The Determinants of 

Forest Service 

Northeastern Forest Hardwood Lumber Price 

Experiment Station 

Research Paper 

N E-558 

William G. Luppold 

Jennifer M. Jacobsen 

1985 
The Authors 

William G. 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 receiving 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 on the hardwood lumber market. 

Jennifer M. Jacobsen attended Randolph-Macon Woman's College 

where she received her B.A. in Biology and Economics in 1978. At Virginia 

Polytechnic Institute, she received her M.S. in Agricultural Economics in 

1981. Currently, she is a research associate at Virginia Polytechnic Institute 

examining the international\lumber markets. 

Abstract 

Increased export activity in the hardwood and oak lumber markets 

coincided with rising prices of these commodities, which also coincided 

with an increase in the overall price level of all commodities. To determine 

the effect that exports have on the prices of hardwood and oak lumber, 

relative price models for these commodities were developed. Relative, 

rather than actual or nominal, price models were used to remove the 

effects of inflation. The models indicated that exports to Europe have had 

and will have an influence on hardwood lumber prices. Oak price seems to 

be more sensitive to changes in exports than overall hardwood lumber 

price. However, the main determinants of hardwood lumber and oak lumber 

prices were found to be domestic demand and millstock levels. 
Introduction 

Before 1973, exports of hardwood lumber were a minor part of 

the U.S. hardwood lumber market. 

Except for a temporary intrusion of 

Japanese buyers into the hard 

maple market in the early 197O9s, 

there was little export activity in the 

hardwood lumber market until 

European buyers started to increase 

their purchases of oak lumber. In 

1973, European demands accounted 

for only 5 percent of hardwood 

lumber exports; by 1980, exports to 

Europe accounted for 34 percent of 

the domestic hardwood lumber 

exported (Fig. 1). More significantly, 

the European share of oak exports 

increased from less than 6 percent 

in 1973 to more than 45 percent in 

1980. These increases occurred 

during a period when total hardwood exports increased 91 percent 

and oak lumber exports increased 

182 percent. 

The export boom in the hardwood lumber market brought greater 

profits to producers and distributors 

of hardwood lumber, and to a small 

extent, improved the balance of payments with Western Europe. One 

suspected drawback of increased 

exports was increased lumber price, 

especially for oak. 

The allegation that increased 

exports lead to increased hardwood 

lumber price results from the strong 

correlation between increased 

exports (Fig. 1) and increased nominal' lumber price (Fig. 2). The movement of hardwood lumber and No. 1 

Common oak lumber prices seems 

to parallel exports to Europe, even 

though exports are primarily composed of grades Firsts and 

Seconds. Exports of higher grades 

indirectly affect overall prices of 

hardwood lumber because 

increasing the price of higher grade 

lumber increases the domestic 

Nominal price is the price that 

exists in the marketplace. Real price is 

the nominal price divided by the true rate 

of inflation. Relative price is nominal 

price divided by a nominal price of 

another commodity or commodity group. Relative price may be a reasonable measure of real price if the adjusting index is 

based on a broad composite of 

commodities. 

demand pressures for lower grade 

lumber. 

The trends exhibited in Figure 2 

must be interpreted with some 

skepticism since inflation and 

expectations of further inflation 

were also prevalent during the 

period when exports increased. 

From 1973 to 1980, when oak price 

increased 116 percent, the general 

price index for all commodities rose 

by 100 percent. To assess the true 

effect of exports on the hardwood 

lumber market, the effects of inflation should be accounted for. 

The prices of oak and hardwood lumber relative to the price of 

all commodities are shown in Figure 

3. Although the relative price of oak 

has fluctuated above the 1967-100 

baseline, these fluctuations are not 

nearly as dramatic as the increase 

in nominal oak price. The relative 

price of hardwood lumber has also 

tended to fluctuate above the baseline, but not to the same degree as 

oak lumber price. These fluctuations 

may indicate that exports did have 

some effect on domestic hardwood 

lumber prices; however, other 

factors such as demand and supply 

YEAR 

(SOURCE: U.S. DEPARTMENT OF COMMERCE) 

Figure 1.-Indexes of quantities of oak and hardwood lumber exported to European 

and non-European countries. (Source: U.S. Department of Commerce) 
Model Development 

forces within the domestic hardwood lumber market could also 

have contributed to these fluctuations. The objective of this paper is 

to isolate and measure the determinants of oak and hardwood 

lumber price to assess the impact 

of exports on prices of oak and 

hardwood lumber. 

Luppold (1982) developed an 

equation for nominal hardwood 

lumber price as part of a system of 

equations depicting hardwood 

lumber demand, supply, and price. 

The price equation was estimated 

using ordinary least squares (OLS) 

procedures because the hardwood 

lumber market was assumed to be 

- Relative Price of Oak Lumber 

--- Relative Price of Hardwood Lumber 

recursive, with quantity of hardwood 

lumber demanded being a function 

of past lumber price, and because 

the error term associated with the 

estimated equations was found to 

be uncorrelated. 

The specification of Luppold's 

(1982) price equation included variables representing past lumber price, 

quantity of lumber demanded 

domestically, quantity of lumber 

exported, and millstocks. Past price 

was included as a measure of price 

expectations, domestic demand and 

exports were included to account 

for the effects of these demands on 

price, and millstocks were included 

to determine the effects of changes 

in inventories. In this type of model 

specification, supply does not enter 

directly into the price equation; but 

the effects of supply are reflected in 

changes in inventories. Therefore, 

the inclusion of the domestic 

demand and millstock variables 

accounted for the demand and 

62 64 66 68 70 72 74 76 78 80 

YEAR 

Figure 2.-Indexes of oak and hardwood lumber prices. 

62 64 66 68 70 72 74 76 78 80 

YEAR Source - Bureau of Labor Statistics 

Figure 3.-Indexes of relative prices of oak and hardwood lumber (relative to the 

price index for all commodities). 
supply forces in the domestic hardwood market, while the export 

variable accounted for the demand 

forces outside the domestic.market. 

The weakness in Luppold's 

specification is that one cannot 

separate the influence of exports 

from the influence of inflation and 

expectations of inflation since all 

followed similar paths. Therefore, 

the influence of exports could have 

been over- or underestimated in 

Luppold's specification. A real-price 

model or its operational proxy, a 

relative price model, would resolve 

this problem. The models to be 

presented in this paper are relative 

price models with the price expectation variable. 

Another difference between the 

specification of the current price 

equations and Luppold's (1982) 

specification is that European and 

non-European exports are represented by separate variables. This 

allows us to separate the effects of 

European exports from those of 

exports in general and also to test 

whether European exports affect 

domestic lumber price differently 

from non-European exports. The 

specific definition of the variable to 

be included in the hardwood lumber 

and oak lumber relative price equations is outlined in Table l. 

Table 1.-Dependent variables for the hardwood lumber and oak lumber price equations 

Variable 

Actual variable used in 

hardwood lumber price model 

Actual variable used in 

oak lumber price model 

Quantity demanded Quantity of hardwood lumber domestically 

domestically consumed in current year 

Exports to Quantity of hardwood lumber exported to 

Western Europe Western European countries 

Exports outside of Quantity of hardwood lumber exported to 

Western Europe other than Western European countries 

Millstocks Average level of millstocks of hardwood 

(inventories) lumber at end of current year and past year 

Quantity of hardwood lumber domestically 

consumed multiplied by the proportion of 

oak lumber produced 

Quantity of oak lumber exported to 

Western European countries 

Quantity of oak lumber exported to other 

than Western European countries 

Average level of millstocks of hardwood 

lumber multiplied by the proportion of oak 

lumber produced in current year and past 

year. 
Data Base Model Estimation 

The data base used in the estimation of the hardwood lumber 

price equation and the oak lumber 

price equation extended from 1960 

through 1980. All data were 

obtained or derived from secondary 

sources. 

Indexes for hardwood lumber 

price, oak lumber price, and the 

producer price index of all commodities were obtained from U.S. 

Department of Labor, Producer 

Price and Price Indexes. Since no 

aggregate oak price representing all 

grades and species was available 

through the time period under 

study, the price of No. 1 Common 

red oak was used as the dependent 

variable in the oak price equation. 

Quantities of hardwood lumber 

and of oak lumber exported were 

obtained from U.S. Exports, 

Schedule 5, Commodity by Country. 

Millstock and lumber production 

figures were obtained from U.S. 

Department of Commerce, Bureau 

of the Census, Current Industrial 

Reports: Lumber Production and 

Mill Stocks. Quantity of hardwood 

lumber demanded domestically was 

derived by subtracting exports and 

changes in millstocks from production figures. 

The quantity of oak lumber 

demanded and the millstocks of oak 

lumber were estimated by multiplying the proportion of oak lumber 

produced by domestic quantity 

demanded and by millstocks, 

respectively. The proportion of oak 

lumber produced was calculated by 

dividing oak lumber production by 

total hardwood lumber production. 

The statistically estimated price 

equations for hardwood lumber and 

oak lumber are presented in Table 2. 

Both equations fitted the data relatively well, as indicated by the R2's 

and the "t" statistics. The nonintercept variables representing 

exports to Europe, millstocks, and 

domestic demand were significant 

at the 0.10 level or better. The 

variable representing non-European 

exports was insignificant in both 

equations. The Durbin Watson (DW) 

statistics of both equations fell into 

the inconclusive range, so the 

hypothesis of autocorrelation could 

not be accepted or rejected. 

The price equations were estimated by taking the natural logarithms of the independent and 

dependent variables, then estimating their relationships by OLS 

procedures. The equations resulting 

from the transform data are in multiplicative form, and the resulting 

parameter estimates can be directly 

interpreted as price flexibilitie~.~ 

Flexibilities are used in interpreting price equations as elasticities are 

used to analyze demand and supply 

equations. Mathematically, a flexibility is the (aPIaQ) (QIP) where Q represents a 

quantity and P represents commodity 

price. This contrasts with the elasticity 

aQ P 

formula of .p~. Given the multiplicative form, P = Qb, where b is the estimated parameter, (aPIaQ), (QIP) = b Qb- 1 

(QIQb) = b. 

Table 2.-Ordinary least squares estimates for 

hardwood and oak lumber price 

equations (t statistics in 

parentheses) 

Item Hardwood lumber Oak lumber 

Intercept 4.&6* - 0.066 

(2.32) (0.141) 

Quantity demanded 0.610** 1 .44a 

domestically (3.50) (2.51) 

Exports to 0.01 7* 0.074* * 

Western Europe (1.52) (3.41) 

Exports outside of - 0.046 - 0.119 

Western Europe (0.81 5) (0.942) 

Millstocks - 0.662* * - 0.931 * * 

(6.47) (4.78) 

R2 0.822 0.819 

DW 1.31 0.90 

t* = Significant at the 0.01 level 

= Significant at the 0.05 level 

a = Significant at the 0.10 level 
Analysis 

"Price flexibility" is the 

percentage change in price 

resulting from a 1-percent change in 

an independent variable (Tomek and 

Robinson 1972). Flexibilities have 

been widely used to analyze agricultural markets in which demand and 

supply forces are buffered by the 

existence of a large fluctuating 

inventory. Although hardwood 

lumber does not exhibit the 

seasonal inventory extremes 

common in the soybean, corn, and 

wheat markets, millstocks of lumber 

account for as much as 17 percent 

of the annual production and can 

vary by 45 percent in a single year. 

Flexibilities can be viewed as 

inverse elasticities to the extent 

that the more elastic a demand for a 

commodity is, the lower its flexibility. Luppold (1984) found that the 

European demand for oak lumber 

was quite elastic, and Luppold 

(1 982) found domestic hardwood 

lumber demand to be near unitary 

elasticity. These results are 

supported by the current study, : 

since export demand flexibilities are 

much smaller than domestic 

demand flexibilities. Since the nonEuropean export coefficient wasinsignificant, future use of the term 

"price flexibility of exports" refers 

to exports to Western Europe. . , 

The estimated price flexibilities 

indicate that oak lumber price is 

affected by changes in domestic 

demand, millstocks, and exports to 

a greater degree than is hardwood 

lumber price. This finding may 

explain why oak price tended to 

fluctuate more than hardwood 

lumber price even during the pre1973 period when exports were a 

minor part of the market. The 

increased divergence between oak 

lumber and hardwood lumber price 

fluctuations since 1973 (Figs. 2 and 

3) probably results from the facts 

that (1) changes in oak exports 

affect oak price more than changes 

in hardwood exports affect hardwood price, and (2) changes in oak 

exports to Europe have been greater 

than changes in hardwood lumber 

exports. 

Another interesting fact demonstrated by the estimated price flexibilities is that a I-percent change in 

domestic demand or millstocks has 

a much larger influence on hardwood lumber and oak lumber prices 

than a 1-percent change in exports. 

In the case of oak lumber price, 

exports would have to increase by 

19.5 percent to have the same 

impact as a 1-percent change in 

domestic demand and by 12.6 

percent to have the same impact as 

a 1-percent change in millstocks. 

During the 1972-to-1980 period, 

yearly changes in domestic demand 

averaged 6 percent, yearly changes 

in millstocks averaged 12 percent, 

and yearly changes in exports 

averaged 50 percent. Analysis based 

on these 1972-1980 average yearly 

changes shows that changes in 

domestic demand affected oak 

lumber price 2.3 times as much as 

changes in exports and changes in 

millstocks affected oak lumber price 

3 times as much as changes in 

exports. Similarly, changes in 

domestic demand affected hardwood lumber price 5.2 times as 

much as changes in exports, and 

changes in millstocks affected price 

10.1 times as much as changes in 

exports. 

The above analysis should not 

be interpreted as indicating that 

exports have little discernible effect 

on oak and hardwood lumber prices. 

During the late 19703, when 

domestic demand was increasing 

and millstocks were decreasing, 

increased levels of exports helped 

push lumber prices up even further. 

On the other hand, during 1979 and 

1980, when domestic demand was 

decreasing and inventories were 

increasing, increases in exports 

helped moderate the drops in hardwood lumber and oak lumber prices. 

However, since 1980, changes in 

export demand have moderated; 

therefore, the effect of exports on 

hardwood lumber prices has 

moderated. 
Conclusions Literature Cited 

Increases in exports of hardwood and oak lumber to Europe did 

contribute to the increases in the 

nominal and relative prices of these 

commodities during the 1970's. 

Exports affected oak lumber price 

more than hardwood lumber price 

because: (1) The increase in oak 

exports to Europe was 20 percent 

greater than the exports of all hardwood lumber to Europe, and (2) a 

1-percent change in exports affects 

oak price 3.3 times as much as a 

1-percent change in hardwood 

lumber affects hardwood lumber 

price. However, changes in 

domestic demand and millstocks 

have had more influence on hardwood lumber and oak lumber prices 

than changes in exports. Furthermore, changes in exports of hardwood lumber have leveled during 

the last 5 years. Therefore, exports 

of hardwood and oak lumber can be 

thought of as contributing to the 

formation of hardwood lumber 

prices, but domestic demand and 

level of millstocks have been and 

will be the major factors that 

influence domestic hardwood 

lumber prices. 

Luppold, William G.An econometric 

model of th'e hardwood lumber 

market. Res. Pap. NE-512. 

Broomall, PA: U.S. Department of 

Agriculture, Forest Service, North. 

eastern Forest Experiment 

Station; 1982. 15 p. 

Luppold, William G. An analysis of 

European demand for oak lumber. 

Res. Pap. NE-538. Broomall, 

PA: U.S. D,epartment of 

Agriculture, Forest Service, 

Northeastern Forest Experiment 

Station; 1984. 7 p. 

Tomek, William G.; Robinson, 

Kenneth L. Agricultural product 

prices. Ithaca, NY: Cornell 

University Press; 1972. 378 p. 

U.S. Department of Commerce, 

Bureau of the Census. Current 

industrial reports: lumber production and mill stocks. Washington, 

DC: U.S. Department of 

Commerce; 1961-1980. 

U.S. Department of Commerce, 

Bureau of the Census. U.S. 

exports, Schedule B. commodity 

by country. Washington, DC: U.S. 

Department of Commerce; 

1961-1979. 

U.S. Department of Labor. Producer 

prices and price indexes. 

Washington, DC: U.S. Department 

of Labor, 1961-1980. 
Luppold, William G.; Jacobsen, Jennifer M. The determinants 

of hardwood lumber price. Res. Pap. NE-558. Broomatl, 

PA: U.S. Department of Agriculture, Forest Service, Northeastern Forest Experiment Station; 1985. 6 p. 

Econometric equations were estimated to determine the 

effects of domestic foreign hardwood lumber demands on 

oak and hardwood lumber prices. Oak price seemed to be 

more sensitive to changes in exports than overall hardwood 

lumber price.' However, the main determinants of hardwood 

lumber and oak lumber prices were found to be domestic 

demand and millstock levels. 

ODC 722.4 

Keywords: Economics; demand; oak 

*U. S. GOVERNMENT PRINTING OFFICE: 1985-505-028:20000 
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. 

0 Delaware, Ohio. 

Durham, New Hampshire, in cooperation with the University of 

New HampsYre. 

0 Hamden, Connecticut, in cooperation with Yale University. 

0 Morgantown, West Virginia, in cooperation with West Virginia 

University, Morgantown. 

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

Orono. 

0 Parsons, West Virginia. 

0 Princeton, West Virginia. 

0 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.