AN economnmc ANALYSIS or MARKET FACTORS DETERMINING SUPPLY AND DEMAND FOR .sorrwoon LUMBER v Thesis for the Degree of .Ph‘. Di MICHIGAN, STATE UNIVERSITY. THOMAS]. MILLS 1972 LIBRARY -|~?l" Michigan State University This is to certify that the thesis entitled AN ECONOMETRIC ANALYSIS OF MARKET FACTORS DETERMINING SUPPLY AND DEMAND FOR SOFTWOOD LUMBER presented by Thomas J. Mills has been accepted towards fulfillment of the requirements for EhJL—degree in My «621/ f M 7451 Major professor Date Qua 3/) /77Z Q J 0-7639 “-5 ‘ a av mm; tsuus’ ; 300K BINDERY lNC. . mum swans l ‘ 'mnnm- ABSTRACT AN ECONOMETRIC ANALYSIS OF MARKET FACTORS DETERMINING SUPPLY AND DEMAND FOR SOFTWOOD LUMBER BY Thomas J. Mills This study was undertaken to provide statistical estimations of the impact of various market system variables upon price and con- sumption levels of Douglas-fir, Southern pine, and "structural species" lumber. Lumber market variables are statistically treated as supply and demand function shifters. Quantitatively identified supply and demand functions are then evaluated in terms of their relative impor— tance as determinants of lumber market price and consumption levels. Analysis using this model clearly indicates that supply conditions are the principal price determinants while consumption is almost ex- clusively controlled by the level of demand. The derived demand scheme of successive market interactions is the framework within which Specific variables were grouped for analysis. Two independent demand function estimates were drawn from separate groups of variables, one from consumption level variables in lumber using markets and a second from the supply and demand determinants of these Thomas J. Mills consumption levels in lumber using markets. Two partially independent supply equations were estimated, one from domestic sawmill and foreign source variables and a second from the same group with sawlow price replaced by its stumpage sector determinants. The equations were estimated by applying the two stage least squares statistical model to modeled subsets, each containing a single supply and demand equation for a single species group. Tests showed that the equations were properly identified, contained no serial corre- lation among residuals, and showed little evidence of misspecification. Multicollinearity was handled by excluding from the equations all col- linear variables but one of a collinear group. Demand variables were all inelastic. The most important demand function shifters, as measured by elasticity and average associated c tl._aa,~,,,-auu,- percentage shift of the function, were volume of residential construc- tion and the price of softwood plywood. Supply variables were somewhat more elastic than demand variables with four elasticities above unity. Average sawmill establishment size, which is highly correlated to labor productivity and sawmill wage rates, showed only moderate importance. Log expert volume, lumber tariffs, and U.S./Canada money exchange rate demonstrated low importance. British Columbia lumber production proved very important. Raw'material variables (sawlog price, peeler log price, pulpwood price, and residue utilization) Thomas J. Mills were the most important supply function shifters, especially sawlog price. Pulpwood price demonstrated greater impact upon the lumber market than peeler log prices. Demand price elasticities fall in the very inelastic range below -O.50 and do not vary by species group. Average supply price elasticities over the 1947-70 period are estimated to be within the 1.2 to 1.6 range, again with little species variation. Analysis of shifts in the estimated supply and demand positions from 1947-70 at an assumed price of $100 per thousand board feet showed a species difference in longer run supply response. Douglas-fir supply shifts to the left in response to a rightward demand shift while Southern pine supply shifts to the right in response to a similar shift. By using connection lines between successive price and consumption points as an index of longer run supply response, the longer run Douglas-fir supply elasticity is about 1.0 and for Southern pine as high as 2.0. The reason for this difference probably lies in regional differences in forest ownership patterns, log use alternatives, and barriers to entry. The "structural species" group displays an average of the Douglas-fir and Southern pine longer run supply price elasticity through 1965 and then demonstrates the less elastic supply response typical of the inflexible Douglas-fir species. This supply and demand analysis Thomas J. Mills also demonstrated quite clearly that demand is essentially the sole consumption determinant while supply dominates the price level. Price and consumption projections from 1971 through 2000 showed a price differential between Douglas-fir and Southern pine in the year 2000 of $192 versus $118 per thousand board feet respectively which indicates the economic pressure for regional balancing. "Structural species" consumption is projected to decline from a 1975 high at 1.2 percent annually through 1987 and decline thereafter at a very slow 0.02 percent annually. Projected price declines to a $102 low in 1985 and then rises sharply to $135 by 2000. The 1987 to 2000 rate of increase is 2.25 percent annually. Sensitivity of the "structural species" price projection to possible sawlog and log export changes was tested. These tests showed that the price projection can be lowered but the 1987 to 2000 year trend, which is controlled in the projection by the level of British Columbia lumber production, is unmitigated by sawlog price and log export volumes. Consequently, if lumber prices are to be maintained at low levels beyond the middle 1980's the void currently filled by British Columbia production must be filled in another way. AN ECONOMETRIC ANALYSIS OF MARKET FACTORS DETERMINING SUPPLY AND DEMAND FOR SOFTWOOD LUMBER by J“ Thomas J? Mills A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Forestry 1972 ACKNOWLEDGEMENTS The author wishes to acknowledge appreciation to Dr. Robert S. Manthy, who acted as both advisor and guidance committee chairman, for his valuable suggestions during review and extensive editing help. Gratitude is extended to the National Science Foundation and the United States Forest Service for financial support which the author received. Sincere appreciation is expressed to the author's parents whose patient and continual encouragement helped.immensely in early stages of this educational endeavor. Most of all, the author is deeply indebted to his wife, Chris, for her understanding, encouragement, and continual sacrifice throughout the entire period of graduate study. And last, but far from least, appreciation is extended to the author's daughter, Jennifer, for the loving comic relief she has provided during the final stages of this study. ii TABLE OF CONTENTS LIST OF‘ TABLES O O O C O C O O O O I O 0 LIST w FIwRES O O C O . O O O O O O O O 0 Chapter I. INTRODUCTION . . . . . . . . . . . OBJECTIVE AND SCOPE . . . . . . PROCEDURE . . . . . . . . . . . RELATED STUDIES . . . . . . . . Consumption Projection . . . Price Projection . . . . . . Short-Run Econometric Models Long-Run Econometric Models. Relationship to Other Studies and Techniques II. MODEL STRUCTURE. . . . . . . . . . DEMAND AND SUPPLY VARIABLE GROUPS DATA CHARACTERISTICS. . . . . . III. STATISTICAL METHOD . . . . . . . . STATISTICAL MODEL SELECTION . . TWO STAGE LEAST SQUARES OPERATION INITIAL REQUIREMENTS OF COMPLETENESS AND IDENTIFICATION. . . . . . . . iii Page vi viii \OGDVO‘ 10 l4 16 21 25 25 27 29 TABLE OF CONTENTS.--Cont. Chapter SERIAL CORRELATION AND MULTICOLLINEARITY. . . . . . . VARIABLE SIGNIFICANCE . . . . . . . . . . . . . . . . MISSPECIFICATION. O O O O O O O O O O O O O O O O O 0 IV. RELATIVE IMPORTANCE OF SUPPLY AND DEMAND SHIFTERS. . . . ESTIMATED EQUATIONS . . . . . . . . . . . . . . . . . Primary Demand Level Variables . . . . . . . . . . Secondary Demand Level Variables . . . . . . . . . Primary Supply Level Variables . . . . . . . . . . Primary + Secondary Level Variables. . . . . . . . ESTIMATED ELASTICITIES OF INDIVIDUAL SHIFT VARIABLES. Demand Variable Elasticities . . . . . . . . . . . Supply Variable Elasticities . . . . . . . . . . . ESTIMATED PRICE ELASTICITY ESTIMATES. . . . . . . . . Demand Price Elasticity Estimates. . . . . . . . . Supply Price Elasticity Estimates. . . . . . . . . ESTIMATES OF LUMBER DEMAND EQUATIONS USING GROSS ECONOMIC INDICATORS . . . . . . . . . . . . . . . . V. SHIFTS OF THE SUPPLY AND DEMAND FUNCTIONS. . . . . . . . ESTMTION ACCUch O O O O O O O O O O O O O O O O O CHARACTERISTICS OF SUPPLY AND DEMAND SHIFTS FOR DOUGH S -F IR AND SOUTERN P INE C O O O O O O O O O O Douglas-fir Supply and Demand Shifts . . . . . . . Southern Pine Supply and Demand Shifts . . . . . . Comparison of Douglas-fir and Southern Pine Longer Run Supply Response . . . . . . . . . . . CHARACTERISTICS OF SUPPLY AND DEMAND SHIFTS FOR THE "STRUCTURAL SPECIES" AGGREGATE. . . . . . . . . . . iv Page 30 35 36 38 39 41 43 46 SO 53 55 59 65 67 69 73 76 77 79 80 84 86 9O TABLE OF CONTENTS.--Cont. Chapter VI. CONSUMPTION AND PRICE PROJECTIONS. . . . . . . . . EXOGENOUS VARIABLE PROJECTIONS. . . . . . . . . DOUGLAS-FIR AND SOUTHERN PINE PROJECTIONS . . . "STRUCTURAL SPECIES" PROJECTION . . . . . . . . POLICY SENSITIVITY IN THE "STRUCTURAL SPECIES" SYSTEM. . . . . . . . . . . . . . . . . . . . VII. SUMMARY AND CONCLUSIONS. . . . . . . . . . . . . . LITERATURE CITED . . . . . . . . . . . . . . . . . . . . . APPENDIX A. ORIGINAL DEFLATED DATA. . . . . . . . . . . . APPENDIX B. APPENDIX C. APPENDIX D. APPENDIX E. SOURCE NOTES AND DESCRIPTION OF ORIGINAL DATA ESTIMATED SUPPLY AND DEMAND POSITION AT AN ASSUMED PRICE OF $100/bem, 1947-70 . . . . PROJECTED EXOGENOUS VARIABLES . . . . . . . . METHOD OF CALCULATING THE ARC ELASTICITIES AND THEIR CONFIDENCE INTERVAL . . . . . . . Page 96 97 99 101 108 111 119 123 146 175 178 182 LI ST OF TABLES Table Page 1. Statistical characteristics of the primary demand level equations for lumber, by species group . . . . . . . . . 42 2. Statistical characteristics of the secondary demand level equations for lumber, by species group . . . . . . 44 3. Statistical characteristics of the primary supply level equations for lumber, by species group . . . . . . . . . 47 4. Statistical characteristics of the primary + secondary supply level equations for lumber, by species group. . . 51 S. Elasticity and percentage impact estimates for Douglas- fir lumber demand function shifters. . . . . . . . . . . 56 6. Elasticity.and percentage impact estimates for Southern pine lumber demand function shifters . . . . . . . . . . 57 7. Elasticity and percentage impact estimates for "struc- tural species" lumber demand function shifters . . . . . 58 8. Elasticity.and percentage impact estimates for Douglas- ' fir lumber supply function shifters. . . . . . . . . . . 60 9. Elasticity.and percentage impact estimates for Southern pine lumber supply function shifters . . . . . . . . . . 61 10. Elasticity.and.percentage impact estimates for "struc- tural species" lumber supply function shifters . . . . . 62 11. Price elasticity.estimates for Douglas-fir, Southern pine,.and "structural species" lumber supply and demand . . . . . . . . . . . . . . . . . . . . . . . . . 66 12._ Statistical characteristics of lumber demand equations using gross economic indications, by species . . . . . . 74 vi LIST-OF TABLES.--Cont. Table Page 13. Percentage error of calculated estimates of price and .consumption from observed levels of price and consump- tion for Douglas-fir, Southern pine, and "structural species" . . . . . . . . . . . . . . . . . . . . . . . . 78 14. Projected level of Douglas-fir and Southern pine lumber supply at an assumed price of $100/bem, 1971-2000 . . . 100 vii Figure 10. 11. 12. LIST OF FIGURES Schematic representation of market interactions in a derived demand framework. . . . . . . . . . . . Interrelationship between factors hypothesized to affect the demand side of the softwood lumber market. Interrelationship between factors hypothesized to affect the supply side of the softwood lumber market. Flow chart of the modeled softwood lumber market. . . Estimated.Douglas-fir lumber demand and supply at an assumed price of $100/bem, 1947-70 . . . . . . Observed market equilibrium points for Douglas-fir llmber' 1947-70 0 o o o o o o o o o o o o o o o o 0 Estimated Southern pine lumber demand.and supply at an Observed market equilibrium points for Southern pine lmer' 1947-70 a o o o o o o o o c Q o o o o o o 0 Estimated "structural species" lumber demand and supply at an assumed price of $100/bem, 1947-70 . . . . . Observed market equilibrium points for "structural SPeCieS" l‘lmber' 1947-700 0 o o o o o o o o o o o 0 Projected ”structural species" lumber demand at an assumed price of $100/bem, 1971-2000 . . . . . . . . Projected.Pstructural species" lumber consumption, 1971-2000 C O O O O O O O O O O O O O O C O O O O 0 viii Page 15 18 19 22 81 83 .5 87 91 92 102 102 LIST-OF FIGURES.--Cont. Figure Page 13. Projected "structural species" lumber supply at an assumed price of $100/bem, 1971-2000 . . . . . . . . . 105 14. Projected "structural species" lumber price, 1971-2000. . 105 ix CHAPTER I INTRODUCTION Considerable conjecture and piecemeal evidence has been accumulated about the effect of supply and demand conditions upon price and consumption levels of wood products. Some of this con- jecture centers upon the underlyingkshifgergfbf market supply and demand functions. Information about these shifters is usually “N. w a derived from qggggiptivewstudies‘or from studies that project con- sumption levels. The Congressional hearings originating over concern for the 1968-69 rise in lumber and plywood prices demonstrate how in- formation from these sources is often utilized (U.S. Congress, 1968 and 1969). Conclusions about the relative impact of variables ranging from log exports to housing starts upon wood product price and consumption levels were drawn almost exclusively from descrip- tive information. Major public policy decisions were based upon these conclusions such as the need for a partial log embargo and an increase in the intensity of management on Federal forest land. OBJECTIVE .AND SCOPE The thrust behind this study is the contention that an inte- -q...- grated system of the wood product markets containing statistically ._-k i measured interactions among the.system variables will provide more reliable information for similar policy decisions. This study attempts to accomplish the construction.of such an integrated system. It pro- vides supply and demand.equations.for.a.particular wood product group as a means of determining the impact of various factors upon price and consumption.levels. .The products of concern are Douglas-fir, Southern pine, and "structural species“ lumbera. Four.principal objec- tives are: (1) to determine the extent that potentia1-statistica1 difficulties inherent.in the multi-equation approach are present in the ’ developed model and the extent to which they impair interpre- tation of results. (2) to determine the relative importance of specific variables as supply and demand shifters, (3) to study the importance of supply versus demand.conditions in rterms.of their importance as price and consumption level determinants, and (4) to utilize the estimated supply and demand relations to project consumption and price levels, and-study the sensitivity of these levels to changes in the magnitude of some policy- ..sensitive variables. Lumber as a commodity-was chosen for.three reasons. First, lumber production represents.approximately.45.percent of all domestic roundwood consumed in the U.S. (Hair and Ulrich, 1971, p. 39). Second, lumber is a relatively homogenous primary product. Third, time series data are readily available for the lumber industry. The latter item is particularly.important as lack of data often precludes use of a multi- equation.model.(Hair and Josephson, 1971, p. 19). Within the lumber industry three species groups are identified for.detai1ed study: Douglas-fir, Southern pine, and a group of "struc- tural.species".composed of lumber cut from Douglas-fir, Southern pine, .hemlock, true fir, and larch. These groupings allow for fairly specific producing.and consuming.industry identification and for regional com— parisons. - PROCEDURE The statistical procedure employed to meet the study objectives consists of regression estimated supply.and demand functions for each of the species.groups.. Each function is represented by an endogenous or system determined price-quantity relationship shifted by a group of relevant.exogenous or.external factors.. These relationships can be statistically characterized as: n y = b + b Y + Z b_x, + e . demand function D 0 l D , l 1 i=1 n = c + Y + Z + v 1 f t' n 95 (3 Cl S j-l ijj supp y unc 10 where: 9D and gs = quantity of lumber demanded and supplied, respectively Y and Y3 =.price of lumber demanded.and supplied, respectively .x,.and.x;.= exogenous variables that shift.the.demand and supply 1 ' 3 function, respectively e and v = unexplained variation of yD and gs structural coefficients estimating the change of quantity demanded or supplied associated with a one unit change of the variable while all other factors are held constant b's and c's For.reasons.discussed later, this two equation model was applied sep- arately to each of the species groups considered. Time series of annual observations from 1947 through 1970 were employed in this study for estimation of structural coefficients. Data availability, the desire to avoid the 1940-46 price control period, and the desirability of obtaining observations from a relatively consistent market structure were all reasons for excluding data before 1947. The principal advantage of the econometric method used in this study is that it allows explicit statistical consideration of a number of system parameters directly within the framework of an analytical model. But there are a number of potential disadvantages such as prob- lems of data availability, identification, serial correlation, multi- collinearity, and model missPecification. These problems and the extent of their presence are discussed in detail in Chapter III. The relative importance of various parameters as supply and demand function shifters is measured by three indexes: 1) statistical significance of its estimated coefficient, 2) elasticity with respect to lumber quantity, and 3) elasticity times the average annual per- centage change of the variable. Each of these measures is applied and discussed in Chapter IV. Once the equation coefficients are derived, the estimated posi- tion of the supply and demand functions during the sample period are produced by applying these equation estimates to the actual observations of exogenous variables from 1947—70. Conclusions about the relative impact of supply and demand shifts upon price and consumption levels are then drawn from the estimated annual shift in position of the two functions. This analysis is presented in Chapter V. Lumber consumption and price projections are provided in Chapter VI. These are derived by applying estimated structural coef- ficients to the projected exogenous variables to determine the price level where the supply and demand curves cross. Alternative levels of some policy-sensitive exogenous variables are then used to project the resulting consumption and price changes. RELATED STUDIES Past studies related to this one can be aggregated into four groups: consumption projections, price projections, short term econo- metric analysis, and long term econometric analysis. Consumption Projection Studies undertaken to project the consumption level of wood products generally have employed one of two rather simple techniques, regression analysis or end-use ratios. Regression projections such as \H/‘fih .1...“ — . \-...-.——»”""*"” . ‘ ....,.._.-——‘ .. those used by Stanford Research Institute (1954), Guthrie and Armstrong (1961), Frazier (1965) and Hair (1967) usually involved regressing consumption of the wood product against some relatively gross economic indicator such as Gross National Product (GNP) or population. Con- sumption is projected by applying the estimated structural relationship between the indicator variable and consumption to an exogenously de- rived projection of the indicator variable. Hair's (1967) projection of per capita consumption of numerous paper products probably represents the host detailed wood products application of this technique. In the second approach, end-use ratios are estimated for timber products as they are utilized in their various end-uses such as lumber use per dwelling. Consumption is then projected by applying this use ratio to the projected consumption level in the markets for goods that employ wood products. This technique has been utilized by Stanford Research Institute (1954), U.S. Forest Service (1958, 1965), Landsberg gt_§l, (1963) and Nathan Associates (1968). Price Projection Attempts to project the price of forest products have usually been applied to a limited number of specifically defined products. Dutrow (1971) projected the price of cottonwood stumpage from a three equation recursive model using quarterly data. The level of the endo- genous variables in the first two equations, stumpage price in period t-l and agricultural wages in period t-l, are used in the third equation as regressors of that endogenous variable, stumpage price in period t. Anderson (1969a, 1969b) prepared two single equation models which pro- ject pine sawtimber and Southern pine pulpwood stumpage prices, re- spectively. The two studies are quite similar and entail regression of stumpage price upon timber characteristics, number of buyers, and a V time trend. Since individual timber sales were the unit of observation, multiple observations at the same time point were utilized. Short-Run Econometric Models The single most important characteristic of short-run econometric models is the use of monthly or quarterly observations. Explicit con- sideration must be made for the nature of short—run market equilibrium (or more accurately, disequilibrium) and decision parameters. It is often the case with monthly observations that demand is registered at a price agreed upon by both the supplier and demander but the commodity is not physically supplied until a later date. This short—run disequilibrium situation, due to violation of the economic model assumption of instan- taneous production in a point market, must be considered with such indexes as unfilled orders and can not be depicted by supply and demand functions alone. Different system parameters are decision signals in the short-run than in the long-run due to the effect of time period upon input variability. For example, the input schedule is relatively fixed in the short-run so changes of input costs may have much less effect upon production decisions than the past level of new orders. McKillop (1969) developed a six equation short-run recursive model of the redwood lumber industry using monthly data. One equation was prepared for each of the following endogenous variables: unfilled orders, mill stocks, production, shipments, new orders, and price. He then used these equations to forecast the endogenous variables in more .recent time periods where actual observations were available but not used in model construction. Simpson and Halter (1963) constructed a four equation model of the sanded and unsanded Douglas-fir plywood 7 market using quarterly data. The four equations include specifications for demand, supply, inventory, and unfilled orders. Gregory (1960, 1965) prepared a short-run recursive model of the hardwood flooring market including equations for supply, demand, and price. Gregory estimated the structural relations for the same three equations using six consecutive and non-overlapping monthly time series data sets from 1947 to 1963. He concluded that different co- efficient estimates (some of which changed sign as well as magnitude) . ". . . might indicate substantial change in the structure of the in- dustry . . ." (Gregory, 1954, p. 203) but unfortunately conducted no tests to see if a statistical difference occurs. Long-Run Econometric Models. Given that length of run is based upon the proportion of inputs that are variable, one year observations of the primary wood product industries gives adequate allowance for variation of most inputs and thus constitutes a moderately long-run. Similarly, because one year usually surpasses the production and delivery time for primary wood products, supply and demand relations can be estimated directly with disequilibrium conditions due to production and delivery time quite safely ignored. 10 Holland (1955) provided one of the pioneering attempts at an econometric analysis of a wood product using annual observations. His model contained supply and demand equations for softwood lumber. The structural relationships tested the importance of very few shifters, however, and according to McKillop (1967, p. 10), may have been im- properly specified. McKillop (1967) constructed what is probably the most compre— hensive long-run econometric study of wood product markets to date. Annual observations were utilized in the estimation of supply and demand curves for "all" lumber, softwood lumber, paper, paperboard, building paper and board, and softwood plywood. He used the estimated equations to project price and consumption levels through 1975. A study similar to McKillop's analysis in terms of product aggregations is currently being analyzed by Talhelm and Holland (1971). Monthly observations are being utilized in the estimation of supply and demand functions di- rectly, however, while short-run disequilibrium conditions are being ignored. Relationship to Other Studies and Techniques While all of the studies discussed above are related to this aniilysis only two of the four groups, the consumption projection and J~<31'1g--run econometric approaches, have close relationships. The Pb Ft .FU My Hr .L a OS 11 consumption projection models have the advantages of analytical simpli- city and less severe data requirements. This simplicity allows, and even necessitates, large inputs of investigator judgment, however. For example, the Forest Service has repeatedly assumed that relative prices between a particular wood product and its substitutes would remain con- stant (U.S. Forest Service, 1948; 1958, p. 371; 1965, p. 9; and Hair, 1967, pp. 24-25). The economic plausability of the constant price assumption has been questioned since it means that (1) there is a hori- zontal supply function, (2) the supply curve can be induced to shift to the right such that it intersects the new demand function at the current price level (Vaux and Zivnuska, 1952; Gregory, 1955), or (3) that the 1 price level of each product and its competing group move identically. 1The 1946 Reappraisal study (U.S. Forest Service, 1946a and 1946b) which precipitated the articles by Vaux and Zivnuska (1952) and Gregory (1955) did not explicitly assume the constant price relation- ship. The Reappraisal did define the requirement quantity projected, however, as that quantity which ". . . might be used by consumers af- forded reasonable latitude in choice of readily available materials . . ." (U.S. Forest Service, 1946a, p. l) and further defined the production goal as ". . . at least as much timber as a prosperous people might use if the supply were sufficient to keep forest products available at reasonable prices" (U.S. Forest Service, 1946b, p. 3). Both Vaux and Zivnuska, and Gregory interpreted this as an implicit assumption of constant relative prices between wood products and all commodities. To the extent that this is a correct interpreta- tion of.the Reappraisal study, the articles of criticism are correct except that Vaux and Zivnuska seem to ignore the second possible cause Of constant relative prices, i.e. a shift of the supply function, men- tioned by Gregory . The two more recent Forest Service studies (U.S. Forest Serrvice, 1955 and 1963) make the assumption explicit that constant 12 An even greater restriction is the inability of the consumption model to explicitly and internally implement alternative assumptions. For example, the Nathan Associates study (1968, p. 161) assumes that future price induced substitution rates will be extensions of past rates rather than the more limited substitution assumed by the Forest Service (1965, p. 9). Nathan Associates implemented this alternative price assumption by lowering the projected wood product end-use ratios below those used by the Forest Service. This use ratio adjustment was based solely upon judgment of evidence external to the model. There is no way such price relatives can be specifically inputed into the model. Therefore, the most serious limitation of the consumption pro- jection models is not their failure to produce information concerning the interrelation between numerous exogenous and endogenous variables. The consumption models were not built to supply such information. Like- wise, the extensive use of assumptionsifisrxnztheir major weakness since all methods require assumptions of varying stringencies. Rather, the major weakness is that there is no explicit analytical consideration of parameter interactions internal to the model through which the effect of alternative assumptions can be measured. The econometric approach employed here allows internal consideration of relative parameter importance. relative prices will occur among the substitutes alone and not relative to all commodities. Thus, it becomes necessary to consider the third possible cause, i.e. that all prices of commodities in the substitute group change the same. 13 The method utilized in this study and the information produced is very similar to that found in McKillop's 1967 study. McKillop did not include some system parameters tested in this study, however, and his estimates for softwood lumber price elasticities had questionable magnitudes and wide confidence intervals. Possible causes of these problems may have been the wide industry aggregations and retention of colinear variables. In some respects this study can be viewed as an attempted refinement of an approach handled very well by McKillop. CHAPTER II MODEL STRUCTURE Lumber manufacture(i§;only one stage in the processing chain between the forest and the final market in which timber derivatives are utilized. TheisEquentialminteraction in the deriyedfidemand flow is the system representation used in this study as the framework within which specificwvariables are placed.; A very basic schematic representation of the derived demand interactions is shown in Figure l. The demand for any product is a function of the consumption levels in all markets that use the product as an input. For example, the demand for lumber is a function of the consumption level of resi- dential construction, shipping containers, railroad ties, and other products. Similarly, the demand for logs is a function of such factors as the consumption of lumber, plywood, and pulpwood. Generalized this becomes: Demand = f consum tio . . . consum tion B ( P “All I P Ai) where "A" is the product (residential construction) in which "8" (lumber) is used and there are i different industries or products "A." The same demand can be expressed alternatively as a function of the determinants of the consumption level in markets using the product: 14 15 ...J .xHOSmEoum osmfioo ow>flumo m CH mcofluomumHCH umxume mo coaumusommummu oeucamnomll.a .mam * _ _ ._ _ . . .4 — 4— _ mmomfisum _ mmoH _ Honfisa _ muosooum mswms Hmnasa _ . . 7 p _ _ _ Q umxumfi _ U umxums _ m umxuma _ m umxums _ . . . _ . _ _ _ _ _ 71 llllllllllllllllllll _ a >Hmm5m 1H + _ IIIIII a low IIIIIIIIIIII J a .Hflsoo tll h 0 H on lllllll W. lllllllllllll a osmsoo_+lll 0 .stoo +2 _ m mammsm h . +.. . I O osmaoo.tlll m .stvo +. «4 madame a m possum +lll..¢ .stoo + 16 DemandB = f(supplyAl, demandAl, . . . , supplyAi, demandAi) As diagrammatically shown in Figure 1, the effect of higher markets is transmitted through the demand functions of lower markets. The effect of lower markets is transmitted upward through the supply functions of higher markets. The products of lower markets are inputs for higher markets. With reference to Figure 1, for example, logs are inputs into the lumber industry, and to the extent that input costs affect supply, the lower (log) market has an impact on the higher (lumber) supply function. Just as it is possible to replace consump- tion of higher level products with its supply and demand determinants, the input price can be replaced by its supply and demand determinants as an alternative means of showing lower market effect. Note then that one market equilibrium variable, consumption, transmits the impact of higher markets downward while the second market equilibrium variable, price, carries the impact of lower markets upward through the derived demand chain. It is within this general framework of interrelated markets that the data classification discussed below fist presented. DEMAND AND SUPPLY VARIABLE GROUPS Based upon the derived demand system described above, three groups of demand variables were initially segregated for analysis. 17 These groups are discussed below and presented schematically in Figure 2: (l) demand level 1, (2) demand level 2, (3) demand level 3, consumption levels of lumber using products, equivalent to equilibriums A1 in Figure 1. Residential construction consumption is also represented by the percentage of structures started which contain three or more dwelling units because of the heterogeneity of housing consumption and its effect upon the amount of lumber demanded. major supply and demand determinants of the consumption levels in various lumber using markets, equivalent to supply A1 and demand Ai in Figure l. more detailed representations of the level 2 factors or determinants of the same. Two groups of supply variables were utilized. They are discussed below and presented schematically in Figure 3: (1) supply level 1, (2) supply level 2, level la which includes determinants of domestic supply conditions and level 1b which contains gross indicators of foreign supply factors. These two sublevels together are equivalent to supply B in Figure 1. level 2a which includes determinants of sawlog prices as influenced by stumpage price or stumpage conditions, equivalent to market D in Figure 1, and level 2b which contains monitors of the demand from other markets for logs, equivalent to some demand Di in Figure 1. Parameters for transportation cost were included on the supply side. This is opposite to the traditional approach of placing them on the demand side but is done under the assumption that lumber sellers rnrtlmd scent pr. I softwood plywood pr. I structural steel pr. I building board pr. I building constr. wages Femary an. m is I constr. materials pr. [ pop. age dist. [ headship age dist. I population per capita disposable income diet. of families by income sap-iditures m heua ing I I pop. in cities price of substitute materials resid. constr. coat/sq.tt. or value/dwelling no. households median family income or per capi ta disposable income 18 H Supply: resid. constr. a upkeep value of resid. constr. put-in-place or no. dwelling starts 1 starts with 3 or more dwelling units value of resid. upkeep a repair put-in-place lesid. Constr. Market r—-d Demand: resid. constr. a upkeep 1 f [ population mobility r 1 price of substitutes I prime lending rate building oonstr . wages price of substitute constr. materials pr. [index of mfgt. activity I O spent on services#‘_~_}'—JI railroad rev . /ton-mi ls l #1 l index of mfgt. activity non-resid. constr. cost/sq.ft. Supply: non-resid. constr. Demand: non-resid. constr. Supply: shipping containers demand level 3 fig. 2.--1nterrelationahip between factors hypothesized to affect the demand side of the softwood lumber market. demand level 2 .----- Demand: shipping containers value of non-resid. put-in-place lesid. Upkeep a Repair Market tone-lies of interCity freight no. new box cars installed no. new cross ties installed I index of mfgt. actfl—U demand level 1 Ion-resid. Conetr. Market 4 Shipping Container Market Railroad Con-tr. a Repair Market J Lumber Used in Mlqt. lumber using markets l9 . quMIE encuosm anon-seas usage .6851 goroNOe 05 us eon.- .Sdosa era assuus cu vase-enuongn encuusu cosausn mas-codesasuusuCHllé .3..- ." ~s>s~ finance l . M. II» .80 use! .3: «as» weal: _ eucssalueuea 3.3.6 sou—40¢ c3 suom 3 L e~«0.8u\.>eu osougsu # TL seal—none use: he» e35 .233 UT .93.. uoalsdé _ .693 noel: 5:238 _ eusssalusueo Samoa anal-em oauesda 4.— ] envious s2.2. seen-ox. a... 833on 9333 an . . . a «ease SE:- n . soda.- oooamusn — [— auuduau Hi.— .u.D — Il— sase uuovoual>fllll sea...“ son 009350 «0 slice I.— »35 e323 I [ragga usfisel I «seed .maosum E — ll— so« an module T 2&5 us)?— I sauna unavanosus — .ususel .ooua \eusuaoiaae usual—so as: L365 332208. flu —l. oeoosnesasa \eusoaucel . eons sill-3.38 xenon-.31.. geese Sneak-ones nausea easel». en r i 1m. aeol- asausa Sui — gasses TI. gates eased!— assesses negates . m. m accuses .m.m 1| .83.. Seals. esuosme an I .8?!— easel-us agave-Ass ease eeeoOe wees: .ge eased!— IL e..- 33. .e.a IL .aowmms caduceus!- vss .uml .e.m L 81. 3.13 .ed _ .I. Vi 34. 20 price to compete in the market of concern whether the prices are listed f.o.b. mill or not. When these variable categories were first developed, the inten- tion was to estimate three separate demand functions for Douglas-fir, Southern pine, and the "structural Species" group from each of the three groups of demand variables. Similarly, it was originally intended that two supply functions would be estimated for each species group, one using supply level 1 variables and a second using supply level 1 vari— ables with the sawlog price replaced by its supply level 2 determinants. Preliminary analysis of multicollinearity between variables and variable significance lead to substantial regrouping and removal of some variables presented in Figures 2 and 3, however. Two major rearrange- ments occurred. Demand level 2 variables were highly correlated among themselves so demand level 2 and demand level 3 variables were combined as a single group from which significant and independent variables could be selected. On the supply side the sawlog competition variables of supply level 2b proved to have sufficient explanatory power beyond their influence upon sawlog price to warrant placement of the sawlog competi- tion variables in supply level 1 along with the sawlog price itself. Given these two major changes in the arrangement of variables shown in Figures 2 and 3, and given exclusion of individual variables because of the multicollinearity and significance tests discussed in the next chapter, the two groups of demand variables and two groups of 21 supply variables shown in Figure 4 result. Two demand equations were estimated for each species group, one from the primary demand variables or consumption levels in lumber using markets and one from the secondary demand variables or supply and demand determinants of these consumption levels in lumber using markets. Likewise, two supply equations were estimated, one from the primary supply variables or lumber market supply factors and one from the primary supply variables (excluding the sawlog price) plus the secondary supply variables or stumpage factors. Here- after this second supply equation will be referred to as the primary + secondary supply equation and equations drawn from the other groups will be known by the market levels as shown in Figure 4. Not all of the variables shown in any one market level of Figure 4 were used in the equation for each species group but all were used in at least one species group. DATA CHARACTERISTICS Many variables pertinent to the lumber market have been excluded from Figures 2 and 3 and therefore from Figure 4 and the subsequent analysis. Parameters such as log quality, land tax and construction productivity were excluded because of the desire to represent the system in an operational form. Only those variables for which data are avail- able are considered in the analysis. Thus variables exluded were not He>sa madman musoooose 22 svsusas .m.m .s0aun amen-sue sensuaocsnxs oeou eeeuos sea-.3 7:: :3. aflL L .usxuss nonfioa vootque vsasooa an» ac uusnu ronmun.v .mam ~e>sa aammse ausflaum use: .eusu aasu ueAISH .M.lluml00 fl! .ooun season .u.m fill socscuxs fill mecca soecs0\.u.o uneasy weal...— .o.o T essoaeeu sadness uo sl5~o> I sound oodles I#l1 551.333.. L b.8673?» nexus: weal: manure wen-5A ssaunuaasvs caduAISeeou a scene u 8.8“.- Ni." o3 weal: Hesse ocssso kneaded venue» 3: scan seouo ass .0: 333-5 ease as.» as: .0: sesamlcuuusa .oassulsoo no sods> 345. 05:86 sued no n 5a... 3.3». x J [j 33». 9:326 .2. T .IL eventual»!— .uueooo 1.. .oqesu no sense seed—I551 r. Mel-en s masses .1 .3esu no sense geese ace-so assocooee jigs Jena no needl— 1— .uneuaonefifial J I—.un Hesse aswsuosuue TH T—T .a 600.53 602.5qu E l— 3332. 8332.8 a e305 an sequin no .ueao IF 83.908 .0: % 53.. ee- a; L fifilnuiga 23 always excluded because they were considered unimportant. Data restric- tions also forced the use of proxy variables for some system parameters such as precipitation level in the Pacific Northwest rather than the number of days logs could not be removed from the woods due to wet con- ditions. Similarly, some time series could only be derived by splicing two overlapping partial series together. Data corresponding to the variables identified in Figures 2 through 4 are presented in table form in Appendix A. Corresponding source notes and explanations of the variables are listed in Appendix B. .All variables measured in dollar units or which contain dollar measured components were deflated by the "all commodity" wholesale price index, variable number Bl in Appendix A. This deflation holds the size of the money unit constant over time so that it can be validly compared to the other units of measure employed. The two exceptions to the de- flation process were sawmill establishment size and sawmill productivity since the value-added component of each as measured in current dollars should be a better proxy for lumber production than value-added measured in deflated dollars. That there are data problems, whether through variable exclusion or minor misrepresentations,cuminot be questioned. These problems are judged to be quite minor, however, and do not constitute the "lack of suitable data" problem which is sometimes cited as a reason why multi- equation models can not be employed. ‘Whether this same conclusion of 24 data.adequacy could be made regarding a similar study of the plywood or paper industry is uncertain. CHAPTER III STATISTICAL METHOD In this chapter attention is given to consideration of the (presence of potential statistical problems which either impair the interpretation of results or completely block model implementation. These problems and explicit statements regarding their effect if they are present are discussed in this chapter. Of particular concern are questions of the appropriate statistical model, model completeness and identification, incidence of serial correlation and multicolinearity, determination of variable importance and model misspecification. STATISTICAL MODEL SELECTION As discussed briefly in Chapter I, supply and demand functions are represented in this study as endogenous price-quantity relationships shifted by a number of exogenous variables. since both lumber quantity and lumber price are determined within the system simultaneously, they are correlated with the residual terms. The inclusion of two endogenous variables in a single equation violates the ordinary least squares (OLS) assumption that only one variable is correlated with the residual. If 25 26 OLS was applied to the above system regardless of the violation, the estimated structural coefficients would be biased and biased even on large samples, or in statistical terminology, inconsistent (Wonnacott and Whnnacott, 1970, pp. 152-153). Four alternative statistical models are available which produce asymptotically or large sample unbiased and thus consistent estimates. Two of these approaches are single equation or limited information techniques: two stage least squares (ZSLS) and limited information maximum likelihood (LIML). The remaining two are simultaneous equation or full information models: three stage least squares (BSLS) and full information maximum likelihood (FIML). The full information models are so named because they utilize information about variable levels and equation specification from all parts of the model in the estimation of coefficients for each equation. The limited information techniques are so named, obviously, because they do not utilize all this information from other equations. Since we are dealing with a small sample here, the property of large sample unbias does not automatically reject OLS or lead us to a choice among the four alternatives. Monte Carlo simulation studies conducted to investigate the small sample properties of the five statis- tipal models are summarized by Goldberg (1964, pp. 362-363) and WOnna- cott and annacott (1970, p. 399). Though the summaries presented by 27 these authors are somewhat conflicting and inconclusive, they can be generally stated as follows: (1) OLS has the largest bias but generally the smallest variance, (2) ZSLS has the second smallest variance and generally a low bias, (Also important, it shows less sensitivity to problems of multicolinearity and model misspecification.) (3) LIML provides quite unstable estimates, (4) BSLS and FIML sometimes out perform the other models but not always and, because of their full information approach, the multicolinearity or misspecification in individual equations is not segregated but affects other equations. LIML was rejected because of its high cost and unstability. Since multicolinearity is almost always a problem with economic time series data and model misspecification is always a potential problem, 3SLS and FIML were also rejected. The model chosen was ZSLS. This technique was selected over OLS because lower bias was considered more desirable than the possible lower variance of OLS. The ZSLS model utilized here was also used by McKillop (1967). Talhelm and Holland (1971), however, used 3SLS. TWO STAGE LEAST SQUARES OPERATION The particular statistical operation of ZSLS utilized in this study is adequately described in Ruble (1969) and in more general form in numerous econometric texts (e.g. Wonnacott and Wonnacott, 1970, 28 pp. 355-364; Goldberg, 1964, pp. 329-336). Conceptually, ZSLS involves the application of OLS in two sequential steps. In the first stage, the endogenous variable on the right-hand side of the equation (lumber price Y) is purged of its correlation with the residual term by estimat- ing lumber price (Y) as a linear combination of variables not correlated with the residual. This purge is accomplished by regressing lumber price on a number of exogenous variables called instruments. If the number of instruments exceeds the number of sample observations, we have a completely deterministic situation where Y = Y just as always the case in such a situation with OLS. Therefore, the first stage would accomplish nothing and the final estimates from the ZSLS process would be identical to the OLS estimates of the second stage alone (Ruble, 1968, p. 105). To bypass this difficulty, a subset of instruments was selected which did not exceed the number of observations. The instruments in this subset were selected on the basis of including exogenous variables which have the most direct effect upon lumber price (Fisher, 1965, p. 627). Therefore, exogenous variables from the particular supply and demand equation for the species in question were used as instruments in the first stage estimation of lumber price of that species. In the second stage, since the replacement of Y by Y leaves only one variable (lumber quantity) correlated to the residual and thus removes the objection to using OLS, OLS is applied to the adjusted set of variables, 29 adjusted in that Y replaces Y. It is the second stage that produces the structural coefficient estimates presented in the next chapter. INITIAL REQUIREMENTS OF COMPLETENESS AND IDENTIFICATION By using subsets of instruments in the first stage, the ZSLS model is actually applied to a number of subsystems of the lumber in- dustry as described in Figure 4. Since each subsystem contains two equations, a single supply and demand function for a single species, and two unknowns, the appropriate lumber quantity and price, each sub- system is complete in a statistical sense. Observations of lumber consumption are used in the estimation process to represent both the quantity demanded and supplied. Simi- larly, observations of the market equilibrium price are used to repre- sent both the supply and demand price. In short, we have only a group of price-consumption points from which we must estimate two equations which are properly identified as supply and demand functions rather than some cross between the two (Wonnacott and wonnacott, 1970, pp. 172- 189). Two conditions are required for identification (Goldberger, 1964, p. 316). First, there must be as many predetermined variables excluded from a particular equation E1 which are included in other equations in the same equation subset as there are endogenous variables on the 30 right-hand side of the equation E1. By this condition each equation in the lumber industry model constructed here is over-identified by having more excluded predetermined than endogenous variables on the right side. Over-identification reduces to exact identification in the ZSLS operation, however, and causes no statistical problems (Wonnacott and Wonnacott, 1970, p. 190). Second, the predetermined variables excluded from each equation E1 must in reality be excluded. That is their true coefficient in E1 is zero. Initial inspection based upon economic logic suggested this condition was met. When this condition was later tested during equation estimation by an F statistic developed by Basmann (1960), the initial conclusion was substantiated. The null hypothesis that the coefficients were zero in respective El's could not be rejected in any equation at the 10 percent alpha level. Given that each subsystem containing a single supply and demand equation is statistically complete, and both identification conditions are fulfilled, it is possible to proceed with equation estimation and investigation for the presence of statistical problems. SERIAL CORRELATION AND MULTICOLLINEARITY One potential statistical problem is serial correlation among residuals of an equation. The presence of serial correlation results in unbiased coefficient estimates but the estimated variance 31 underestimates the true variance (Wonnacott and WOnnacott, 1970, pp. 136-143). If this correlation exists, the statistical framework of the equations must be modified. The Durbin-Watson statistic was utilized to test for the presence of serial correlation and in each case there proved to be no significant correlation or else the tabulated statistic lay in the uncertain range between the critical values of significant and nonsignificant serial correlation. Another potential problem, multicollinearity, is a state of high correlation between the observations of two or more variables, meaning they are not linearly independent and a rather constant relationship exists between their sample observations (WOnnacott and Wonnacott, 1970, pp. 59-63). The statistical problem precipitated by multicollinearity is unbiased but unstable coefficient estimates as reflected in inflated coefficient standard errors. Therefore, addition of an observation slightly different from the consistent relation between observed vari- able levels, or removal of one collinear variable from a group of col- linear variables in an equation may cause coefficient point estimates and standard errors to vary considerably. Along with this statistical problem occurs an information prob- lem of equal severity. If two variables are collinear, ". . . it becomes very difficult, if not impossible, to disentangle their separate influ- ences and obtain a reasonably precise estimate of their relative ef- fects" (Johnston, 1963, p. 201). Although this multicollinearity 32 condition does not allow us to measure the independent relationship between collinear variables and the quantity supplied or demanded, this does not constitute an information loss. In fact, the entire problem is the lack of initial information. No analytical method can very well estimate independent relationships if no observations are supplied which demonstrate independent actions. Removal of all collinear vari- ables but one does not overcome this information difficulty either. The coefficient of the retained collinear variable represents not only the effect of a one unit change of the retained variable but also the associated change of excluded collinear variables which occurred in the sample observations. Therefore, to the extent that multicollinearity occurs, we find ourselves faced with one of the most serious restric- tions to the application of regression analysis results. Statistical confidence on the estimated model is measured only over the data range utilized in estimating the system structure, whether the data range in question is the range of observed levels of independent variables or the observed range of variable correlations. There is no desirable solution to the multicollinearity problem if selective data transformations fail to remove collinearity. In this study transformations did fail. This problem was met by removing from the equation all but one variable of a collinear group such that all variables in each equation are independent of each other but one variable represents the associated effect of a collinear group. This 33 provides for a stable coefficient estimate of the collinear group rela- tionship to endogenous variables and allows a simpler equation that gives as much statistical explanation of the endogenous variable move- ments as an equation containing collinear variables. Properly identifying the actual incidence of multicollinearity is difficult. Since in reality we deal with varying degrees of collinear interactions, the question comes to selecting those variables that introduce more harm from standard error inflation and thus coefficient instability than help from reduction in unexplained variation of the endogenous variable. Three partially reinforcing criteria of identify- ing multicollinearity were applied to variables found in the same equa- tion. In the first step, one of a pair of variables was excluded from further analysis if the simple correlation, r, between the two was above approximately .95. This rejection was conditional upon their economic equivalence, however. If both were somewhat equivalent, such as medium family income and per capita income (r = .99), one was dropped. If the economic relation was much more indirect, such as sawmill wages and establishment size (r = .95), both were retained for further study. Factor analysis was applied as a second tool to identify multi- collinear variables. One of a pair of variables was excluded as being collinear if both had a high loading in one factor such as .90 or higher and neither had a moderate loading such as .25 or above in other factors. 34 In the third test, variables not excluded as being collinear by their simple correlations or factor analysis were combined in test run equations. Variables suspected of being collinear were then sequentially removed and the structural relations re-estimated. The presence of multicollinearity was identified by a small decrease in the equation's R2 (coefficient of determination) associated with a substantial de- crease of the standard errors of other variables. A small change in R2 indicates that the removed variable adds nothing to the reduction of unexplained variation not already accounted for by other variables. The associated decrease of standard errors does signal that the variable was collinear, however, and not just non-significant, which a small decrease in R2 might also indicate. Certain rather important policy variables as well as variables usually used to depict the system had to be removed by test run screen- ing. For example, the number of households, construction wages, and median family income were excluded as collinear to softwood plywood price in the Southern pine and "structural species" secondary demand level equation. Similarly, British Columbia lumber production, sawmill wage rate, and sawmill productivity were excluded from the "structural species" primary level supply function because of collinearity with sawmill establishment size. It is readily admitted that the application of the above three collinearity tests involves considerable judgment, especially the equation 35 test runs. The results showed, however, that a less conservative appli- cation of the more objective factor analysis alone would have removed about the same variables removed by the above three step sequence. The results also indicate that either the factor analysis or the test run screening is superior to a simple correlation rejection level alone, especially a high simple correlation level such as the .98 employed by McKillop (1967, p. 35). For example, British Columbia lumber produc- tion and Pacific region sawmill establishment size have a simple corre- lation of only .92. Yet when the British Columbia lumber production is excluded from an equation containing Pacific sawmill establishment size and other basic variables in the Douglas—fir primary supply func- tion, there is sufficient multicollinearity to cause a drop of the establishment size coefficient standard error from 5.4 to 2.7 (50%) while the R2 dropped less than 0.1%. Whether this indicates sufficient collinearity to warrant exclusion of a variable is certainly a matter of judgment. In this study it was judged sufficient evidence to warrant removal, however, and British Columbia lumber production was excluded. VARIABLE S IGN IF ICANCE Variables retained through the multicollinearity exclusion pro- cess were then subjected to a test of significance. If it could not be shown that there was at least a 70% probability that the estimated 36 coefficient sign was in fact the true sign, as measured by a one tail Student t test, the variable was excluded from the equation. Variables on the supply side removed through this process included work stoppages in sawmills and transportation industries, precipitation level in the Pacific Northwest or its squared transformation, and electricity price. Similarly, cross tie and rail car consumption were excluded on the demand side from the Douglas-fir and "structural species" equations. Since the calculated t value is derived from the ratio of estimated coefficient over the standard error of the coefficient estimate, and since the coefficient is only asymptotically unbiased, any test of significance on the ZSLS estimates are subject to bias. The extent of this bias is undeterminable but since the t test removed those variables which eco- nomic logic also judged relatively unimportant, the test provides information which the author felt sufficient to act upon. MISSPEC IF ICATION 'Anytime variables are not included in an equation, for whatever reason, there is the potential that model misspecification will result. If the excluded variable Xl has any independent explanatory power not already included in the equation, the relationship of both the excluded variable and some included variable X2 to the endogenous variable may be partially and erroneously attributed to the included variable alone 37 (WOnnacott and Wonnacott, 1970, pp. 71-75). Therefore, exclusion may result in biased coefficient estimates and increased standard errors. Misspecification may have been introduced into this study at three points: original exclusion, multicolinearity exclusion, or ex- clusion due to non-significance. Some important variables may have been originally excluded due to data unavailability but because of the system representation used in this study their impact should be minimal. Variables excluded due to multicolinearity or non-significance were excluded on the basis that they had no individual importance but multicolinearity and significance are themselves continuums such that any exclusion will remove some explanatory power. Because of the ex- tensive colinearity testing and low significance level utilized for exclusion, however, the amount of misspecification resulting from these should be minimal. TCHAPTER IV RELATIVE IMPORTANCE OF SUPPLY AND DEMAND SHIFTERS The method discussed in Chapter III was applied to the industry representation outlined in Chapter II using specific data series found in Appendix A. As noted earlier, two demand functions were developed for each species definition, one using the variables which monitor the consumption level of lumber using markets (primary demand determinants), and one using the supply and demand determinants of these lumber product consumption levels (secondary demand determinants).' Similarly, two supply equations were estimated for each species definition. One was estimated from parameters of domestic production, foreign supply, and sawlog competition (primary supply determinants), and a second was estimated from the same as the first with sawlog price replaced by its stumpage sector determinants (primary + secondary determinants). In this chapter results will be presented which pertain to the second study objective, that of judging the relative importance of system parameters as supply and demand function shifters. This will be accomplished by presenting the estimated equations along with associated significance levels and elasticities of particular variables. 38 3 9 ESTIMATED EQUAT IONS Tables 1 through 4 contain the structural coefficient estimates for each equation along with various statistical parameters of the estimates. Each variable is immediately followed by a code identifying the exact data series and description in Appendix A and B. The struc- tural coefficients represent the estimated change in quantity demanded or supplied associated with a one unit change of the variable in ques- tion while holding all else constant. This definition is modified to the extent multicollinearity is present, as discussed in Chapter III. Each coefficient estimate is characterized by three parameters. First, the calculated t value, equal to the coefficient estimate over the standard error of the coefficient estimate, is in the column follow- ing the coefficient. Second, the next column shows the probability of certainty that the sign of the estimated coefficient is the true sign as measured by a one-tailed Student's t test. Third, the last column in each table registers the plus-and-minus band corresponding to a 90 percent confidence interval around the estimated coefficient, and is the range within which we can be 90 percent confident that the true value lies. Similar to the statistical parameters of the coefficient esti- mate, each equation described in Tables 1-4 is also characterized by its 2 . squared multiple correlation coefficient, R , the calculated Durbin-Watson 40 serial correlation statistic, and the percentage significance level at which the Basmann phi ratio null hypothesis that the equation is iden— tified can be rejected. The signs of the estimated coefficients can be classed in three groups. The first group, and by far the largest, contains variables which monitor relatively single natured phenomenon and carry the "cor- rect" or expected sign. Second, there are variables which monitor two or more opposing forces and the sign indicates which force is overrid- ing. Third, there are several estimates that do not seem to exhibit correct signs but were stable in combination with many other variables and had significant t tests. It is important to remember that these equations were esti- mated from annual observations from 1947 through 1970. As such, the estimated relationships mirror somewhat of an "average" of the system structure as that structure existed and changed throughout the sample period. To use these results as an exact statement of what existing parameter interrelationships are requires that reality coincide with several very restrictive assumptions concerning such things as data ranges and continuation of sample period multicollinearity. Even these "average" estimates provide some statistical information, however. Observed lumber consumption, Appendix A series E5, E9, and E27 for the respective species groups, was used to represent both lumber quantity supplied and demanded during equation estimation. 41 Primary_Demand Level Variables Most of the coefficients estimated for the primary demand deter- minants, Table l, were comparable to what economic logic would dictate. The Douglas-fir demand equation shifts to the right as the volume of residential construction increases. However it shifts to the left as more multi-family structures are started and as the volume of maintenance and repair increases. These negative signs perhaps indicate that both provide substitutes for full scale new single family dwellings and thus represent net demand decreases at the same price. The volume of resi- dential construction and the multi-family structure index in the Southern pine function are opposite of what they are in the Douglas- fir equation and opposite of what economic logic dictates. One explan- ation in the face of the highly significant and stable estimates is that there is greater substitution of Douglas-fir for Southern pine in the lumber market during construction booms. This is somewhat incon- sistent with the positive Southern pine housing start coefficient, how- ever. The residential construction signs in the "structural species" are the same as in Douglas-fir demonstrating that the dominate effect upon a larger lumber aggregate which incorporate close species sub- stitutes is as expected. 42 TABLE l.--Statistical characteristics of the primary demand level equations for lumber, by species group. m Variable . . . . . 99% codea Variable Coeffic1ent t ratio % Slg. confidence interval Douglas—firb E38 Douglas-fir price 2.4589 0.2164 -- 19.6433 Constant 8605.1898 6.1547 99 2417.4035 Dl Vol. resid. constr. 0.2188 4.9584 99 0.0762 D3 % starts with 3 or more dwelling units -10583.0652 -8.6464 99 2116.2591 D4 Vol. maint.+ repair -0.2733 —1.8394 95 0.2569 Southern pineC E39 Southern pine price 33.8991 1.8864 95 31.2683 Constant 943.3706 0.8007 75 2050.0753 D1 Vol. resid. constr. —0.1858 -3.2920 99 0.0981 D2 Dwelling starts 3.1170 5.9419 99 0.9128 D3 % starts with 3 or more dwelling units 2249.0318 3.0173 99 1296.9554 D9 No. cross ties 0.0331 1.1064 80 0.0520 D10 No. box cars 42.5179 5.1943 99 14.2427 Structural speciesd E40 Structural species price -3.l747 -0.ll37 -- 48.5879 Constant 19209.9714 5.5922 99 5977.1778 D1 Vol. resid. constr. 0.2973 2.1579 97.5 0.2397 D2 Dwelling starts 2.0102 0.9674 80 3.6157 D3 % starts with 3 or . more dwelling units -13515.7859 -4.1238 99 5702.8028 D4 Vol. maint. + repair -O.8154 -2.3989 97.5 0.5914 D5 Vol. non-resid. constr. 0.0929 1.0995 85 0.1470 aThe variable code pertains to the codes in Appendix.A and B. bSquared multiple correlation coefficient = .8272; Durbin-Watson 7 statistic = 1.90; Basmann phi ratio = cSquared multiple correlation coefficient = statistic = 2.52; Basmann phi ratio = dSquared multiple correlation coefficient = statistic = 2.35; Basmann phi ratio = .355. .937. .7243; .722. .9670; Durbin-Watson Durbin-Watson 43 Secondary Demand Level Variables Of the secondary demand level estimates, a few represent the net effect of opposing forces but most have straightforward correct signs, Table 2. Softwood plywood registers as a strong lumber substi- tute by the substantial positive shift of demand associated with an increase in plywood price. Likewise, an increase in mortgage rates, as monitored by FHA secondary market yields, curtails demand in all species. The price of building board mirrors two opposing tendencies, one to act as a substitute for lumber in the form of boards and one to act as a complement for lumber dimension stock. Building board is estimated as a net substitute for Douglas-fir lumber and a net comple- ment for Southern pine lumber. Similarly, structural steel is repre- sented as a net lumber substitute in the "structural species" demand equation described in Table 2. One estimate that may be contrary to expected results is the negative sign of the coefficient of the national population mobility variable in the Southern pine equation. If the coefficient does not merely represent a regional situation it seems to indicate that mobile generally people sell one home before buying another instead of vice versa. 44 TABLE 2.-vStatistica1 characteristics of the secondary demand level equations for lumber, by species group. . 90% Variable . . . . . . Codea Variable CoeffiCient t ratio % Slg. confidence interval , b Douglas-fir E38 Douglas-fir price -7.1694 -0.3320 -- 37.5742 Constant —9193.0858 -2.7798 99 5754.3536 D15 No. households 0.1716 2.6457. 99 0.1127 029 Softwood Plywood pr 56.1204 2.6884 99 36.3231 D31 Building board pr 34.5625 1.3916 90 43.2153 D39 Secondary FHA 1% -310.9465 -l.7695 95 305.7667 D55 % families having income $5-10 thou. 115.2325 2.4081 97.5 83.2630 . c Southern Pine E39 Southern pine price 29.2838 0.9827 80 51.8597 Constant 14106.4159 3.3266 99 2378.4607 029 Softwood plywood pr 26.1436 1.7496 95 26.0006 D31 Building board pr -83.2349 -4.5689 99 31.6984 D39 Secondary FHA i% -496.2835 -2.2097 97.5 390.7946 D53 % pop. mobility -220.l648 -l.4300 9O 267.8967 D60 % pop. age 0-24 as ' household heads 332.9874 0.6880 70 842.0465 a . . The variable code pertains to the codes in Appendix A and B. Squared multiple correlation coefficient = .8219; Durbin-Watson statistic = 2.21; Basmann phi ratio = .213. CSquared multiple correlation coefficient = .9134; Durbin-Watson statistic = 1.99; Basmann phi ratio = .495. Table.2.—-Cont. 45 90% V ' bl aria e Variable Coefficient t ratio % sig. confidence Code . interval Structural Species E40 Structural species price 31.9760 0.7008 75 79.3875 Constant 4997.5322 1.2530 85 6939.9249 D29 Softwood plywood price 60.9376 1.9735 95 53.7265 D30 Structural steel price 1446.6995 3.4389 99 731.9953 D39 Secondary FHA i%. -896.1964 -l.8601 95 838.3123 D60 % pop. age 0-24 as household heads 1397.4660 1.5758 90 543.0427 D28 Change mfgt index 39.4566 1.0541 80 65.1316 Squared multiple correlation coefficient = .6496, Durbin-Watson statistic = 2.57; Basmann phi ratio = .269. 46 Primary Supply Level Variables The results of the primary supply level equations given in .Table 3 present some of the most interesting and most perplexing re- sults. Sawmill establishment size, to which productivity and wage rate variables were previously found to be colinear and therefore were excluded, carries a positive sign. This is expected since an increase in establishment size probably corresponds to more efficient produc- tion, more advanced technology, and therefore lower costs. Interest- ingly, the magnitude of the establishment size coefficient is one-third as large in the Douglas-fir equation as in the Southern pine equation probably resulting from the relatively smaller and more inefficient mills located in the South. The peeler log price variable in the Douglas-fir equation is intended to monitor the pressure of the plywood industry at the peeler log-sawlog margin. The average peeler log price can change for at least two reasons. First, if there is a relative increase in demand of plywood over lumber, the peeler-sawlog margin of profitability will shift to lower size and quality logs. The average peeler log price may decrease, however, if the lower cost logs added to the peeler log price average outweigh the effect of the price increase for larger size and quality logs. Second, technological advances which allow profitable utilization of smaller peeler logs can increase the input 47 TABLE 3.--Statistica1 characteristics of the primary supply level equations for lumber, by species group. - 90% Vagggzge Variable Coefficient t ratio % sig. Confidence interval Douglas-fir E38 Douglas-fir price 145.9743 6.0918 99 41.8385 Constant -17018.3280 -4.6583 99 6378.6972 S6 Average sawmill size 10.8698 4.0083 99 4.7349 819 Douglas-fir sawlog price -231.4199 -4.6566 99 86.7714 826 U.S./Canada money exchange rate 71.2235 3.1451 99 39.5390 852 Douglas-fir log export -4.7912 -3.1084 99 2.6912 S55 Douglas-fir peeler log price 27.4736 2.2675 97.5 21.1554 T3 Lumber rail rate 7970.5809 4.0907 99 3402.0088 Southern PineC E39 Southern pine price 97.8272 4.6604 99 36.5245 Constant 11562.9997 3.2663 99 6159.7432 S7 Average sawmill size 30.8986 1.4643 90 36.7152 823 Softwood chip residue, South -0.4541 -1.8827 95 0.4196 825 Lumber tariff 343.1870 0.8661 80 689.4736 526 U.S./Canada money exchange rate -68.3921 -1.9055 95 62.4517 SS7 Southern pine pulp- -619.679l -2.3014 97.5 468.5249 wood price a ' . ‘ ' . . The variable code pertains to the codes in Appendix A and B. b . Squared multiple correlation coefficient = .9183; Durbin-Watson statistic = 2.76; Basmann phi ratio = Q .709. C . . . . . Squared multiple correlation coeffiCient = .8982; Durbin—Watson statistic = 2.19; Basmann phi ratio = .120. 48 Table 3.--Cont. , 90% Va:::::e Variable Coefficient t ratio % sig. Confidence interval Structural Species E40 Structural species price 237.3802 5.7602 99 71.9538 Constant 4233.2588 0.5857 —- 12618.6894 520 Softwood sawlog price -12.4818 -1.8103 95 117.1670 826 U.S./Canada money . exchange rate 144.8248 2.1118 95 119.7373 828 B.C. lumber prod. 1892.9390 5.4928 99 601.7142 SS3 Softwood log export -0.5138 -1.0737 95 0.8354 858 Softwood pulpwood ' price -243.9394 -2.2197 97.5 91.8798 T3. Lumber rail rate 3863.6176. 0.9052 80 7453.3297 Squared multiple correlation coefficient = .7846; Durbin-Watson statistic = 2.61; Basmann phi ratio = .629. 49 .of smaller logs. At the same time the price of high quality peeler logs may even decline if plywood demand is constant. Therefore, it is pos- sible.and even probable that a decline in the average peeler log price is associated with increased pressure upon the sawlog market and thus will cause a negative shift of the lumber supply function. The esti- mated peeler log coefficient is consistent with this logic. A similar situation occurs in the case of the volume of chip residues from Southern pine sawmills. The sale of chip by-products increases the profitability of lumber production from lower quality and smaller logs, which would exert a positive shift of the supply function. If the sawmills actually chip what was once cut for lumber, however, a negative shift of the supply function would occur. This would occur when mills chip low grade lumber, either because the lumber market is weak or because the mill can use a larger percentage of its operating time producing more profitable high grade lumber. According to the estimated Southern pine supply equation, there is a 95 percent certainty that a net decrease in lumber supply is associated with an increase in chip production. Three primary supply level variables have signs contrary to those expected by economic theory: U.S./Canadian money exchange rate, lumber tariff rate, and rail transportation cost. The exchange rate and tariff rate should carry opposite signs in the Douglas-fir or "structural species" function than they do in the Southern pine 50 equation. The estimated signs are of the opposite sign in the Southern pine equations but in all three equations the signs are contrary to the expected. Since the variable signs and significance levels were con- sistent under numerous test runs and transformations, they could not be discarded. Similarly, the railroad cost variable should have a negative rather than a positive sign yet the estimate was positive whether it was included on the supply or demand side of the model. Primary + Secondarquupply Level Variables When the sawlog price was removed from the primary supply level equations and replaced by the stumpage sector determinants of sawlog price, the few variables which successfully faced the multicolinearity tests had estimated coefficients with correct signs. 'As shown in Table 4, increased Forest Service timber sales and money spent on timber access roads both shift the supply functions to the right. An increase in the stumpage price from Forest Service timber sales, a variable which is perhaps less immediate than the stumpage price of the species itself but a more interesting policy variable, causes a shift of the supply function to the left. That is,the coefficient of the stumpage price variable is negative meaning that quantity supplied at the same lumber price is less as stumpage price increases. The individual species stumpage price variables were excluded because they proved 51 TABLE 4.--Statistica1 characteristics of the primary + secondary supply level equations, by species group. , 90% Variabie. ' Variable Coefficient t ratio % sig. Confidence Code . interval , b Douglas-fir E38 Douglas-fir price 87.6556 4.9877 99 30.6850 Constant -7450.4051 -2.7456 99. 4737.8979 826 U.S./Canada money exchange rate 46.7869 1.9441 95 42.0194 852 Douglas-fir log export —5.7849 -4.0387 99 2.5009 555 Douglas-fir peeler log.price 21.2742 1.4324 90 25.9317 T3 Lumber rail rate. 1856.5470 1.0026 80 3233.0605 $38 F.8. stumpage price -81.7334 -3.3066 99 43.1581 839 Road cost 6.8788 1.6403 90 7.3218 Southern PineC E39 Southern pine price 103.9045 5.2424 99 34.6058 Constant 14875.4913 3.8204 99 6798.4551 S7 Average sawmill size 42.5821 1.9896 95 37.3692 823 Softwood chip residue, South -0.7560 -2.6346 99 0.5011 825 Lumber tariff 431.9187 1.1377 85 662.8442 826 U.S./Canada money . exchange rate -92.8521 -2.5682 97.5 63.1259 SS7 Southern pine pulp- wood price -886.8S88 -3.0162 99 513.3748 530 F.S.”region 8 timber sales ' 3.1913 1.9393 95 2.8732 a . . . The variable code pertains to the codes in Appendix A and B. b' , , , Squared multiple correlation coeffiCient = .8823; Durbin-Watson statistic = 2.37; Basmann phi ratio = .281. c . . . . Squared multiple correlation coeffiCient = .9134; Durbin—Watson statistic = 1.95; Basmann phi ratio = .849. Table.4.--Cont. 52 , 90% Va::::le Variable Coefficient t ratio % sig. Confidence interval Structural Species E40 Structural species price 247.1900 6.2620 99 68.9230 Constant 5043.972? 0.9771 80 9013.4028 826 U.S./Canada money exchange rate 130.5845 2.6561 97.5 85.8391 828 B.C. lumber prod. 1542.3198 4.0704 99 661.5868 SS3 Softwood log export -1.1580 -2.2230 95 0.9094 558 Softwood pulpwood price . -287.0258 -3.5637 99 140.6256 S38 F.S. stumpage price -lll.2927 -2.4221 97.5 80.2281 839 .. -Road cost 16.5977 1.1155 85 25.9782 d . Squared multiple correlation coefficient = .8207; Durbin-Watson statistic = 2.68; Basmann phi ratio = .296. 53 non-significant. Lack of structural significance probably lies in the poor quality of the time series data on species stumpage prices. It seems that, at least for estimated coefficient signs, it can be safely stated that the estimated equations are about what economic logic would dictate. There is little basis on which to judge coeffi- cient magnitudes, however. ESTIMATED ELASTICITIES OF INDIVIDUAL SHIFT VARIABLES Even though the significance levels in Tables 1 through 4 give some information relevant to the objective of judging the relative importance of function shifters, coefficient estimates must be pre- ,sented in some standardized unit of measure before their relative im- portance can be readily judged. The measurement used for standardiza- tion in this study is elasticity. Elasticity is the percent change of the quantity of lumber supplied or demanded associated with a one per- centage increase in the exogenous variable of concern, ceteris paribus. For example, a demand price elasticity of -0.2 means that quantity de- manded decreases 0.2 percent for every 1.0 percent increase in lumber price. See Appendix E for the method used in calculation. The elasticity estimates were calculated using the arithmetic mean of lumber consumption and the variable in question over the sample observation period on the presumption that they are closest to "normal" 54 levels. As such, the elasticity estimates are somewhat of the average ,of.1947-70 levels. Although no significance levels are presented in the.following elasticity tables, Tables 5 through 10, the probability levels in the above Tables 1 through 4 concerning coefficient signs are applicable to the same null hypothesis concerning the sign of the elas- ticity estimate. That is, if the coefficient estimate for variable D1 in Table l is significantly different from zero at the 99 percent con- fidence level, so is the corresponding elasticity estimate. Elasticity provides unit standardization but, because variables exhibit considerably divergent average annual percentage changes, cal- culated elasticities may not monitor the average relative impact between variables. To demonstrate this aspect of relative importance, the arithmetic mean of absolute annual percentage changes in the level of each exogenous variable over the sample period was determined. The elasticity estimate derived from the 1947-70 sample was then multiplied by this mean absolute annual percentage change to derive the average percentage change in lumber quantity supplied or demanded associated with movements of the variable in question. Thus, in each elasticity table three values are shown for each variable: the elasticity, the average absolute annual percentage change, and the average annual per- centage impact on lumber quantity due to the mean sample period changes of the specific variable. 55 Demand Variable Elasticities As shown in Tables 5 through 7, the elasticity of all variables included in the final demand equations were inelastic, having a value of less than unity. This is contrary to the results of McKillop's (1967, p. 46) softwood lumber demand equation where over half of the variable elasticities were greater than unity. The secondary demand variables display higher elasticity estimates on the average (elasti- city, e = 0.39) than do the primary demand level variables (e = 0.26). This tendency is much more pronounced in the Douglas-fir and Southern pine equations than the "structural species" demand equations but per- sists throughout. Because of higher absolute average percentage changes, however, the average percentage impact upon quantity demanded of primary demand level variables (average absolute percentage impact, aapi = 3.04) is greater than secondary level variables (aapi = 1.76). Therefore, while there are exceptions, it seems that changes in the consumption level of individual lumber-using products exerts more impact upon lumber demand than do the specific supply and demand factors that determine the consumption level for these lumber-using products. Multiplication of elasticities by the average percentage change also allows for ready identification of the most important individual variables. The value of residential construction is associated with greater shifts of the lumber demand functions than any other lumber 56 TABLE 5.--Elasticity and percentage impact estimates for Douglas-fir lumber demand function shifters. Variable , , , Avera e Avera e a Variable ElastiCity g , 9 Code a. % change % impact Primary level: D1 Volume of residential construction 0.5087 9.85 5.01 D3 % starts with 3 or more dwelling units -0.2417 16.44 3.97 D4 Volume of maintenance and repair -0.1874 6.07 1.14 b absolute average 0.3126 3.37 Secondary level: D15 Number Households 0.9112 2.09 1.90 D29 Softwood plywood price 0.5328 7.49 3.99 D31 Building board price 0.2857 2.72 0.78 D39 Secondary FHA % yields -0.1764 5.55 0.98 D55 % families having income of $5-10 thousand 0.4803 3.08 1.48 b absolute average 0.4772 1.83 3- . . The variable code pertains to the codes used in Appendix A and B to identify data series. b The arithmetic mean of the absolute elasticity and average annual percentage function shift. 57 TABLE 6.--Elasticity and percentage impact estimates for Southern pine lumber demand function shifters. Variable. . . , Avera e Avera e a Variable ,. . ElastiCity g , g Code . % change % impact Primary level: D1 Volume of residential construction -0.5843 9.85 5.76 02 Number of dwelling starts 0.6348 10.68 6.77 D3 % starts with 3 or more dwelling units 0.0694 16.44 1.14 D9 Number of cross ties installed 0.1118 7.84 0.88 D10 Number of box cars installed 0.1282 47.18 6.05 b absolute average 0.3057 4.12 Secondary level: D29 Softwood plywood price 0.3394 7.49 2.54 D31 Building board price -0.9286 2.72 2.52 D39 Secondary FHA % yields -0.3813 5.55 2.12 D53 Percent population mobility -0.6000 3.65 2.20 D60 Percent population ages 0-24 as house- hold heads 0.1569 4.93 0.77 b absolute average 0.4817 2.03 a . . . . The variable code pertains to the codes used in Appendix A and B to identify data series. b . . The arithmetic mean of the absolute elastiCity and average annual percentage function shift. 58 TABLE 7.--Elasticity and percentage impact estimates for "structural species" lumber demand function shifters. Average Variable , , . Average a Variable ElastiCity , . Code .%_change % impact Primary level: 01 Volume of residential construction 0.3081 9.85 3.03 D2 Number of dwelling units. 0.1349 10.67 1.44 D3 % starts Wlth 3 or more dwelling units -0.1376 16.44 2.26 D4 Volume of maintenance and repair -0.2493 6.07 1.51 D5 Volume of non-residential construction 0.0705 8.21 0.58 absolute average 0.1800 1.76 Secondary level: 029 Softwood plywood price 0.2579 7.49 1.93 030 Structural steel price 0.3546 3.90 1.38 039 Secondary FHA % yields -0.2267 5.55 1.26 060 Percent population ages 0-24 as household heads 0.2169 4.93 1.07 028 Change manufacturing activity 0.0082 absolute average 0.4817 2.03 a . The variable code pertains to the codes used in Appendix A and B to identify data series. b . . The arithmetic mean of the absolute elastiCity and average annual percentage function shift. 59 product demand level variable except for the multi-family building index in the Southern pine equation. The price of softwood plywood (aapi = 2.12) as a substitute for lumber is evidently the most impor- tant secondary demand variable affecting lumber demand. Softwood ply- wood is especially important in the Douglas-fir equation (aapi = 2.54), demonstrating that a sheathing substitute has more impact upon Douglas- .fir than it does upon its Southern pine lumber substitute. This dif- ference in plywood elasticities is consistent with the estimation that building board (a sheathing substitute) is a net substitute for Douglas- fir lumber but a net complement for Southern pine lumber. The reason . for this may be the nature of residential construction in the regions served by the Douglas-fir and Southern pine lumber industries respec- tively and the end use differences of the two species, but very little data are available to substantiate this. FHA secondary market yields have only moderate to low impact upon the overall demand level (aapi = 1.45), as does the change in household headship rates in the 0-24 age class (aapi = 0.92). Beyond this, no general groupings are readily apparent. Supply Variable Elasticities The estimated elasticity of supply variables shown in Tables 8 through 10 averaged higher (average primary e = 0.58 with four above 60 TABLE 8.--Elasticity and percentage impact estimates for Douglas-fir supply function shifters. Variable Variable Elasticit Average Average ~Codea . ‘ y % change % impact Primary level: 86 Average sawmill size 0.4550 4.90 2.23 519 Douglas-fir sawlog price -1.3866 5.49 7.61 526 U.S./Canada money exchange rate 0.7161 1.64 1.17 552 Douglas-fir log export volume -0.0455 56.57 2.57 SSS Douglas-fir peeler log price 0.2782 5.50 1.53 T3 Lumber railroad rate 1.1371 3.50 3.47 absolute average 0.6697 3.10 Primary i Secondary level: 526 U.S./Canada money exchange rate 0.4704 1.64 0.77 852 Douglas-fir log export volume -0.0550 56.57 3.11 855 Douglas~fir peeler log price 0.2154 5.50 1.18 T3 Lumber railroad rate 0.2648 3.05 0.81 S38 F.8. stumpage price —0.l353 23.17 3.13 539 Timber access road cost 0.0447 22.08 0.99 absolute average 0.1976 1.67 a . The variable code pertains to the codes used in Appendix A and B to identify data series. b . . The arithmetic mean of the absolute elastiCity and average annual percentage function shift. 61 TABLE 9.--E1asticity and percentage impact estimates for Southern pine lumber supply function shifters. Variable , . , Average Average .V abl El t t . . Codea ari e as 1C1 y % change % impact Primary level: S7 Average sawmill size. 0.2986 6.28 1.86 523 Softwood chip residue use, South -0.1426 45.18 6.45 525 Lumber import tariff. 0.0497 7.72 0.38 826 U.S./Canada money exchange rate -0.9303 1.64 1.53 SS7 Southern pine pulpwood price —1.3631 1.82 2.48 absolute average 0.5568 2.54 Primary + Secondary level: S7 Average sawmill size 0.4115 6.28 2.58 523 Softwood chip residue use, South -0.2375 45.18 10.73 825 Lumber import tariff 0.0625 7.72 0.48 826 U.S./Canada money exchange rate -1.2630 1.64 2.07 SS7 Southern pine pulpwood price -1.9508 1.82 3.55 S30 F.8. region 8 timber sales 0.3334 11.64 3.88 absolute average 0.7097 3.88 a The variable code pertains to the codes used in Appendix A and B to identify data series. b The arithmetic mean of the absolute elasticity and average annual percentage function shift. 62 TABLE 10.--Elasticity and percentage impact estimate for "structural species" lumber supply function shifters. Variable. Variable Elasticit Average Average Codea ' y % change % impact Primary level: 820 Softwood sawlog price -0.5674 4.09 2.32 826 U.S./Canada money exchange rate 0.6492 1.64 1.06 528 B.C. lumber production 0.4661 6.38 2.97 SS3 Softwood log export volume -0.0157 36.83 0.58 558 Softwood pulpwood price. -l.1440 2.13 2.44 T3. Lumber railroad rate 0.2457 3.05 0.75 absolute average 0.5146 1.69 Primary + Secondary Level: A 826 U.S./Canada money exchange rate 0.5853 1.64 0.96 828 B.C. lumber production 0.3739 6.38 2.39 S53 Softwood log export volume -0.0354 36.83 1.30 858 Softwood pulpwood price -l.3460 2.13 2.87 S38 F.8. stumpage price -0.0821 23;17 1.90 839 Timber access road cost 0.0465 22.08 1.03 absolute average 0.4115 1.74. aThe variable code pertains to the codes used in Appendix A and B to identify data series. b . . . . The arithmetic mean of the absolute elastiCity and average annual percentage function shift. 63 unity) and showed more variation in magnitude between variables than found in any of the-demand equations. Multiplication by the average percentage change in the variables over the 1947-70 sample period .tended to moderate the average impact and variation between variables, . however (aapi = 2.44). Average sawmill establishment size, which is correlated to average sawmill labor productivity at .92 in the Pacific region and .97 in the Southern region, showed only moderate to low elasticities (e = 0.38) and average percent impact (aapi = 2.04). To the extent that productivity and establishment size monitor many .of the same factors, these results are somewhat contrary to those pre- sented by McKillop (1967, p. 46). McKillop estimated sawmill produc- tivity to have one of the largest elasticities among the supply vari- ables. The tariff rate on lumber imports into the United States ex- hibited one of the lowest elasticities (e = 0.05). The U.S./Canadian exchange rate had moderate elasticities (e = 0.77) but low average percentage impacts (aapi = 1.25) because of its generally stable level. Another international factor, log exports, has low elasticities and moderate to low average impacts (aapi = 1.57). Log exports registered higher importance in the Douglas-fir supply equation (aapi = 2.57) than in the "structural species" function (aapi = 0.58), as might be expected. This relatively minor log export impact as measured by the 1947-70 aver- age runs somewhat contrary to the attention awarded log exports by some 64 analysts concerned with lumber price increases during 1968 and 1969. British Columbia lumber production, a proxy for lumber import pressure, has a relatively large elasticity (e = 0.47) and very large average impact (aapi = 2.97) upon the "structural species" supply, the only equation in which it was retained due to multicollinearity in other equations. Perhaps the most interesting supply elasticity results concern the raw material factors in the lumber market system: sawlog prices, pulpwood price, peeler log price, stumpage price, and chip residue recovery. As a group, they average quite high elasticities (e = 0.64) and even higher relative average annual percentage impacts (aapi = 3.5). Sawlog price is one of the most important shift variables of this raw material group and of all the supply variables. The Douglas-fir supply function is more susceptible to changes in the log price (aapi = 7.61) than the "structural species" supply (aapi = 2.32), a difference pos- sibly due to a relatively more inelastic log supply function for Douglas-fir than "structural species" logs. Similarly, pulpwood factors exhibit high importance (aapi = 2.46) indicating that sawlog availability is receiving substantial pressure at the sawlog-pulpwood margin of log size and quality; more pressure than at the peeler log- sawlog margin (aapi = 1.53). In summary, results indicate that the consumption levels of lumber using products are relatively more important as lumber demand 65 .shifters than are the more indirect supply and demand determinants of those.consumption levels. The value of residential construction and the price of softwood plywood showed the greatest importance as demand function shifters. 0n the supply side average establishment size, log exports, lumber tariffs, and U.S./Canadian exchange rate have an esti- .mated moderate to low impact. Raw material factors, especially sawlog price and pulpwood variables, exhibit relatively greater importance as supply function shifters as does the British Columbia lumber production level. ESTIMATED PRICE ELASTICITY ESTIMATES The elasticity of the lumber price variable is interpreted the same as the elasticity of the shifter variables. Price elasticity is the percentage change of the quantity of lumber supplied or demanded associated with a one percent increase in lumber price, ceterbis paribus. These are calculated at the arithmetic mean level of lumber consumption and price over the 1947-70 sample period just as they were for the shifter variables. Price elasticities so calculated are recorded in Table 11 along with a 90 percent confidence interval band for each point estimate. 66 ammm. msam. mmmm. sadism mmHN.H mqmm.H «mom.o sumscoomm + sumsaum nqmm. moqm. Amos. Nona.a amoe.a vao.H shadow sumshum «Ham. amps. omae. oemfl. mama. Hmno.u camsmo sumocoomm mmmm. meme. moan. omao.u whom. ammo. wcmams sumsflum .H.o mom .sumoaummam .H.o mom sunoaummao .H.o mom sumoflummam . . . Hm>ma coflumsvm =mmflommm Amusuosuum: mcflm cumnusom MHMImmHmsoo .Ucmewp can hammdm Hmnfida :mmflommm HMHSDUSHUm: cam mcfim cumcusom .Hflmsmmamsoo How mwumeflumm wufloflummHm woflumll.aa mqm msosmmoxo can woflum HmQEsH map >3 How pmucsooom cmosmfimc wuflusmsq HmnEdH :H coaumflum> mo ammusmouwm on» mmHSmmmE A my COAHMCHEHmumo mo usmfloflmmmoo ones m . . . . . . I . . mfioosa m Ammo mom vHN em H «H mo mmm we mes ms 6m 50 mm . u. =mmaommm amusuonhum= mma. mm.a 6H. em.H mq.ou Hm.mm mv.em mzo mac. mm. Hm. mm.emv mfl.mooau Hm.~m Hm.oea mecca“ mufimmo “mm mafia cumnpsom mac. mm. mm. mo.H ma.vu mm.om 0m.ooH mzo Hoo. mm. vs. ee.mmm em.mmman om.eH . om.am mecca“ «sumac umm “Hulmwamsoo Hoo. mm. we. 6m.o mo.ma mo.ea om.m~ mzo Houum .pum ucmflofimmmoo Houum .vum .usofloammwoo Dana combos wanmflum> ccmamm baabuso m :0 mac mmflommm I m a m . Mm manmflHd> msosmmoxm moflum umnadq xm .msoum mwfiommm ha .muoumoHUCH DAEosoom mmoum means mcowumsvo pcmamp Hmnfisa mo moflumfiumuomnmno HMUflumflumumll.NH mqmme 75 the "structural species" estimates are similar to the secondary demand level estimates. The Douglas-fir and Southern pine price elasticity estimates are very positive, however, which is not surprising since they are not properly identified as demand equations. Similarly, all the exogenous variable coefficient estimates are opposite of their ex- pected signs, probably as a result of the gross missepcification signaled by the very low Rz's. In short, the contents of Table 12 indicate that gross economic indicators alone simply are not adequate for the estimation of demand functions for these lumber species. Hair (1967) was more successful in estimating consumption when he applied gross indicators to quite nar- rowly defined paper products, as is indicated by his Rz's which were in the .90's. McKillop's (1967, pp. 42-47) elasticity estimates show that gross economic variables only have high importance to the exclusion of any other variables having high importance in the paper demand func- tion. In the demand for any of the other wood products the gross eco- nomic variables had lower elasticities. The results of this study in conjunction with McKillop‘s suggest that paper is the only wood product with which Hair could have been successful in estimating narrowly de- fined product class consumption levels with gross economic indicators. CHAPTER V SHIFTS OF THE SUPPLY AND DEMAND FUNCTIONS The results presented in Chapter IV give an indication of the relative importance of various shift variables and the supply response in the one year run. Recall the one year run conclusions were drawn from equations estimated from annual observations from 1947-70 and from certain mean values of the 1947-70 variable levels. Some infor- mation must be presented to show how supply and demand interact before we can tell how these variables affect the actual market equilibrium, however. For example, even an important supply function shifter has no impact upon consumption if the position of demand dominates the consumption level. This chapter is concerned with the relationship between the supply and demand positions as estimated for 1947-70, their relative impact upon the price and consumption levels, and the nature of supply responses to demand shifts. Once this relationship between supply and demand shifts is identified we will have some indication of the supply response over a longer time span than the one year run im- plicit in the previously discussed coefficient estimates. 76 77 ESTIMATION ACCURACY Before moving onto estimation of supply and demand shifts, it is appropriate to find how closely the estimated supply and demand functions can predict the observed 1947—70 lumber consumption and price levels. The only information available so far concerning this predic- tability is the R2 of supply and demand functions which may not indi- cate the accuracy with which the two interact. The 1947-70 coefficient estimates for the secondary demand level and the primary supply level equations for each species were applied to the observed exogenous variable levels in each of the sample years, ti. This gives the level of supply or demand at a lumber price of zero in ti. By use of the estimated lumber price coefficient, it was possible to extend the slope of the two functions from the zero price level until they crossed and thus indicated the estimated lumber price and consumption levels in ti. The percentage error between actual and estimated consumption and price is shown for each of the three species groups for each year of the sample in Table 13. Evidently the equations are fairly accurate since the average absolute consumption error across all three species groups is only 3.2 percent. The average absolute price error is even lower, 2.4 percent. Only one estimated equilibrium error is in excess of 10 percent, that of Southern pine consumption in 1956 with an error 78 TABLE l3.--Percentage error of calculated estimates of price and con- sumption from observed levels of price and concumption for Douglas-fir, Southern pine, and."structural.specdes" lumber. (In Percent) J ——_—— 4 _’ 1——__— L Douglas-fir Southern pine "Structural species" Year .11 price consumption price consumption price consumption 1947 0.19 -0.34 -5.52 -5.79 1.87 -2.08 1948 -0.64 -0.28 -0.81 1.01 -0.59 0.68 1949 1.41 2.66 -2.31 1.86 5.54 7.85 1950 -0.41 0.72 -l.69 -8.49 -0.43 -2.63 1951 3.08 0.73 5.47 6.29 -0.33 1.41 1952 -3.25 -2.75 6.68 1.89 —4.22 -5.51 1953 1.22 1.98 -0.59 7.60 1.92 2.60 1954 -l.52 -1.39 1.57 5.09 -4.31 -4.36 1955 -1.60 -0.71 -2.50 2.13 -3.16 -0.38 1956 -0.26 -2.25 -5.18 -12.71 0.35 -2.22 1957 2.07 7.15 -3.01 -5.96 3.77 5.46 1958 2.65 -0.77 -l.61 -l.49 -2.31 -1.71 1959 -4.82 -8.86 2.27 -4.09 -0.61 -5.02 1960 -l.00 —0.28 -0.95 2.80 -l.00 1.05 1961 2.66 3.09 -2.07 -1.55 2.77 2.79 1962 3.58 1.19 0.75 7.55 3.71 1.92 1963 2.04 8.87 0.87 3.75 -2.19 4.34 1964 -l.37 -3.03 4.42 2.74 -0.62 -1.12 1965 1.88 -0.42 8.10 0.74 3.94 -0.24 1966 -2.77 -2.63 1.94 2.45 -0.49 -0.93 1967 -2.82 -l.69 4.05 4.53 -0.77 -2.13 1968 0.09 -O.22 1.57 5.29 -l.81 -0.36 1969 2.33 5.32 -6.53 —1.33 3.62 6.25 1970 0.62 -2.81 —1.78 -7.96 -2.51 -4.82 t abs°1u e 1.85 2.51 3.01 4.37 2.20 2.74 avg.a a . . The arithmetic mean of the absolute annual percentage errors. 79 of 12.7 percent. There is some tendency for the largest errors to occur at turning points in the trend of demand shifts, especially for Douglas- fir, but there are many exceptions. Perhaps the most interesting results of this accuracy test is . 2 the comparison between percentage error and the R of the supply and . . . . 2 demand equations. Southern pine, which has the highest average R of the supply and demand equations used in this test (.90), has the largest average equilibrium estimation errors (3.69). On the other hand, the . 2 "structural speCies" class has a much lower average R (.71) but lower price and consumption errors than Southern pine (2.47). This indicates 2 . .. that the R of indiVidual supply and demand equations may prOVide little information on the accuracy of equilibrium estimation. CHARACTERISTICS.OF SUPPLY AND DEMAND SHIFTS FOR DOUGLAS-FIR AND SOUTHERN PINE The relationship between the market equilibrium and shifts of supply and demand functions is derived from a study of changes in the estimated quantity of lumber demanded and supplied during each of the sample years at a constant lumber price. This quantity level is pre- dicted by applying the estimated exogenous variable coefficients to the observed level of these variables in each sample year and applying the estimated lumber price coefficient to an assumed $100 per thousand 80 feet board measure (bem). Note that an increase (decrease) of quan- .tity demanded (supplied) at a constant price is directly related to a rightward (leftward) shift of the demand (supply) function. An increase in the quantity of lumber demanded of X bem as it is measured above is synonymous with a shift of the demand function to the right by ..X bem since we have held the lumber price constant. Similarly, a decrease in the quantity of lumber supplied at a constant price is synonymous to a leftward shift of the supply function and vice versa. The tabularized estimates of quantities supplied and demanded at $100/bem are presented in Appendix C. -Doggla59fir Supply and.Demand Shifts The estimated quantity of Douglas-fir lumber demanded at $100/bem, Figure 5, increased until 1955 then decreased at the rate of about 2 percent annually until the 1968 increase. Estimated quan- tity supplied is quite erratic but generally lower than demand at $100/bem through 1956. In 1957 supply shows an increase relative to demand and then decreases similar to demand until 1968. One of the most important pieces of information available here concerns the response of the supply function position to demand function shifts. The supply of Douglas-fir lumber shows a consistent tendency to shift opposite from demand. Douglas-fir supply shifts to the left 81 Billion Board Feet ..L' ' ' ' Demand 10 (L 1 1 L 1 l 1950 1955 1960 1965 1970 Fig. 5.--Estimated Douglas-fir lumber demand and supply at an assumed price of $100/bem, 1947-70. 82 when demand shifts to the right and vice versa. This is indicated by the negative correlation of -0.54 between the estimated percentage shifts of the supply and demand functions. Figure 6 provides a graph of observed year-to-year price and consumption equilibrium in the Douglas—fir lumber market. The graph adequately demonstrates the impact of contrary shifts in supply and demand functions. The connection lines between successive equilibrium have a steeper slope than the estimated slope of the supply function where this slope is equal to the lumber supply price coefficient. Calculation of the estimated exogenous variable coefficients times the observed variable levels during the sample period shows that changes in the sawlog price variable is very heavily associated with these contrary supply function shifts. Ferguson (1969, pp. 247-248) forwards an argument concerning the longer run supply response in an increasing cost industry, one where a rightward shift of the demand function induces increased input costs which cause the supply function to shift to the left. He concludes that the connection lines between successive equilibrium points traces out the longer run supply response of the industry if the equilibrium change is caused by a demand shift and its induced supply shift. Employing this same logic and given the evidence above, it seems plausible to conclude that the longer run supply response of Douglas-fir lumber is less elastic than'the 1.61 estimated in the primary supply level equation. The nature of this Slflfll 140 135 130 125 120 115 110 105 100 95 ? 83 69 I 55 50 52 59 70 47 D l 8 Billion loud root melon 10 Pig. 6.--Obocrvod market oquilihriu points for Douglas-fir labor, 1941-70. 11 12 84 longer run response is indicated by the slope of lines connecting suc- cessive equilibrium points in Figure 6. This is entirely consistent with the lower elasticity estimate of 0.97 from the primary + secondary supply level equation which explicitly contains a stumpage price vari- able and thus internalizes this external pecuniary diseconomy of in- dustry scale. Southern Pine:Supplyyand-Demand.Shiftss The calculated supply and demand positions of Southern pine lumber from 1947-70 at a price of $100/bem are given in Figure 7. The illustrated relationships demonstrate a much different situation than the above discussed Douglas-fir market exhibits. The level of both quantity supplied and demanded gradually decreased, and thus shifted to the left, from 1947 to 1960 at about 3.5 percent annually. Both functions shift to the right during the early 1960's and then decrease more gradually thereafter. The overall trend of Southern pine supply and demand shifts is probably due to a slower rate of second growth removal than existed before 1947 and the increased importance of the plywood and pulp indus- tries throughout the sample period. Year-to-year supply and demand shift relationships are still apparent, however, and are not too clouded by this overall trend. Generally, the supply and demand functions shift 85 Billion Board Feet 12 *- - 2 j I l L l 1950 1955 1960 1965 1970 Fig. 7.--Eetimated Southern pine lumber demand and supply at an assumed price of $100/14m, 1947-70.. 86 in the same direction. There is a +0.39 correlation between the esti- mated percentage shifts of the Southern pine supply and demand func- .tions. As demand shifts to the right so does supply and vice versa. Likewise, the equilibrium connection lines.in Figure 8 have a flatter slope than the one year supply function slope coefficient from the primary supply level equation. This indicates that the longer run supply response is more elastic than the Southern pine primary level equation estimate of 1.46. Comparison of.Douglas-fir and Southern Pine “Longe ‘Run Supply Response One of the most noticeable contrasts between the Douglas-fir and Southern pine lumber markets is the difference in the stability of the supply function. Southern pine supply only averages a 3.34 percent shift annually from 1947-70 while Douglas-fir shifts an average of 5.45 percent annually from 1947-66 even though the drastic 1967-70 Douglas- fir supply shifts are removed from the average. Their price changes, which are dominated by supply shifts, show the same tendency. The 1947-70 average lumber price for the two species is an almost identical $106/bem yet Douglas-fir price has a standard deviation of 9.0 while that for Southern pine is only 6.3. Recall now the three aspects of timber and industry flexibility discussed in Chapter IV. Theoretically, the amount of flexibility Slim- 140r— 135 '- 130 )- 125 r' 120 ’ 115!- 110)- 105 P 1M)- 95'- 69 87 eetimeted elope of the average ammal supply curve 52 50 47 49 l l l ‘ l a a a 9 10 ll Billion Board feet Commune Pig. 13.-W market equilibrim pointe for Southern pine luber, 1947-70. 12 88 should be affected by different ownership distributions, the extent that alternative log markets exist, and by the extent barriers to entry occur. The Southern pine region is more flexible than the Douglas-fir region on all three of these counts, yet there was no apparent effect upon the relative one year run price elasticity estimates for the primary level equations. These flexibility factors may affect the longer run supply re- sponse, however. Given a situation where year-to-year supply shifts occur in response to demand shifts, which is quite logical in a derived demand chain, we have concluded that the connection lines between suc- cessive annual equilibrium positions trace out an approximate longer run supply response. Statistical associations alone do not allow de- ductions of cause.and effect, but we do have a situation here where greater flexibility is associated with a more elastic longer run supply response. Similarly, in the Douglas-fir system the contrary supply response is associated with the sawlog price variable and the primary + secondary level Douglas-fir equation containing a stumpage price variable produces a lower price elasticity estimate. Economic logic indicates that at least part of the low flexibility would produce a less price elastic stumpage supply. A relatively inelastic stumpage supply can precipitate external diseconomies of industry scale and thus a less elastic supply price response. Thus, it is difficult to conclude 89 that a cause-effect relationship does not exist between flexibility factors and longer run supply response. What is difficult to determine is the magnitude of the longer run supply response difference. So far we merely have evidence that the direction of our economic logic concerning the difference between the one year supply elasticity and the longer run response is correctly related to industry and timber flexibility. The problem comes in trying to determine which supply shifts are in response to annual demand shifts alone. Since this determination is quite difficult, perhaps all we can do is use the estimated one year run elasticities as bench marks. The longer run Douglas-fir response is less elastic than the primary level equation estimate of 1.61. It probably falls in the neighborhood of the 0.97 of the primary + secondary estimate since most of the annual supply shift is in response to sawlog price changes. With Southern pine, however, it would appear that the longer run supply response to price is more elastic than the primary level equation estimate of 1.46. The equilibrium line connections indicate that the longer run elasticity may go as high as 2.0. 9O CHARACTERISTICS OF SUPPLY AND DEMAND SHIFTS FOR THE "STRUCTURAL SPECIES" AGGREGATE The "structural species" aggregate overcomes some of the detail problems of species comparisons and presents a larger and quite definite product class for analysis. The estimated quantity of "structural species" lumber supplied and demanded at $100/bem from 1947-70 is illustrated in Figure 9. Estimated demand is quite erratic and fluc- tuates about what seems to be a very gradually declining moving average. The quantity of lumber supplied is also erratic but displays two quite distinct subperiod.sections. From 1947-57 quantity supplied is rela- tively stable.and below quantity demanded at $100/bem. During 1956-58, however, the supply function shifts to the right (quantity supplied increases at $100/bem) without a corresponding shift of the demand function. From 1947-57 supply fluctuates with a range similar to that occupied by the quantity demanded. The impact of this 1956-58 rightward supply function shift relative to the demand curve is readily apparent in the plot of ob- served price and consumption equilibrium, Figure 10. From 1947 through 1957 consumption varied within a range of approximately 19.6 to 24.0 billion board feet and within a rather narrow price band which has about the same slope as the lumber price coefficient of the primary level supply equation. From 1958 through 1964, after the relative shift of supply to the right occurred, consumption falls within the 91 Billion Board Feet l I l I 23 Demand _- A ’ r - I \\ 21 I \__ , ~\ - I \ f\\ l\ I \ ..a/ \ d/ ‘\ I \ - I " \ I \ I V \ 19 ‘ - I ‘ . ‘ I \ I _ | I 17 | l - ‘. I ‘ l ‘ _ l I ‘.I 15 u _ l 1 i 1 II I- III II 1950 1955 1960 1965 1970 Fig. 9.--Estimated “structural species" lumber demand and supply at an assumed price of $100/bem, 1947—70. S/Mfln 140 )— 125 " 115 " 110 " 105 "' 100" 95)- Fiq. lO.--Obeerved market equilibrium pointe for 'etructurel epeciee" labor, 92 ’ eetimated elope of the average annual eupply curve 55 50 47 49 I + l I l l l l l l 19 20 21 22 23 24 25 Billion Board feet Coneumtion 1947-70. 93 same extremes. Lumber price, however, falls in a price band parallel too but lower than the 1947-57 band. This demonstrates that almost the sole determinant of the "structural species" consumption level is placement of the highly in- elastic demand function and that change in consumption levels is domi- nated by demand function shifts. Similarly, the major determinant of lumber price levels is the supply function. Minor price changes result from demand shifts along a stationary and less than perfectly elastic supply function such as the 1.17 elasticity estimated here. Radical price changes only seem to occur in response to substantial supply shifts, however. This is adequately demonstrated by the drastic supply shifts of 1967-70, Figure 9, and the corresponding movement of observed price during the same period, Figure 10. A rather disturbing element of the "structural species" aggre- gate is that the 1965 to 1969 trend is almost diametrically Opposed to the 1947 to 1964 trend. The difference is not in the observation that price changes are dominated by supply shifts and consumption changes are dominated by demand shifts. Rather, a substantial difference is evident in the relationship between supply responses to demand shifts. The estimated percentage supply and demand shifts from 1946 through 1964 show a slightly positive simple correlation, r, of +0.16; The correla- tion between percentages supply and demand shifts from 1965 through 1970 is very negative (r = -0.55). 94 Since the "structural species" group is the sum of the flexible South, the relatively inflexible Douglas-fir region, and a smattering of the moderately flexible Intermountain and Rocky Mountain regions, . we would expect the "structural species" group to exhibit an average between.the contrary Douglas-fir supply and demand shifts (r = -0.52) .and the like shifts of Southern pine (r = +0.39). During the period from 1947 through 1964 this is exactly what happens. The correlation between the percentage shifts of "structural species" supply and demand .at a lumber price of $100/bem is a moderate +0.16. Therefore, supply shifts to the right slightly as demand does such that from 1947 through 1964 the longer run supply response is only slightly more price elastic than the 1.17 of the primary supply level equation. This conclusion is somewhat substantiated by the more price elastic supply level primary + secondary estimate of 1.22 where the stumpage price variable is expli- citly included in the equation. From 1965 through 1970, however, there is a strong negative correlation between the supply and demand shifts (r = -0.55) similar to the response typical of the inflexible Douglas-fir region. Analysis of the estimated coefficients of the primary supply level equation times their respective observed variable levels indicate that decreasing British Columbia lumber production and increased pulpwood prices are the major changes associated with the gradual 1963-67 supply decline. In- creased log exports played a minor role. In 1968 and 1969, however, 95 the.drastic leftward shift of supply is very heavily associated with an increase in the price of sawlogs. Note in Figure 9 that increased sawlog price dominance did not occur until demand increased in 1968. This sawlog dominance lagged into 1969 even though lumber demand had backed off. This suggests that in the 1965—70 period, and especially the years of 1968 and 1969, the aggregate "structural species" group exhibits the same evidence of external diseconomies characteristic of the Douglas-fir system. There is little to suggest the reason for this substantial change in the nature of "structural species" supply and demand inter- actions. Southern pine, which should lend a more flexible factor to the aggregate, represents an even larger percentage of the "structural" aggregate in recent years. In 1960 "structural species" consumption was 26 percent Southern pine and in 1970 it was 33 percent Southern pine. While there is little evidence to suggest a cause of the changes of the relations, change did occur. CHAPTER VI CONSUMPTION AND PRICE PROJECTIONS Using equation estimates presented and discussed in Chapter IV, projections are made annually for the thirty year period from 1971 through 2000. Once structural coefficients are available for the modeled supply and demand relationships, projection of price and con- sumption levels is a fairly easy process. Ease does not indicate ac- curacy, however, as there are important assumptions inherent in the model that will most certainly be violated during the projection period. First, the data range implicit in the sample observations is the only range over which there can be any measured confidence concerning the estimated structdral relations. These data bands are passed in this study as they are in probably every other study. Second, there is an assumption that colinear variables will maintain their relationship during the projection period. Perhaps the most severe assumption is that the structural relationships observed during the sample period will continue to exist during the projection period even within the same data range let alone an extended range. Another difficulty is obtaining projections of the exogenous variables to which the estimated structural relations are applied. Furthermore, the farther into the 96 97 future the projection extends, the greater the chance of error from violation of these assumptions. All projection techniques are subject to the problems noted above or to toher equally serious limitations. Thus the selection of a single projection technique is comparable to trying to select the boat that sinks the slowest. The equation system used in this study has a greater problem by assuming more relations constant by including numerous variables rather than profiting from whatever compensating errors might be covered in an aggregate analysis. The ability to con- sider changes in specific variables internally and explicitly seems to justify the added risk, however. EXOGENOUS VARIABLE PROJECTION Secondary demand level equations and primary supply level equa- tions are used for projections just as they were used in the analysis of past supply and demand shifts in Chapter V. No projected annual series of the variables contained in these equations were known to be available from alternative sources. That which was available was Bureau of Census projections of total households and 0-24 year-old headship rates for five year increments from 1970 through 1990. Esti- mates available in this form were interpolated between the five-year points and extrapolated beyond. For other variables a linear regression 98 of.the variable against time, an approach used by McKillop (1967, .pp..50-51) on some variables, was attempted but discarded as producing . unlikely variable levels such as a wholesale price of $3 per thousand square feet for softwood plywood in the year 2000. 'Therefore, most projected exogenous series were based upon subjective judgments. Past rates of change in exogenous series were studied along with the changes in factors identified as affecting these rates of change. Probable future changes in the level of these deter- mining parameters were then assumed to have certain effects upon the .rate of change of exogenous variables. Projected exogenous series were then derived from these rates of change in determining factors. .While this may be a questionable process, it seems to be the best avail- able and iS*a step any projection.technique must become involved with. The exogenous series obtained in this manner are tabularized in Ap- pendix D. One difficulty with a detailed system approach such as employed here is that the exogenous-endogenous dichotomy maintained through structural estimation and projection is a questionable expediency. For example, Chip residues from sawmills and plywood price, considered exo- genous in this study, are probably as much determined by the endogenously determined lumber consumption and price variables as by anything else. A lessening of this problem is one of the major advantages of the broader approach employed by McKillop (1967) and Talhelm and ' 99 Holland (1971) where numerous wood products are considered simultan- eously. Unfortunately there is a trade-off between detail and scope. The detailed approach taken here is more appropriate for identifying supply and demand relations for a well defined relatively homogeneous product class. DOUGLAS-FIR AND SOUTHERN PINE PROJECTIONS Supply and demand levels at a lumber price of $100/bem were projected for Douglas-fir and Southern pine. At this price Douglas-fir supply is projected to steadily decrease at the rapid rate of approxi- mately 0.35 billion board feet per year. Southern pine supply is pro- jected to increase at a modest rate of 0.08 billion feet per year until 1985 and decline thereafter at a rate of 0.18, Table 14. The previous analysis of supply and demand shifts concluded that price is dominated by the position of the supply function. The rapid shift of Douglas-fir supply and only moderate shift of Southern pine supply indicate the presence of a large price differential. The projected price of Douglas- fir lumber in the year 2000 is $192/bem while Southern pine is only $118/bem. The likelihood is low that such a large price differential be- tween two close lumber substitutes would exist in a market system. The model used here would have to be modified to incorporate the regional 100 TABLE l4.v-Projected level of Douglas-fir and Southern pine lumber supply at an assumed price of $100/bem, 1971—2000. Year . -Douglas-fir. - Southern pine 1971 7.42 5.25 1972 .7.12 6.18 1973 6.66 6.48 1974 6.36 7.25 1975 5.90 7.71 1976 5.49 8.48 1977 4.97 8.94 1978 4.45 9.25 1979 3.94 9.86 1980 3.47 10.17 1981 2.89 10.78 1982 2.30 10.94 1983 1.72 11.24 1984 1.13 11.39 1985 0.55 12.01 1986 0.16 12.30 1987 -0.23 12.27 1988 -0.62 12.72 1989 -1.02 12.85 1990 -l.24 12.98 1991 -l.47 12.81 1992 -1.69 12.63 1993 -l.9l 12.45 1994 -2.14 12.28 1995 -2.36 12.10 1996 —2.59 11.93 1997 -2.81 11.75 1998 -3.04 11.57 1999 -3.26 11.40 2000 -3.48 11.22 101 shift of lumber production which this price differential indicates will occur. Specifically, the lumber price ratio between the species would have to be included in both demand equations.' Similarly, supply side changes must incorporate the shift of capital investment or at least the effect of greater investment upon such parameters as sawlog price and pressure at the sawlog-pulpwood margin. In brief, both the system para- meters and the model form itself would have to be changed to adequately incorporate the results of the regional shift that the projected priCe differential indicates will occur. Even as it now stands, however, the model used here does provide an economic measure of the pressure for regional relocation that has often been measured but in physical terms alone. For example, the U.S. Forest Service (1965) used a physical supply approach to estimate that there would be a 4 percent increase in the sawtimber cut in the Pacific Coast States between 1962 and 2000 but a 235 percent increase of saw- timber cut in the South for the same time period. " STRUCTURAL SPEC IES " PROJECTION The level of "structural species" demand at an assumed lumber price of $100/bem is projected to increase until 1975 and then decline through 2000, Figure 11. The 1975-2000 projected rate of demand deCline 102 Fig. ll.“Projected."structural species" lumber demand at an assumed price of $100/be , 1971-2000. Fig. 12.--Projected "structural species" lumber consumption, 1971-2000. 103 Billion Board Feet L, t I I I I I I I I 1950 1960 1970 1980 1990 Figure‘ll. Billion Board Feet #— - - - - - 23 h ’l“\ 22 ‘ --‘~ ~ ' I “. I 21 , \ 20 “‘~- 19 * 44 l l J 1 1950 1960 1970 1980 1990 l l l 1 Figure 12. 104 (0.84 percent annually) is substantially greater than the estimated decline rate for 1947-70 (0.13 percent annually). Projected supply increases from 1970 through 1981 at 0.9 per- cent annually compared to the estimated 0.6 percent annual increase for the 1947-65 period, Figure 13. .From 1981 through 2000, however, supply is projected to decrease by 3.2 percent annually at the $100/bem price level. The rightward supply shift through 1981, as is indicated by an increase in quantity supplied at a constant price, is associated with the projected high rate of increase in British Columbia lumber production through 1960. Projected British Columbia production rises slowly from 1980 through 1990, however, and then slowly declines to what is considered to be a sustainable level in 2000.‘ After 1981 the shift of the supply function to the left is associated with the pro- jected high rate of softwood sawlog price increase ($2/bem per year 'through 1985 and $l/bem annually thereafter compared to $1.40/bem from 1947-70) and the projected increase of log exports (205 million board feet increase annually 1970-80, 150 from 1980-90, and 75 from 1990-2000 compared to the average 230 million board feet rate experi- enced from 1959-70). Consumption and price projections derived from these supply and demand projections are presented in Figures 12 and 14, respectively. Consumption is projected to maintain a relatively high plateau of about 22.7 billion board feet from 1972 through 1977. Consumption declines Fig. 13. 105 --Projected "structural species" lumber supply at an assumed price of $100/bem, 1971-2000. a b Fig. 14. 1971-2000. expected supply projected supply given a lower log export volume or a slower sawlog price increase projected supply given zero log exports projected supply given a slower sawlog price increase and zero log exports --Projected "structural species" lumber price, expected supply projected supply given a lower log export volume or a slower sawlog price increase projected supply given zero log exports 'projected supply given a slower sawlog price increase and zero log exports 1 06 Billion Board Feet I I I I I I I I I I I P — 24 22 20 18 16 14P- \\\- 12'- \- I. é 1 1 1 4 1 4 1 1 1 J L 1950 1960 1970 1980 1990 2000 Figure 13 . $me 150 " 140 " 130 120 110 100 80 1950 1960 1970 1980 1990 2000 107 from 1977 through 1987 at 1.2 percent annually and very gradually de- clines from 1987 through 2000 at about 0.02 percent annually. The projected 2000 level is 19.5 billion feet or 5 percent below the 1947-70 average of 21.6 billion board feet. The consumption change projected here is substantially different from projections of "all lumber" available from other major studies. The U.S. Forest Service (1965, p. 41) projected a 35 percent increase in "all lumber" consumption from 1970 to 2000. The medium projection by Landsberg and others (1963, p. 812) for "all lumber" increases 90 percent for the same period. The Forest Service projection for lumber used in residential construction raises even more (45 percent) but the Landsberg'gt_§l, projection for lumber used in construction increases about the same as their "all lumber" category. The real price of "structural species" is projected to decline from a 1972 high of $ll4/bem to a relatively stable 1980-87 plateau of $102/bem. After 1987, however, the projected price rises quite rapidly to $135/bem by the year 2000, Figure 14. The year 2000 pro- jection of $135/bem is 20 percent greater than the $106/bem 1947-7O average. The overall 30-year rate of increase is a very modest 0.65 percent annually. Between 1987 and 2000 price increases at the rather high rate of 2.25 percent annually, due primarily to the rapid shift of the lumber supply function to the left. 108 Comparison of the "structural species" price projection with McKillop's (1967, p. 62) price projection, the Douglas-fir projection, and the Southern pine price projection provides somewhat of a consistency check. McKillop's prediction of the non—deflated softwood lumber price, which increases $5/bem from 1965 to 1970 and then declines $2/bem I from 1970 to 1975, compares quite closely with the above results through 1975. McKillop's projections do not extend beyond 1975, however, and no other major study projected price. Moving onto a species comparison, the "structural species" year 2000 projection of $135/bem lies between the $118/bem Southern pine and $192/bem Douglas-fir projection as it should. Since the Douglas-fir regional industry and timber situation is relatively more inflexible than the Southern pine situation, it seems probable that a regional shift to the South would cause the Douglas-fir price to fall farther than the Southern pine price would rise. This would put the market price somewhere below the $155 midpoint of the $188—l92 range: the "structural species" projection of $135/bem is consistent with this expectation. POLICY SENSITIVITY IN THE "STRUCTURAL SPECIES" SYSTEM One of the underlying motivations behind this analysis was the contention that a detailed supply and demand model such as the one de- veloped here would be desirable for explicit testing of the effect which 109 changes in policy—sensitive variables have upon future price and con— sumption levels. This section deals with such sensitivity analysis. Two major pieces of Federal legislation resulted from the con- cern over the 1968 and 1969 lumber and plywood price rises, one regarding an export embargo on logs removed from federal land and a second regard- ing a more intensive level of forest management on Federal lands. Both of these factors have been considered in the model employed in this study. The level of log exports is explicitly included in the "struc- tural species" supply equation. The effect of management intensity can be expressed through its impact upon sawlog prices. In order to test the possible impact of changes in these vari- ables, the'projected exogenous series discussed above were replaced one at‘a time by the following alternative series: (1) a slower rate of log export whose rate of increase is only one—sixth that of the expected series, (2) zero log exports which is comparable to a complete log embargo, (3) a lower sawlog price projection which raises only two-thirds as fast as the expected series, (4) a combination of the log embargo and slower sawlog price rise. Since we concluded in Chapter IV that the demand functions for the three species groups considered here are almost perfectly price in- elastic and since these proposed policy changes shift the supply func- tions, the policy alternatives will be visible in terms of a price change. Projected consumption will be unchanged. ‘Both the lower log 110 price and lower log export alternatives shift the supply curve to the right by about the same amount and therefore have about the same impact upon "structural species" lumber price, Figures 12 and 14. The proposed .1owering in either log price or exports will result in a price projec- tion approximately 5 percent lower than the expected trend, reaching a level of $127/bem by the year 2000. A complete log embargo results in a price projection of $118/bem, 13 percent below the expected level in the year 2000. A combined use of both the complete log embargo and lower sawlog price trend results in a price projection 18 percent below the expected trend to a level of $llO/bem in 2000. This is only $4 above the $106 average for 1947—70. These alternatives demonstrate that even though some variables have had a greater average annual impact upon the supply or demand function in the past, a less important variable may be enough more sensitive to policy manipulation to overcome its lower per unit impact. For example, the absolute average annual shift of the "structural species" supply function by sawlog price was an estimated 2.32 percent versus only 0.58 percent for softwood log export but the greater sus- ceptibility of export volume to control may make it a better policy tool. ‘CHAPTER VII SUMMARY‘AND‘CONCLUSIONS The impact of future changes in the factors that influence the price and consumption of wood products are typically derived from studies employing rather simplistic analytical techniques. As a result, it is difficult or impossible to reliably estimate the impact of alter— native levels of sensitive variables upon the supply and demand of timber products. The econometric model developed here is designedrtO‘overcome this information deficiency. An integrated model of the supply and the demand factors determining the market price and consumption level of Douglas-fir, Southern pine, and "structural species" lumber is developed and exercised. The principal objectives of the study include: 1) dis- covery of the presence of multi-equation statistical problems, 2) measure the relative importance of supply and demand shifters, 3) analyze the impact of supply and demand movements upon price and consumption levels, and 4) project consumption and price levels and study the sensitivity of these levels to changes in policy-sensitive variables. Using the derived demand representation as a guide, numerous hypothesized system variables were grouped for analysis. Two totally lll 112 .independent groups of demand variables were collected, one containing monitors of the consumption level in lumber using markets and one con- .taining the supply and demand determinants of these consumption levels. Two.partially independent groups of supply variables were also collected, one containing determinants of domestic supply, foreign supply, and log competition, and a second containing the same variables with sawlog price replaced by its stumpage sector determinants. This division allows estimation of two independent demand price elasticities. It also allows partially independent estimates of supply price elasticity and analysis of the difference in price elasticity when sawlog price is replaced by stumpage price. Data requirements necessary to implement the system representa- tion utilized were substantial. Obtaining consistent annual time series observations for a period as long as the 1947-70 time span used here is always difficult. Data restrictions precluded the study of some para- ~ meters and required the use of proxy variables in some cases. On the whole, however, the data collected is of sufficient quality that it does not hamper study results. Statistically, the system structure was estimated as a number of independent subsystems, each containing a single supply and demand func- tion for a particular species group. Since both price and quantity of lumber supplied or demanded are contained in a single equation and since both are determined endogenously, the ordinary least squares (OLS) 113 statistical model would have produced biased and inconsistent estimates. The two stage least squares (ZSLS) model was deemed to be most appro- priate for this study since it is unbiased on large samples and rela- tively insensitive to multicollinearity and misspecification problems. Since each two equation subsystem has two unknowns (lumber price and lumber quantity) each subsystem is statistically complete. The Durbin-Watson test showed that significant serial correlation among estimated residuals was absent. Similarly, the Basmann phi ratio and economic logic both suggest that the estimated equations contain such variables that they are properly identified as supply and demand func- tions. System misspecification, the exclusion of important variables, may be present but the completeness of the system representation and the few indications of its presence suggest its effect is minimal. The only statistical problem having widespread incidence in this study was multicollinearity among variables. Its presence was detected by the sequential use of simple correlation coefficients, factor analysis, and equation test runs. These tests indicated that factor analysis is the best and a simple correlation the worst single test of multicollinearity. When multicollinearity is present, it is obviously impossible to untangle the joint impact of collinear variables to esti- mate independent impacts. Therefore, to the extent that multicollinearity is present, interpretation of the estimated elasticities used to measure relative variable importance is hampered. Similarly, use of the 114 estimated equations as projection tools is hampered because we only have measured confidence on the structural estimates within the range of variable relations observed in the sample set. Although the difficulties resulting from multicollinearity are substantial and represent the single most important statistical problem encountered in this study, its importance should not be over-emphasized. This collinearity does not hamper precise estimation of past supply and demand positions and interactions. Projections are not hampered if the collinearity continues or if the structural estimates hold beyond observed ranges of multicollinearity. Finally, it should be noted that multicollinearity is a property of the system itself and not a function of the particular analytical technique applied to that system. Aggre- gate techniques applied to the same system may ignore or fail to locate multicollinearity but do little or nothing to overcome the difficulties. Relative importance among various system parameters as supply and demand function shifters was measured by an elasticity estimate and the estimated average percentage change in lumber demanded or supplied associated with the movements of the particular variable. On the demand side, consumption levels in lumber using markets are relatively more important individually than the supply and demand determinants of these consumption levels. Not surprisingly, the volume of residential con- struction and the price of softwood plywood were the most important single variables in the two groups of demand variables. On the supply 115 side, the volume of log exports proved to have relatively low importance and the average establishment size, which is highly correlated to aver- age productivity, only has an estimated moderate to low importance. .British Columbia lumber production was the only variable outside the group.of raw material prices which showed high importance; in the struc- tural species aggregate it was the most important supply shifter. The raw material variables (sawlog price, stumpage price, pulpwood price, peeler log price, and chipped residues) proved to be the most important supply shifters. Sawlog price was very important as a supply shifter. .Pulpwood price was more important than veneer log price, indicating that sawlog market prices are more affected by conditions in the pulpwood than in the veneer log market. It must be remembered that these results are derived from 1947-70 annual observations and mean variable levels during that period. As such they implicitly measure the average annual condition and may not adequately mirror the effect of radical trends within the period. For example, the relatively low importance allocated to the log export vari- able probably is a result of the low export volumes from 1947-59 and the elasticity estimates may understate the impact of export levels like those since 1959. The following one year run price elasticity conclusions can be drawn from the study. The demand price elasticity is very inelastic and 116 probably well below -O.50. The annual run supply price elasticity lies between 1.2 and 1.6 with little difference between species. Analysis of supply and demand interactions over the sample period show that Douglas-fir supply will shift to the left in response .to a demand increase while Southern pine will shift to the right. Fur- thermore, the leftward shift of the Douglas-fir supply function.is_ heavily associated with an increased sawlog price and as such indicates the presence of significant external diseconomies embodied in a highly inelastic stumpage supply function. To the extent that the connection .lines between successive market equilibrium points represents longer run supply responses, the longer run supply response of Douglas-fir may be as low as 1.0 and of Southern as high as 2.0. Through 1964 the "structural species" aggregate exhibited an average of the inflexible Douglas—fir and flexible Southern pine influ- ences such that the longer run supply response is only a little more elastic than the 1.17 annual run estimate. From 1965 through 1970, especially 1968-70, however, the whole "structural‘species" aggregate behaves as the inflexible Douglas-fir class. Sawlog price rises strongly when demand increases. The reason for this character change is unknown. A clear conclusion of the study is that lumber consumption changes are primarily controlled by demand function shifts. Price changes may result from a demand function shifting over the less than perfectly elastic supply function, but substantial price changes are 117 the.result of supply shifts.' It may be said that the demand shift is the force which induces the operation of external diseconomies on the supply side, but the especially large changes in lumber price such as .those of 1968 and 1969 are directly the result of supply side determi- nants and most dominately stumpage prices. "Pric ‘projections for Douglas-fir and Southern pine lumber pro- vide an indication of the economic pressure for a regional shift of lumber. The extent of the pressure for change from the Douglas-fir region to the South and degree of disequilibrium if change does not .occur is indicated by the projected $192 versus $118 price differential in the year 2000. The "structural species" consumption projection decreases from a 1975 high at a rate of 1.2 percent annually through 1987 then declines at'a very slow 0.02 percent annually thereafter. This projection con- trasts strongly with the increased consumption levels developed in most other studies. The "structural species" price projection declines from a $ll4/bem high to $102 in 1985 and then rises sharply to $135 by 2000. The overall increase in projected real prices from 1970 to 2000 is quite low but the 1987 to 2000 rate of increase is a very high 2.25 percent annually. Modification of the exogenously projected log export and log price variables indicated that projected lumber price can be reduced. For example, a complete log export embargo combined with a slower rate 118 of increased sawlog price decreased the expected price trend by 18 per- cent resulting in a year 2000 price of only $4/bem above the 1947-70 average. It is quite apprent, however, that the export embargo and the slower increase in log price are only temporary measures. The 1987-2000 rate of lumber price increase is unmitigated by changes in these two policy sensitive variables. The 1987-2000 rise is dominated by the associated exogenously projected decline in British Columbia lumber production. Apparently, then, action must be taken to fill the void currently contained by British Columbia production if the rate of lumber price increase is to be maintained at recent levels beyond the late 1980's. Whether it should be a public goal to maintain lumber prices at or close to their current levels is a question beyond the scope of this analysis. What this analysis does provide is some information con- cerning how market parameters for the major construction lumber species interact, and some expectation of what will occur if the levels of pro- jected exogenous variables are realized. LITERATURE CITED LITERATURE CITED Anderson, Walter C. 1969a Pine Sawtimber Price Behavior in South Carolina. Southern Forest Experiment Station, Research Paper SO-42, U.S. Forest Service, U.S.D.A., 12 pp. 1969b Determinants of Southern Pine Pulpwood Prices. Southern Forest Experiment Station, Research Paper SO-44, U.S. Forest Service, U.S.D.A., 10 pp. Basmann, R. L. 1960 On Finite Sample Distribution of Generalized Classical Linear Identifiability Test Statistics. Journal of the American Statistical Association 55:650-659. Dutrow, George F. 1971 Disequilibrium Model for Stumpage Price Analysis. Forest Service 17:246-251. Ferguson, C. E. 1966 Microeconomic Theory. Revised edition, 521 pp., Homewood, Illinois: Richard D. Irwin, Inc. Fisher, Franklin M. 1965 Dynamic Structure and Estimation in Economy-wide Econometric Models. Chapter 15, pp. 589-686 in The Brookings Quarterly Econometric Model of the United States, edited by J. S. Duesenberry, G. Fromm, L. R. Klein, and E. Kuh, Chicago: Rand McNally. Frazier, George D. 1965 Estimated Demand for Lumber and Plywood in Hawaii by the year 2000. Pacific Southwest Forest and Range Experiment Station, Research Paper PSW—23, U.S. Forest Service, U.S.D.A., 9 pp. 119 120 Goldberger, Arthur S. 1964 Econometric Theory. 399 pp., New York: John Wiley and Sons, Inc. Gregory, G. Robinson. 1955 An Analysis of Forest Production Goal Methodology. Journal of Forestry 53:247-252. 1960 A Statistical Investigation of Factors Affecting the ‘ Market for Hardwood Flooring. Forest Science 6:123-134. 1965 More on Factors Affecting the Market for Hardwood Flooring. . Forest Science 11:200-203. 3 Guthrie, John A. and Armstrong, George R. 1961 Western Forest Industry, an economic outlook. 324 pp. Published for Resources for the Future, Inc. Baltimore: The John Hopkins Press. 'fina- ' Hair, Dwight 1967 Use of Regression Equations for Projecting Trends in Demand for Paper and Board. Forest Resource Report no. 18, U.S. Forest Service, U.S.D.A., Washington: U.S. Government Printing Office, 178 pp. and Josephson, H. R. 1971 Forecasting Demand, Long-run. In Forecasting in Forestry and Timber Economy, Folia Forestalia 101:16-21. Johnston, J. 1963 Econometric Methods. 300 pp. New York: McGraw-Hill Book Company. Landsberg, Hans H.; Fischman, Lenond L.; and Fisher, Joseph L. 1963 Resources in America's Future, patterns of requirements and availabilities, 1960-2000. 1017 pp., published for Resources for the Future Inc., Baltimore: The John Hopkins Press. McKillop, W. L. M. 1967 Supply and Demand for Forest Products-—An Econometric Study. Hilgardia 38:1-132. 121 McKillop, W. L. M. 1969 An Econometric Model of the Market for Redwood Lumber. Forest Science 15:159-170. Mead, Walter J. 1966 Competition and Oligopsony in the Douglas-fir Lumber Industry. 276 pp. Berkeley: University of California Press. Nathan, Robert R., Associates Inc. 1968 Projections of the Consumption of Commodities Producible on the Public Lands of the United States 1980-2000. Pre- pared for the Public Land Law Review Commission, Washing- ton, D.C., 429 pp. Ruble, William L. 1968 Improving the Computation of Simultaneous Stochastic Linear Equation Estimates. Agriculture Economic Report no. 116 and Econometric Special Report no. 1, Dept. of Agriculture Economics, Michigan State University. Simpson, R. S. and Halter, A. N. 1963 Forecasting Price, Production, and New Orders in the Douglas-fir Plywood Industry. Special Report no. 165, Agriculture Experiment Station, Oregon State University. Stanford Research Institute. 1954 America's Demand for Wood. A report done for Weyerhaeuser Timber Company, 404 pp. Talhelm, Daniel R. and Holland, Irving. .1971 An Econometric Analysis of the Demand and Supply of Wood Products-~Preliminary Results. Paper presented at the National Society of American Foresters Meeting, Cleveland, Ohio. U.S. Congress 1969a Timber Management Policies. Hearings before the Subcom- mittee on Retailing, Distribution, and Marketing Practices of the Select Committee on Small Business, U.S. Senate, 90th Congress, 2nd session, Washington: U.S. Government Printing Office, 577 pp. U.S. Congress. 1969 122 Rising Costs of Housing: Lumber Price Increases. Hear- ings before the Committee on Banking and Currency, U.S. House of Representatives, 9lst Congress, 2nd session, Washington: U.S. Government Printing Office, 894 pp. U.S. Forest Service. 1946a 1946b 1958 1965 Vaux, Henery J 1971 Gaging the Timber Resources of the United States. Report no. 1 in A Reappraisal of the Forest Situation, Washing- ton: U.S. Government Printing Office, 62 pp. Potential Requirements for Timber Products in the United States. Report no. 2 in A Reappraisal of the Forest Situation, Washington: U.S. Government Printing Office, 70 pp. Timber Resources for America's Future. Forest Resource Report no. 14. Washington: U.S. Government Printing Office, 713 pp. Timber Trends in the United States. Forest Resource Report no. 17. Washington: U.S. Government Printing Office, 235 pp. Forecasting Supply, Long-term. In Forecasting in Forestry and Timber Economy. Folia Forestalia 101:28-34. and Zivnuska, John A. 1952 Forest Production Goals: A Critical Analysis. Land Economics 28:318-27. Wennacott, Ronald J. and Wonnacott, Thomas H. 1970 Econometrics. 445 pp., New York: John Wiley and Sons, Inc. 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APPENDIX E METHOD OF CALCULATING THE ARC ELASTICITIES AND THEIR CONFIDENCE INTERVAL APPENDIX E METHOD OF CALCULATING THE ARC ELASTICITIES AND THEIR CONFIDENCE INTERVAL L. The arc elasticity estimates were calculated using the standard elasticity formula: Mama—b4 T A lumber quantity/lumber quantity A variable level/variable level elasticity = where (l) lumber quantity and variable level were represented by the mean 1947-7O level of lumber consumption and the variable in question. (2) A lumber quantity is the estimated coefficient of the par- ticular variable. (3) A variable level is 1.0 to correspond with the use of the variable coefficient as the A lumber quantity. The width of a plus-and—minus confidence band around this elasticity estimate can be derived by replacing the variable coeffi- cient used for A lumber quantity by the standard error of the coef- ficient estimate times an appropriate tabulated student's t ratio. 182