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Forest Science, Vol. 33, No. 4, pp. 932-945.
Copyright 1987 by the Society of American Foresters
An Econometric Analysis of the Southern
Softwood Stumpage Market: 1950-1980
DAVID H. NEWMAN
ABSTRACT. This paper presents an aggregate regional model of the southern softwood
solidwood (combined lumber and plywood) and pulpwood stumpage markets. The deri-
vation of stumpage supply includes direct substitution possibilities by stumpage pro-
ducers. The derivation of stumpage demand follows a profit maximization framework
and includes the effects of input substitution as well as production capacity. Three-stage
least squares regression techniques provide simultaneous parameter estimation of the
market system. Solidwood stumpage is a complement in production with pulpwood;
however, in solidwood production, an asymmetrical relationship exists as pulpwood is a
substitute good. With respect to demand, solidwood stumpage responds to a greater
extent to changes in final good price than does pulpwood. FOR. S½I. 33(4):932-945.
ADDITIONAL KEY WORDS. Regional supply and demand, market equilibrium.
THE SOUTHERN TIMBER MARKET represents a major source of softwood
stumpage production in the United States. In 1976, 45% of the country's
total softwood timber removals and 50% of the total additions to softwood
inventories came from the region (USDA Forest Service 1982, p. 143). The
region's share of total removals and growth is projected to increase to 51%
and 61% respectively by 2030 (Haynes and Adams 1985, p. 81). These pro-
jections are based on a number of assumptions about the characteristics of
the stumpage market, particularly the participant's responses to internal as
well as external market changes.
Previous analyses of southern timber markets focus almost exclusively on
own price responses in demand and supply. Works by Robinson (1974),
Adams and Haynes (1980), Haynes and Adams (1985), and others empha-
size national timber supply issues. As a result, issues such as cross-regional
market substitution receive greater attention than do within-region product
substitution issues. These models therefore ignore the response of indi-
vidual stumpage producers to changes in substitute market prices as well as
many local market characteristics. In addition, stumpage demand specifica-
tions are quite restrictive as the models assume either completely inelastic
price responses, zero cross-product effects with other inputs into produc-
tion, or both.
In order to gain a clearer understanding of the regional market responses,
this study examines the supply and demand for southern softwood stumpage
alone. The study uses three-stage least squares for simultaneous parameter
estimation in the two primary stumpage markets: solidwood (combined
lumber and plywood) and pulpwood. The analysis differs from earlier re-
gional supply and demand analyses as it considers direct substitution in
The author is Visiting Assistant Professor of Forest and Resource Economics at the School
of Forestry and Environmental Studies, Duke University, Durham, NC 27706. Funding for this
research was received from the Southeastern and Southern Forest Experiment Stations and the
Washington Office of the USDA Forest Service. The author thanks Ralph Alig, George Du-
trow, William Hyde, Stephen Swallow, T. Dudley Walla6e, and the journal's reviewers for
helpful advice. Any remaining errors are the author's responsibility. Manuscript received
March 31, 1987.
932/FOREST SCIENCE
stumpage output between these two products. A simple theoretical frame-
work of the stumpage market system allows the derivation of stumpage de-
mand and supply within a profit maximization framework. The study uses a
three-input production technology that includes capital, labor, and
stumpage inputs to model stumpage demand. For stumpage production,
timber inventory serves as a proxy for production costs. The model's theo-
retical structure is based on stumpage marked models derived for Sweden
and Finland (Brannlund et al. 1985a and 1985b, Johansson and Lofgren
1985, and Kuuluvainen 1986).
The first section presents the theoretical model of stumpage supply and
demand. The second section presents the data sources used to test the
model. The specification of the model and the econometric results for both
pulpwood and solidwood markets follows. The paper concludes with a dis-
cussion of the results and their implications for southern timber markets.
A MODEL OF SOFTWOOD STUMPAGE DEMAND
AND SUPPLY
Softwood stumpage demand derives from its use as a raw material either in
the production of solidwood products (lumber and plywood) or in the pro-
duction of pulp and paper products. Firms purchase the stumpage in the
market along with other inputs to produce their particular output. For each
firm j, assume a twice continuously differentiable production function for
either solidwood or pulpwood products:
Qot = qo(Lot, Kot, Sot) (1)
i = sw or pp
j=l ..... N
t = 1950 ..... 1980
Qot is the quantity of either solidwood or pulpwood production by firm j in
periot t; and LOt, Kot, and Sot are the quantities of labor, capital, and raw
material which firm j uses in period t.
The end products trade competitively in national and international
markets, and as such the final good prices, Fsw and Fee (prices for solidwood
and pulpwood products) are exogenous to the region. The profit function for
firmj in period t is thus:
max Vot = FitqgLot, KOt, Sot ) - witLot - ritKo. t
Wit' tit' Pit -- PitSot (2)
where wit, rit, and Pit are the respective prices of labor, capital, and
stumpage for the particular industry.
Applying Hotelling's lemma, the firm's derived demand for stumpage in
period t is a function of the demand for its output and the prices of all inputs
into production. It is derived by differentiating the profit function with re-
spect to stumpage price (Varian 1978, p. 31). Thus:
Ogo. t/OPi t = Sdo(Pit, Fit, wit , tit ) (3)
(_) (+) (.9) (.9)
where the signs below the variables represent the expected effects on
stumpage demand of a positive change in the price of the input or the final
good. The signs for the wage and capital coefficients are uncertain as they
DECEMBER 1987/933
depend on whether stumpage is a technical complement or substitute with
other inputs. There is some uncertainty in the literature with respect to the
nature of the relationship between timber and other inputs in the production
processes. A number of studies show stumpage, capital, and labor to be
gross substitutes in production (Stier 1980, Abt 1984, de Borger and Buon-
giorno 1985). Other studies using similar estimation techniques find wood
and labor to be complements (Merrifield and Haynes 1983), or wood and
capital to be complements (Humphrey and Moroney 1975). This confusion
restricts a priori expectations with regards to the sign of the other input
price coefficients.
If all the firms in the region maintain the same production function and
face the same input prices, the regional stumpage demand specification can
be found by aggregating the N individual firm's demand functions. Thus:
N
sdi(Pit, Fit, wit , rit ) = • sd•/(pit, Fit, wit , rit ) (4)
j=l
We do not derive the aggregate stumpage supply functions for solidwood
and pulpwood markets through the explicit use of individual firm production
functions. The heterogeneous ownership and management structure of
southern forestland complicates the aggregation of individual stumpage
supply functions as was done by Brannlund et al. (1985a) and Kuuluvainen
(1986). Numerous factors influence the individuals output of softwood
stumpage such as multiple potential outputs (both timber and nontimber),
long delay between production decisions, potential economies of scale,
technological change, large capital inputs, and the presence of various gov-
ernment subsidies (capital gains taxation in the past, regeneration and stand
improvement subsidies, and others). These concerns recommend hypothe-
sizing a simplified supply function that still accounts for the costs and re-
turns from forest management. In situations where owner-specific data is
available, a complete production function specification is possible, though
still problematic (See Brannlund et al. 1985b).
Aggregate stumpage supply, for both pulpwood and solidwood products,
is assumed to be a function of the received price for both of these goods and
the harvesting costs. The amount of standing softwood inventory (It) serves
as a proxy for harvesting costs. Thus:
Ssit = SSi(Pswt, Pppt, It) (5)
(?) (?) (+)
The expected signs for the price variables depend on whether the solid-
wood or pulpwood supply regression is specified. Generally these signs are
offsetting, since a ceteris paribus positive change in the price of one good
received by a stumpage producer, depending on the relative ease of shifting
outputs, will lead to a shift in production toward that good. Thus, for solid-
wood supply, the own price (Pswt) displays a positive effect on supply while
the sign on the coefficient for the price of the alternate product, pulpwood
(Pp•,t), is likely to be negative. The opportunity for the immediate switching
of production from solidwood to pulpwood is relatively easy as timber
nearing solidwood size is already large enough to be cut for pulpwood.
The own price coefficient (P•,•,t) for the pulpwood supply function is posi-
tive, but the sign on Pswt is uncertain. This uncertain sign occurs because
firms often sell pulpwood as a byproduct of a solidwood harvest. The possi-
bility therefore exists that the two outputs are net complements in produc-
934/FOREST SCIENCE
tion, thus potentially giving a positive sign on the solidwood coefficient.
This positive sign occurs if these complementary production effects are
greater than the expected substitution effects that occur from a relative in-
crease in solidwood price.•
In both functions, a positive supply effect occurs from increasing timber
inventory. As inventory increases, the marginal harvesting costs from per-
ceived economies of scale decrease. This lowers the supply cost and there-
fore increases total supply. Numerous timber supply studies have pre-
viously used this assumption, and it has received some empirical verifica-
tion through several international comparative studies (Gregory 1966,
Styrman and Wibe 1986).
Finally, a market clearing assumption of equality of supply and demand
completes the supply and demand system. Thus:
Ssi(Pswt, Pppt, It) -- Sdi(Pit , Fit, wit, tit) (6)
The market model makes two important simplifying assumptions to allow
estimation. First, prices and price expectations do not affect inventory. The
effects of price expectations on total forest inventory are not well under-
stood empirically. Inventory changes occur relatively slowly over time so
that precise incremental shifts as a result of price changes are difficult to
measure. As a result, no reliable contemporaneous relationship between
prices and inventory has been shown to exist. Thus, the inclusion of a price
expectations operator on inventory into the market system would do little to
decrease the potential for bias from this source in the estimation process.
We also assume that competitive stumpage markets exist. This assump-
tion allows the use of real prices in the stumpage demand equations, as
opposed to the marginal revenue from stumpage bought. On the local level,
various degrees of monopsonistic or oligopsonistic power exist in subre-
gions of the South. This is because the cost of bringing the wood to the mill
is a major cost of stumpage production, which restricts the total distance
that wood is competitively shipped. The likelihood of bias from this as-
sumption is relatively small. The analysis focuses on the regional level,
which represents perhaps the most competitive stumpage market in the
country (with respect to active firms participating in the market), if not the
world. Forest industries in the South have shown extensive growth in pro-
duction and market penetration over the period of the analysis, the pulp and
paper industry in particular. As a result there has been increasing competi-
tion for stumpage resources, which reduces the opportunity for extended
imperfect market abuses.
DATA
The analysis uses aggregated time series data for stumpage and other input
prices. The time period of the data runs from 1950 to 1980. Price variables
• This situation of complementary outputs occurs in the Johansson and Lofgren (1985,
chapter 9) study. They footnote that this complementary condition implies that the present
value function for the individual stumpage producer is discontinuous since the twice contin-
uously differentiable present value function implies OSsJOpvv = OSvv/OPsw. The likelihood of a
discontinuous present value function as a result of discrete price changes has long been realized
by forest economists and results in the potential of multiple optimal forest rotations (see
Newman 1985, p. 4).
DECEMBER 1987/935
are adjusted to the common base year of 1967 by means of the Department
of Commerce's All Commodities Producer Price Index.
STUMPAGE QUANTITY (Ssw ,, Spp,)
Solidwood stumpage is the total quantity of softwood roundwood, in thou-
sand cubic feet (mcf) used for either lumber or plywood production in each
of the 12 southern states covered by the Southeastern and Southern Forest
Experiment Stations of the USDA Forest Service. We aggregate these state
quantities to derive a regional production figure. The aggregation process
does not compensate for roundwood exports to or imports from outside the
region since both are relatively small quantities. Pulpwood stumpage is the
quantity of softwood coming in the form of roundwood pulpwood used in
the production pulp and paper products. (Sources are U.S. Department of
Commerce annual lumber reports MA-24T; Southern Plywood Association
annual plywood production compilation; and the Southern Pulpwood Pro-
duction Resource Bulletins from the two regional USDA Forest Service
Forest Experiment Stations.)
STUMPAGE PRICE (Pswt, Pppt)
The analysis uses a regionally weighted average stumpage price for each
product. No allowance is made for any price difference between plywood
and solidwood in the solidwood price. The price difference for plywood
peeler logs in the late 1970s was about 20%, but no early price series exists
for plywood stumpage prices. This brings in a relatively small bias since (1)
the quantity of plywood stumpage production is small relative to lumber
(only 16% in 1970 rising to a high of 27% in 1980); and (2) plywood logs can
also be sold for solidwood.
Reported southern region pulpwood prices are for wood delivered to the
mill. In order to estimate the stumpage price, the difference between deliv-
ered and stumpage price for sales reported by the Louisiana forest extension
service was calculated. This value was then subtracted from the regional
data. The Louisiana figures are the only estimates of the difference between
stumpage and delivered price that exist for the length of this time series. No
alternative methods are known for estimating direct stumpage costs, and
this method is used by others in supply and demand studies for the region
(see Haynes and Adams 1985, p. $8). The method seems reasonable, as the
broad changes that have occurred in Louisiana's forests and forest indus-
tries are similar to those that have occurred in the other southern states. 2
(Source: Ulrich 1985.)
FINAL GOOD PRICE (Fswt, Fppt)
Real producer price indexes for lumber and wood products and for pulp and
paper products serve as final good price variables. National price indexes
are used for both products since they are traded in national markets com-
peting against substitute goods from other regions. National indexes avoid
the problem of simultaneity bias in estimation. This problem occurs if
2 Timber Mart South has reported stumpage and delivered prices of wood since 1977. The
correlation of their regional average prices with the Louisiana prices since that time is 97% and
98% respectively.
936/FOREST SCIENCE
changes in southern production affect the national price causing the market
price to shift. The degree of market power exhibited by the region depends
on the particular product with the pulp and paper industry exhibiting much
more market power than does solidwood. 3 While some potential therefore
exists for price-setting behavior in the paper products market, the presence
of stiff foreign competition from Canada and other paper-producing regions
in this country reduces this effect in the regression analysis presented here.
(Source: Ulrich 1985.)
STANDING TIMBER INVENTORY (It)
The USDA Forest Service reports total softwood standing live timber inven-
tory for each southern state. These reports come out at approximate ten-
year intervals. In order to fill in the intervening years for the standing inven-
tory, the following formula is used:
I t = It_ • + [G* - (St - S*)] (7)
where G* is the average annual net growth between survey years and S* is
the average stumpage production between survey years. The net increment
to inventory in any single year may be positive or negative, regardless of the
average growth rate for the survey period. The total sou[hern inventory
figure is the aggregate of the individual state values. [Source: Newman
(1986, Chapters 2 and 3) provides the compilation of this variable.]
USER COST OF CAPITAL (rswt, r•t)
Values are calculated by standard industrial classification (SIC) code and
are a composite of long- and short-term capital. The series are constructed
in part from Moody's bond rate, the industry's depreciation rate, the effec-
tive investment tax credit rate for the industry and the effective corporate
tax rate for the industry. (Source: Wharton Econometrics Service.)
WAGES (Wsw t, Wppt)
These values are the average hourly wages for workers and are also calcu-
lated by SIC code. The nominal values are derived by dividing the total
wage bill by the total hours worked. (Source: Bureau of Manufacturers Re-
ports of the U.S. Census Bureau.)
Wages and the user cost of capital data are national, since regional series
of sufficient length are not available. The bias from using national figures is
uncertain. In regard to the user cost of capital, the bias is probably small
since well functioning capital markets are assumed to operate throughout
the country. As a result, the regional costs should not differ from the rest of
the nation's. The bias from the wage series may be somewhat more serious
since a major reason that has been put forth for the large forest industry
movement to the South is the assumed wage difference that exists between
the South and the rest of the country. The coefficients for this variable
should thus be judged with caution.
3 The South produced 65% of all the softwood pulpwood in the United States in 1982 but
produced only 35% of the softwood lumber (Ulrich 1985, Tables 29 and 33).
DECEMBER 1987/937
ECONOMETRIC ESTIMATION AND RESULTS
Two separate functional forms were used to model the supply and demand
relationship of solidwood and pulpwood. Both linear and log-log formula-
tions of the equation systems were tested, but the linear results are reported
here as they generally performed better (Newman 1986). Since production
decisions in the model affect both the solidwood and pulpwood markets
contemporaneously, the two market's structural equations may be distur-
bance-related. For this reason, the analysis uses three stage least squares
regression to estimate the model's coefficients as it produces more efficient,
unbiased estimates in this situation (Judge et al. 1982, Chapter 13).
Adjustments to the theoretical demand specifications for both the solid-
wood and pulpwood markets improve the estimation power of the equation
system. 4 The solidwood equation includes lagged solidwood production
(Sswt-,) in the regression. This variable incorporates two important demand
characteristics not contained in the original demand specification. First,
lagged production acts as an expectations operator of future demand in that
present demand is positively related to expectations of future prices; and
second, it serves as a measure of the actual production capacity. 5 For both
these reasons, the expected sign of the lagged production coefficient is posi-
tive and 0 < h •< 1 (Nerlove 1958). The summed lagged production of both
pulpwood and wood residues used in pulp production (SpARt_ 1) is included
for the pulpwood demand equation. The residues component is added to
better account for the actual pulping capacity in the previous production
period, because in 1980 residues made up 33% of the total raw material
input.
The estimation structure for the pulpwood and solidwood linear regres-
sion system is:
SSppt =
SSp t -•-
SSsw t
SClsw t =
where the ai and [3i are the estimated coefficients, and the Ei are the re-
siduals from the estimation.
Tables 1 and 2 present the regression results for both structural forms and
the reduced form stumpage price equation. The tables also contain the elas-
ticity estimates for the variables calculated at the mean of the data. In gen-
eral the signs and sizes of the elasticity measures for both systems of equa-
4 The major benefit in the parameter estimation from the addition of the Ssw,- i and S•,Am- • to
the demand specification is a reduction in the degree of autocorrelation in the system (autocor-
relation statistics generally improve substantially) and a great reduction in the model variance
(many more significant variables, though generally of lower magnitudes).
5 A reviewer noted that the same formulation occurs if we assume that there is an unobserv-
able desired level of stumpage and the adjustment toward this desired level is not an instanta-
neous process. Thus, the effect of lagged production can be seen to verify either an expecta-
tions or an adjustment model.
938/FOREST SCIENCE
TABLE 1. Three-stage least squares regression results and elasticities of the pulp-
wood stumpage market: 1950-1980. a
Variable S%et Savv, Peet
Intercept - 776,013
( - 4.28)*
Pppt 4921.47
(2.52)**
[0.231
I t 0.02246
(17.83)*
[1.20]
Pswt 491.12
(2.05)**
[0.08]
Fppt
Wppt
SpART- 1
dfe 26
R 2 0.952
DW 1.034
CV 5.3%
F 171.89*
731,725 76.802
(1.28) (0.76)
-9091.91 --
(- 1.77)***
[-0.43]
-1.334 x 10 -7
(- 1.57)***
-0.0184
(-0.44)
1800.4 0.2939
(0.29) (0.34)
[0.12]
304,257.3 22.218
(3.12)* (3.42)*
[0.68]
-2,341,434 - 157.73
( - 3.06)* ( - 3.07)*
[-0.15]
0.2265 8.774 x 10 -6
(2.26)** (0.50)
[0.28]
24 23
0.869 0.578
1.116 1.217
9.1% 10.8%
31.84' 5.25*
a Values in parenthesis are t ratios.
* Significant at the 0.01 probability level
** Significant at the 0.05 probability level
*** Significant at the 0.10 probability level
Values in brackets are elasticities evaluated at the mean of the data.
tions are consistent with the production theory and within expected bounds.
The low values for the Durbin Watson (DW) statistic in the pulpwood equa-
tions indicate a problem of autocorrelation in that system, even with the
addition of SpARt_ 1' This may be a result of the poor fit for the reduced form
of the pulpwood price equation. Parks (1967) shows an efficient method for
evaluating contemporaneous and serial correlation, but the statistical
package used in this analysis will not perform this method for a system of
equations. Because of the presence of the lagged dependent variable in the
solidwood demand equation, the Durbin h statistic is used. This statistic
tests as a normal deviate so the null hypothesis of no serial correlation in
solidwood demand is accepted (Pindyck and Rubinfeld 1981, p. 194). The
DW statistic for solidwood supply falls in the uncertain range.
DECEMBER 1987/939
TABLE 2. Three-stage least squares regression results and elasticities of the solid-
wood stumpage market: 1950-1980. a
Variable Ss•wt S •w t P •t
Intercept 888,908
(5.27)*
Psi, 3072.3
(8.21)*
[0.55]
I t 0.00648
(3.89)*
[0.39]
Pppt -- 11,279
(- 6.66)*
[-0.591
Fswt
Wswt.
Sswt - 1
dfe 26
R e 0.934
DW 1.475
Durbin h
CV 6.6%
F 122.65'
- 1,645,097 - 473.3
(-3.28)* (-5.48)*
-3162.4 --
(- 2.22)**
[-0.571
- 1.14 x 10 -9
(-o.ool)
1.771
(3.71)*
21,733.9 4.497
(3.13)* (6.77)*
[1.721
114,890.7 - 11.899
(2.27)** (-0.33)
[0.211
1,024,928 319.311
(1.40) (2.49)**
[0.08]
0.786 0.00008
(6.05)* (2.95)*
[0.781
24 23
0.938 0.949
-- 1.699
0.821
6.9% 7.0%
72.62* 71.52'
a Values in parenthesis are t ratios.
* Denotes significance at the 0.01 probability level
** Denotes significance at the 0.05 probability level
Values in brackets are elasticities evaluated at the mean of the data.
PULPWOOD STUMPAGE SUPPLY AND DEMAND
The supply equation for the pulpwood system shows a much better fit with
higher R 2 and F values and a lower coefficient of variation (CV) than does
the demand equation. Parameter estimates in the presence of autocorrela-
tion are unbiased but inefficient. With positive correlations, the standard
error of the regression is generally reduced, and summary statistics may
therefore be biased upwards (Pindyck and Rubinfeld 1981, p. 153). Caution
regarding the interpretation of these regressions should therefore be taken.
Turning first to the pulpwood supply equation, the own price elasticity is
positive and very inelastic with an estimated value of 0.23. The cross elas-
ticity with solidwood is as hypothesized (positive) and is smaller in magni-
940/FOREST SCIENCE
tude at 0.08. The inventory elasticity is positive and greater than one so that
a 1% increase in the standing inventory leads to a 1.2% increase in the pulp-
wood stumpage output. While this value seems large, it is not unreasonable
in view of the strong growth in the southern pulp and paper industry over
the years spanning this analysis. All the variables are significant at least at
the 0.05 probability level or better.
For the pulpwood stumpage demand equation, own price is inelastic and
significant at the 0.10 level while the final good price is positive but not
significantly different from 0. A degree of substitutability exists between
stumpage and labor, since an increase in labor price leads to an increase in
stumpage requirements, while capital and stumpage are slight technical
complements in production. Both of these coefficients are significant at the
0.0! level. Finally, lagged pulpwood and residue input has the expected
sign, although it is low in magnitude.
The signs of the coefficients of the reduced form price equation are all as
expected though the goodness of fit, as measured by the R 2, CV, and F
values, is not very high. As shown in Figure 1, the overall predictive power
of this model for stumpage is only fair; the model fails to predict several
shifts occurring in production. The general trends track very well, however.
The cause for this may rest in the poor predictive ability of the endogenous
stumpage price variable. The poor explanatory power of the final good price
contributes to this as it is a composite price index used and as such may be a
poor indicator of the range of prices for pulp and paper products.
No other studies of southern production have modeled pulpwood in the
manner of this study. Most have modeled pulpwood demand as predeter-
mined, i.e., completely inelastic, due to either the relatively fixed demands
of pulp mills, the greater importance of solidwood production, or the pres-
ence of imperfect markets (Robinson 1974, Haynes and Adams 1985). Thus,
it is not possible to directly compare the results for pulpwood presented
here to other studies. The low demand elasticity corroborates the inelastic
demand assumptions that these studies use. The estimated supply elasticity
is consistent with, though lower than, previous sawtimber supply estimates.
This result is reasonable, since a technical complement in production (solid-
wood stumpage) is modeled in the regression.
SOLIDWOOD STUMPAGE SUPPLY AND DEMAND
Solidwood stumpage supply results are shown. in Table 2. The significant
negative sign of the pulpwood price coefficient implies that pulpwood is a
net substitute for solidwood stumpage. This difference between the solid-
wood and pulpwood equations conforms to the scenario discussed in the
theoretical section with respect to the effect of substitute product prices on
output decisions. Also, the price coefficients, though still inelastic, are
much larger in magnitude than for pulpwood supply. Solidwood producers
therefore respond to short-term changes in market variables to a greater
extent than do pulpwood producers. Finally, standing inventory has a much
lower elasticity with respect to solidwood supply than it did for pulpwood
supply. All variables are significant at the 0.0! level.
Comparing the solidwood stumpage demand function to the pulpwood
demand function also shows major differences. Own price is inelastic and
significant, but there is a significant and elastic stumpage response from an
increase in the final good price. This response did not occur in the pulpwood
equations and may be a relic of the earlier structure of the lumber industry
DECEMBER 1987/941
in the South. Prior to the mid 1960s, the industry contained many small
production units with relatively low capital inputs that could gear up quickly
or shut down with apparent changes in the lumber market. As the move to
larger, more heavily capitalized integrated firms has continued over the past
20 years, this pattern of boom and bust production will decrease in magni-
tude.
Both the labor and capital cost coefficients have small positive elasticities
indicating slight substitution possibilities between these two inputs and
stumpage. This substitution possibility is not as strong for capital as it is for
labor. The capital price coefficient is significant at the 0.20 level, while the
wage coefficient is significant at the 0.01 level. The sign of the lagged pro-
duction coefficient is again as predicted, and its value is much larger than
was the case for pulpwood. This is due to the altered composition of the
lagged variable.
Finally, the signs of the reduced form price equations are consistent with
the signs of the other equations. The effect of inventory changes on own
stumpage price is much reduced from the situation in pulpwood, while the
final good price has a large and significant effect. The predictive power of
the stumpage model, as shown by Figure 2, appears much better than for
pulpwood.
The estimated elasticities for the solidwood equations conform with pre-
vious studies (Robinson 1974, Haynes and Adams 1985). Those studies
showed own price elasticities from -0.3 to -0.5 for demand and 0.3 to 1.0
for supply. This study shows a somewhat higher demand elasticity, possibly
because of the addition of the substitute good, pulpwood, in the equation
and a similar, but clearly inelastic supply elasticity. The inventory elasticity
is somewhat lower.
2400000
• 2000000
• 1600000
z
¸
'"r 1200000.
8OOO00
1950
OBSERVED
....... PREDICTED
•0 1970 1980
YEAR
FIGURE 1. Actual and predicted southern pulpwood stumpage supply.
942/FOREST SCIENCE
2400000
2000000
1•00000
1200000
8OO000
FIGURE 2.
-OBSERVED .z'•
....... PREDICTED ,
1950 •960 1970 1980
YEAR
Actual and predicted southern solidwood (lumber and plywood) stumpage supply.
DISCUSSION AND IMPLICATIONS OF THE
ECONOMETRIC RESULTS
This paper presents an econometric analysis of the joint production possibil-
ities in softwood stumpage supply in the South. It uses three stage least
squares regression techniques on a system of supply and demand for the
pulpwood and solidwood markets. The study makes two contributions to
the U.S. timber supply and demand literature. First the study implements a
supply function that allows stumpage production based on the relative
prices of substitute outputs. Other statistical studies of regional supply and
demand either omit or completely separate substitute outputs. 6
The use of a three-factor demand specification for stumpage and the in-
clusion of an expectations variable mark the second major contribution of
the analysis. In market systems analyses, stumpage demand has often been
modeled as a function of final good demand alone, allowing no possibility
for substitution in production with other inputs. In this analysis the model
specification allows for both substitutes in production and for an expecta-
tions operator, lagged production.
This study quantifies substantial asymmetries between the pulpwood and
6 In the only other regional study to examine the effects of joint forest production, Greber
and Wisdom (1985) use a mathematical programming model to explicitly examine forest
product interdependencies. They focus on fuelwood, pulpwood, and sawlog production in the
coastal plain and piedmont regions of Virginia. By systematically altering fuelwood prices, they
are able to examine production behavior for these three goods. They find strong complemen-
tary behavior between fuelwood and sawlogs but find that fuelwood and pulpwood are pri-
marily substitutes. They do not examine pulpwood and solidwood interdependencies.
DECEMBER 1987/943
solidwood market structures with respect to both supply and demand. The
complementary role of solidwood in pulpwood supply found in Sweden (Jo-
hansson and Lofgren 1985) is empirically shown to hold in the South. The
relatively high degree of substitution possibilities exhibited by pulpwood in
solidwood supply reflects the observed behavior of southern forest owners
who have managed their stands with continually shorter rotation lengths
over the last 30 years.
The relatively low estimated inventory elasticity in solidwood supply
function compared to pulpwood conforms with recent theoretical analysis of
timber supply, which shows an inverse relationship between inventory elas-
ticity and rotation length (Binkley 1985). The importance of this is that
standing softwood inventory is often used as a measure of the effectiveness
of improvements in biological forest production (Newman 1986). As a re-
sult, the total value of the expected benefits derived from increasing inven-
tory will be reduced since pulpwood stumpage receives a much lower price
in the market.
The inelastic own demand price response for both solidwood and pulp-
wood systems was expected (Zaremba 1962), but the large final good price
response for solidwood stumpage is important. Projections show future de-
clines in solidwood product demand resulting from decreased housing starts
(USDA Forest Service 1982, p. 25). An even stronger negative effect on
future solidwood stumpage demand is anticipated by the results of this anal-
ysis. Even with this drop in demand, stumpage prices are projected to rise
substantially as softwood timber inventory is expected to decrease over this
period. We cannot directly comment on this prediction as inventory is exog-
enous to the model, but the strong price responses suggest that market
forces may work to moderate projected price rises.
The apparent substitution between wood and the other inputs, particu-
larly labor, in the production of final goods creates a possible dilemma for
policy analysts. If the substitution possibilities presented are symmetric,
shifts occurring in biological forest productivity which increase stumpage
supply levels will have a lower effect on job creation in the processing
sector. An increase in output will occur, but increasing quantities of
stumpage may also be substituted for labor in the production process. Thus,
attempts to improve local community welfare through timber-based expan-
sion alone may ultimately be low.
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