld, 1 9 7 6 ) . Because sample sizes for long-reach and grapple yarding operations (13 and 15 respectively) are r e l a t i v e l y small, and to ensure that 112 predicted p r o b a b i l i t i e s across systems sum to one, the equations were estimated using unweighted OLS regression procedures. Furthermore, since the error term is not normally di s t r i b u t e d , the conventional tests for autocorrelation using the Durbin-Watson s t a t i s t i c can not be applied. Thus, the DW s t a t i s t i c s were not given in Equation 4.9, and no conclusion can be drawn about possible autocorrelation. If sample sizes are increased through further study, and the equations are developed using weighted least-squares estimation, then the errors would be normally d i s t r i b u t e d and the hypothesis for autocorrelation could be tested. System probability prediction could also be improved by recognizing that various yarding methods are commonly used together on a single operation. Therefore, p r o b a b i l i t i e s should also be developed for the various combinations ( C o t t e l l , 1980). This suggests that even greater sampling is required, since for the four yarding methods sampled here (separating long-reach into tension skidder and slackline yarding), there are 15 d i f f e r e n t combinations. If the logging systems on each sample are ranked by the proportion of volume logged, the number of possible permutations would equal 64. If additional systems are sampled, the permutations would be greater. Even i f i t is assumed only three systems, of six possible, w i l l be used on a single operation, there are 120 possible permutations for predicting system p r o b a b i l i t y . The implication is that an extremely large sampling e f f o r t would be required. For this reason i t may better to continue 113 modeling pr o b a b i l i t y for single systems, and where two or more systems have nearly equal p r o b a b i l i t y of occurring, a combination could be i d e n t i f i e d as the system chosen, with weighting provided by the individual system p r o b a b i l i t i e s . 4 . 5 SUMMARY To develop stock estimates of accessible timber supplies requires some means of predicting net values of harvesting physical stocks. In choosing a s t a t i s t i c a l approach to determine values the analyst is l e f t with two a l t e r n a t i v e s : (a) d i r e c t l y develop net value relationships, or (b) calculate net value from separate predictions of logging cost, and revenue. The l a t t e r approach was further developed in this chapter, since i t allows more detailed analysis of the s p e c i f i c forces that influence economic reco v e r a b i l i t y of timber supplies. S i m i l a r l y , in developing logging costs the estimation of productivity relationships to which factor costs can be applied is favored over direct unit cost relationships, primarily because i t permits separate analysis of the forces influencing unit costs. Other reasons elaborated for choosing a time (or productivity) vs. cost analysis were: (a) d e f i n i t i o n of cost centers may pose problems in obtaining wide variations in resource c h a r a c t e r i s t i c s ; (b) reluctance of industry to provide samples of operational costs; and (c) problems of comparability in i n t e r - f i r m accounting data. 114 In developing productivity relationships to determine timber supplies for y i e l d planning on public lands, only those variables that are or could be a part of inventory s t a t i s t i c s can be used for explanatory purposes. That i s , some variables, which are important to a more precise determination of productivity w i l l not be known and could not be s a t i s f a c t o r i l y projected, such as; season of logging, landing locations and their c h a r a c t e r i s t i c s , crew c h a r a c t e r i s t i c s , weather, etc.,. These variables must be omitted from the productivity analysis. With th i s in mind, a preliminary analysis of data on logging operations in coastal B r i t i s h Columbia was completed, to determine i f any s i g n i f i c a n t relationships could be developed between logging c h a r a c t e r i s t i c s and resource variables. The logging process was disaggregated into homogeneous phases" and equations were hypothesized for predicting length of roads constructed, f a l l i n g and bucking productivity, yarding productivity and t o t a l production. Since the type of yarding system for which an area is engineered may influence the prediction in each phase, single equations were hypothesized for each system by logging phase. Three 'systems' were represented by the sample data: (a) highlead, (b) grapple, and (c) long-reach (tension skidder and slackline) yarding. Analyses of the sample data show that a wide variation in resource c h a r a c t e r i s t i c s was obtained as desired. Also, since the sampling was d i s t r i b u t e d over six major companies 115 operating in the coastal region i t is f e l t that the data are representative of current logging operations and level of e f f i c i e n c y . However, r e l a t i v e l y small sample sizes for grapple and long-reach operations, extensive range in ch a r a c t e r i s t i c s on highlead operations, close association between grapple and highlead samples, and narrow d i s t r i b u t i o n of long-reach observations between sampled logging firms, l i k e l y reduced current data c a p a b i l i t i e s for determining true differences between systems. Results of the regression analysis are encouraging in that s i g n i f i c a n t relationships can be i d e n t i f i e d using only resource variables. As a result the estimated equations were able to explain a substantial proportion of t o t a l variations in each phase with r e l a t i v e l y low standard errors. However, there is a f a i r amount of in t e r c o r r e l a t i o n among resource variables. Hence, the accepted equations l i k e l y suffer from some degree of m u l t i c o l l i n e a r i t y , which requires careful interpretation of the res u l t s . S p e c i f i c a l l y , the re l a t i v e influence of a single independent on dependant variable can not be d i r e c t l y concluded from the estimated c o e f f i c i e n t s in some of the equations. It is also necessary to be careful in interpreting the reason some variables were s i g n i f i c a n t , since they may represent the combined variations caused by other variables ( i . e . in essence these could be considered proxy or instrumental v a r i a b l e s . ) . In predicting road length, f a l l i n g and bucking productivity, and volume harvested, the hypothesis of a 116 separate equation for each system was rejected in favor of a single equation across a l l systems. The prediction of yarding p r o d u c t i v i t i e s i s , however, dependent on the system used. To u t i l i z e the present equation for prediction purposes, therefore, requires knowledge of the yarding method that w i l l most l i k e l y be used on future operations. For this purpose, linear probability equations were estimated for each system. The equations predict the p r o b a b i l i t y a method w i l l be chosen given resource c h a r a c t e r i s t i c s on the proposed cutting area. Given the current data, the equations provide acceptable explanation of expected p r o b a b i l i t i e s . However, as mentioned e a r l i e r , the d i s t i n c t i o n between systems provided by the samples available may be r e l a t i v e l y narrow, and thus better predictions of system p r o b a b i l i t i e s w i l l depend on greater sampling. In general, the sample size is small r e l a t i v e to the number of variables relevant for prediction in each phase, and to the variation in observable values for most variables. As suggested in this chapter, improved relationships w i l l depend on increasing the sample size and ensuring a more uniform d i s t r i b u t i o n of samples across possible values for each variable. Further improvement can be acheived by reducing the p o s s i b i l i t y of s i g n i f i c a n t m u l t i c o l l i n e a r i t y . One means of approaching this problem is to eliminate int e r c o r r e l a t i o n s of independent variables through the i d e n t i f i c a t i o n of new variables, or, by i d e n t i f y i n g and running regressions on p r i n c i p a l components. 117 CHAPTER 5 ECONOMIC TIMBER SUPPLY OF THE U.B.C. RESEARCH FOREST 5.1 INTRODUCTION The purpose of t h i s chapter is to i l l u s t r a t e how economic stock timber supplies could be estimated using equations such as those developed in the previous chapter, and how cost, price and productivity trends could be e x p l i c i t l y considered in adjusting stock estimates over time. To acheive this objective, the University of B r i t i s h Columbia Research Forest was selected as a representative forest management unit. The procedures outlined here could be followed, with some modifications, for supply estimation on any management unit in coastal B r i t i s h Columbia (e.g. Timber Supply Area, Tree Farm License, e t c . , ) . Augmented with a model of manufacturing costs and lumber recovery, stock timber supplies from forests of the i n t e r i o r region could be s i m i l a r l y estimated. The basic components of an economic timber supply modeling process are shown in Figure 5. The dashed lines represent temporal- flow adjustments, which are not necessary for the calculation of recoverable timber stocks in the current period. However, these adjustments are necessary for stock estimation in future periods; a c r i t i c a l requirement of short or long-term development, harvest and s i l v i c u l t u r a l planning. 118 Figure 5. Economic Timber Supply Modeling Procedures Physical Inventory Site Data Ownership, Product Market Records Collection and Infrastructure T Stochastic Processes Deterministic] Processes Subjective Constraints Technological Change and Productivity Data Preparation and Collating I Production Simulation Growth and Depletion Cost and Revenue Calculation Input Factor Costs By Type Product Prices By Type Economic j Stock I Timber Suppl} u J Cost & Price Trends 119 5.2 DESCRIPTION OF THE RESEARCH FOREST Prior to d e t a i l i n g the s p e c i f i c data and means of completing the supply modeling on the Research Forest, a brief review of i t s ' management history and current status w i l l be presented. 1 This i s not meant to be a comprehensive analysis, rather, i t is presented to provide a general understanding of timber reco v e r a b i l i t y on the forest. The Research Forest is approximately 35 kilometers distant from Vancouver, and is accessible year-round by paved highways. The area (5157 hectares; the University of B r i t i s h Columbia Research Forest, undated) was established as an educational forest in 1947 and is representative of " . . . t y p i c a l lower coast topography mountain lakes, steep slopes and rock outcrops in the north, and more gentle slopes of g l a c i a l t i l l in the south. Elevations in the forest range from sea level at P i t t Lake to 1025 metres on the slopes of Mount Blanchard. . ." (the University of B r i t i s h Columbia Research Forest, undated). Excluding the steep slopes on the northeastern boundary, much of the eastern half of the Forest is young (less than 50 years) second growth mixed-conifer and deciduous types that have naturally regenerated following r a i l r o a d logging in the 1920's. Most of the western half of the Forest i s older (greater than 100 years) second growth mixed conifer types information in this section , i f not e x p l i c i t l y referenced, is based upon Annual Reports of the Research Forest (1961-1980), and draft appendices to the Forest Management Plan which is in preparat ion. 120 that regenerated following a major f i r e in 1868. Remnants of the old growth Douglas-fir (Pseudotsuga menz i e s i i (Mirb.)Franco), western hemlock (Tsuga heterophylla (Raf.)Sarg.), and western redcedar (Thuja p i i c a t a Donn) forests that dominated the area, can be found on the steep slopes of P i t t Lake, Mount Blanchard, across the northern boundary, and around the high elevation northern lakes (Gwendoline, Eunice and Katherine). Prior to 1967, road construction on the Forest was designed solely for timber harvesting; no d i s t i n c t development plan had been formulated. In the 1967-1968 f i s c a l year the need for planned access to the Forest was e x p l i c i t l y considered in the formulation of a proposal for a " . . . general road development plan for the whole Forest. . . in which a l l aspects of our management (research, demonstration, crop-growing, protection and harvesting). . . (are) taken into consideration." (the University of B r i t i s h Columbia Research Forest, August 1968). . Construction based upon this plan (Adamovich, 1967) has culminated in an integrated network of main and secondary roads that provide general access to a l l parts of the Forest. From th i s base, spur and four-wheel drive access (or temporary) roads have been constructed as needed to recover timber values. Logging on the Research Forest has progressed from the southwest to northeast (Figure 6) and has generally been limited, as is t y p i c a l of coastal logging development, to the lower cost, most accessible areas. 121 F i g u r e 6. U.B.C. Re s e a r c h F o r e s t P r i m a r y Cover D i s t r i b u t i o n N I LEGEND Major reserves and/or Protection Immature, Second-Growth Mixed Conifer and Deciduous Logging Since Forest Established Main Entrance Map Source: Univ. of B. C. Res. For. Brochure 122 Logging a c t i v i t y was most intense from the mid 1950's through the 1960's. Concern over the rate of harvesting on the Forest increased in the late 1960's, and as a result of a revised y i e l d analysis which showed that ". . .on the basis of the AAC calculations of 1966. . ., by 1981 a l l mature stands (except those excluded from production as reserves, protection. . .) w i l l have been logged. . ." (Walters, 1970), The annual harvest rate was reduced from approximately 11,000 cunits to 6000 cunits. Following consideration of additional reductions to productive areas and expected growth rates on immature stands, the calculated AAC was reduced again in December of 1971 to 4600 cunits. Continued reassessments have led to the current harvest rate of approximatly 4000 cunits (11,300 cu. m.). Over the past two decades management objectives of the Forest have become increasingly non-timber oriented. Based on the concept of "best-use forestry", the U.B.C. Faculty of Forestry proposed a resource management plan in 1971, that designated sections of the Forest to single or combined management for " . . . wood production, recreation, watershed management, game management, education, community development, and forestry . . ." (University of B r i t i s h Columbia Research Forest, 1972. p. 11). Under the proposed plan, wood production w i l l be the primary objective only on the southern one t h i r d of the Forest (excluding education reserves and protection areas), and a minor objective subject to w i l d l i f e management constraints on the northcentral and northwestern 123 areas of the Forest. Throughout the Forest logging has been excluded from a number of areas designated as research, education, ecological or protection reserves. 2 The largest of these reserves are the Loon Lake Camp Education Reserve, and P i t t Lake and Golden Ears (northwestern boundary) protection reserves, of approximately 102, 233 and 169 hectares respectively, almost 10 percent of t o t a l Forest area (251, 576 and 418 acres). In t o t a l , a l l - reserves account for the majority of remaining old-growth timber on the Forest. In retrospect, development and management of the Research Forest has proceeded in a manner t y p i c a l of forest development and management in coastal B r i t i s h Columbia. Logging has been progressing from the low elevation, most accessible s i t e s to high elevation, steep slope, increasingly inaccessible areas. Although some would readily c r i t i c i z e the h i s t o r i c a l l y high harvest rates (Perrin, 1979) i t must be remembered that decisions on the Forest, as elsewhere in the province, were based upon the best estimates of the sustained y i e l d capacity of the Forest, given current understanding of the inventory. Add i t i o n a l l y , increasing awareness of and demand for non-timber forest values by society in general, has resulted in unforeseen withdrawals of forest lands from timber production throughout the province, as well as in the Research Forest. Because of the unique orientation of the Research 2In addition to the major protection reserves, protection areas are also designated by leave s t r i p s around lakes and each side of main creeks (approximately 30.5 m wide; 121.9 m around Loon Lake), (appendix 13(2), p. 14). 124 Forest as an educational f a c i l i t y , the magnitude of area withdrawn and thus the impact on timber harvesting capacity of the Forest has been proportionately greater than for the province as a whole. Because the balance of the Forest inventory, not in reserves, is young second-growth timber, i t has been projected (Sanders, 1980) that harvest le v e l s w i l l begin declining in this decade, given current levels of logging costs, product prices and management intensity. It is expected that harvest lev e l s w i l l begin to rise in the 1990's as immature stands acheive harvestable size and value. This scenario could of course d i f f e r i f substantial real increases in log values, real decreases in harvesting costs, development of new logging technology, increased management intensity and/or an easing of reserve r e s t r i c t i o n s occur. 5.3 PROCEDURES In th i s section, the s p e c i f i c actions are detailed for completing each step of the general procedures (Figure 5) to estimate recoverable timber supplies on the Research Forest. Excluding most of the i n i t i a l data preparation and c o l l a t i n g , a l l c alculations of production, costs, revenues, growth, etc., were c a r r i e d out using a computer program (ETS) written for this study (program l i s t i n g in Appendix 2). 5.31 Data Col l e c t i o n , Preparation And Collating Fortunately, timber type boundaries are overlayed on a 125 topographic map of the Research Forest so that c o l l a t i n g much of the s i t e , stand and tree c h a r a c t e r i s t i c s was f a i r l y straight forward. Individual stands were i d e n t i f i e d f i r s t by timber type and second by location. Thus, where a timber type occurred in more than one d i s t i n c t location on the Forest, a separate stand was i n d e n t i f i e d for each location. If individual stands were less than one hectare in area they were combined with an adjacent stand. Stand and stock tables, and summary s t a t i s t i c s of the 1964-1966 inventory were used to determine and record for each stand: age, s i t e index, t o t a l height, stems per hectare, weighted average diameter at breast height, and stem d i s t r i b u t i o n by species. From the topographic map (scale 1:5000), t o t a l stand area and stand area in protection or reserve forests were measured with a compensating polar planimeter. As areas of exposed bedrock (rock outcrops) were i d e n t i f i e d on the map, these areas were also measured with the planimeter so that percent of area in exposed rock and thus an index could be determined. F i n a l l y , median elevation and average ground slope were determined from the topographic map for each stand. In the way of inventory and s i t e c h a r a c t e r i s t i c s , information was s t i l l needed on t e r r a i n v a r i a b i l i t y , brush density, obstacles, c u l l (decay, waste and breakage), merchantable height, log volume and volume per hectare. For determining the l a t t e r three i t was decided to use a computer program designed by Province of B r i t i s h Columbia (1977), 126 which, given input on tree species, inventory zone, diameter at breast height, maturity c l a s s , t o t a l height, log length, and u t i l z a t i o n standards, w i l l provide values for number of logs per tree, volume per log for each log of the tree and stem volume to u t i l i z a t i o n standards, to name a few. After calculations had been completed for each species in the stand, weighted stand average merchantable height, log volume and volume per hectare were calculated, using stem d i s t r i b u t i o n by species for weighting. Stand average c u l l was also determined as a weighted average of species c u l l estimates. Species estimates were determined as a function of stand age and average diameter using the "Net Volume (loss) Factors" ( B r i t i s h Columbia Forest Service, 1966) for inventory zone 2. Regression equations were estimated for predicting stand t e r r a i n v a r i a b i l i t y (Equation 5.1), brush density (Equation 5.2), and the extent of obstacles (Equation 5.3), using the sample data on coast logging operations given in Chapter Four. This information is necessary for prediction of phase pr o d u c t i v i t i e s in f a l l i n g and yarding, using Equations (4.7) and (4.8) estimated in Chapter Four. (5.1) T = 1.692 + 0.2628 EX + 0.01711 S R2 = 0 . 356 SEE = 0.5485 (5.2) B = 3 . 207 T - 1.393 T 2 + 0 .1865 T 3 - 2.126 EX + 1.423 EX2 - 0.2216 EX 3 R2 = 0.265 SEE = 0.665 (5.3) 0 = 0.3818 T + 0.00352 E - 0.0000034 E 2 - 0.2014 EX 127 - 0.3983 EX2 + 0.1654 EX3 - 0.07865 S + 0.0027 S 2 -• 0.000022 S 3 R2 = 0.583 SEE = 0.5922 A l l c o e f f i c i e n t s (polynomials in orthogonal form) are s i g n i f i c a n t at or greater than the 95 percent confidence l e v e l , with 64 observations on each equation. The f i n a l category of data col l e c t e d .on the Forest, concerning the transportation network, included two separate measurements on each stand for which road access existed as of 1979, and a t h i r d measurement for a l l stands. F i r s t , t o t a l length of existing roads (kilometers) on the stand were measured with a "map measurer", including boundary roads, by road class (main, secondary, spur and "cat" or four-wheel dr i v e ) . Second, actual hauling distance (kilometers) to the main gate (access control point) of the Forest was measured, also with the map measurer. F i n a l l y , for a l l stands on the Forest the s t r a i g h t - l i n e distance (kilometers) between approximate stand center and the main gate was measured. In this way, the actual hauling distance of stands with access could be related to s t r a i g h t - l i n e distance (Equation 5.4) so that actual hauling distances could be predicted for those stands presently without access. The concept i s i l l u s t r a t e d in Figure 7. (5.4) AHDi = ^ QSLDi + £i where: AHDi = actual hauling distance in kilometers from stand i to the main gate. SLDi = s t r a i g h t - l i n e distance in kilometers from stand i to the main gate. - c o e f f i c i e n t to be estimated through regression € i = prediction error of AHD for stand i 7.- I l l u s t r a t i o n Of Hauling Distance Concept i LEGEND Hypothet ica l Stand "Bes t " E x i s t i n g Hauling Route — — - Chord Between Stand and Main Gate V Ac tua l Haul Distance of Stand t SLD-—> St ra ight L ine Distance of Stand t 129 Where more than one route could be chosen the "best" route was determined by the shortest hauling distance, as constrained by road c l a s s . That i s , i f - there was a substantial difference in distance, the shortest route was selected. If hauling distances were similar, the route with most distance traveled on higher quality roads was selected. If distance by road class and t o t a l distance were similar, again the shortest route was selected. Assuming the current road network provides equal access to a l l areas on the Forest, then a single relationship should be s u f f i c i e n t , explaining most of the observed variations in hauling distance. I f , however, the " f i t " of a single equation model i s f a i r l y poor, then i t is l i k e l y that some sections of the Forest are r e l a t i v e l y less developed than others, and separate equations estimated by section would improve overall f i t . An equation was estimated for actual haul distance, using the data c o l l e c t e d on stands with access, and is given below in Equation 5.5. An intercept term was not included in the estimation, since actual haul distance should be zero when s t r a i g h t - l i n e distance is zero. Given the high R2 value and low standard error of the estimate, i t was decided that a single equation for the Forest would be s u f f i c i e n t . (5.5) AHD = 1 . 220 SLD, R2 = 0.940 SEE = 0.837 N = 258 ( 0.0 0 8 9 ) 130 This approach results in actual haul distance estimates not related to road class. Thus, when ca l c u l a t i n g hauling costs a single travel speed for the entire distance w i l l be used, rather than a separate speed for each road c l a s s . A more detailed approach to haul distance estimation was reported by Bradley (1972), which e x p l i c i t l y incorporated road quality in an analysis of transportation distances. Whether the added precision i s j u s t i f i e d , in a planning context, depends on a consideration of the increased cost of estimation, and ultimately, the difference in projected hauling costs estimated by the two approaches. For timber types number 107 and greater, no stand tables were available from which average stand diameter (DBH), stems per hectare (SPH) or species d i s t r i b u t i o n could be cal c u l a t e d . 3 Equations were estimated for predicting DBH (Equation 5.6) and SPH (Equation 5.7), using data co l l e c t e d on stands of timber types less than 107. (5.6) DBH = 12.054 - 0.1189 SI - 0.1557 AGE + 0.0015 AGE2 ( 3.9 4 8 ) ( 0.0 4 2 1 ) ( 0. 0 0 4 1 ) ( 0 .0 0 0 0 t) - 0.000003 AGE3 + 1.295 H - 0.0132 H 2 ( 0 . 0 0 0 0 0 0 6 ) ( 0 . 0 3 4 4 ) ( 0 .0 0 2 1 4 ) R2 = 0.701 SEE = 4.60 N = 340 (5.7) InSPH = 10.119 - 1.1651 InDBH ( 0.0 5 8 6 ) ( 0.2 0 7 2 ) R2 = 0.697 SEE = 0.143 N = 340 Where: DBH = average stand diameter in centimeters SPH = stems per hectare ( a l l species). SI = stand s i t e index; height in meters at 100 years. 'Types number 107 - 120 are a mix of mature old-growth and older second-growth stands. Types number 121+ are young immature second growth covering the area logged in the 1920's - 1930's on the eastern half of the Forest. 131 AGE = stand age in years. H = average stand height (total) in meters, ln = natural logarithm. Co e f f i c i e n t s of the DBH equation are a l l s i g n i f i c a n t at or greater than the 99 percent confidence l e v e l . C o e f f i c i e n t s of the SPH equation are a l l s i g n i f i c a n t at the 99.9 percent confidence l e v e l . Although exact species d i s t r i b u t i o n could not be i d e n t i f i e d , approximate species d i s t r i b u t i o n s were a r b i t r a r i l y assigned according to the number and order of alphabetic species codes associated with each type. If only one species was indicated then 100 percent of stem d i s t r i b u t i o n was assigned to that specie. Given two species, the f i r s t or major species (e.g. f i r given an FC code) was assigned two-thirds, and the second or minor species was assigned one-third of stem d i s t r i b u t i o n . Where three species were indicated, 50, 30 and 20 percent of stem d i s t r i b u t i o n was assigned to the f i r s t , second and t h i r d species respectively. If a deciduous type was indicated, the percent assigned was equally divided between the three species categorized on timber types less than 107: Alder (Alnus rubra Bong.), Maple (Acer macrophyllum Pursh) and Cottonwood (Populus trichocarpa Torr. and Gray). For lack of better information, i t was assumed that species d i s t r i b u t i o n would remain constant over time. In t o t a l , 557 stands were i d e n t i f i e d . Of this t o t a l , 445 stands are of mature old-growth, immature or mature second-growth timber for which a l l data described above was 132 c o l l a t e d . The remaining 112 stands are areas that were logged through 1979. On these stands information was not readily available on current species d i s t r i b u t i o n , s i t e index, height, diameter or stems per hectare. Because even the oldest of these stands w i l l not l i k e l y be recoverable by the end of the supply estimation period in t h i s i l l u s t r a t i o n , and due to time l i m i t a t i o n s , i t was decided to eliminate these stands from further c a l c u l a t i o n s . A stand by stand l i s t i n g of the data assumed-to be constant over time (area, site index, elevation, slope, exposed rock, haul distance, straight l i n e distance, species d i s t r i b u t i o n and percent of area in protection) is given in Appendix 3. 5.32 Logging Production Simulation This section d e t a i l s the methodology in determining length of roads constructed, f a l l i n g and bucking productivity, yarding productivity, loading productivity, ' hauling productivity and actual volume harvested, for each stand on the Forest. The methods involve a combination of stochastic and deterministic processes, and, subjective c r i t e r i a . In Chapter Four an equation (Equation 4.6) was estimated for predicting the required length of roads for logging an area. However, i t was pointed out that this equation would l i k e l y provide inconsistent results on immature stands where growth (vis-a-vis annual change in stems per hectare and log volume) would have a greater ef f e c t on road requirements than s i t e a c c e s s i b i l i t y . Since many of the stands on the Research 1 3 3 Forest are immature, an equation was estimated which related road length to area only. The results of th i s estimation (Equation 5 . 8 ) when compared to the o r i g i n a l road length equation shows that only a s l i g h t l y poorer explanation is obtained. ( 5 . 8 ) RL = 3 7 . 1 2 8 A, R2 = 0 . 7 9 4 SEE = 5 2 7 . 6 1 N = 4 9 ( 2.7 3 3 ) However, the equation u n r e a l i s t i c a l l y implies that variations in site a c c e s s i b i l i t y between stands of equal area has no impact on the required length of roads. The solution to this dilemma, as discussed in Chapter Four, l i e s in the development of new explanatory variables or p r i n c i p a l components. For t h i s i l l u s t r a t i o n i t was decided to use both equations; the o r i g i n a l on stands greater than 8 0 years, and the above equation on stands less than 8 0 years. The calculated road requirements were then compared to the length of roads already existing on the stand. Where no roads previously existed, t o t a l stand roads were set equal to calculated road length, for which road construction costs were calculated. If the exis t i n g roads on a stand were less than the calculated road requirements, road length was increased by the difference. Hence, construction costs were also calculated only for the difference. F i n a l l y , where existing roads exceeded calculated requirements no additional roads were constructed or costs calculated. 134 F a l l i n g and bucking productivity on each stand was calculated using the equation developed in Chapter Four (Equation 4.7), and the recorded or calculated data on t e r r a i n , obstacles, merchantable height, volume per hectare and diameter at breast height. Before yarding productivity could be estimated, the most l i k e l y yarding system had to be chosen. Using the linear p r o b a b i l i t y equations (Equations 4.10 to 4.12), and necessary stand data, p r o b a b i l i t i e s were estimated for each system. That system with the greatest probability of occurring was chosen as the system used. Given the yarding system, productivity of yarding the stand was estimated using the relavent coeffients estimated for each system (Equation 4.8), and necessary stand data. If f a l l i n g or yarding productivity of a stand was estimated to be negative, no further production or cost calculations were completed for the current period. That i s , a negative productivity was taken as an indication that the stand was not economically recoverable, regardless of cost or price assumptions. 4 R e a l i s t i c a l l y , a negative productivity could be indicative of other p e c u l i a r i t i e s . F i r s t , a negative productivity may indicate that a method of f a l l i n g or yarding other than those represented by the equations, would actually be used. Second, i t may also indicate that the equations are being used outside their relevant range, resulting in a negative productivity even though the predicted logging system is the 'true' system. 135 Calculations of loading and hauling productivity are based upon procedures followed by the B r i t i s h Columbia Forest Service, Valuation Division in carrying out stumpage appraisals (Province of B r i t i s h Columbia, 1979b and 1980e). In loading, a base productivity is f i r s t calculated as 120 percent of projected yarding productivity. Second, base productivity is increased by one percent for each one percent that stand slope is less than 40 percent (e.g. given a stand slope of 26%, base loader productivity is increased by 40 - 26 = 14%) . Hauling productivity is calculated in three steps. F i r s t , t o t a l or return t r i p time per load was calculated as the sum of loading time per load, driving time per load (trip) and unloading time. Using an approximate average load size of 40 cubic meters determined from the coast logging data, loading time per load was calculated as load size (m 3/load) divided by loader productivity (m 3/hour). 5 To calculate driving time i t is necessary to know t o t a l hauling distance, loaded and unloaded driving speeds (or average return speed). The method of estimating hauling distance on the Forest has already been discussed. Since the bulk of a l l timber (logs) harvested from the Forest i s sold to Whonnock Lumber Company, the m i l l in Whonnock was assumed to be the delivery point for a l l loads, and a one-way haul 5Since the greatest haul distance from the Forest to delivery point w i l l involve highway hauling, load average was extrapolated from those sampled operations with primarily highway hauling and no intermediate dump and rehaul. 136 distance of 16.25 kilometers, from the Research Forest main gate to Whonnock, was estimated from area maps. Based upon the design speed of main and secondary roads on the Research Forest, unloaded travel speed was assumed to average 40 kilometers per hour (25mph). Unloaded travel speed on the highways between the Forest and Whonnock was assumed to average 72 kilometers per hour (45mph). From the data on coastal logging operations i t was determined that loaded travel speed would be approximately two-thirds of unloaded travel speed; thus, values of 27 and 48 kilometers per hour (approximately 17 and 30 mph) were used for Forest and highway loaded travel speeds respectively. Driving time.is then equal to the sum of Forest and highway haul distances divided by the respective loaded and unloaded travel speeds. Unloading time was assumed to be 10 minutes (0.17 hours) as indicated by coastal logging operations and the allowance given in stumpage appraisals (Province of B r i t i s h Columbia, 1979b). Equation (5.9) below summarizes the calculations for return time per load. (5.9) RPL = Loading Time + Driving Time + Unloading Time = ALS + HDF + HDH + HDH + HDF + UT LP LTSF LTSH UTSH UTSF = 40m 3/load + HDF +16.25+ HDF +16.. 25 + 0.17hrs. LP 27kph 48kph 40kph 72kph = 40mVload + HDF ( 0 . 062037 ) + 0.73hrs. LP where: RPL = return time per load (hours) ALS = average load size (cubic meters) LP = loader productivity (cubic meters/hour) HDF = haul distance on the forest, one way (km) HDH = haul distance on the highway, one way (km) 137 LTSF = loaded t r a v e l speed on the f o r e s t (km/hour) LTSH = loaded t r a v e l speed on the highway (km/hour) UTSF = unloaded t r a v e l speed on the f o r e s t (km/hour) UTSH = unloaded t r a v e l speed on the highway (km/hour) UT = unloading time (hours) Because l o a d s i z e , highway haul d i s t a n c e , t r a v e l speeds and unloading times are c o n s t a n t i n t h i s i l l u s t r a t i o n , i t can be seen (Equation 5.9) t h a t v a r i a t i o n s i n r e t u r n time per l o a d are u l t i m a t e l y dependent on loader p r o d u c t i v i t y and h a u l i n g d i s t a n c e ( i . e . stand l o c a t i o n ) on the F o r e s t . The second step i n c a l c u l a t i n g h a u l i n g p r o d u c t i v i t y r e q u i r e s d i v i d i n g h a u l i n g s h i f t l e n g t h by the r e t u r n time per l o a d , as e s timated above, to determine the number of loads per s h i f t (Equation 5.10). F i n a l l y , h a u l i n g p r o d u c t i v i t y i s c a l c u l a t e d as volume hauled per s h i f t ( l o a d s per s h i f t m u l t i p l i e d by average l o a d s i z e ) d i v i d e d by s h i f t l e n g t h (Equation 5.11). For t h i s i l l u s t r a t i o n , a 9 hour s h i f t l e n g t h was assumed f o r h a u l i n g . (5.10) LPS = _SL = 9 h r s . / s h i f t RPL RPL (5.11) HP = LPS*ALS = LPS*40m 3/load SL 9 h r s . / s h i f t where: LPS = loads per s h i f t SL = s h i f t l e n g t h ( h o u r s / s h i f t ) RPL = r e t u r n time per l o a d (hours/load) HP = h a u l i n g p r o d u c t i v i t y (cubic meters/hour) ALS = average.load s i z e (cubic meters/load) 138 Two problems a r i s e i n a t t e m p t i n g t o p r e d i c t a c t u a l volume h a r v e s t e d (Q) u s i n g t h e e q u a t i o n e s t i m a t e d i n C h a p t e r Four ( E q u a t i o n 4.9). R e c a l l i n g t h e s t r u c t u r e of t h e e q u a t i o n a s ; (5.12) Q = ^ Y T + faVnet where: YT = y a r d i n g t i m e (machine h o u r s ) Vnet = s t a n d i n g t i m b e r volume (net of c u l l ) / 3 1 , / 3 2 = e s t i m a t e d c o e f f i c i e n t s i t i s c l e a r t h a t f i r s t , p r e d i c t e d h a r v e s t can exceed the s t a n d i n g t i m b e r volume due t o t h e u n c o n s t r a i n e d l i n e a r s p e c i f i c a t i o n ; and s e c o n d , y a r d i n g i n p u t demands were e s t i m a t e d as a p r o d u c t i v i t y (YP i n m 3/hour) not t o t a l time ( Y T ) , t h u s no v a l u e s a r e a v a i l a b l e t o complete the c a l c u l a t i o n of h a r v e s t volume. The l a t t e r problem can be d e a l t w i t h by r e a l i z i n g t h a t (5.13) YP = Q/YT, o r , (5.14) YT = Q/YP Hence, s u b s t i t u t i n g (5.14) i n t o the h a r v e s t e q u a t i o n (5.12) and r e a r r a n g i n g , an e q u a t i o n i s o b t a i n e d ; (5.15) Q = (/3 z*Vnet*YP)/(YP - fa) w h i c h uses the e s t i m a t e of y a r d i n g p r o d u c t i v i t y c a l c u l a t e d e a r l i e r . The f i r s t p roblem s t i l l r e m a i n s , a l t h o u g h i n r e v e r s e o r d e r . That i s , i n e q u a t i o n (5.12) i n c r e a s e s i n YT . beyond a c e r t a i n l i m i t , f o r a g i v e n V n e t , would r e s u l t i n p r e d i c t e d h a r v e s t volumes g r e a t e r than s t a n d i n g t i m b e r volume; whereas, i n e q u a t i o n (5.15) decrea.ses i n YP, below the i n v e r s e of the YT l i m i t , w i l l y i e l d the same r e s u l t s . S i n c e Vnet i s 139 c a l c u l a t e d .on a c l o s e - u t i l i z a t i o n b a s i s , i t i s u n l i k e l y that p r e d i c t e d harvest w i l l exceed estimated timber volume. T h e r e f o r e , . to use e q u a t i o n (5.15) a c o n s t r a i n t was i n c o r p o r a t e d to set h a r v e s t volume (Q) equal to net s t a n d i n g timber volume (Vnet) whenever p r e d i c t e d Q exceeded Vnet. 5.33 Costs In a d d i t i o n to ' c o s t i n g out' the e s t i m a t e s of phase p r o d u c t i v i t i e s c a l c u l a t e d i n the p r o d u c t i o n s i m u l a t i o n , c o s t e s t i m a t e s a l s o had to be d e r i v e d f o r timber c r u i s i n g , l o g g i n g e n g i n e e r i n g , road maintenance, crew t r a n s p o r t a t i o n , stand treatment f o l l o w i n g l o g g i n g , s c a l i n g , and a d m i n s t r a t i o n and overhead. Road c o n s t r u c t i o n and maintenance c o s t s were developed from h i s t o r i c c o s t s on the Research F o r e s t . No attempt was made to a s s e s s c o s t s by road c l a s s , s i n c e the estimated l e n g t h of roads b u i l t i s c l a s s independent. For the p e r i o d 1962-1976, r e a l c o s t s (1976=100) per k i l o m e t e r of roads c o n s t r u c t e d i n each year were determined and an average c o s t per k i l o m e t e r , over the e n t i r e p e r i o d , was c a l c u l a t e d . T h i s c o s t of $28173.62/km was a p p l i e d a g a i n s t the estimated l e n g t h of roads b u i l t to l o g each stand on the F o r e s t . Annual road maintenance c o s t s w i l l vary g r e a t l y , depending on the occurrance of s p e c i a l p r o j e c t s (e.g. major r e s u r f a c i n g and/or r e d i t c h i n g , e t c . ) i n a d d i t i o n to r e g u l a r g r a d i n g and snow removal. 'Rather than attempt to p r o j e c t the years i n which major maintenance p r o j e c t s w i l l occur, a r e a l 140 a v e r a g e maintenance c o s t per k i l o m e t e r was d e v e l o p e d u s i n g t o t a l maintenance c o s t s and t o t a l l e n g t h of roads on the F o r e s t , over the p e r i o d 1S62-1976. U s i n g the e s t i m a t e d v a l u e of $257.62/km, maintenance c o s t s were c h a r g e d a g a i n s t the t o t a l s t a n d i n g t i m b e r volume ( n e t ) of a r e a s on w h i c h h a r v e s t i n g i s a l l o w e d . T h e r e f o r e , maintenance c o s t s per c u b i c meter were d e v e l o p e d a n n u a l l y as shown i n E q u a t i o n ( 5 . 1 6 ) . The u n i t maintenance c o s t i s then c h a r g e d a g a i n s t the t i m b e r volume on each s t a n d i n the F o r e s t i n the c u r r e n t p e r i o d f o r an e s t i m a t e of the r o a d maintenance c o s t component of t o t a l l o g g i n g c o s t . (5.16) UMC = RMC*TARDS i TVi where: UMC =' u n i t maintenance c o s t ($/m 3) RMC = road maintenance c o s t (s/km) TARDSi = t o t a l a r e a roads i n p e r i o d i (km) T V i = t i m b e r volume on the F o r e s t i n p e r i o d i (m 3) A l l r e m a i n i n g c o s t s , e x c l u d i n g y a r d i n g , were d e v e l o p e d d i r e c t l y from p r o c e d u r e s and/or c o s t s used i n stumpage a p p r a i s a l s f o r c o a s t a l B r i t i s h C o l u m b i a ( P r o v i n c e of B r i t i s h C o l u m b i a , 1979b and 1980e). P r o c e d u r e s f o r c a l c u l a t i n g y a r d i n g c o s t s a r e a c o m b i n a t i o n of t h o s e used by Sauder and Nagy (1977), Warren (1977) and P r o v i n c e of B r i t i s h C olumbia (1979b and 1980e). Most c o s t s c o u l d be e x p r e s s e d as a s i n g l e h o u r l y r a t e or d i r e c t l y i n terms of c o s t per c u b i c meter h a r v e s t e d ( T a b l e 7 ) . H o u r l y phase c o s t s were c o n v e r t e d t o u n i t c o s t s by d i v i d i n g i n t o phase p r o d u c t i v i t y . L o a d i n g , crew t r a n s p o r t a t i o n , t i m b e r c r u i s i n g , e n g i n e e r i n g and s t a n d t r e a t m e n t c o s t s a r e not. e x p r e s s a b l e as a unique v a l u e s i n c e .141 .-they depend on c h a r a c t e r i s t i c s t h a t v a r y by s t a n d . T a b l e 7. L o g g i n g C o s t s By Component Component Co s t T a i l i n g & B u c k i n g 1 - Y a r d i n g 2 33.75/hr H i g h l e a d 168.91/hr ,160.73/hr 241.49/hr G r a p p l e L o n g - r e a c h : H a u l i n g 3 U n l o a d i n g , S o r t i n g & Bo o m i n g 4 S c a l i n g 5 l A d m i n i s t r a t i o n & O v e r h e a d 6 44.59/hr 3.08/m3 0.17/m3 5.64/m3 1 .180 s h i f t s / y e a r , 6.5 h o u r s / s h i f t * .200 s h i f t s / y e a r , 8.0 h o u r s / s h i f t 3 9 h o u r s / s h i f t * :dr y l a n d s o r t , no r e h a u l s ..stick s c a l e * " a l l o t h e r s " t e n u r e c a t e g o r y ( P r o v i n c e of B r i t i s h Columbia,1980e) L o a d i n g c o s t per c u b i c meter ( E q u a t i o n 5.19) i s e q u a l t o the sum of a base c o s t ($/m 3) and d e p r e c i a t i o n a l l o w a n c e ( $ / m 3). U s i n g an e q u a t i o n t h a t the B r i t i s h Columbia F o r e s t . S e r v i c e has d e v e l o p e d f o r stumpage a p p r a i s a l s ( P r o v i n c e of B r i t i s h C o l u m b i a , 1980e), base c o s t i s c a l c u l a t e d ( E q u a t i o n 5.17) as a t h i r d degree p o l y n o m i a l of l o a d e r p r o d u c t i v i t y . Assuming 200 8-hour s h i f t s per y e a r , a d e p r e c i a t i o n a l l o w a n c e of $10.42 per hour was c a l c u l a t e d u s i n g the a n n u a l d e p r e c i a t i o n a l l o w a n c e g i v e n f o r a p p r a i s a l s . T h i s i s the n c o n v e r t e d t o a c o s t p e r c u b i c meter when d i v i d e d by l o a d e r p r o d u c t i v i t y ( E q u a t i o n 5.18). (5.17) BLC = 6.5045-0.026828LP+0.00004882LP 2-0.00000003LP 3 (5.18) LDA = HDA = $10.42 LP LP 142 (5.19) LC = BLC + LDA •where: BLC = base loader c o s t allowance ($/m 3) LP = loader p r o d u c t i v i t y per s h i f t ( m 3 / s h i f t ) LDA = loader d e p r e c i a t i o n allowance ($/m 3) •-HDA = h o u r l y d e p r e c i a t i o n allowance f o r l o a d i n g LC = u n i t l o a d i n g c o s t ($/m 3) ^Round-trip t r a n s p o r t a t i o n c o s t s were c a l c u l a t e d f o r crew t r a v e l between the Research F o r e s t ' s main gate ( m a r s h a l l i n g p o i n t ) and stand being logged, u s i n g procedures d e t a i l e d f o r co a s t stumpage a p p r a i s a l s . B a s i c a l l y , t r a n s p o r t a t i o n c o s t per .cubic meter was c a l c u l a t e d as the sum of v e h i c l e , d r i v e r and crew c o s t s per c u b i c meter. The d e t a i l s of each component are .given i n E q u a t i o n s (5.20) to (5.23) below. No allowance was •given f o r a "town run" s i n c e the area i s l o c a t e d near main ...population c e n t e r s . (5.20) VC = VFC+[2*TD*FC] = $31. 64 +[TP*0 .19/km] VF 32m3 (5.21) TT = TD*120 = TD*120 TS 40kph -C5.22) DC = DCPM*TT = $0 .87/min. *TT LPS LP*8 h r s . (5.23) CC = (FBC + OCC)*TT = ($0.72/min.+$3.30/min.)*TT, i f TT<90min. = ($0.72/min.+$4.95/min.)*TT, i f 90<TT<250min. = ($1.08/min.+$4.95/min.)*TT, i f TT>250min. (5.24) TC = VC + DC + CC where: VC = v e h i c l e c o s t ($/m 3) VFC = v e h i c l e f i x e d c o s t ($) TD = t r a v e l d i s t a n c e (km) FC = f u e l c o s t ($/km) VF = v e h i c l e f a c t o r ; volume of d a i l y p r o d u c t i o n s e r v i c e d by one v e h i c l e ( P r o v i n c e of B r i t i s h Columbia', 1980e) TT = t r a v e l time (minutes) TS = t r a v e l speed (kph) DC = d r i v e r ' s c o s t ($/m 3) DCPM = d r i v e r ' s c o s t per minute ($/min.) loader p r o d u c t i v i t y per s h i f t , 8 nr. s h i f t LPS 143 ( - • / s h i f t ) CC =' crew c o s t ($/m 3) FBC = f a l l i n g and b u c k i n g crew c o s t ($/min.) OCC = o t h e r crew c o s t ($/min.) TC = t o t a l crew t r a n s p o r t a t i o n c o s t Timber c r u i s i n g c o s t s were d e t e r m i n e d u s i n g t h e c o s t s per c u b i c meter a l l o w e d i n stumpage a p p r a i s a l s , which a r e dependent on volume per h e c t a r e and a r e a of each s t a n d , and range from 3 t o 52 c e n t s per c u b i c meter ( h i g h e r c o s t s on s m a l l s t a n d s of low v o l u m e ) . E n g i n e e r i n g c o s t s a r e e s t i m a t e d as 5 p e r c e n t of the sum of r o a d c o n s t r u c t i o n , f a l l i n g , y a r d i n g and l o a d i n g c o s t s per c u b i c meter . ( P r o v i n c e of B r i t i s h C o l u m b i a , 1980e). F i n a l l y , s t a n d t r e a t m e n t c o s t s per c u b i c meter, a g a i n d e v e l o p e d from c o a s t stumpage a p p r a i s a l c o s t s , were c a l c u l a t e d as the sum of spot s l a s h b u r n i n g c o s t s ($0.02/m 3), r e s i d u e s u r v e y s ($0.01/m 3) and r e s i d u a l f a l l i n g a l l o w a n c e ($15.20/ha). The l a s t component was c o n v e r t e d t o a volume b a s i s by m u l t i p l y i n g by s t a n d a r e a and d i v i d i n g by t i m b e r volume ( n e t ) . A f t e r c a l c u l a t i n g the c o s t f o r each phase or component of t h e l o g g i n g p r o c e s s , t o t a l l o g g i n g c o s t ($/m 3) was d e t e r m i n e d as the sum of a l l phase c o s t s . 5.34 Revenues D e t e r m i n i n g the v a l u e of h a r v e s t e d t i m b e r r e q u i r e s knowledge of the t y p e and q u a l i t y of p r o d u c t s r e c o v e r e d , and t h e i r c u r r e n t market p r i c e s . U n f o r t u n a t e l y , p r o d u c t r e c o v e r y i n f o r m a t i o n i s not commonly a v a i l a b l e from i n v e n t o r y d a t a . T h i s has o f t e n l e d t o h a r v e s t revenues b e i n g c a l c u l a t e d on the b a s i s of s p e c i e s d i s t r i b u t i o n and average market p r i c e of l o g s 144 by species, which requires the assumption that product . d i s t r i b u t i o n of future harvests w i l l be s i m i l a r to product d i s t r i b u t i o n currently on the market. In t o t a l , for a l l producers supplying a given market, product d i s t r i b u t i o n of .harvests may be si m i l a r to product d i s t r i b u t i o n on the market in the previous year, with temporal changes in d i s t r i b u t i o n .being f a i r l y gradual and predictable. However, th i s assumption i s highly untenable in an analysis of the l i m i t s to economic timber r e c o v e r a b i l i t y , since, the d i s t r i b u t i o n of products recoverable w i l l vary from stand to stand depending on timber type and q u a l i t y . It i s t h i s v a r i a t i o n that must be .considered in determining harvest revenues, to e x p l i c i t l y .recognize that the value (or q u a l i t y ) of the timber on a given stand i s of equal (or possibly greater) importance to logging costs in l i m i t i n g r e c o v e r a b i l i t y . As elsewhere, inventory -data on the Research Forest lack the product information •-necessary to analyse the true v a r i a t i o n in timber values as -suggested above. Rather than automatically assume that d i s t r i b u t i o n of the harvest by product type on the Forest would p a r a l l e l that of the market in general, a simple an a l y s i s of h i s t o r i c product recovery from the Forest was undertaken. Products recovered from past timber sales have generally included; sawlogs and pulpwood, poles, p i l i n g s , cedar shakes and blanks. Production of shakes and blanks, by salvaging cedar snags from the area k i l l e d by f i r e in 1 S 6 8 , was an important source of revenues on the Forest during the f i r s t 10 145 to 15 years .of operations. As noted in the 1968-1969 Annual Report, the l a s t usable material had been salvaged by 1967 and,. . • . " . . . a 20-year period of manufacture of shakes and blanks from cedar. . , was brought to a close. Although suitable material w i l l be salvaged occasionally in the future the volume w i l l be minimal." (University of B r i t i s h Columbia Research Forest, 1970. p. 1 ) . An analysis of recoverable timber supplies i s concerned with the recovery of primary forest products, that i s , products for which i n i t i a l logging operations were undertaken. Since current and future shake and blank production (barring major f i r e s in old-growth cedar) w i l l occur as salvage following regular logging operations, t h e i r recovered values w i l l be excluded from the analysis (as w i l l t h e i r a d d i t i o n a l costs of recovery). Sawlogs have, h i s t o r i c a l l y , comprised the bulk of product volumes recovered from the Research Forest. Pulpwood, poles and p i l i n g s have formed a r e l a t i v e l y small, though increasing, portion of the t o t a l harvest. Pulpwood has generally been recovered through relogging operations, while, pole and p i l i n g recovery have been integrated with sawlog operations or occasionally been the primary product in second-growth logging. The proportion of annual harvests in "small-timber" products can be expected to increase as future logging moves into predominantly second-growth stands. The i n e v i t a b i l i t y of the forthcoming change in product recovery from the Research Forest, and need for new information, was recognized in the 146 1 9 6 7 - 1 9 6 8 Annual Report "With the growing dependence. . . on second-growth stands and the p o s s i b i l i t y of high value products i t i s e v i d e n t that new i n v e n t o r i e s of these stands w i l l be r e q u i r e d based upon product c r u i s i n g to supplement c u r r e n t volume c r u i s i n g . " ( U n i v e r s i t y of B r i t i s h Columbia Research F o r e s t , 1969. p. 1 ) . -However, no a d d i t i o n a l product i n f o r m a t i o n has yet been c o l l e c t e d or compiled w i t h i n v e n t o r y data, so t h a t product r e c o v e r y from f u t u r e h a r v e s t s can be r e a d i l y p r o j e c t e d . For t h i s reason, harvest revenues f o r each stand were determined s o l e l y from the value of timber i n sawlogs. Over the p e r i o d 1968 to 1979, d i s t r i b u t i o n of annual l o g h a r v e s t s by s p e c i e s and grade were r e p o r t e d i n Annual Reports of the Research F o r e s t . Mean v a l u e s f o r the percent of •species volume in each grade over t h i s p e r i o d were c a l c u l a t e d f o r d o u g l a s - f i r , western hemlock, western red cedar and c y p r e s s (Chamaecyparis nootkatensis(D.Don)Spach), and are g r a p h i c a l l y shown i n F i g u r e 8 . When compared with s p e c i e s and grade d i s t r i b u t i o n of l o g volumes on the Vancouver Log Market i n a recent p e r i o d , the Research F o r e s t d i s t r i b u t i o n was found to be skewed more to lower grades f o r d o u g l a s - f i r and western red cedar, and, had a s i m i l a r ( s l i g h t l y more skewed) d i s t r i b u t i o n f o r western hemlock and c y p r e s s * Thus, u s i n g average market p r i c e by s p e c i e s would have o v e r s t a t e d timber v a l u e s f o r stands of predominantly D o u g l a s - f i r and western red cedar. 147 Figure 8. A v e r a g e - G r a d e ' D i s t r i b u t i o n of Annual H a r v e s t s on the R e s e a r c h Forest: 1968-1979 Specie And Grade (F • D» F i r , H » W. Hcmlcck, C « W. R. Cedar. «nd' Cy « Y. Cedar) 148 I n s u f f i c i e n t grade information on the other three conifer species considered in t h i s analysis (balsam f i r (Abies  balsamea(L.)Mill.), sitka spruce (Picea sitchensis (Bong.)Carr), and white pine (Pinus monticola Dougl.)) required that grade d i s t r i b u t i o n on the Forest be assumed to follow that on the market. Although the annual variations in grade d i s t r i b u t i o n by species on the Forest did not indicate any discernable trends, because of increasing second-growth harvests i t i s l i k e l y that even greater proportions of future harvests w i l l be of lower log quality than that in h i s t o r i c grade recovery. Also, since the grade d i s t r i b u t i o n i s based on stands selected for their merchantability, i t is unlikely that the d i s t r i b u t i o n w i l l be representative of timber value on stands at the margin of economic rec o v e r a b i l i t y . To enhance the s e n s i t i v i t y of harvest revenues to timber size, minimum diameter l i m i t s (based upon information presented by Smith (1977)) were used to define the average timber size a stand must reach before assuming h i s t o r i c grade d i s t r i b u t i o n . Below this l i m i t i t was assumed a l l timber would f a l l into grades three and four --with the proportions of timber in each grade again depending on assigned diameter l i m i t s . Using market prices on the Vancouver Log Market (three month period ending September, 1980), the species-grade d i s t r i b u t i o n s discussed above and the assumed diameter r e s t r i c t i o n s , a schedule of log prices by species was developed for the Research Forest (Table 8). 149 Table 8. Log Prices Used in Revenue Calculations -- By Species, Diameter Limits And Grade Categories 1 Diameter L i m i t s 2 Specie <20 20-25 25+ 20-36 36+ <41 41-48 48+ Grade Categories 3 4 3 A l l 4 3- A l l T $ / m ^ T Douglas-Fir (F) 26. ,47 39. . 56 54. ,91 W.Red Cedar (C) 13, .19 29. .90 39. .30 W. Hemlock (H) 30. .19 37, , 44 42, ,00 Balsam (B) 27 , .60 31. .98 43, ,66 S.Spruce (Ss) 31. .17 50, .40 95, , 53 W.Pine (Pw) 13. .08 19. .65 21, .96 Cypress (Cy) Dec iduous (D) 7, .00 17.00 20.00 20.85 54.84 105.11 1Log prices, net of royalty charges, based upon Vancouver Log Market prices (three month period ending Sept. 1980) for a l l coniferous species; personal survey for deciduous prices. 2Limits for coniferous species based upon work by Smith (1977). 3Grade categories applicable to coniferous species only. Category 4 prices are 75 and 25 percent of market prices for grades 4 (rejects) and 3 respectively; percentages are reversed for category 3 prices. The " a l l " category assumes harvest w i l l follow h i s t o r i c grade d i s t r i b u t i o n s , by specie, on the Research Forest (F, C, H and Cy), or, current market specie-grade d i s t r i b u t i o n (B, Ss and Pw). 150 The price of deciduous logs was determined from a telephone survey of several companies and log brokers in the Vancouver region, that were or had recently purchased or sold hardwood logs. A l l prices are net of royalty charges per cubic meter. 5.35 P r o f i t And Risk In the section on costs, procedures were discussed for c a l c u l a t i n g payments to a l l factors of production, excluding the entrepreneur. In this section the c a l c u l a t i o n of returns, or p r o f i t , to the entrepreneur for investment in logging is presented. The procedures followed in this analysis are b a s i c a l l y the same as those developed for stumpage appraisals (Province of B r i t i s h Columbia, 1980e). One major difference, however, is that the base investment against which the p r o f i t r a tio is applied, is operating costs only, not operating costs and stumpage. Stumpages could be ignored since the allowance for p r o f i t and risk is being calculated for a contracted logging operator. The Research Forest as tenure holder, recovers the timber values through log sales, from which payments must be made to the contractor for services rendered (price includes the p r o f i t allowance calculated here), and to the crown for the incremental or unearned value solely attributable to the timber. In this case, with the payment of r o y a l t i e s , the incremental value is implied to be constant over a l l levels of logging intensity (or cost). 151 An additional p r o f i t allowance could have been calculated for the Research Forest, with t o t a l logging costs (operating and contractor's p r o f i t ) and royalty payments comprising the base investment against which the p r o f i t r a t i o i s applied. However, thi s was not undertaken, as e x p l i c i t p r o f i t objectives have not been i d e n t i f i e d for logging on' the Forest. It appears the primary concern is that logging generate net revenues of any dimension, within y i e l d constraints, to offset other costs of Forest operation. 6 A p r o f i t and risk r a t i o was calculated for each species in the stand, since a component of the r a t i o is determined by species value (market r i s k ) . Other components of the ratio include: decay, waste and breakage risk ( c u l l ) ; c a p i t a l investment r i s k ; risk of chance (logging d i f f i c u l t y ) , and; a basic allowance (10% - coast). As a surrogate measure of c a p i t a l investment, the type of yarding system used on the stand defined the c a p i t a l risk allowance -- lowest r a t i o for grapple and highest for long-reach yarding. The risk of chance i s a f a i r l y subjective measure that depends on the appraisers' conception of r e l a t i v e interactions between timber maturity, slope, t e r r a i n , location, and other c h a r a c t e r i s t i c s of the stand. In this analysis the d e f i n i t i o n was si m p l i f i e d 6 I t should not be misconstrued that I am suggesting the Forest generate a p r o f i t , comparable to other market returns, on i t s general operations. Many components of the Forest's operation return values that are non-pecuniary and accrue to society in general. However, as one component, timber harvesting should be p r o f i t a b l e , or, the investment should be placed elsewhere to generate operating revenues. 152 by using only stand age and slope as variables determining the risk of chance? with the lowest allowance for mature stands on level to gently sloping ground, and highest allowances for immature stands on steep slopes. The t o t a l p r o f i t r a t i o for the stand was determined by weighting species ra t i o s according to their occurrance in the stand. This completes the description of s p e c i f i c procedures used to determine economic stock timber supply for any given year. At this point, for each stand on the Research Forest, the sum of operating costs (Section 5.33) and p r o f i t allowance (Section 5.35), is subtracted from t o t a l revenues (Section 5.34) to obtain an estimate of net stand value. Timber volumes on a l l stands with a non-negative net value are then summed to provide an estimate of stock timber supply in the current year. The following three sections d e t a i l the procedures followed for e x p l i c i t l y incorporating the periodic changes in timber inventories, logging costs and product prices — to determine the flow of recoverable timber supplies over time. 5.36 Harvesting P r i o r i t i e s The f i r s t adjustment to timber inventories in each year, prior to stand growth analysis and net value ca l c u l a t i o n s , i s to reduce inventories by the volume logged in the previous year. B a s i c a l l y two approaches can be taken. In the f i r s t appproach the highest net value stands are 'logged' in the previous year, up to a predetermined t o t a l allowable or expected harvest. This assumes that either no e x t e r n a l i t i e s 153 exist, or, that the highest value of the forest i s in timber products, and opportunity costs of other uses have been e x p l i c i t l y included in the costs of harvesting. The second approach, constrained economic harvest, should be taken i f there are e x t e r n a l i t i e s which can not, r e l i a b l y , be assigned pecuniary values. Constraints can include location, maximum allowable cutting age, timber types, s i t e index and location, to name a few. In th i s analysis a combination of the two approaches was used to determine stands harvested in each year. F i r s t , a l l stands in reserve and protection areas were excluded from the recoverable inventory; based on the assumption they had been determined through previous analyses to have higher values in uses other than timber production. Second, harvesting p r i o r i t y for the area remaining in timber production was then determined by ranking stand net values in descending order. The maximum annual harvest was set at 11,326.8 cubic meters (4000 CCF). Stands were 'logged' u n t i l their cumulative timber volumes were ± 10% of the harvest l i m i t , thus the actual log (scaled) volume w i l l not equal t h i s harvest rate. 5.37 Stand Growth To enable flow adjustment of the physical timber inventory over time, a simple growth modeling process was developed. Since i t would be necessary to estimate changes in diameter, height, log volumes, c u l l , stems per hectare and volume per hectare, and that the changes in each should be 154 r e a l i s t i c with r e s p e c t to changes i n a l l o t h e r s , i t was dec i d e d not to use B.C.F.S. volume-age e q u a t i o n s . Had they been used, changes p r o j e c t e d in other timber c h a r a c t e r i s t i c s , using separate r e l a t i o n s h i p s , may not have been c o n s i s t e n t with the volume changes. Instead, decadal change eq u a t i o n s were developed (as suggested by D. D. Munro (1980)) f o r diameter (Equation 5.25), t o t a l h e i g h t (Equation 5.26) and stems per he c t a r e (Equation 5.27), using y i e l d t a b l e s f o r hemlock (Barnes, 1962) and d o u g l a s - f i r (McArdle and Meyer, 1949). C o e f f i c i e n t s f o r each e q u a t i o n , by s p e c i e ( y i e l d t a b l e ) type and s i t e index are giv e n i n Appendix 4. A l l c o e f f i c i e n t s g i v e n are s i g n i f i c a n t at the 95 percent c o n f i d e n c e l e v e l . The f i r s t s t e p of the a n a l y s i s i n each s u c c e s s i v e year i s to c a l c u l a t e annual change i n diameter, h e i g h t and stems per h e c t a r e , f o r a d j u s t i n g t h e i r p r e v i o u s year i n v e n t o r y v a l u e . Annual change was taken simply as one-tenth of dec a d a l change. A f t e r these adjustments had been made, new l o g volumes and merchantable h e i g h t s c o u l d be c a l c u l a t e d u sing the program by Province of B r i t i s h Columbia (1977), and new e s t i m a t e s of c u l l c o u l d be c a l c u l a t e d u s i n g the s u b r o u t i n e developed f o r t h i s study, both d i s c u s s e d e a r l i e r . F i n a l l y , gross and net volumes per hectare c o u l d be c a l c u l a t e d from the above. (5.25 )A l 0DBH = ^ k + / 3 , i K D B H t + ^ j k D 3 H t ^ / s j l / J B H t a + ^ J k D B H t 4 (5.26.)AleHGT = $ik H G ™ t + /^jl< HGT^ 2 + f^iv, H G T t 3 +/3«jk H G T i * (5.27)A ( oSPH = 0<ik + / 9|Jk S P Ht + / 9 i j k S P H t l + / 5 3 i K S P H t ' + / ^ 4 i K S P H t « where :A ) 0DBH = ten-year change i n stand diameter (cm) at br e a s t height 155 = DBH t M O - DBH t DBH^ = stand diamete'r at breast height in period t at beginning of decade ^JioAnU^ respectively, intercept and slope c o e f f i c i e n t s for diameter change equations, estimated through regression analysis for s i t e index j , species k and for a polynomial of degree m A,-0HGT = ten-year change in stand t o t a l height (meters) = H G T t M e - HGTt KGT^ = stand t o t a l height in period t at beginning of decade °^ ik ' A* 1 ' k = respectively, intercept and slope c o e f f i c i e n t s for height change equations, estimated through regression analysis for s i t e index j , species k and for a polynomial of degree m Zkj0SPH = ten-year change in stems per hectare = SPH-t.,,0 - SPH t SPHj. = stems per hectare in period t at beginning of ^ ^ decade • °* Jk \fi •njk= respectively, intercept and slope c o e f f i c i e n t s for stems per hectare change equations, estimated through regression analysis for s i t e index j , species k and for a polynomial of degree m j = 80, 90, 100...190 for F i r types; 80, 90, 100..,160 for Hemlock types k = 1, F i r types; 2, Hemlock types m = 3, F i r DBH change; 4, Hemlock DBH change; 4, HGT change for both types; 3, SPH changes for both types No attempt was made to develop or incorporate a growth model for cutover lands. Thus, i f the analysis were continued beyond the 20-year period i l l u s t r a t e d here, eventually, physical inventory would decline to zero. Since the areas logged w i l l a l l be less than 20 years old by the end of the analysis period, i t is unlikely any w i l l have reached the size of economic r e c o v e r a b i l i t y . Hence, omission of these stands from t h i s analysis w i l l not af f e c t the projections of economic stock timber supplies.' 156 5.38 Cost And Price Trends To test the f u l l s e n s i t i v i t y of the model in simulating the impact of temporal changes in cost, price and p r o d u c t i v i t i e s , a detailed time series analysis by type of factor input, phase of the logging process and type of product, would be necessary. Such a detailed analysis was beyond the scope of this t h e s i s . However, to incorporate some measure • of temporal changes in market forces a f f e c t i n g recoverable timber supplies, a general analysis of cost and price trends in logging was undertaken. No attempt was made td conduct a similar analysis of general logging productivity, since trends.in p r o d u c t i v i t i e s by phase (as disaggregated here) would be d i s t i n c t l y d i f f e r e n t than an overa l l productivity measure. Cost and Price trends were analysed for logging in B r i t i s h Columbia so that r e l a t i v e adjustments could be made in logging costs and revenues calculated in the supply analysis. For the period 1926 to 1977, logging industry data (Coast and Interior combined) was c o l l e c t e d from S t a t i s t i c s Canada records, on t o t a l annual: volume production (converted to cubic meters), value of shipments; and beginning in 1940, employment (manhours, a l l personnel); wages and s a l a r i e s ; supply costs (materials, fuel and e l e c t r i c i t y , repairs and maintenance, stumpage costs); and net c a p i t a l stocks. Using the data, an annual wage rate (wages and salaries/employment = $/manhour); labor, c a p i t a l and supply cost per cubic meter (wages and s a l a r i e s , c a p i t a l costs, 157 supply costs/production = $/m3); and, price per cubic meter (value of shipments/production), were c a l c u l a t e d . 7 A l l values were adjusted to real terms. Reviewing the calculated unit costs over time, i t appeared the dramatic fluctuations around the war years (1940-1946) were not a normal indication of annual variations around long-term trends. Hence, the analyses of cost trends were carried out for the period 1947 to 1977. Over this period, both labor and supply costs per cubic meter of production have been declining in real terms; labor much more noticeably than supply. The continous decline in the labor share of t o t a l logging costs can be attributed to the substitution of c a p i t a l for labor over this period, as real average wage rates steadily increased. As implied above, c a p i t a l costs per cubic meter of production have been increasing over this period, although rather slowly and with substantial c y c l i c a l v a r i a t i o n s . 8 Combining labor, c a p i t a l and supply costs, i t was found that t o t a l unit logging costs have been slowly decreasing over th i s period. 7 T o t a l annual c a p i t a l costs were calculated by applying an assumed 4% real interest charge against net c a p i t a l stocks, based upon an analysis of long-term real rates of return on i n d u s t r i a l bonds by Jenkins (1977). 'Since net c a p i t a l stocks are fixed inputs for which costs are incurred regardless of production l e v e l , the c a p i t a l share of t o t a l costs (regardless of real increases in stocks) w i l l increase (decrease) in low (high) production years. 158 Using the data described above, equations were estimated for the annual wage rate, wood and c a p i t a l price indices, and annual production, for projecting future values for labor, c a p i t a l and supply costs per cubic meter of production. The f i r s t four equations, necessary to complete projections of the last three, were hypothesized to be functions of current to previous years' production. Since the unit factor cost equations are es s e n t i a l l y shares of t o t a l unit cost, the error terms were expected to be correlated across equations. Hence, these equations were estimated as a set of "seemingly unrelated" equations ( i t e r a t i v e Zellner estimation: Pindyck and Rubinfeld, 1976) using UBC Shazam (White and Grieg, 1979). The estimated equations and s t a t i s t i c s are given below (standard errors in parentheses). (5.28) lnPL t = 1.0084 lnPL t_, ( 0 .0 0 7 0 ) R2 = 0.860 SEE = 0.0757 (3.7% of mean) (5.29) lnCAPI t = 0.0832 + 1.0699 lnCAPIt_, ( 0 .0 2 1 3 ) ( 0 .0 3 0 8 ) R2 = 0.979 SEE = 0.3636 (5.9% of mean) 0.1355 + 1.1139 lnWOODIt_, ( 0 .0 2 7 6 ) ( 0 .0 3 2 2 ) R2 = 0 . 979 SEE = 0.0435 (5.6% of mean) 1.0039 l n Q t M ( 0 .0 0 1 9 ) R2 = 0 . 903 SEE = 0.1070 (10.1% of mean) (5.30) InWOODI, (5.31) lnQ t = (5.32) (LC/Q) t = 5.4984 - 0.13099 PL* - 1.5466 (Q t/Q t -i ) ( 1.6 3 4 3 ) ( 0. 0 8 3 0 ) ( 1.1 0 3 5 ) + 0.58351 (LC/Q)t_, ( 0 .0 9 0 6 ) R2 = 0.716 SEE = 0.6373 (9.0% of mean) 159 (5.33) (KC/Q)t = 0.76854 + 0.025278 CAPI+ - 0.6917 ( Q t / Q t ) ( 0 .0 3 8 8 ) ( 0 .0 2 6 0 ) ( 0 .0 3 8 4 ) + 0.91254 (KC/QL, ( 0 ,0 4 9 8 ) R2 = 0 . 939 SEE = 0.0199 (3.3% of mean) (5.34) (SC/Q)t = 2.5498 - wOODIt - 0.85103 (Qt/Qt_, ) ( 0 .7 9 5 6 ) ( 3 4 1 4 ) ( 0.5 7 7 3 ) + 0.43737 (SC/Q)t_, ( 0.1 3 6 8 ) R2 = 0.264 SEE = 0.3315 (11.5% of mean) System R2 for Equations 5.32 to 5.34 = 0.9930 where: PL t = real average earnings of labor in period t, ($/hr) CAPIt = c a p i t a l price index in period t, (1977=100) W00DIt = wood products price index in period t, (1977=100) Q t = volume of wood produced in period t (Mm3) (Qt/Qt-* ) = r a t i o of current to past years' production (LC/Q)t= real unit labor cost in period t ($/m3) (KC/Q)t= real unit c a p i t a l cost in period t ($/m3) (SC/Q)t= real unit supply cost in period t ($/m3) The analysis of unit price trends was ca r r i e d out for the entire period of 1926 to 1977, since values in the war years did not appear to deviate greatly from normal variations observed in other years. Inspection of unit prices over this period revealed a very s l i g h t increasing trend, in real terms, at a simple compounded rate of approximately 1.3 percent per year, with c y c l i c a l movements of approximately six years duration on average. To incorporate the c y c l i c a l nature of log prices, an equation was estimated (5.35) which related the current unit price to prices over the previous six years. The equation was actually estimated over the period 1926 to 1969, with the remaining years (1970-1977) used in testing the equations' forecasting a b i l i t y . Over this period real unit prices were predicted with a root mean square error of approximately 8.3 percent of their mean value. 160 (5.35) PLOG+ = 2.064 + 6.79074 PLOGt_, - 0.029147 PLOG*., ( 2 .6 2 6 ) ( 0 .1 * 6 4 ) ( 0 .9 8 6 ) * " - 0.10117 PLOGt_, + 0.14316 PL0G t_ 4 ( O. 0 8 4 9 ) ( 0 .0 8 6 1 ) + 0.27231 PLOGt.5 - 0.14522 PLOG. . ( O . l 0 O 9 ) ( 0 .1 5 4 8 ) R2 = 0.731 SEE = 2.1942 (9.9% of mean) where: PLOG^ = real unit price of logs in period t ($/m3) PLOG-fc.^  = real unit price of logs in period t-n; n = l , 2 , . . . , 6 Before projecting future cost and price l e v e l s , certain constraints were incorporated to maintain realism. F i r s t , annual production could not be allowed to increase i n d e f i n i t e l y due to regulated harvest l e v e l s . In the recent Five-Year Forest and Range Resource Program (Province of B r i t i s h Columbia, 1980c) i t was proposed that timber harvesting on public forest lands be continued at the current l e v e l of approximately 75 m i l l i o n cubic meters per annum. Allowing for timber production from private lands, and for increases in allowable cuts due to management i n t e n s i f i c a t i o n , an upper l i m i t to annual production in the province was set at 90 m i l l i o n cubic meters. Second, due to the s p e c i f i c a t i o n of the unit factor cost equations, projected values could become negative for labor and supply, or u n r e a l i s t i c a l l y high for c a p i t a l . If the expected trends actually began to be realized, there would be factor substitutions in reverse of h i s t o r i c trends, or, (more l i k e l y ) development of new technologies that would s i g n i f i c a n t l y a l t e r r e l a t i v e factor costs per unit of production. Therefore, factor costs were constrained to a region defined, a r b i t r a r i l y , by approximately 1 6 1 50 percent of their lowest and 1 5 0 percent of their highest recorded values. Projections of rea l wage rates, price indices, production, unit factor costs and unit prices, for the period 1 9 8 0 to 2 0 0 0 , are given in Table 9. The r e l a t i o n s h i p between unit price and t o t a l unit cost over t h i s period i s shown in Figure 9. Unit log prices increase throughout the period while logging costs decrease, hence recoverable timber supplies can be expected to generally increase. However, due to the constraints that were s p e c i f i e d