United States 

Department of 

Agriculture 

Forest Service 

An Econometr c Model 

Northeastern Forest 

Experiment Station 

of the Hardwood 

Researc ti 

Paper PI E-512 Lumber Mar 

William G. Luppold 
The Author 

William G. Luppold attended 

the University of Florida, where he 

received his BSA and MSA in Food 

and Resource Economics in 1974 

and 1977, respectivety, and Virginia 

Polytechnic Institute, where he was 

awarded a Pk. D in Agricultural 

Economics in 1981. He then joined 

the Northeastern Forest Experiment 

Station, Forestry Sciences Laboratory at Princeton, West Virginia, 

where he is currently conducting 

economic research on the hardwood 

lumber market, 

Manuscript received for 

publication 16 February 1982 

Abstract 

A recursive econometric model 

with causal flow originating from 

the demand relationship is used to 

analyze the effects of exogenous 

variables on quantity and price of 

hardwood lumber. Wage rates, interest rates, stumpage price, lumber 

exports, and price of lumber demanders' output were the major fa@- 

tors influencing quantities demanded and supplied and hardwood 

lumber price, 
Introduction 

The hardwood lumber industry 

dates back to colonial times, when 

hardwood lumber was used in the 

manufacturing of homes, ships, 

bridges, furniture, and a multitude 

of other major and minor products. 

As softwood, steel, plastic, and 

other industries developed and new 

technology and production methods 

were introduced, many of the uses 

of hardwood lumber changed. Today, hardwood lumber is used 

primarily by producers of furniture, 

cabinets, and pallets. Other users of 

hardwood lumber include manufacturers of rail ties, hardwood flooring, and a variety of specialty items. 

Traditionally, the hardwood 

lumber market consisted of 

numerous buyers and sellers, trading in a slowly changing market 

environment. The price of hardwood 

lumber historically followed an 

oscillating and slowly upwardtrending path. The quantity of hardwood lumber produced and demanded also fluctuated, but did not 

show any significant trend upward 

or downward during the last 30 

years. However, since 1975, hardwood lumber price has increased 

dramatically while lumber production remained relatively stable. 

Between 1975 and 1979, the 

price of hardwood lumber increased 

at an ~nnual rate of 10.4 percent, or 

about 40 percent above the rate of 

increase for all crude materials used 

in manufacturing. Furthermore, the 

price of higher grade oak, the 

predominant hardwood species, increased at an annuai rate of 18.4 

percent. Still, lumber production in 

the 1970's remained below the average levels of the previous two decades. 

The economic behavior of the 

hardwood lumber market during the 

late 1970's caused industrial users 

concern about future price and 

availability of hardwood lumber. 

Questions that arose included: what 

effects have increasing stumpage, 

labor, and capital costs had on Iumber production; and how will lumber 

users react to increasing lumber 

prices? Also, what effects have the 

increased hardwood lumber exports 

during the 1970's had on the price? 

In order for lumber suppliers 

(producers) and demanders (users) 

and forest resource planners to address these questions, information 

is needed on the effects of wage 

rates, stumpage prices, lumber exports, interest rates, and other 

important factors on the demand, 

supply, and price of hardwood lumber. Suppliers and demanders can 

incorporate such information when 

making lumber production and 

usage decisions. More market 

information will result in better 

allocation of resources by lumber 

demanders and suppliers. Such 

information will also contribute to 

the stock of knowledge available to 

resource planners, allowing them to 

better anticipate the effects of alternative policies on the hardwood 

lumber market. 

To provide this needed information, I developed an econometric 

model to quantify economic 

relationships in the hardwood lumber market. The model considered 

major factors affecting the demand, 

supply, and price of hardwood lumber. With this model, the impacts of 

changes in important factors on 

lumber usage, production, and price 

can be assessed. 

Model Development 

The econometric market model 

uses aggregated yearly production, 

usage, and price data. Aggregate 

data that combine all grades and 

species of hardwood lumber were 

used because inventory and subsequent lumber usage data were not 

available by grade and species. 

Yearly observations were used 

because monthly observations were 

not updated. Also, since many firms 

are vertically integrated in this industry, it was assumed that these 

firms behaved rationally (maximized 

profits) at the various levels of their 

production processes. 
The hardwood market model 

consisted of four relationships-three equations, representing demand, supply, and the 

price of hardwood lumber, and one 

equilibrium identity. The overall 

model was similar in form to the 

general commodity market model 

presented by Labys (1975). The 

model was recursive, with current 

quantity of lumber demanded being 

a function of past lumber price. A 

similar demand equation was presented by McKillop (1969) for the 

redwood industry. Figure 1 is schematic of the relationships in the 

model and the causal flow between 

these relationships. 

The major factors assumed to 

affect hardwood lumber demand, 

supply, and price and the expected 

influences of these factors are 

listed in Tables 1, 2, and 3. The 

individual equations included in the 

model are discussed briefly below. 

The Demand Equation 

The specification of the demand equation was based on the 

derived demand relationships developed by Mosak (1938). Quantity 

of hardwood lumber demanded 

(used) was expressed as a function 

of lagged quantity demanded, current prices of output, past prices of 

inputs, and time. 

dependent on supply and 

Figure 1.-The directional flow of demand, supply, and price in the hardwood lumber market in the United States. 
%able I .---Major factors, variables, expected relationships between variables, 

and units included in the hardwood lumber demand equation. 

"Te designations in parentheses in the variable column are those 

used for the same variables in equation "I 

Factor Variable Expected relationship 

Dynamic adjustment variable Quantity of hardwood lumber, lagged 1 year (lagged quantity demanded) 

Price of output Weighted price index of wholesale furniture price and price of 

manufactured goods (output price) 

Past price of 2-year moving average of the price index for hardwood lumber, 

hardwood lumber lagged 1 year (past lumber price) 

Past wage rates 2-year moving average of wage rates in manufacturing lagged 1 

year (past wage rates) 

Past price of capital %year moving average of interest rate on 4- to 6-month prime 

commercial paper, lagged 1 year (past interest rates) 

Trend removal Time trend (time) 

Positive, but less than 1 

Positive 

Negative 

Negative 

Negative 

No a priori expectations 

Table 2.-Major factors, variables, expected relationships between variables, 

and units included in the hardwood lumber supply equation. 

The designations in parentheses in the variable column are those 

used for the same variables in equation 2 

Factor Variable Expected relationship 

Dynamic adjustment variable Quantity of hardwood lumber supplied, lagged 1 year (lagged 

quantity supplied) 

Lumber price Price index of hardwood lumber (lumber price) 

Stumpage price 2-year moving average of current and past year stumpage price 

in national forest, plus the cost of borrowing money 1 year 

(stumpage price) 

Wage rates Price of labor in sawmills (wage rates) 

Price of capital 

Trend removal 

3-year moving average of interest on 4- to 6-month prime commercial paper (interest rates) 

Time trend (time) 

Positive, but less than 1 

Positive 

Negative 

Negative 

Negative 

No a priori expectations 

Table 3.-Major factors, variables, expected relationships between variables, 

and units included in the hardwood lumber price equation. 

The designations in parentheses in the variable column are those 

used for the same variables in equation 3 ---- - - -- 

Factor Variable -- ------I___----.___ 

-- 

Price expectation Lagged price index of hardwood lumber (lagged lumber price) 

variable 

Quantity demanded Quantity of hardwood lumber demanded (quantity demanded) 

inventory Quantity of hardwood lumber held in inventory by producers and 

wholesalers at year's end (inventory) 

Exports Quantity of hardwood lumber exported (exports) 

-- 

Expected relationship 

Positive, but less than 1 

Positive 

Negative 

Positive 
The demand equation was 

specified as a function of past input 

prices because of the economic behavior of the two major hardwood 

lumber users, furniture and pallet 

producers. Furniture manufacturers' 

usage of lumber and other inputs is 

a function of past input prices and 

current output prices because of 

the process by which furniture is 

designed and marketed. Design and 

input mix decisions are made before 

production and are based on expectations of future input prices. These 

expectations are usually based on 

prices during the planning period 

and previous years. 

The quantities of lumber and 

other inputs used in the production 

of pallets are also contingent upon 

past prices because pallet producers cannot constantly change 

their production processes. Pallet 

producers do change production 

processes and equipment, but these 

changes take time. 

The selection of an appropriate 

output price variable for the demand 

equation was difficult because 

furniture is a final product, while 

pallets are an industrial product. 

Furniture manufacturers react to 

wholesale prices of furniture. Pallet 

producers are usually locked into 

some formal or informal contractual 

arrangement with pallet users, so 

pallet production is usually based 

strictly on orders. Since pallet cost 

is a very small part of the pallet 

user's production and distribution 

costs, the price of the pallet user's 

output is relevant in the derived demand for lumber. Therefore, the output price used in the hardwood lumber demand equation was the 

weighted average of the wholesale 

price of furniture and a measure of 

pallet demanders' output price. 

Lagged quantity demanded was 

included in the specification of the 

demand equation in order to incorporate a distributed lag structure, 

thus allowing for dynamic adjustment. This method of incorporating 

a distributed lag was developed by 

Nerlove (1958) and was based on the 

idea that dependent variables may 

adjust to changes in the independent variables over several time periods. 

Time was included in the 

specification to remove any trend 

that was present in the data. Trend 

might have been present in the data 

base because of increases in labor 

productivity or input utilization. The 

price of substitute materials was 

not included in the aggregate demand relationship because a number of substitutes have been developed, implemented, then replaced by yet other substitutes 

during the period included in the 

data base. 

lmports of hardwood lumber 

were not used in the final calculation of quantity demanded because 

there is no adequate price index 

representing imported hardwood 

lumber, so misspecification might 

occur if imports were included in 

the demand equation. When imports 

were included in the calculation of 

quantity demanded, the equation 

did not explain the turning points as 

well as the final form of the equation, which excluded imports. 

The Supply Equation 

Quantity of lumber supplied 

(produced) was expressed as a function of lagged quantity supplied, 

price of hardwood lumber, wage 

rates, stumpage costs, current and 

past interest rates, and time. The 

time variable was included to remove some of the trend that might 

otherwise tend to be picked up by 

the lagged quantity variable. 

The roundwood input used in 

lumber production may be purchased in the form of stumpage or 

sawiogs, or both. Stumpage price 

was included in the supply relationship because stumpage is the basic 

input, whereas sawlogs are a transitional input. Because stumpage may 

be held for a period before harvesting, previous stumpage price 

was hypothesized to influence current quantity supplied. Stumpage is 

a high-cost input; therefore, interest 

rates must be considered as part of 

the cost of purchasing stumpage. 

Previous purchases of capital equipment also affect current lumber 

production. Consequently, past and 

current interest rates were included 

in the supply equation. 

The Price Equation 

Price of hardwood lumber was 

specified as a function of lagged 

price, quantity demanded, level of 

inventory, and quantity exported. Although only high-grade lumber is 

exported, an increase in exports not 

only leads to an increase in the 

price of the highest grade of lumber, but also affects all grades of 

lumber. 

Since export demand may be a 

function of current hardwood lumber price, an argument might be 

made for domestic price and export 

demand being jointly determined. 

However, there is an information lag 

concerning the volumes of lumber 

exported, while information about 

the price of domestically produced 

lumber is almost instantaneous. Because of the information flows, the 

causal flow between domestic price 

and export demand was hypothesized to originate from the export 

demand relationship and then flow 

to the domestic price relationship. 

Similar recursive flows in which all 

endogenous variables have a time 

period "t" subscript have been discussed by Wold and Jureen (1953). 

Imports may also affect domestic hardwood lumber price; however, 

much of the hardwood lumber imported is high-value tropical species 

such as teak, mahogany, and balsa. 

These high-value tropical species 

compete with less than 5 percent of 

the domestically produced hardwood lumber and, thus, should not 

significantly affect domestic hardwood lumber price. But imports of 

temperate hardwood species from 

Canada can affect domestic hardwood lumber price since these 

species are similar, if not identical, 

to domestic species. However, the 
Equation 1: 

In(quantity demanded) = 11.19 + 

(1.68) 

inclusion of Canadian imports into 

the hardwood lumber price equation 

resulted in a highly insignificant coefficient of the wrong sign for this 

variable. The magnitudes of the 

existing coefficients changed at 

most by .02 and the R2 only increased by ,0029 percent. In fact, inclusion of Canadian imports into the 

price model only affected the equation by consuming a degree of freedom that resulted in a 25-percent 

decrease in the F statistic and increases in the standard errors of the 

coefficients. Consequently, hardwood lumber imports were omitted 

from the price equation. 

The Equilibrium Identity 

The last relationship included 

in the model was an identity, rather 

than an equation to be statistically 

estimated. The identity stated that: 

Quantity 

demanded = (quantity supplied) + 

(lagged inventory levels) 

- (current inventory 

levels) - (exports) 

The identity allowed the market 

model to be in equilibrium with respect to quantities produced, demanded, and held in inventory, lmports were not included in the equilibrium identity since they were excluded from the demand and price 

equations. 

Data Base 

All equations were estimated 

from secondary data. The data base 

consisted of annual observations 

from 1959 through 1978, being limited by the stumpage price series 

that began in 1959. The data series 

representing quantity of hardwood 

lumber demanded was calculated 

using the equilibrium identity presented above. A complete listing of 

all data used in calculating quantity 

demanded is listed in Appendix A. 

The quantity of hardwood lumber supplied and inventories of 

hardwood lumber were obtained 

from Current Industrial Reports: 

Lumber Production and Mill Stocks 

(U.S. Department of Commerce 

1959-1978). Exports of hardwood 

lumber were calculated from figures 

presented in U.S. Exports Schedule 

B, Commodity by Country (US. Department of Commerce 1959-1978). 

The price indexes of manufactured goods, furniture, and hardwood lumber were derived from information published in the Statistical Abstracts of the United States 

(US. Department of Commerce 

1959-1978). Wage rates in manufacturing, wage rates in sawmills, interest rates of commercial paper, and 

stumpage price in national forests 

were also collected from the Statistical Abstracts. 

Model Estimation and Evaluation 

Since quantity demanded is a 

function of past lumber prices, the 

demand equation was estimated by 

ordinary least squares (OLS); and, 

since error terms of the price and 

supply relationships were hypothesized to be independently distributed, the parameters of the price and 

supply relationships were estimated 

using OLS procedures. The statistics in parentheses represent standard errors. The "2" statistic represents "Z"values calculated for the 

nonparametric runs test, which is a 

test for serial correlation. This test 

was used in lieu of a DW statistics 

since DW statistics are invalid in 

equations that include lagged dependent variables. Ail relationships 

were estimated by taking the natural 

log of both sides of the individual 

equations, resulting in a multiplicative form; therefore, the estimated 

coefficients represent elasticities 

and flexibilities. The results of the 

estimate procedure are: 

.287 In(lagged quantity demanded) 

(.151) 

+ 1.72 In(output price) 

('503) 

- .961 In(past lumber price) - t.249) 

1.14 In(past wage rates) - (-372) 

.076 In(past interest rates) + 

(.056) 

Equation 2: 

Intquantity supplied) = ,518 + 

(1.23) 

.256 In(lagged quantity supplied) 

(. 1 45) 

+ .634 In(lumber price) - (. 1 24) 

,400 In(stumpage price) - (.097) 

.676 I n(wage rates) - (.114) 

.I85 In(interest rates) + 

t.049) 

Equation 3: 

lumber price) + .336 In(quantity 

(, 243) 

demanded) - .336 In(inventory) + 

(. 150) 
In order to estimate the hardwood market model using OLS, it 

was hypothesized that the supply 

and price equations were not jointly 

determined. A likelihood ratio test 

developed by Anderson (1958) indicated no correlation between error 

terms since the null hypothesis 

could not be rejected at the .05 

level. Thus, no joint determination 

appeared to exist between the supply and price equation. A more detailed discussion of the likelihood 

ratio test employed and the results 

of the test are presented in Appendix B. 

Model Evaluation 

The goodness of fit of a particular equation, as measured by multiple correlation coefficient (RZ) and 

the F statistics, indicated that all 

equations fitted the data quite well. 

Most of the estimated coefficients 

in the model were significant at the 

.O1 level and all variables were significant at the .10 level. Since the 

resulting 2 values of the nonparametric runs tests were all below the 

critical value of 1.76, the alternative 

hypothesis (autocorrelation exists) 

could not be accepted in any of the 

equations at the .05 level of significance. Thus, autocorrelation did not 

appear to be present in any of the 

equations. 

The quality of an econometric 

model is only partially measured by 

the value of the R2 or the magnitude 

of the "t" test on individual variables. In fact, the true strength of a 

model lies in its ability to account 

for the fluctuations in the production, use, and price of the commodity. The explanatory abilities of the 

supply, demand, and price equations are presented in Figures l, 2, 

and 3. 

Figure 2.-Observed vs predicted of quantity of hardwood lumber 

supplied, 1961 - 1978. 

MMBF 

7900~ 

The supply equation in Figure 2 

performed extremely well, catching 

five of the six turning points that 

occurred in the data base. The one 

missed turning point occurred when 

the equation showed an upturn in 

1967, a year before its actual occurrence. Overall, the explanatory ability of the supply equation was 

judged excellent. 

The demand equation (Fig. 3) 

accounted for all major turning 

points that occurred in the data 

base. Not only were all major turning points accounted for, but so 

were the magnitudes of these 

changes. However, the minor turning points, which occurred in rapid 

succession during the early 1970'~~ 

were missed. Thus, the demand 

equation's explanatory ability was 

judged as only good, and not outstanding. 
Figure 3.-Observed vs predicted of quantity of hardwood lumber 

demanded, 1961 - 1978. 

MMBF 

"0° T 

5400~::::::::::::~ 

1959 1964 1969 1974 1979 

TIM € 

Although the price equation 

(Fig. 4) had the highest R2 of all the 

estimated relationships, the ability 

of this equation to account for turning points was poor. The inability of 

the price equation to catch turning 

points can be attributed to the influence of lagged price. The high estimate for the coefficient of expectation (the coefficient on lagged price) 

in the price equation caused the estimated turning points to occur a 

year after the actual turning points. 

However, the general ability of the 

price equation to account for price 

trend implied that this equation 

could be used for long-term price 

forecasts with few difficulties. 

Model Interpretation 

The statistical results presented and discussed in the previous 

section were not analyzed or interpreted. The purpose of this section 

is to provide meaning to the statistical results. 

Figure 4.-Observed vs predicted of price of hardwood lumber, 

1961 - 1978. 

% of 7967 

250 

200 

150 

100 

50 

1959 1964 1969 1974 1979 

TIME 
Elasticities, Flexibilities, and Net 

Effects 

In the model estimation section, the estimated coefficients of 

the demand and supply equations 

represented elasticities, and the coefficients of the price equation represented flexibilities. These coefficients represented the effects of a 

1-percent change of an independent 

variable on a dependent variable 

without accounting for interactions 

between equations. The term "net 

effects" is used in this study to describe the effects of a 1-percent 

change of an independent variable 

on the dependent variables of all 

equations when interactions are allowed to occur between the various 

relationships in the model. The elasticities, f lexibilities, and net effects 

are discussed in subsequent sections. 

Interpreting Elasticities and 

Flexibilities 

Demand and supply elasticities 

and price flexibilities are presented 

in Table 4. While elasticities and 

flexibilities are conceptually simple 

to understand, the use of these 

measurements was limited in this 

study because they do not account 

for interactions with the other relationships in the model. However, 

price flexibilities can be used in calculating the effect of changes in exports, quantity demanded, and inventory on price. These price flexibilities are shown in the right-hand 

column of Table 4. Too, elasticities 

can be used to determine how much 

an output price must change to 

counteract a change in an input 

price in order for quantity produced 

or demanded to remain constant. A 

few examples of the arithmetic used 

in calculating these counterbalancing changes are demonstrated below. Table 5 is a summary of these 

counterbalancing changes. 

Lumber users can use elasticities to determine how much lumber 

price must change, given an increase in an input price, in order for 

lumber production to remain constant. For example, a 1-percent increase in wage rates means that 

lumber price must increase 1.07 percent for quantity supplied to remain 

constant. This figure is obtained by 

dividing wage rate elasticity of supply (.676) by lumber price elasticity 

of supply (.634). Another way to 

view this procedure is to say that 

the ,676-percent decrease in lumber 

production, due to a 1-percent increase in wage rates, is counteracted by a 1.07-percent increase in 

lumber price since (1.07) x (.634) = -676. 

It was slightly more difficult to 

determine how much lumber price 

must increase to counteract a 1- 

percent increase in stumpage price 

since the stumpage price coefficient was based on a 2-year movir;g 

average. Because a moving average 

was used, a change in the stumpage 

price was interpreted as affecting 

lumber production during the year 

of the change (the first year) and 

also the year after the change (the 

second year). Therefore, the number 

resulting from dividing the stumpage price elasticity of supply (.40) by 

the lumber price elasticity of supply 

(-634) must be divided by 2. This can 

be shown arithmetically as 

(.401.634)/2 = ,315; so, lumber price 

must increase by '315 percent during the first year in order to counteract a 1-percent increase in stumpage price. Similarly, a ,315-percent 

increase in lumber price during the 

second year is also necessary to 

counteract the initial increase in 

stumpage price. 

The amount lumber price must 

change to counteract a change in 

interest rates was developed similarly. However, since the interest elasticity of supply was estimated using 

a 3-year moving average, lumber 

price must increase by (.1851.639)/3, 

or .10 percent during the first, second, and third years in order to 

counteract a change in interest 

rates during the first year. Also, 

since all input price elasticities in 

the demand equation were based on 

a 2-year moving average, lagged 1 

year, a change in price of one of 

these inputs affected demand during the subsequent 2 years (Table 

6). 

lnterpreting the Net Effects 

The net effects displayed in Table 6 were calculated using a computer program that allowed concurrent changes between the various 

relationships of the market model. 

The net effects, obtained from the 

recursive model, were sequels to 

impact and interim multipliers obtained from a simultaneous system. 

However, since recursive systems 

continually oscillate, the net effects 

represented changes in production, 

usage, and price from what would 

have occurred had there been no 

change in wage rates, interest rates, 

etc. The net effects of changes in 

lumber users' output price, wage 

rates, interest rates, exports, and 

stumpage price on quantity demanded (usage), quantity supplied 

(production), and price are discussed below. 

Price of lumber users' output. 

Lumber users' output price is by far 

the most influential single force in 

the hardwood lumber market when 

measured by net effects. Increases 

in this variable are usually caused 

by an increased aggregate demand 

at the national level. When lumber 

users' output price increases by 1 

percent, quantity of lumber demanded increases by 1.7 percent, production increases by 1 percent, and 

price increases by almost 1.7 percent. In the second year after the increase in output price, production 

and us,-ge increase by 1.6 and 1.4 

percent, respectively, and price increases by 2.1 percent. 

Wage rates, The calculated net 

effects showed that a 1-percent increase in lumber producers' and 

users'wage rates initially caused 

quantity supplied to decrease by .3 

percent and price to increase by .58 

percent. During the second year after the increase in wage rates, pro- 
Table 4.-Elasticities of demand and supply and 

price flexilbilities" (in percent) 

Variable Quantity 

demanded 

Quantity 

supplied Price 

Price of lumber users' 

ou t pu t 

Wage rates 

lnterest rates 

Stumpage price 

Exports 

Price of turn ber 

Quantity demanded 

inventory 

a Does not inciude lagged dependent variable. Lagged dependent variables incorporate dynamics into the model, and the coefficients are coefficients of adjustments or expectation. 

b Calculated from a 2-year moving average, lagged f year (t-1, and t-2). 

Not applicable. 

d Calculated from a &year movingaverage (t, t-1, and t-2). 

& Calculated from a 2-year moving average (t, and t-If. 

Table 5.-Using elasticities to calculate the percentage increase in output 

price necessary to counteract a 1-percent change in input price 

Variable that changes Amount lumber price Amount demanders' output 

by 1 percent Year would have to increase price would have to 

in Year 1 for lumber production increase for lumber usage 

to remain constant to remain constant 

Wage rates 

Interest rates 

Stumpage price 

Lurn ber price 

Table 6.-Net effects of a lepercent change in exogenous 

variables on endogenous variables during the 

year of the change and the year after 

(in percent) 

First year Second year Exogenous 

variable Quantity Quantity Price Quantity Quantity 

demanded supplied demanded supplied 

Price of lumber 

users3utput + 1.72, -t- 1-04 s f .65 -i- 1.39 -a- 1.59 -r- 2.10 

Wage rates 8 - .30 -6. .58 --- 1.42 - .75 - .01 

Interest rates 0 - .08 +.I63 - .16 --- -10 -t .I61 

Stumpage price 0 - .07 +.20 - .09 - .I5 +.42 

Exports O i- -08 -+ .12 - .06 + .1Q + .I3 
duction and usage decreased by .75 

and 1.42 percent, respectively, while 

price decreased by .Ol percent. 

Lumber price actually decreased 

during the second year after increases in wage rates because lumber users, faced with increases in 

wage rates and lumber price, decreased their lumber use more than 

lumber suppliers decreased production. However, increased wage rates 

at a national level increase aggregate demand and, thus, output 

prices. Increased output price affects lumber price to a greater extent than it affects lumber production or lumber usage (see lumber 

users' output price). Therefore, increases in wage rates by themselves may not affect lumber prices, 

but the effect of increased wage 

rates and subsequent increased output price can result in increased 

lumber prices. 

Interest rates. The effect of interest rates on usage, production, 

and price of hardwood lumber appears to be small; however, when interest rates move from 10 to 12.5 

percent during the course of a year, 

the increase is 25 percent. If interest rates increase by 25 percent, 

lumber production decreases by 2 

percent and lumber price increases 

by 4 percent during the first year. 

During the second year after the increase, lumber usage decreases by 

4 percent, lumber production decreases by 2.5 percent, and price increases by 4 percent. 

Stumpage price. As indicated in 

Table 6, an increase in stumpage 

price affected lumber price more 

than it affected either production or 

usage. A 1-percent increase in 

stumpage price initially led to a '07- 

percent decrease in production and 

a .20-percent increase in price. During the second year after the increase in stumpage price, lumber 

price increased by -42 percent, 

while usage and production decreased by approximately .09 and 

.15 percent, respectively. 

Exports. The effects of exports 

are somewhat understated by the 

net effects listed in Table 6 because 

exports changed by as much as 90 

percent in I year during the 1970's. 

Given a 10-percent increase in exports, quantity supplied increased 

by .8 percent and price increased by 

1.2 percent during the first year. If 

exports continued at the high level 

during the second year, domestic 

demand would decrease by .6 percent because of the higher price. 

However, increased exports caused 

price to increase by 1.3 percent, and 

thus caused production to increase 

by 1 percent. 

The Results of the Model 

and Recent Market Behavior 

The behavior of the hardwood 

lumber market during the 1970's and 

early 1980's was characterized by 

rapidly rising price and relatively 

stable production and usage. An examination of why the market behaved in this manner will be of interest to both industry members 

and resource policymakers and will 

also demonstrate how information 

obtained from the previous analysis 

can be used to explain real-world 

market behavior. Since the market 

behaved slightly differently in the 

1970's from the early 1980's, each of 

these time periods is discussed 

separately. 

The 1970's 

Hardwood lumber production 

and usage remained stable, or even 

decreased, during the 1970's, relative to the 1960's and 1950's. The 

price of hardwood lumber increased 

126 percent between 1970 and 1979, 

compared to 15 percent from 1960 

to 1969. One question that we must 

address at this point is: how did the 

factors that affect the hardwood 

lumber market contribute to the increased price and stable, or even 

declining, production and usage of 

hardwood lumber? 

One alleged cause of increased 

price of domestic hardwood lumber 

is increased lumber exports. Exports increased by more than 250 

percent during the 1970's, but the 

econometric model indicates that 

increased exports accounted for, at 

most, 25 percent of the increased 

lumber price. However, since increased exports have consisted 

mainly of high-quality oak and ash, 

the prices of grades 1 F and FAS of 

these species have been more affected by exports. 

Domestic demand for hardwood 

lumber was ruled out as a major 

contributor to increased lumber 

price since demand did not increase 

during the 1970's. This indicates 

that the large increase in lumber 

price must have emanated primarily 

from the supply side; i.e., at the mi!! 

level. The fact that price increased 

126 percent while production stayed 

stable supports this hypot kesis. 

During the 1970's, hardwood 

lumber producers faced rapidly increasing labor, roundwood input, 

and capital costs, Wage rates in 

sawmills increased by 127 percent, 

stumpage prices increased by 51 

percent, and interest rates increased by more than 22 percent. 

Using the information presented in 

Table 5, I estimated that lumber 

prices could increase by 175 percent in order to counteract the increases in production cost. However, better utilization of inputs, as 

probably represented by the positive 

time-trend coefficient, partially 

counteracted increased costs; thus, 

lumber price increased by only 126 

percent. 

Increases in production costs 

also caused lumber demand to remain stable during the last decade. 

During the 1970'~~ wage rates in furniture and other types of manufacturing nearly doubled and lumber 

price increased by 127 percent. According to the information contained in Table 5, output price could 
increase by 132 percent in order to 

counteract increases in costs. However, output prices only increased 

by approximately 90 percent, indicating that gains in input utilization 

were enough to counteract some of 

the increased input costs by the 

end of the decade. 

The 1980's 

Lumber prices of most hardwood species fluctuated during 

1980 and 1981. Although prices of 

IF and FAS red and white oak remained high, prices of most other 

species and lower grades of oak decreased t hru 1980 and increased 

only slightly in 1981. 

Lumber production increased in 

1980 and 1981, reaching pre-1970 

levels, while inventories were at the 

highest point in the last 30 years. 

All the while, domestic hardwood 

lumber demand decreased. These 

occurrences seem contradictory, 

since production does not usually 

increase during periods of increasing inventories and decreasing demand, and lumber price does not 

usually increase while domestic demand is decreasing and inventories 

remain high. 

The answer to these apparent 

contradictions can be found by 

looking at the export market. Exports to Europe remained high during 1980 and 1981, despite devaluation of European currencies against 

the dollar and slowed economic 

growth in most European countries. 

The increases in exports were predominantly FAS and IF red and 

white oak. Europeans paid high 

prices for the best grades, and thus 

kept these prices high. However, 

the lower grades did not sell because of decreased domestic demand; thus, inventories increased to 

the highest levels ever recorded. 

Conclusions 

One implication of the market 

model is that the hardwood lumber 

market is recursive. However, it differs from other recursive markets, 

such as wheat and other agricultural 

commodities, because demand, 

rather than supply, is a function of 

lagged price. This can cause demand and supply forces to be continually out of synchrony, causing 

continual fluctuations in production 

and usage. 

A Problem of Uncertainty 

A problem in markets with recursive attributes is the uncertainty 

created by constant fluctuations in 

quantities demanded and supplied 

and subsequent fluctuations in 

price. Uncertainty tends to discourage current and potential demanders from committing themselves to 

future use of hardwood lumber, and 

current and potential suppliers may 

be discouraged from purchasing expensive equipment and incorporating new technology. 

Slower implementation of technology affects the price of hardwood lumber on the supply side and 

contributes to nonincreasing demand. The end result of uncertainty 

is a potential misallocation of resources, less efficient production 

practices, and lower production and 

usage. 

Problems Affecting Supply 

lncreasing production costs 

forced suppliers of hardwood lumber to increase lumber price or go 

out of business, In Table 5, the 

single most influential factor affecting lumber production costs is wage 

rates. Lumber price can increase by 

as much as 1.07 percent for each 

1-percent increase in wage rates. 

Given that wage rates have increased more than any other input 

cost and will probably continue to 

do so in the future, high priority 

should be given to ways of increasing labor productivity. It should be 

remembered that better management and better work incentives 

may be just as important as labor 

saving machinery in increasing output per man-hour. 

Stumpage costs also contributed to the large increases in lumber 

prices. Although very little can be 

done to increase the interim stumpage supply, research in better 

utilization of existing stumpage 

would dampen future increases in 

lumber price, and better maintenance of existing stumpage and 

growing stock would also help keep 

lumber production costs down in 

the long run. 

lncreasing interest rates increased the cost of capital and, 

thus contributed to higher production costs. Given the current increases in interest rates, increasing 

labor productivity by better management and increased work incentives 

may be, at least, a temporary 

alternative to increased capitalization. 

Problems Affecting Demand 

Hardwood lumber users also 

faced steadily increasing production 

costs because of increases in wage 

rates and lumber price. Lumber 

price increases are not expected to 

subside in the future; therefore, if 

lumber costs are to be reduced, 

lumber users must strive for better 

utilization and increased use of less 

expensive, lower grade lumber and 

timber. Similarly, lumber users 

must increase labor productivity if 

future increases in labor costs are 

to be minimized. 
Another problem facing hardwood lumber users is overcapacity. 

Furniture manufacturers increased 

production capacity during the 

1970's in anticipation of increased 

demand, but the increase in demand 

did not materialize. Pallet producers 

increased production capacity with 

new equipment, but demand did not 

increase as fast as production 

capacity. Given this overcapacity, 

increasing labor utilization by managerial methods is a viable alternative to increasing production by increased capital expenditures. 

Outside Forces Affecting 

the Hardwood Lumber Market 

Much of the economic behavior 

of the hardwood lumber market is 

caused by forces that originate outside the market. The hardwood lumber market is small relative to other 

agricultural and industrial markets; 

therefore, interest and wage rates 

are not affected by actions occurring within the hardwood market. 

Output prices of goods manufactured from hardwood lumber are influenced by aggregate national demand and exports of hardwood lumber are affected by outside forces 

such as exchange rates and income 

levels of other countries. 

Producers and users of hardwood lumber have had to contend 

with forces affecting their market 

and will continue to do so. Thus, 

timely and accurate information on 

how these forces are expected to 

move in the future and the net effects of their movements aid in 

making more profitable production 

and usage decisions. Also, because 

of the effects of outside forces, 

lumber price cannot simply be 

assumed to follow some predescribed path in production and 

usage project ions; rat her, projections should be based on future 

movements of the outside forces 

and the interactions of usage, 

production, and price. 

Future Research Needs 

The analysis presented in this 

study presents an initial framework 

that can be used to understand the 

economic behavior of the hardwood 

lumber market. However, this research is only a starting point, as 

several important topics were only 

briefly discussed. 

It is crucial to the hardwood 

lumber industry to better understand and predict the fluctuations in 

hardwood lumber production, 

usage, and price. To anticipate 

these fluctuations, further research 

is needed to isolate and measure 

the relative contributions of internal 

and external forces. Such research 

should also be extended to simulate 

future levels of production, usage, 

and price under various market 

conditions. 

The supply equation presented 

in this study was based on aggregate data that lumped all species 

from all regions together. However, 

lumber demanders usually use specific species of lumber produced in 

a particular region. Therefore, future 

research concerned with estimating 

lumber supply equations by region 

and species would be highly beneficial to lumber users. 

In recent years, exports have increasingly affected domestic lumber 

price. In order to better anticipate 

export-induced price changes, the 

factors that affect exports must be 

quantified. Information gained by 

estimating export demand relationships would help in predicting 

future prices of hardwood lumber. 

The estimated price equation 

was also based on aggregate data. 

But lumber is produced, marketed, 

and priced on a species-and-grade 

basis so quantifying lumber price 

equations on that basis would be 

useful to both lumber demanders 

and suppliers. 

Increased labor costs without 

subsequent increases in labor 

productivity have contributed to the 

lack of growth in the hardwood lumber industry. Better labor utilization 

would help curb these costs increases. Research aimed at increasing labor productivity and improving 

utilization of all inputs into production and use of hardwood lumber is 

nesessary to increase the growth 

potential of this industry. 

The research discussed above 

would provide information that 

would be beneficial to current and 

potential lumber demanders and 

producers in making both short-run 

and long-run decisions. Since timely 

and accurate information reduces 

the amount of uncertainty felt by industry members, the end result of 

better information will be better 

planning and better resource allocation. 

Literature Cited 

Anderson, T. W. An introduction to 

multivariant statistical analysis. 

New York: John Wiley and Sons; 

1958. 374 p. 

Labys, W. C. Quantitative models of 

commodity markets. Cam bridge, 

MA: Ballinger Publ. Co.; 1975. 404 

P* 

McKillop, W. L. An econometric 

model of the market for redwood 

lumber. For. Sci. 15(2):159-170; 

1969. 

Mosak, J. L. interrelationships of 

production, price and derived demand. J. Polit. Econ. 

46(6):761-788; 1938. 

Nerlove, M. Distributed lags and 

estimation of long-run supply and 

demand elasticities, theoretical 

considerations. J. Farm Econ. 

40(2):301-311; 1958. 
U.S. Department of Commerce. 

Current industrial reports: lumber 

production and mill stocks. 

Washington, DC: U.S. Bur. 

Census; 1959-1978. 

U.S. Department of Commerce. 

Statistical abstracts of the United 

States. Washington, DC: U.S. Bur. 

Census; 1959-1978. 

U.S. Department of Commerce. U.S. 

exports schedule B. commodity 

by country. Washington, DC: U.S. 

Bur. Census; 1959-1978; Rep. 

FT410. 

U.S. Department of Commerce. U.S. 

imports for consumption and genera1 imports. Washington, DC: 

U.S. Bur. Census; 1960-1963; Rep. 

FT110. 

U.S. Department of Commerce. U.S. 

imports for consumption and general imports. Washington, DC: 

U.S. Bur. Census; 1964; Rep. 

FT125. 

U.S. Department of Commerce. U.S. 

imports for consumption and general imports. Washington, DC: 

U.S. Bur. Census; 1965-1978; Rep. 

FT246. 

Wold, Herman; Jureen, Lars. Dee 

mand analysis: a study in econometrics. New York: John Wiley 

and Sons; 1953.358 p. 
Appendix A 

Quantity Data Used in Model 

Estimation 

The data representing hardwood lumber exports used in this 

study do not include products 

manufactured from hardwood lumber. Products such as rail ties, hardwood flooring, and wood siding are 

no longer lumber and are not used 

as lumber. Although an argument 

can be made for untreated rail ties 

being considered as lumber, export 

data did not separate treated and 

untreated ties until after 1977. Since 

export information used in this 

study differed from previously published data, and imports were not 

used in calculating quantity demanded, a listing of all quantity 

data used in model estimation is 

presented below. Imports of 

Canadian lumber calculated from 

U.S. lmports for Consumption and 

General Imports, Report FT110 

(1960-1963), Report FT125 (1964), 

and Report FT246 (1965-1978), published by U.S. Department of Commerce, Bureau of Census, are also 

listed since this series was used in 

a preliminary estimate of the price 

model. These import statistics do 

not include any products manufactured from hardwood lumber. 

Quantity data used in the analyses, in million board feet 

Quantity Quantity Inventories Quantity Canadian 

Year supplied exported at sawmills demanded imports 
Appendix B 

Statistical Test for Joint Determination 

In estimating the price and 

supply equations by ordinary least 

squares (OLS) procedures, it was 

assumed that these two relationships were not jointly determined. If 

these relationships are not jointly 

determined, then the error terms between these relationships will be 

uncorrelated. The test presented in 

this appendix indicates that no significant correlation exists between 

these estimated relationships; therefore, OLS procedures resulted in 

best, linear, and unbiased estimates. 

The Test 

The hypotheses to be tested are: 

H,-the disturbance terms are 

not correlated 

Ha-t he disturbance terms are 

correlated 

The test statistic is: 

- K Ln(W) x2 F, 1 - d.f. 

where: 

K = (n + 1) - (2P + 11)/6 

n = degrees of freedom for the 

system of equations 

P = number of equations in 

the system 

W = the determinant of the 

correlation matrix of the disturbance 

terms across equations of the 

model 

F =r P x (P - 1)/2 

The correlation matrix of the disturbance terms of the supply and price 

equation is presented below: 

The system is composed of two 

equations and there are 24 degrees 

of freedom for the entire system of 

equations, therefore: 

The critical value of xZ, with 1 degree of freedom at the .05-percent 

level, is 3.841; therefore, we cannot 

accept the alternative hypothesis 

that the error terms are correlated at 

the .05 level of significance. 
Luppold, William G. An econometric model of the hardwood 

lumber market. Res. Pap. NE-512. Broomall, PA: U.S. Clepartment of Agriculture, Forest Service, Northeastern Forest Experiment Station; 1982.15 p. 

A recursive econometric model is used to analyze the effects 

of wage rates, interest rates, stumpage price, lumber exports, 

and output prices on the production, demand, and price of 

hardwood lumber. 

ODC 721.1 

Keywords: Demand, supply, price 
Headquarters of the NoPtheastern Forest Experiment Station are in 

Broomall, Pa. Field laboratories are maintained at: 

Arnherst, Massachetts, in cooperation with the University of 

Massachusetts. 

Berea, Kentucky, in cooperation with Berea College. 

0 Burlington, Vermont, in cooperation with the University of 

Vermont. 

Delaware, Ohio. 

0 Durham, New Hmpshire, in cooperation with the University of 

New Mimplillire, 

Hamden, Connwticut, in cooperation with Yale University. 

Morgantown, West Virghia, h coopration with West Virginia 

University, Morgantown. 

Orono, Maine, in cooperation with the University of Maine, 

Orono. 

Parsons, West Virginia. 

0 Princeton, West Virginia. 

Syracuse, New York, in cooperation with the State University of 

New York College of Environmental Sciences and Forestry at 

Syracuse University, Syracuse. 

0 University Park, Pennsylvania, in cooperation with the 

Pennsylvania State University. 

0 Warren, Pennsylvania. 

"-U.S. GOVERPXEKT PRINTIKG OFFICE: 1982-505-012:38