United States 

De~artmentof The Effect of Changes Agriculture 

Forest Service in Lumber and Furniture Prices 

Northeastern Forest 

Experiment Station 

on Wood Furniture Manufacturers9 

Research 

Lumber Usage 

Paper NE-514 

1983 William G. Luppold 
The Author 

William €3. Luppold attended 

the University of Florida where he 

received his B.S.A. and M.S.A. in 

food and resource economics in 

1974 and 1977, respectively. After re 

ceiving a Ph.D, in agricultural economics from Virginia Polytechnic Institute in 1981, he joined the Northeastern Forest Experiment Station's 

Forestry Sciences Laboratory at 

Princeton, West Virginia. He is currently conducting economic research concerning the hardwood 

lumber market. 

Manuscript received for 

publication 7 June 1982 

Abstract 

Wood furniture manufacturers' 

demands for oak, maple, poplar, 

open-grain, and close-grain lumber 

are estimated using cross-sectional, 

time-series techniques. The analyses indicate that the demand for 

open-grain species is more price responsive than the demand for closegrain species. The calculated crossprice elasticities indicate that furniture producers do substitute 

species through style decisions. 

However, poplar lumber has a negative cross-price elasticity, indicating 

that it is used with, rather than substituted for, other species. 
Introduction 

Wood furniture manufacturers 

are the major demanders of higher 

grade hardwood lumber; they use 

more than 24 percent of all hardwood lumber consumed in the 

United States. Because furniture demand is expected to increase as the 

"baby boom" generation establishes new households, demand for 

hardwood lumber by wood furniture 

manufacturers is expected to increase. This could lead to significantly increased lumber prices if 

current conditions in the hardwood 

lumber market persist. 

One major problem within the 

hardwood lumber market is lack of 

information on the inner workings 

of the market itself, Inadequate information makes markets inefficient 

because productive resources tend 

to be poorly allocated. Poor allocation of productive resources increases production costs and leads 

to increased consumer prices. The 

objective of this study is to provide 

some of this much needed information by quantifying the relationship 

between furniture manufacturers' 

demand for hardwood lumber and 

the prices of hardwood lumber and 

furniture. 

Such information would benefit 

lumber distributors, the furniture industry, and furniture consumers. 

Lumber distributors (producers and 

wholesalers) could use such information to better anticipate current 

and future demands for various 

species of hardwood lumber. The 

furniture industry would benefit 

from the actions of lumber distributors because adequate supplies 

would more likely be available at the 

time they are needed. Consumers 

would benefit from the eventual decrease in the relative price of furniture. 

Model Development 

Wood furniture manufacturers 

use many different species of hardwood lumber. The amount of a particular species used by a manufacturer is dependent on the price category and style of furniture being 

produced and the price of furniture 

in general. The price of one species 

may affect the demand for, or usage 

of, another species because of the 

relationship between past lumber 

prices and current styles being introduced at the furniture markets. 

Of course, this relationship is much 

weaker for a manufacturer specializing in high-priced 18th century reproductions than for a manufacturer 

producing several lines of popularpriced furniture. 

In this study, the quantity of 

hardwood lumber of a particular 

species demanded by a furniture 

manufacturer is assumed to be affected by: (1) the past prices of lumber of that species (own price), (2) 

the past prices of complementary 

and substitute species (cross price), 

(3) the wholesale price of furniture 

and (4) past quantity of lumber demanded. 

Lagged quantity is included in 

the model as an aggregation variable. This allows the demands of 

firms of various sizes to be estimated in the same equation. This 

variable also accounts for style expectations, since past lumber use is 

representative of past furniture 

styles produced by the firm. 

The major variables included in 

the general model and the expected 

relationships between the variables 

and the quantity demanded are specified in Table 1. This general specification is the basis for all estimated demand equations presented 

in the next section. 

Table 1.-The major factors, variables, expected relationships between variables and quantity 

demanded, and units for furniture manufacturers~umber demand equations 

Factor Variable Expected 

relation Units 

Lumber price of the 

species being demanded 

Lumber price of 

substitute or 

complementary species 

Wholesale price of 

wood furniture 

Lagged quantity 

Price index of lumber of the Negative Index (1974 = 100) 

species being demanded, lagged 

1-112 years (own price) 

Weighted price index of Positive Index (1974 = 100) 

substitute or complementary (substitute) 

species, lagged 1-112 years Negative 

(price of substitutes, complements) (complement) 

An index of the wholesale price Positive Index (1967 = 100) 

of furniture (furniture price) 

Quantity of lumber of the species Positive Million board feet 

being demanded, lagged 1 year 

(lagged quantity) 
Specification of Substitute 

and Complement Price Variables 

Since each estimated equation 

represents the demand by furniture 

manufacturers for a specific species 

of lumber, the variable representing 

the price of substitutes or complementary species is different for 

each equation. The variable representing the price of substitute 

species in the oak equation is the 

weighted price index of ash, pecan, 

elm, hackberry, maple, and white 

pine lumber. These species have 

some characteristics that may encourage a manufacturer to use 

them, rather than oak, when designing a suite. The first four species 

are chosen because they have an 

open grain. Maple is included because it and oak are intermediatepriced species. White pine is included because it is a substitue for 

oak in heavy, "over designed" furniture. 

The variable representing price 

of substitute lumber in the maple 

equation is the weighted price index 

of cherry, gum, and oak lumber. It is 

felt that these species have certain 

characteristics that allow them to 

be substituted for maple. Cherry 

and gum are close-grain species 

with some characteristics similar to 

maple lumber, while both oak and 

maple are intermediately priced. 

The cross-price variable for 

open-grain lumber contains the 

weighted price index of all lumber 

not considered open grain. While 

the price of substitute lumber in the 

close-grain equation is the weighted 

price index of all non-close grain 

lumber, no cross-price variable is included in the demand for all lumber 

because the weighted price of all 

species of lumber is included in the 

own-price variable. 

The weighted price index of all 

species other than poplar is used as 

the price of complements in the 

poplar demand model. We assume 

that poplar is used with, rather than 

substituted for, other species of 

lumber. It should be noted that the 

data base for the poplar demand 

equation does not contain any promotional furniture producers. Promotional furniture producers use 

poplar in exterior parts and may 

substitute poplar lumber for sweet 

gum, black gum, or other inexpensive woods that can be easily embossed. 

Data Base 

The quantity data used in this 

paper were originally collected for a 

study of wood furniture manufacturers' demands by Luppold (1981). 

These data consist of lumber usage 

statistics, by species, for the years 

1974 through 1979 by 11 wood furniture producers. These producers 

employed 250 or more production 

workers each and were located in 

Virginia, North Carolina, and South 

Carolina. All firms included in the 

final sample produced several different lines of furniture and used several different species of hardwood 

lumber. Lumber price data were obtained from the Hardwood Market 

Report (Lems ky 1972- 1978) and 

wood furniture price data were collected from Wholesale Prices and 

Price Indexes (US. Department of 

Labor 1974- 1979). 

The firms included in the data 

base are representative of the larger 

wood furniture manufacturers in the 

Southeast. Wood furniture firms in 

this region account for more than 50 

percent of the national production, 

and firms employing 250 or more 

workers account for about 75 percent of the materials used in wood 

furniture manufacturing (US. Department of Commerce 1980). 

Equation Estimation 

Demand relationships were 

estimated for oak, maple, and poplar 

lumber, as well as for open-grain 

lumber, close-grain lumber, and all 

lumber as an aggregate. These estimated relationships are presented 

and compared in this section. 

Since the data base consists sf 

lumber usage over time by several 

firms, the equations were estimated 

by the ordinary least squares (ObS) 

and cross-sectional time-series 

(CSTS) techniques. Results from 

both estimation procedures are presented to show the advantages and 

disadvantages of each technique, 

The Parks (1 967) cross-sectional 

time-series algorithm was used because it accounts for contempsraneously correlated errors between 

cross sections that may result from 

the omission of unknown or unmeasurable variables. The Parks 

method also adjusts for aulocorrelation within time series and heteroskedasticity across cross sections, 

A rigorous development of the 

Parks method is presented in the 

Appendix. 

Because pooled cross-sectisnai 

and 'rime-series data are used, estimated responses to changes in 

prices (price elasticities) cannot be 

strictly interpreted as being either 

longrun or shortrun in nature. However, since there was much more 

variation in the prices over time 

than there was over the firms, the 

resulting elasticities are mare representative of shortrun responses. 

The results of the QLS eslimates are presented in Table 2, 

while the CSTS estimates are presented in Table 3. The standard errors associated with atmast a81 the 

parameters are reduced by as much 

as 94 percent by using "ike Parks 

estimation procedure. Fur"iher, the 

magnitudes of the coefficients do 

not differ significantly between the 

OLS estimates and "Ehe CSTS estimates except for the mapie mode!, 

The decrease in standard error witkout a radical change in the magnitude of the estimated coefficients 

indicates that the Parks method did 

yield statistically more efficient estimates than did OLS, 
"I"abls 2.mOrdinary least squares estimates of wood furniture 

manufacturers' demand for hardwood lumber, by species, 

1975- 1979 (standard errors in parentheses) 

Oak Maple Poplar Open All 

lumber lumber lumber grain grain lumber 

lumber lumber 

l ntercept - 3832 

(3 1 39) 

Own price - 32.61d 

(26.86) 

Price of 59.64a 

substitutes and (22.91) 

complements 

Price of 5.03 

furniture (29.1) 

bagged .857a 

quantity (. 065) 

R2 ,905 

F-value 59.6 

Degrees of 25 

freedom 

Meanquantity(Mbf) 5470 

a = Significant at the .O1 level. 

b = Significant at the .05 level. 

c = Significant at the .10 level. 

d = Significant at the .I5 level. 

NA = Not applicable. 

Table 3.-Cross=sectional time-series results of wood furniture 

manufacturers' demand for hardwood lumber, 1975-1979 

(standard errors in parentheses) 

Oak Maple Poplar Open Close All 

lumber lumber lumber grain grain lumber 

lumber lumber 

Intercept 

Own price 

Price of 

substitutes and 

complements 

Price of 

furniture 

Lagged 

quantity 

Degrees of 

freedom 

Mean quantity (M bf) 

a == Significant at the .O1 level. 

h = Significant at the ,05 level. 

c = Significant at the .1O level. 

d = Significant at the .15 level. 

NA = Not applicable. 
lnterpretling the Results 

The effect of changes in lumber 

or furniture price on quantity of iumber demanded is exhibited in Table 

4 in the form of price elasticities. 

These elasticities indicate the percentage change in quantity demanded resulting from a 1-percent 

change in price. Own-price elasticity 

represents the effect of a change in 

price of a particular species on the 

demand for that species, while 

cross-price elasticity represents the 

effect of a change in prices of other 

species. 

As previously mentioned, the 

elasticities are more representative 

of shortrun responses to changes in 

prices, since most of the variation 

in the data base occurred in the 

time-series data rather than in the 

cross-sectional data. Since furniture 

producers respond to past lumber 

prices and current furniture price, 

the estimated lumber-price elasticities are indicative of the likely response 1 to 2 years after a change 

in lumber price, and the furnitureprice elasticity represents the response in the current year to a 

change in furniture price. 

In general, open-grain lumber 

was found to be more price-elastic 

with respect to its own price and 

the price of substitutes, and less 

price elastic with respect to furniture price than was close-grain lumber. One exception to this rule was 

maple, which had the highest ownprice elasticity and the lowest 

furniture-price elasticity. These results indicate that open-grain lumber demand is more affected by 

lumber price and close-grain lumber 

demand is more affected by furniture price. 

Another general observation 

that can be made is that the crossprice elasticities are nearly as high 

or higher than the own-price elasticities in the oak, open-grain, closegrain, and poplar equations. This indicates that prices of other lumber, 

when taken as a group, affect demand for a particular species by 

about the same amount as the price 

of that species. Again, one exception to this rule is maple, which appears to have a very low cross-price 

elasticity. 

The estimated cross-price elasticity of poplar is negative. This 

finding supports the hypothesis that 

poplar is a complement to other 

lumber and not a substitute. The 

low own-price elasticity was also expected, since poptar is used as an 

interior lumber with a number of different exterior species. 

The own-price elasticity for all 

lumber demanded is - .09, which is 

quite low. This is not surprising 

since wood furniture manufacturers 

must use wood. The furniture-price 

elasticity of .49 is also quite low 

when compared with the demand 

equations for the different species. 

The elasticities calculated from 

the estimated maple demand equation are much different for the elasticities of the other equations. 

These results may be due to some 

peculiar characteristics of maple, 

but also may result from the rele 

tively poor statistical fit of the 

maple equation. The OLS estimates 

for the maple equation had a low R2 

and incorrect signs for three of the 

four nonintercept variables. Although the CSTS results had the 

correct signs on all variables, the 

standard errors associated with the 

estimated parameters were relatively high. 

Table 4.--Own-price, cross-price, and furniture-price elasticities for wood 

furniture manufacturers' demand for hardwood lumber, 1975-1979 

Model Crossprice Furniture-price 

elasticity elasticity 

Oak lumber 

Maple lumber 

Poplar lumber 

Open-grain lumber 

Close-grain lumber 

All lumber 

a All elasticities were calculated at the means using the cross-sectional time-series parameter estimates, by the following formula: 

a quantity demanded (mean of price) 

a price (mean of quantity demanded) 

NA = Not applicable. 
Implications 

Two major implications of this 

study are: (1) past lumber and current furniture prices affect wood furniture manufacturers' demand for 

lumber, and (2) current demand for a 

particular species is affected by 

past prices of other species. With 

respect to the second implication, it 

should be noted that most furniture 

manufacturers do not directly substitute one species for another; 

rather, past lumber prices affect current design and style decisions. The 

degree to which past lumber prices 

affect current design varies from 

firm to firm. But the sizes of the 

estimated cross-price elasticities 

relative to the own-price elasticities 

indicate that large firms do consider 

past lumber prices when developing 

and promoting different styles of 

furniture. 

Another implication is that 

wood furniture manufacturers' demand for hardwood lumber, as a 

whole, is quite inelastic with respect to the price of hardwood lumber. However, these manufacturers' 

demand for lumber of specific 

species or groups of species is 

much more elastic. Of the individual 

species and species groups, opengrain, oak, and maple lumber are 

more price-elastic than poplar and 

close-grain lumber. 

Furniture manufacturers' demand for close-grain lumber is relatively inelastic with respect to the 

price of close-grain lumber and the 

price of substitute species, but is 

relatively elastic with respect to 

price of furniture. These results indicate that the demand for species 

used in traditional types of furniture, such as cherry and mahogany, 

is not greatly affected by the prices 

of substitute species, but is influenced by the price of wood furniture. 

Maple lumber demand is different from the demand for other 

close-grain species in that maple 

demand is relatively price-elastic. 

However, demand for maple lumber 

is similar to the demand for closegrain species in that cross-price 

elasticity is relatively low and 

furniture-price elasticity is relatively 

high. These results may suggest 

that maple lumber demand is greatly affected by the price of maple 

lumber and the price of wood furniture, but these results must be interpreted with caution since the statistical fit of this equation was relatively poor. 

The estimated results of the demand for open-grain lumber indicate 

little difference between own-price 

elasticity, cross-price elasticity, and 

furniture-price elasticity. This indicates that the price of open-grain 

lumber, the price of substitute species, and the price of furniture have 

about an equal effect on the demand for open-grain species. 

Oak lumber demand is different 

from the demand for all open-grain 

species in that the absolute values 

of the cross-price and own-price 

elasticities are up to 35 percent 

larger than the furniture-price elasticity. However, the furniture-price 

elasticity for oak is very close to the 

furniture-price elasticity for all opengrain species. These results imply 

that the demand for oak lumber is 

more responsive to changes in the 

price of oak and other species than 

it is to changes in the price of furniture. 

The estimated demand for poplar lumber indicates a relatively inelastic own-price elasticity and a 

relatively elastic furniture-price elasticity. The negative cross-price elasticity indicates that poplar lumber is 

used in conjunction with, rather 

than as a substitute for, lumber 0.5 

other species. The results also indicate that poplar lumber demand is 

elastic with respect to the price of 

wood furniture. 
Summary and Conclusions 

Furniture manufacturers are the 

major demanders of higher grade 

hardwood lumber. Their demands 

are expected to increase in the 

future because of an expected increase in furniture demand. lncreased lumber demand will inevitably lead to increased lumber price. 

The level lumber price will reach is 

uncertain since many factors affect 

it; however, increasing the efficiency of the hardwood lumber market would help to keep future price 

increases at a minimum. 

One major ingredient of market 

efficiency is good market information. The objective of this study was 

to provide some of the needed information by developing and estimating relationships that measure the 

effect of lumber and furniture prices 

on wood furniture manufacturers' 

demand for lumber. 

Equations representing furniture manufacturers' demands for 

oak, maple, poplar, open-grain, 

close-grain, and all varieties of lumber were estimated using OLS and 

CSTS techniques. The results indicate that wood furniture manufacturers do substitute species to reduce costs; but this substitution 

takes place over time and not immediately. Such substitutions will 

cause fluctuations in the prices of 

individual species rather than in the 

aggregate price of hardwood lumber. 

Future analysis using crosssectional time-series data from 

more firms and in separate regions 

would provide greater and more refined information on wood furniture 

manufacturers' lumber demands. Information pertaining to the substitution of other wood products and 

nonwood products for lumber would 

also be of great value in predicting 

future market behavior. 

In conclusion, wood furniture 

manufacturers' demand for lumber 

sf various species is price-sensitive. 

Lumber distributors should realize 

this before making long run commitments. Forest industry groups and 

policymakers should also realize the 

degree to which one species can 

substitute for another before advocating legislation aimed at ensuring 

adequate domestic supplies of any 

particular species. 

Literature Cited 

Lemsky, A., ed. Hardwood market report. Memphis, TN: Abe Lemsky; 

1972- 1978. 

Luppold, W. Demand, supply, and 

price of hardwood lumber: an ece 

nometric study. Blacksburg, VA: 

Virginia Polytechnic Institute and 

State University; 1981. 139 p. Dissertation. 

Parks, R. W. Efficient estimators of a 

system of regression equations 

when the disturbances are both 

serially and contemporaneously 

correlated. J. Am. Stat. Assoc. 

62:500-509; 1967. 

U.S. Department of Commerce. 

Household furniture; 1977 census 

of manufacturing. lnd. Ser. 

MC77-1-25A. Washington, DC: 

U.S. Department of Commerce; 

1980. 

U.S. Department of Labor. Wholesale 

prices and price indexes. Washington, DC: U.S. Department of Labor; 

1974- 1979. 
Appendix 

The Parks Method of 

Cross-Sectional Time-Series 

Estimation 

When equations are estimated 

with ordinary least squares and 

pooled cross-sectional and timeseries data, the resulting parameter 

estimates are unbiased and consistent. However, these estimates may 

be inefficient because of the effects 

of autocorrelation and heteroskedasticity. The Parks method is an 

Aitken's generalized least square 

procedure that incorporates prior information of the disturbance term in 

the estimation of the parameters. 

The resulting parameter estimates 

have the properties of consistency, 

unbiasedness, asymptotic eff iciency, and asymptotic normality. 

The general form of a statistical 

rnodei containing k variables and 

using pooled cross-sectional and 

time-series data can be expressed 

as: 

The sample data are represented by T time-series and N 

cross-sectional observations for a 

total of N x T observations. The 

statistical model can be expressed 

in matrix notation as follows: 

Where Y is an (N x T) x 1 vector of observations of the dependent variable, X is an (N x T) x 

(k + 1) matrix of observations of 

predetermined variables, B is a (k + 

1) x 1 vector of parameters and E is 

an (N x T) x 1 vector of disturbance terms. The ordinary least 

squares estimates for the model 

are: 

B = (xfx)-l X'Y PI 

Given the general model, the 

following assumptions are made: 

(i) E(E, hl) = R, where: 

(ii) = oij 

(ii) the predetermined variables 

are nonstochastic and are independent of the disturbance 

term. 

(iii) the number of observations 

exceeds the number of predetermined variables plus the 

intercept. 

The specification of the behavior of the disturbance term for 

models estimated using time-series 

data pooled cross-section and time. 

series is: 

(i) E(Eit2) = Oii 

where: 

pit hl N(O, hi) 

E(E~,~-pit) = 0 for all i, j 

Ebitt pjt) = +ij(i + j) 

Ebit, pis) = O(t # S) 

Condition (i) allows crosssectional heteroskedastici ty, condition (ii) allows mutual correlation of 

the disturbance term across cross 

sections and, condition (iii) permits 

a separate first-order autoregression 

scheme for each cross section. The 

autoregressive disturbance term, pit, 

is assumed to be normally distributed with a constant variance and 

zero covariance between time 

periods for the same cross-sectional 

unit (furniture firm). The autoregressive disturbances during the same 

time period are correlated across 

cross sections, but the autoregressive disturbance for firm i, in period 

t, and firm j, in period s, for s = t 

are assumed to be independent. 

Finally, Ej,t- ?, and pit are assumed to 

be independent. 
Given the specification of the 

behavior of the disturbance term, 

the following relationships can be 

developed: 

(i) E(glt2) = +iill - Pi2 = Uii 

(ii) E(&iqt) = 41iijl - Pi Pj = Oil 

(iii) E(L~~~~) = pit-Soii if t is greater 

than s 

(iv) E(qt, qs) = pif - '0ij (i = j) 

i,j= 1 ,....., N 

The initial disturbance term, 6, 

associated with the pooled crosssectional time-series data is assumed to have the following properties: 

The matrix for the Parks model is: 

where: 

The Parks method estimates an 

P matrix by first estimating a value 

for from an ordinary least square 

estimate. Using ordinary least 

squares, the following equation is 

estimated: 

Yit* = Bo* + Bl*Xlt* + . . . . + 

~~*x~~* + pit* [41 

where: 

Bo* = Bo(1 - ,pi) 

Faom the residuals ~f the above 

estimation, pit* is calculated. 

From these residuals, estimates 

of gii, +ij, oil, and oil are obtained by: 

This procedure yields consistent estimates of oii and gij, therefore, a consistent estimate of $2 is 

obtained. Finally, using the Aitksn's 

procedure, 

B = (xf@-lx)-l (xa- ly) 151 

where 2 is a consistent estimator 

for a. The asymptotic variancecovariance matrix of B is: 
* U. S. GOVERNMENT PRINTING OFFICE: 1983-605-024 

Luppold, William G. The effect of changes in lumber and fur. 

niture prices on wood furniture manufacturers' lumber 

usage. Res. Pap. NE-514. Broomall, PA: U.S. Department of 

Agriculture, F~rest Service, Northeastern Forest Experiment 

Station; 1983. 8 p. 

Wood furniture manufacturers' demands for oak, maple, poplar, open-grain, close-grain, and all species of lumber were developed using cross-sectional time-series estimation techniques. 

ODC 721.1 

Keywords: Economics; oak; maple; poplar 

? 
Headquarters of the Northeastern Forest Experiment Station are in 

Broomall, Pa. Field laboratories are maintained at: 

Amherst, Massachusetts, in cooperation with the University of 

Massachusetts. 

0 Berea, Kentucky, in cooperation with Berea College. 

Burlington, Vermont, in cooperation with the University of 

Vermont. 

Delaware, Ohio. 

Durham, New Hampshire, in cooperation with the University of 

New Hampshire. 

Hamden, Connecticut, in cooperation with Yak University. 

Morgantown, West Virginia, in cooperation with West Virginia 

University, Morgantown, 

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

Orono. 

Parsons, West Virginia. 

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.