Interregional Aspects of Timber Inventory Projections
Except where reference is made to the work of others, the work described in this
dissertation is my own or was done in collaboration with my advisory committee.
This dissertation does not include proprietary or classified information.
Maksym Polyakov
Certificate of Approval:
David N. Laband
Professor
Forestry and Wildlife Sciences
Lawrence D. Teeter, Chair
Professor
Forestry and Wildlife Sciences
C. Robert Taylor
Professor
Agricultural Economics
and Rural Sociology
Stephen L. McFarland
Dean
Graduate School
Interregional Aspects of Timber Inventory Projections
Maksym Polyakov
A Dissertation
Submitted to
the Graduate Faculty of
Auburn University
in Partial Fulfillment of the
Requirements for the
Degree of
Doctor of Philosophy
Auburn, Alabama
17 December 2004
Vita
Maksym Polyakov, son of Oleksandr Polyakov and Lyudmyla Polyakova, was
born on December 24, 1968 in Kyiv, Ukraine. He graduated from the Ukrainian
Agricultural Academy with an Engineer of Forestry degree in 1992. After gradua-
tion he worked as an engineer and senior engineer at the State Forest Management
Planning Institute for eight years. During the same period, with the support of
the Swedish International Development Agency (SIDA) he pursued a study of land
management at the Royal Institute of Technology, Stockholm, and graduated with a
Master of Science in Land Management degree in 1999. In 1995 he began graduate
study by correspondence at the Scientific Research Institute of the Ministry of Econ-
omy, Kyiv, Ukraine. He defended his dissertation and graduated with a Candidate
of Economical Sciences degree in 1999. From 1999 to 2000 he worked part time as a
lecturer at the Forestry Faculty of National Agricultural University, Kyiv, Ukraine.
He entered graduate school at Auburn University in January 2001. He is married to
Olena Polyakova and they have a son, Petro, and daughter Oksana.
iii
Dissertation Abstract
Interregional Aspects of Timber Inventory Projections
Maksym Polyakov
Doctor of Philosophy, 17 December 2004
(Cand.Sc., Economical Scientific-Research Instutute, Kyiv, Ukraine, 1999)
(M.S., Royal Institute of Technology, Stockholm, Sweden, 1999)
(Eng.For., Ukrainian Agricultural Academy, 1992)
84 Typed Pages
Directed by Lawrence D. Teeter
The overall goal of this study is to explore interregional aspects of modeling
timber supply. Three separate papers are presented in this dissertation.
Thefirstpaper(Chapter3)presentsaneconometricanalysisoffactorsinfluencing
demand and supply of pulpwood in Alabama. The softwood and hardwood pulpwood
markets were modeled simultaneously as a partial equilibrium system, where equal-
ities of supplies and demands determine prices. Estimation of the parameters was
done using two-stage least squares. Price elasticities of supply were found to be simi-
lar to those previously reported for the U.S. South (Newman 1987, Carter 1992). The
substitution role of sawtimber in hardwood pulpwood supply is consistent with find-
ings for Sweden and the U.S. South (Br?annlund et al. 1985, Newman 1987). Results
indicate that softwood and hardwood demands are complementary and that a sub-
stitution relationship exists between Alabama and Mississippi pulpwood. Regression
results can be used for short run predictions.
iv
Four different specifications of a gravity model and a fixed gravity coefficient
model were evaluated, and their capabilities to predict pulpwood trade were compared
in Chapter 4. Root mean square error was used as a measure of models? predictive
performances. The gravity model estimated using non-linear least squares (NLS) with
fixed error methods (FEM) and the fixed gravity coefficient model (FGCM) showed
the best results, while results for the FGCM were second best and this method is
much easier to use.
In Chapter 5, an interregional trading model for stumpage products was devel-
oped that recognizes the importance of demand centers (centers of forest products
manufacturing activity) and inventory in forecasting future harvests and trade flows.
A gravity model was constructed that considers the relative position of each region
vis-?a-vis all others as a producer of stumpage and as a consumer of stumpage prod-
ucts. The fixed gravity coefficient model was incorporated in a multi-region version of
DPSupply (Teeter 1994, Zhou and Teeter 1996, Zhou 1998) referred to as the Interre-
gional DPSupply System (IDPS). Projections for growth, harvest and trade in forest
products were made for the thirteen state southern region through 2025. Aggregate
trends in inventory are similar to those reported in the Southern Forest Resource
Assessment. Inventory trends by product (pulpwood, sawtimber) and type (hard-
wood, softwood) differ by state and are used to illustrate the advantages of explicitly
recognizing interregional trade in the projection system.
v
Acknowledgments
The author would like to expresses his gratitude to his advisor, Dr. Lawrence
D. Teeter, for guidance, advice, and financial support. He also wants to thank his
committee members, Drs. David N. Laband and C. Robert Taylor, for their encour-
agement and assistance. The author would like to acknowledge Dr. John D. Jackson
for his help with econometric issues, Anne Jenkins, Southern Forest Experimental
Station, for her assistance with TPO data, and Dr. Xiaoping Zhou for help with
understanding details of the DPSupply model.
The author also wishes to thank faculty and graduate students of the Forest
Policy Center for their help and encouragement.
The author is grateful to his wife Olena, son Petro, and daughter Oksana for
their love and understanding. He is also greatly indebted to his parents, Oleksandr
Polyakov and Lyudmyla Polyakova for their support, love and encouragement.
vi
Style manual or journal used Forest Science, Guide to Preparation and
Submission of Theses and Dissertation
Computer software used SAS 8.0, LIMDEP 7.0, FORTRAN 77, ArcGIS 8.3,
Microsoft Excel 2000, LATEX2? with auphd.sty.
vii
Table of Contents
List of Tables x
List of Figures xi
1 Introduction 1
2 Literature Review 3
2.1 Econometric analysis of roundwood markets . . . . . . . . . . . . . . 3
2.2 Gravity Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Interregional Trade in Multi-Regional Input-Output Models . . . . . 8
2.4 Timber Supply and Demand Models . . . . . . . . . . . . . . . . . . 11
3 Econometric Analysis of Alabama?s Pulpwood Market 17
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Pulpwood Market Model . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.4 Model Estimation and Results . . . . . . . . . . . . . . . . . . . . . . 22
3.5 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 26
4 Modeling Pulpwood Trade within the U.S. South 28
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2.1 Gravity Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2.2 Fixed Trade Coefficient Models . . . . . . . . . . . . . . . . . 34
4.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.4 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.4.1 Gravity Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.4.2 Fixed Gravity Coefficient Model . . . . . . . . . . . . . . . . . 42
4.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.6 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 45
viii
5 Incorporating Interstate Trade in a Multi-region Timber In-
ventory Projection System 46
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.2 An Interregional DPSupply Model with Stochastic Prices . . . . . . . 46
5.2.1 Overview of the Model . . . . . . . . . . . . . . . . . . . . . . 46
5.2.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.2.3 Modeling future trading activity in forest products . . . . . . 49
5.2.4 Harvest Decisions . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2.5 Area Change . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.3.1 Inventory adjustment . . . . . . . . . . . . . . . . . . . . . . . 57
5.3.2 Inventory projections . . . . . . . . . . . . . . . . . . . . . . . 58
5.3.3 Interregional Trade . . . . . . . . . . . . . . . . . . . . . . . . 62
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
References 68
ix
List of Tables
3.1 The results of two stage least squares regression and elasticities of
determinants of the Alabama pulpwood stumpage market 1977?2001 . 24
4.1 Descriptive statistics of the variables . . . . . . . . . . . . . . . . . . 38
4.2 Estimation results for bilateral pulpwood trade between states of the
U.S. South without specific effects (models (4.3) and (4.2)) . . . . . 39
4.3 Estimation results for bilateral pulpwood trade between states of the
U.S. South with fixed bilateral and time effects (models (4.4) and (4.5)) 41
4.4 Analysis of variance with main and bilateral interaction effects of the
fixed gravity coefficients for the pulpwood trade between states of the
U.S. South during period 1994?2002 . . . . . . . . . . . . . . . . . . 43
4.5 Root Mean Square Error (RMSE) for the different models and five
different training and learning sets . . . . . . . . . . . . . . . . . . . 45
5.1 Example trade matrices for two selected years for hardwood pulpwood,
2000 and 2025, mcf . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
x
List of Figures
4.1 Pulpwood Production and Pulpmills Located in the South . . . . . . 29
5.1 Interregional DPSupply system . . . . . . . . . . . . . . . . . . . . . 48
5.2 Softwood inventory projections for the 13-state southern region under
three harvest increase scenarios, 2000-2025, billion cubic feet . . . . . 59
5.3 Softwood inventory projections for the 13-state southern region under
three harvest increase scenarios, 2000-2025, billion cubic feet . . . . . 60
5.4 Softwood inventory and harvest projections for North Carolina, Base
Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.5 Hardwood inventory and harvest projections for North Carolina, Base
Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.6 Relative changes in hardwood pulpwood inventory by state, 2000?2025 64
5.7 Relative changes in hardwood pulpwood harvest by state, 2000?2025 . 64
5.8 Dynamics of hardwood pulpwood state-level imports, 2000?2025, Base
Scenario, MCF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.9 Dynamics of hardwood pulpwood state-level exports, 2000?2025, Base
Scenario, MCF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
xi
Chapter 1
Introduction
The South is the major timber production region in the United States. In 1997,
nearly 58% of U.S. industrial roundwood and three-fourths of total U.S. pulpwood
production was produced in the region (Howard 1999, p. 38). The forest sector
is an important part of the Southern states? economy, producing 6% of its gross
regional product. Forestry is the dominant land use in the U.S. South, occupying
56% of the land base (Wear and Greis 2002). A number of projections made in the
1970s and 1980s (e.g., Haynes and Adams 1985), as well as the 2000 USDA Forest
Service Resource Planning Act (RPA) Assessment (Haynes et al. 2003) predicted an
increasing share for the U.S. South both in timber growth and removals.
The constant interest in timber supply and environmental issues calls for more
efforts to improve analyses and projections of forest resource trends. Furthermore, in
recent years, there is a growing interest in information on timber supply in specific
regions (states or parts of the states) and how is it affected by mill expansions, land
use changes, and urbanization (Abt et al. 2000).
Location and availability of timber inventories determine location of timber in-
dustries. In turn, timber industries affect timber inventories, thus impacting them-
selves, as well as the local economies. Mutual interdependence of timber resources
and timber industries occurs not only on a temporal basis, but also on a spatial scale.
Demand for roundwood in most of the states is satisfied from the local resource base,
1
as well as by transporting roundwood products from other states. Thus, interregional
trade is an important determinant of roundwood markets in the U.S. South.
In this situation, single state timber supply models are too restrictive and may
inappropriately indicate bottlenecks in future timber supply. At the same time, ag-
gregating parts of a larger region into a single roundwood demand or supply market
can hide local supply problems, providing little detail on the location of future in-
ventory and harvest activity. Therefore, timber supply and demand modeling on a
subregional (state) level requires accounting for the spatial aspects of timber markets,
and in particular, interregional trade of roundwood products.
The overall goal of this study is to explore interregional aspects of modeling
timber supply. Three separate papers are presented in this dissertation. The first
paper investigates factors determining demand and supply for the pulpwood market
of a single state (Alabama) in the broader context of a regional pulpwood market.
The goal of the second paper is to compare the forecasting performance of various
specifications of a gravity model and a fixed gravity coefficient model, and discuss
their possible applications in interregional (subregional) timber inventory models.
The third paper presents an interregional timber inventory projection model that
recognizes the importance of demand centers, inventory dynamics, and trade flows in
forecasting future inventories, growth, and harvests for the U.S. South by state and
by product on an annual basis.
2
Chapter 2
Literature Review
This chapter reviews some of the existing literature on the topics analyzed in the
following chapters. The first section discusses econometric modeling of roundwood
markets. Section two reviews multi-regional input-output models. Next, the history
and application of gravity models are discussed. Finally, the fourth section provides
an overview of timber supply and demand projection models.
2.1 Econometric analysis of roundwood markets
There exists extensive literature devoted to the analysis of timber products mar-
kets. Two of the earliest were econometric studies by Gregory (1960) and McKillop
(1967). Studies of roundwood product supply and demand were limited to analysis
of a single product, for example, pulpwood (Leuschner 1973, Hetem?aki and Kuu-
luvainen 1992), or several products simultaneously (Br?annlund et al. 1985, Newman
1987). The scope of these studies varies from a national perspective (Br?annlund et al.
1985, Hetem?aki and Kuuluvainen 1992, Haynes and Adams 1985) to regional (New-
man 1987, 1990) and subregional (Leuschner 1973, Adams 1975, Daniels and Hyde
1986, Carter 1992) markets.
The theoretical part of most empirical studies of timber markets is commonly
based on contemporary neoclassical microeconomic theory. Supply and demand are
considered simultaneously, therefore methods are employed which allow for systems of
3
simultaneous equations. Common approaches include two stage least squares (2SLS)
regression, or three stage least squares (3SLS) regression.
Leuschner (1973) conducted an econometric study of the aspen pulpwood market
in Wisconsin based on data covering 1948 to 1969. He assumed that demand for
pulpwood is not affected by price and is shifted by changes in pulpmill capacity.
Supply is affected by price and shifted by the previous year market quantity and
imports. A linear two stage least squares regression was used to estimate the model.
All equation coefficients were found to be significant and had the expected signs. The
elasticity of supply with respect to own price was estimated to be 2.6.
Br?annlund et al. (1985) analyzed Swedish pulpwood and sawtimber markets
based on time-series data covering 1953 to 1981 and assumed that the equality be-
tween demand and supply determines price in the sawtimber market, and that pulp-
wood prices are exogenously determined (because of specific features of the Swedish
pulpwood market). A log-linear model specification was used. All estimated coef-
ficients of the supply curves had signs consistent with the underlying theory, and
most were statistically significant. The own supply price elasticity of pulpwood was
estimated to be approximately 0.7.
Newman (1987) presented an aggregate regional model of the southern U.S. soft-
wood solidwood (lumber + plywood) and pulpwood stumpage markets. This analysis
considered direct substitution in output between these two products. A simple theo-
retical framework of the stumpage market allows the derivation of stumpage demand
and supply within a profit maximization framework. Three-stage least squares regres-
sion techniques provided simultaneous parameter estimation of the market system.
4
The linear specification was used. The study quantified substantial asymmetries be-
tween the pulpwood and solid wood market structures with respect to both supply
and demand. Price coefficients in pulpwood supply and demand equations were sig-
nificant and had signs consistent with the theory. The own price supply and demand
elasticities for the pulpwood market were estimated to be 0.23 and ?0.43 respectively.
Carter (1992) presented a dynamic model of the Texas pulpwood stumpage mar-
ket for the period 1964?1986. The ridge regression form of three-stage least squares
was used in order to address problems of collinearity. A large significant supply elas-
ticity was found with respect to income, larger than own price elasticity. The role of
income is due to the fact that for nonindustrial private forest owners standing timber
plays a role of a store of wealth that can be liquidated in the short run to meet income
targets. The estimates of own price supply and demand elasticities using three-stage
least squares were equal to 0.59 and ?0.42 respectively.
All of the previous studies listed above dealt with softwood pulpwood (Carter
1992), softwood solidwood (pulpwood + lumber) (Br?annlund et al. 1985, Newman
1987), or hardwood pulpwood (Leuschner 1973) markets. Nagubadi et al. (2001) an-
alyzed interactions between softwood and hardwood pulpwood demands, but did not
find any statistically significant substitution effect between hardwood and softwood
in pulp production.
Few econometric studies of roundwood markets include spatial interrelationships
in the analysis. Adams (1975) analyses the two-region pulpwood market of Wisconsin
and Michigan-Minnesota. This analysis includes explicit treatment of pulpwood flows,
market interaction within the region, and inventory-holding behavior at pulp mills.
Following Leuschner (1973), demand in both regions was assumed to be perfectly
5
inelastic, aggregate supply was equal to aggregate demand. Merz (1984) analyses the
pulpwood markets of Wisconsin and the Michigan Upper Peninsula. Unlike in Adams
(1975), transportation costs were taken into account in this two-region spatial equilib-
rium model. However, the study failed to provide conclusive evidence concerning the
appropriateness of a two-region model. Finally, analyzing Texas softwood pulpwood,
Carter (1992) used net softwood pulpwood export from Texas to other states as an
endogenous variable.
2.2 Gravity Model
Spatial interaction models derived from gravitational physics have been used in
the social sciences since the early 1940s (Isard 1960). These models have been em-
ployed to explain the determinants of different types of flows such as migrations,
commuting, recreation traffic, trade, etc. In these models, the degree of interaction
between two regions is strengthened by their ?masses?, represented usually by popu-
lation or income, weakened by the ?distance? between them, reflecting transportation
costs, and influenced by other factors.
In the context of international trade, gravity models were first used independently
by Tinbergen (1962) and P?oyh?onen (1963), who argued that bilateral trade flows
are influenced by the size of each country?s Gross National Product (GNP) and the
distance between them:
Eij = ?0(Yi)?1(Yj)?2(Dij)?3 (2.1)
where Eij is the trade between countries i and j, Yi is the GNP of country i, Yj is the
GNP of country j, and Dij is the distance between countries i and j. Coefficients ?1
6
and ?2 are assumed to be positive, since the greater the sizes of the economies, the
more intensive is trade, while ?3 is negative, because the large distance (high trans-
portation costs) inhibit trade. The values of coefficients were estimated by performing
log transformation and using ordinary least squares regression.
The gravity equation became a popular instrument for trade policy analysis. It
was used to evaluate trade potential as well as the impact of various policy issues
regarding international trade, such as trading groups, currency unions, quotas, or
preferentialtreatment. Despiteitswidespreadempiricaluse, therewasacriticismthat
the gravity equation has no theoretical foundation, however a number of subsequent
researchers have shown that it can be derived from baseline models of trade. Anderson
(1979) showed that the gravity model should be consistent with the generalized trade
share expenditure system models. Bergstrand (1985) derived the gravity model from
the assumption of monopolistic competition and product differentiation.
While used widely to analyze international trade, including trade of forest prod-
ucts (Kangas and Niskanen 2003, Kang 2003), some studies have shown that cross-
sectional gravity analysis gives very wide forecast interval spans around the predicted
values, which makes it almost useless for estimating trade potentials (Breuss and
Egger 1999).
A number of recent studies suggest that a panel framework has many advan-
tages over the cross-section approach (M?aty?as 1997, 1998, Egger 2000). It allows a
researcher to capture the relationships between the relevant variables over a longer
period and to reveal time invariant effects specific to the importer and exporter re-
gions. Acording to (M?aty?as 1997), econometric specification of the gravity model
using panel data is a three-way fixed effect approach, where importer, exporter, and
7
time fixed effects could be viewed as orthogonal vectors of dummy variables. From the
economic point of view, the time effect capture the influence of business cycles, while
importer and exporter effects capture general openness of a country to trade with the
partners. Furthermore, Egger and Pfaffermayr (2003) argue that proper specification
of a panel gravity model should include exporter-by-importer bilateral interaction
effect, the product of importer and exporter fixed effects. The exporter-by-importer
interaction effect accounts for any time invariant bilateral influences which lead to
deviation from a country pair?s ?normal? propensity to trade. However, the use of
bilateral interaction fixed effects makes time invariant variables, such as distance,
border, etc. redundant. In order to estimate coefficients of time invariant variables,
a number of studies use the Hausman and Taylor (1981) instrumental variable esti-
mation technique (Egger and Pfaffermayr 2004, Serlenga and Shin 2004).
2.3 Interregional Trade in Multi-Regional Input-Output Models
Multi-regional input-output models are an extension of classical input-output
models. They can be constructed by either adding a geographic dimension into an
input-outputmodelorbyembeddinganinput-outputmechanismintoamulti-regional
trading model. In this overview we will be interested in the multi-regional trading
part of multi-regional input-output models.
Hua (1990) classified multi-regional input-output models into four types accord-
ing to the way interregional coefficients of these models are calculated.The coefficients
of Type 1 models are obtained by dividing each column of the interregional trade ma-
trix of a good by total regional consumption. These are the most widely used column
8
coefficient models (Moses 1955, Polenske 1970). In models of Type 2, or row coeffi-
cient models, coefficients are obtained by dividing each row of the matrix by regional
production (Polenske 1970). Type 3 and Type 4 models, known also as potential or
gravity coefficient models (Leontief and Strout 1963), assume that trade of a commod-
ity i between regions g and h (Xigh) is proportional to the total supply of a commodity
in the supply region (Xigo) and total demand of a commodity in the demand region
(Xioh):
Xigh = X
i
goX
i
oh
Xioo Q
i
gh ? i,g,h (2.2)
where Xioo is the total amount of commodity i produced in an economy and Qigh is
the gravity coefficient. However, the coefficients in Type 3 models are determined
from the base year data while coefficients in the Type 4 models are determined using
exogenous variables, such as distance.
Leontief and Strout (1963) developed four methods to derive gravity coefficients.
The point estimate is used when base-year statistics comprise information on regional
inputs and outputs Xigo, Xioh, as well as regional absorptions Xigh,g = h, and interre-
gional flows Xigh,g negationslash= h. In this case gravity coefficients are computed directly from
(2.2), the coefficients obtained by this method are used in Type 3 models.
The exact solution is used when interregional flows Xigh,g negationslash= h are not available.
In the system of equations with 3m known variables (Xigo, Xioh, Xigh,g = h) it is not
possible to determine m2 ?m unknown variables (Qigh,g negationslash= h).
In order to determine gravity coefficients, Leontief and Strout (1963) suggested
the following:
Qigh = (Cig +Kih)digh?igh ? i,g,h; g negationslash= h (2.3)
9
where digh is the distance between regions g and h; ?igh indicates whether trade between
g and h exist; Cig is the relative position of region g as a producer; Kih is the relative
position of region h as a consumer. Now m2?m unknown variables (Qigh, g negationslash= h) are
expressed as a combination of 2m unknown (Cig and Kih) and 2m exogenous variables
(digh and ?igh) and the system could be solved when base year trade data are not
available.
A least squares regression estimation procedure is used when interregional flows
Xigh,g negationslash= h are not available and works in a way similar to generating the ?exact
solution?, but uses the least squares method instead of the system of linear equations.
The simple solution is what the name indicates.
Xigh = X
i
goX
i
oh
Xioo b?
i
gh ? i,g,h (2.4)
where ?igh denotes whether trade between two regions exists, and b is a gravity co-
efficient common for all the pairs of regions where trade exists. The data required
to implement this model are regional inputs and outputs Xigo, Xioh, and regional
absorptions Xigh,g = h.
b = X
i
oo ?
summationtextm
r=1 X
i
rr
summationtextm
g=1
summationtextm
h=1
XigoXioh
Xioo
, ?igh = 0 ? g = h (2.5)
The use of interregional trade coefficients in predictive models relies on their
stability, which is the key assumption of multi-regional input-output models. Stability
of interregional trade coefficients has been a concern since the early applications of
these models (Moses 1955).
10
Polenske (1970) conducted a testing of row, column, and gravity fixed coefficient
models within an input-output framework to estimate 1963 Japanese production.
Among the methods used to estimate the gravity fixed coefficient, the point esti-
mate method produced the coefficients that gave the lowest estimation errors. The
overall predictive capability of the column coefficient and the point estimate gravity
trade models produced comparable results, while the row coefficient method was least
accurate.
2.4 Timber Supply and Demand Models
Approaches to modeling timber supply and demand can be classified from two
points of view: how they model the timber product market (gap models, market
models), and how they treat spatial aspects (non-spatial, quasi-spatial, and spatial
models).
Gap models attempt to determine differences between demand for and supply
of timber products assuming a predetermined price level. Demand, supply, and in-
ventory are first projected independently, then demand is compared with supply, and
conclusions are made about resulting prices (whether they will be lower or higher
than assumed). Thus, price-quantity relationships are not used explicitly.
Market models are characterized by explicit functional representations of mar-
ket processes which determine both price and quantity. Usually this is done by
modeling the relationship between price, aggregate production, aggregate consump-
tion, and aggregate timber inventory, by product, and, if applicable, by region. This
approach requires determination of empirical coefficients of these relationships (elas-
ticities). Examples of models using this approach are the Georgia Regional Timber
11
Supply model (GRITS) Cubbage et al. (1991), the Timber Assessment Market Model
(TAMM) Adams and Haynes (1980, 1996), and the Subregional Timber Supply Model
(SRTS) Abt et al. (2000). The alternative is to model growth of individual represen-
tative stands and the decisions of owners whether to cut, which, when combined with
aggregated demand, allows derivation of regional supplies and price levels (Teeter
1994, Zhou 1998).
Non-spatial models are characterized by explicit functional representation of mar-
ket processes which determine both price and quantity, but treat only one geograph-
ical region. Suppliers and purchasers are treated as if they participate in a single
aggregate regional market. Usually these models are applied to a state or to regions
of similar size. Examples of nonspatial models are GRITS for Georgia (Cubbage et al.
1991) and DPSupply for Alabama (Teeter 1994, Zhou 1998).
Quasi-spatial and spatial models address spatial dimensions of timber markets.
In quasi-spatial models, spatial dimensions are modeled, but simplified: a) there is a
connection between one supply region and one demand region; or b) there are many
supply regions and one demand region, for exampple, SRTS (Abt et al. 2000).
Spatial models fully acknowledge the existence of multiple supply and demand
regions. There are a number of regions separated by transportation costs. For each
region and product there is a relationship between price, production and consump-
tion. As a result, a competitive equilibrium exists for prices, amounts produced and
consumed, and transportation costs between regions, so that the net return for each
source is maximized and the distribution of products takes place at a minimum cost.
An example of a spatial model at the national level is TAMM (Adams and Haynes
1980, 1996).
12
The Interregional Timber Supply Model (Holley et al. 1975) modeled the U.S.
softwood market through 17 supply regions, 23 demand regions, and 11 aggregate
final products. ITM considered production costs, wood conversion coefficients, and
transportation costs. Given the forward projection of consumption in each demand
region and starting with existing inventories and production capacities in each region,
the model traced least cost, most efficient geographical patterns of industrial location
and timber harvesting over time. Softwood inventory in each supply region was
updated using the TRAS (Larson and Goforth 1970) growth model. The approach to
handling the multi-regional market was Linear Programming (LP). A large scale LP
transportation and harvesting/processing model minimized overall costs of meeting
consumer requirements in a given time period. Although it does not incorporate
the economic concept of supply and demand as determinants of quantity and price
over time, it models effect of the market mechanism in meeting exogenous regional
demands.
The Timber Assessment Market Model (Adams and Haynes 1980, 1996) modeled
the U.S. softwood market considering 9 supply regions (including Canada), 6 demand
regions, and 4 aggregate final products. Quantity and price of timber products in
each region were determined as a result of the interaction of regional demand and
supply as well as trade of timber from and to other regions. Coefficients of sup-
ply and demand equations (elasticities) were calculated using econometric models of
demand and supply. Coefficients for lumber and plywood demand equations were
estimated separately for each demand region. Demands for pulpwood and fuelwood
were determined outside of the model, regional demands were obtained by disaggre-
gation of national level demands. Coefficients for stumpage supply equations were
13
estimated separately for public and private sectors in each region. The model does
not distinguish between pulpwood and sawtimber stumpage. The TRAS system was
used as a growth model in the early implementation of the system followed by the
Aggregate Timberland Assessment System (ATLAS) more recently. Because reaching
an equilibrium assumes changes in both prices and quantities, it is not possible to use
LP techniques for interregional allocation. The model utilizes Reactive Programming
which is an iterative procedure in which successive approximations to the equilibrium
solution are computed. Despite the fact that it is one of most advanced and widely
accepted timber supply models, it treats the U.S. South as one supply region and does
not allow for analysis of subregional inventory changes, harvest shifts, and impacts
of reallocation within the forest industry.
The Subregional Timber Supply Model for the U.S. South (Abt et al. 2000) works
with 52 supply regions (for each FIA forest survey region), 2 ownership classes, and 5
management classes. Inventory is aggregated by 10-year age classes. Timber supply
for each region is a function of price, inventory, and supply shifters. Aggregate de-
mand is a function of price and demand shifters. SRTS takes exogenously determined
aggregate regional harvest levels and solves for the implicit demand, price, and sub-
regional harvest shifts. Assumptions imply a competitive market with regions and
ownerships facing the same price trend, although levels could differ across subregions.
There is no demand associated with a single point, instead demand is assumed to be
mobile, either through shifts in procurement regions or new capacity, and is assumed
to respond to regional differences in stumpage prices. In reality, the ability to real-
locate production capacities could be not as elastic as this model assumes because
of the barriers between subregions represented by distances and transportation costs,
14
which are ignored in SRTS. Thus, it is not clear how the model will respond to an
explicit change in subregional demand, e.g. resulting from closure of a pulpmill.
DPSupply (Teeter 1994, Zhou 1998) was used to analyze timber supply for Al-
abama, South Alabama, and Mississippi. The elementary growth and harvesting unit
is a FIA sample plot. A network of FIA sample plots covers the territory with a
grid size of approximately 3 miles. In DPSupply each FIA sample plot is assumed
to represent one stand. This makes DPSupply different from most other models
which deal with aggregated timber inventory. FIA sample plots were grouped by four
management types (pine plantations, natural pine, oak-pine, and mixed hardwoods),
two size classes, and two ownerships classes (industrial and non-industrial private).
Public forests were not considered due to their insignificant share (less than 5%) in
timber production. A growth model was developed using two consecutive FIA data
sets. Unlike most of other models which consider only the volume of ?growing stock?,
DPSupply operates with the volume of ?live trees,? which is about 10% greater than
the volume of ?growing stock?, and the difference could be harvested as pulpwood.
Growth and timber product distribution models were built for each management type
and size class. Volume per acre and average diameter at breast height (dbh) in a given
year are modeled as a function of volume and dbh in previous year: Vt+1 = V(Vt,Dt);
Dt+1 = D(Vt,Dt).
Timber product distribution models estimated using a multinomial logit method
(Teeter and Zhou 1999) are used to distribute the aggregate volume on potential
harvest plots to product classes. The dynamic programming module uses a recur-
sive procedure to determine optimal harvest decisions (clearcutting, thinning, or no
action) for each combination of volume and dbh class, management type, ownership
15
class, and stumpage price level. The assumption of this model is that forest owners
manage their forests in order to maximize net present value. The projection mod-
ule works in the following way. For each year of the projection period, this module
?grows? each stand according to growth functions, and, given exogenous demand and
an array of optimal decisions from the dynamic programming module, ?harvests? the
necessary number of stands using a linear programming procedure, and ?regenerates?
harvested stands. DPSupply used a different approach to model the timber products
market than the previous two models, but it is non-spatial model, which limited its
ability to analyze interregional aspects of roundwood markets.
16
Chapter 3
Econometric Analysis of Alabama?s Pulpwood Market
3.1 Introduction
The Southern timber market is the major source of both softwood and hardwood
pulpwood in the U.S. This region accounts for 65 percent of total U.S. pulpwood pro-
duction over the past ten years (Howard 2001). Currently, 94 pulpmills are operating
and drawing wood from the 13 Southern States. Southern mills? pulping capacity
of 123 thousand tons per day accounts for more than two-thirds of the nation?s cur-
rent pulping capacity (Johnson and Steppleton 2003). Alabama leads the South in
total roundwood pulpwood production (10 million cords), number of mills (14), and
is second only to Georgia in pulping capacity (18,605 tons per day) (Johnson and
Steppleton 2003).
The constant interest in timber supply and environmental issues calls for more
efforts to improve analyses and projections of forest resource trends. Furthermore,
in recent years, interest has grown in understanding timber supply in specific regions
(states or parts of states) and how mill expansions, land use changes, and urbanization
affect supply (Abt et al. 2000). The determinants of wood supply and demand are
important elements of timber inventory projection models.
The scope of previous studies of roundwood markets varies from a world per-
spective (Tr?mborg et al. 2000), to national (Br?annlund et al. 1985, Hetem?aki and
17
Kuuluvainen 1992, Adams 1975, Haynes and Adams 1985), and to regional (Daniels
and Hyde 1986, Newman 1987, Carter 1992) markets.
Most empirical studies of timber markets are based on contemporary neoclassical
microeconomic theory. Supply and demand are usually considered simultaneously, us-
ing a system of simultaneous equations. Common approaches include two stage least
squares (2SLS) regression or three stage least squares (3SLS) regression (Br?annlund
et al. 1985, Newman 1987, Carter 1992).
Previous studies of pulpwood markets dealt with softwood pulpwood (Carter
1992), hardwood pulpwood (Leuschner 1973), and softwood solidwood (pulpwood +
lumber) (Br?annlund et al. 1985, Newman 1987). In the latter case, the mutual in-
fluence of pulpwood and sawtimber markets was taken into account by considering
direct substitution in output between solidwood and pulpwood. To our knowledge,
only Nagubadi et al. (2001) analyzed interactions between softwood and hardwood
pulpwood demands, but did not find any statistically significant substitution effect
between hardwood and softwood in pulp production. This paper attempts to esti-
mate demand and supply elasticities as well as identify factors determining demand
and supply for the Alabama pulpwood market. Analysis of hardwood and softwood
pulpwood cross price demand elasticities as well as cross-regional price elasticities are
added goals of the present analysis.
18
3.2 Pulpwood Market Model
The basic economic assumption used in the present model is that of equality of
supply and demand for both softwood and hardwood pulpwood:
QSt ? QSdt ? QSst (3.1)
QHt ? QHdt ? QHst (3.2)
where QSt is the quantity of softwood pulpwood stumpage in year t, QSdt and QSst are
respectively the quantities demanded and supplied in year t; QHt is the quantity of
hardwood pulpwood stumpage in year t, QHdt and QHst are respectively the quantities
of hardwood pulpwood demanded and supplied.
Stumpage demand is derived from its use to produce pulp. Pulpmills have high
fixed costs, and consequently, mill managers must ensure that mills operate contin-
uously (Leuschner 1973). Therefore, aggregated mill capacity is included in the list
of explanatory variables of the pulpwood demand equations. Capacity is expected
to be more significant in models of smaller markets (e.g., state as opposed to region
or nation). Pulpwood demand and pulpmill capacity are expected to be positively
related. At the aggregate level, the pulping industry consumes both softwood and
hardwood pulpwood. Depending on how much the proportions of these inputs are
allowed to vary, softwood and hardwood pulpwood may be either substitutes or com-
plements. The own-price demand elasticity is expected to be negative, the expected
sign of the price of the alternative input depends on whether softwood and hardwood
pulpwood are substitutes or complements. Furthermore, consideration must be made
that a significant proportion of pulpwood consumed by Alabama pulpmills comes
19
from other states. We assume that imported pulpwood substitutes for pulpwood
produced locally. To account for imported pulpwood we include pulpwood stumpage
prices from Mississippi, the major exporter of both softwood and hardwood pulpwood
to Alabama. Thus, demands for softwood and hardwood pulpwood are specified as
follows:
QSdt = F(PSpwt ,PHpwt ,PMSpwt ,Ct) (3.3)
QHdt = F(PHpwt ,PSpwt ,PMHpwt ,Ct) (3.4)
where PSpwt and PHpwt are, respectively, softwood and hardwood pulpwood stumpage
prices in Alabama; PMSpwt and PMHpwt are, respectively, softwood and hardwood
pulpwood stumpage prices in Mississippi; and Ct is the daily pulping capacity of
Alabama?s pulp industry in year t.
It is more difficult to derive the supply equations for pulpwood than the demand
equations. Individual timber growers? production cost data are not readily available
(Br?annlund et al. 1985, Newman 1987) and expenses connected with production are
distant in time. Pulpwood supply is a function of the revenues of forest management
through its own price and the price of alternative outputs (sawtimber). The coeffi-
cients of the own price variable is expected to have a positive sign while the signs of
coefficients for alternative product prices are unclear; they depend on the possibilities
to switch to and from alternative products and on the dynamics of alternative prod-
uct prices. Previous studies report a substitution relationship between pulpwood and
sawtimber in pulpwood supply (Br?annlund et al. 1985, Newman 1987, Carter 1992).
It is reasonable to use standing softwood inventory as in Newman (1987), but data are
20
only available at approximately ten-year intervals, and interpolation does not make
much sense. Another consideration is that stumpage is bought, harvested, and sold
to the pulp mills by a large number of small contractors who have limited financial
resources and managerial skills. The volume sold in previous years would likely affect
the current year?s supply since high sales in previous years provide contractors with
an incentive to stay in business and expand capacity (Leuschner 1973). Therefore, we
assume a positive relationship between current year supply and previous year quantity
(harvest). Thus, the supply equations may be specified as follows:
QSst = F(PSpwt ,PSstt ,QSst?1) (3.5)
QHst = F(PHpwt ,PHstt ,QHst?1) (3.6)
where PSstt and PHstt are, respectively, softwood and hardwood sawtimber stumpage
prices in year t, and QSst?1 and QHst?1 are, respectively, harvests of softwood and hard-
wood pulpwood in the previous year.
3.3 Data
The current analysis uses time series data from 1977 to 2001. All prices are de-
flated to the base year 1982 using the Bureau of Labor Statistics Producer Price Index
for all commodities (http://www.bls.gov/). The quantity of pulpwood stumpage
(QSt ? QSdt ? QSst , QHt ? QHdt ? QHst ) is the total quantity in thousand cords of,
respectively, softwood and hardwood roundwood pulpwood produced in Alabama.
Pulping capacity (Ct) is annualized daily pulping capacity of Alabama?s pulp and
paper industry in thousands of tons. The sources of data on quantity of pulpwood
21
stumpage and pulping capacity are the ?Southern Pulpwood Production? reports,
an annual report series from the USDA Forest Service Southern Research Station.
Stumpage price data are from Timber Mart South (Norris Foundation 1977?2001).
Annual prices of softwood pulpwood, softwood sawtimber, hardwood pulpwood, and
hardwood sawtimber, (PSpwt , PMSpwt , PSstt , PHpwt , PMHpwt , PHstt ) were obtained by
averaging statewide quarterly data; prices are expressed as real U.S. dollars per cord
for pulpwood, and real U.S. dollars per thousand board feet for sawtimber.
3.4 Model Estimation and Results
The present model is a system of four simultaneous linear demand (3.3, 3.4)
and supply (3.5, 3.6) equations with equilibrium constraints (3.1, 3.2). Supply and
demand equations contain two endogenous variables, prices of softwood and hardwood
pulpwood, furthermore, the supply equations contain lagged dependent variables.
Due to the endogenous variables, the ordinary least squares (OLS) method provides
inconsistent estimates of the coefficients (Gujarati 1988, p. 563). Both demand and
supply equations are overidentified, which suggests we should use two stage least
squares (2SLS) regression, as it produces consistent (but biased) parameter estimates
for the system of simultaneous equations.
In order to perform 2SLS, it is necessary to create instrumental variables by
regressing PSpwt , PHpwt on all the exogenous variables (PMSpwt , PSstt , QSst?1, PMHpwt ,
PHstt , QHst?1, Ct), and use predicted values ?PSpwt , ?PHpwt in the following system of
structural linear regression equations:
QSt = ?1 +?2PSpwt +?3PHpwt +?4PMSpwt +?5Ct +epsilon11t (3.7)
22
QHt = ?1 +?2PHpwt +?3PSpwt +?4PMHpwt +?5Ct +epsilon12t (3.8)
QSt = ?1 +?2PSpwt +?3PSstt +?4QSst?1 +epsilon13t (3.9)
QHt = ?1 +?2PHpwt +?3PHstt +?4QHst?1 +epsilon14t (3.10)
where the ?i, ?i, ?i, and ?i are estimated coefficients and the epsilon1it are residuals from
the estimation.
We used a linear regression form because it best accommodates the theoretical
model (the effects are mostly additive) and is reported generally to perform better
in this kind of situation (Newman 1987). The regression results for the structural
(second stage) equations are presented in Table 3.1. The table also contains elasticities
calculated at the means of the data.
The goodness of fit (as indicated by R2) was high in all supply and demand
equations (although its use as a measure of goodness of fit is not fully appropriate
because in 2SLS it is not bounded between 0 and 1, it is still the best available
measure of goodness of fit). The White (1980) test failed to reject the null hypothesis
of homoscedasticity at reasonable levels of significance in all demand and supply
equations indicating no heteroscedasticity is present.
The values of the Durbin-Watson statistics calculated for the demand equations
suggest that no autocorrelation problem exists. Because a lagged dependent variable
was used in the supply equations, the Durbin-Watson d statistic is not valid; therefore
the Durbin h statistic was calculated instead. The value of the statistic suggests au-
tocorrelation is present in the hardwood pulpwood supply equation. For both supply
and demand equations, Newey-West autocorrelation consistent covariance matrices
(Greene 2000) were calculated and the corrected standard errors appear in Table 3.1.
23
Table 3.1: The results of two stage least squares regression and elasticities of
determinants of the Alabama pulpwood stumpage market 1977?2001
Equations Coefficients Value Std. Error p-value Elasticity
Supply QSt Intercept -194.105 421.214 6.4E-01
?PSpwt 84.151 25.068 7.9E-04 0.35
PSstt -0.258 2.094 9.0E-01
QSst?1 0.713 0.134 1.2E-07
R2 0.845
Durbin h -0.761 2.2E+00
QHt Intercept 1322.984 476.849 5.5E-03
?PHpwt 101.900 45.349 2.5E-02 0.35
PHstt -13.219 4.502 3.3E-03 -0.42
QHst?1 0.619 0.191 1.2E-03
R2 0.868
Durbin h 3.837 4.0E-04
Demand QSt Intercept 608.012 662.625 3.6E-01
?PSpwt -416.868 135.929 2.2E-03 -1.72
?PHpwt -264.151 97.834 6.9E-03 -0.57
PMSpwt 518.983 149.793 5.3E-04 1.74
Ct 0.342 0.072 2.4E-06 1.42
R2 0.660
D-W d 1.850
QHt Intercept -3511.743 1060.74 9.3E-04
?PHpwt -226.081 83.610 6.9E-03 -0.77
?PSpwt 4.146 15.404 7.9E-01 0.02
PMHpwt 277.566 95.530 3.7E-03 0.70
Ct 0.342 0.057 2.3E-09 2.26
R2 0.814
D-W d 1.899
24
The own price coefficients in the demand equations are significant at the 1%
level and have the expected signs. Hardwood and softwood pulpwood are shown to
be complements in the softwood pulpwood demand equation; however, data do not
support the same conclusion in the hardwood pulpwood demand equation. The latter
is likely due to the fact that in paper production requiring a mix of softwood and
hardwood pulp, softwood is typically used in larger proportion. Mississippi pulpwood
appears to be a substitute for Alabama pulpwood in both softwood and hardwood
demand equations. The own price elasticities have similar magnitudes (and opposite
signs) as elasticities for Mississippi pulpwood prices (cross-price elasticities) in both
softwood and hardwood demand equations. The estimated coefficients on the pulpmill
capacity variable have the expected signs and are significant at the 1% level.
Estimated coefficients on all the variables in the supply equations are significant
at the 1% level or higher, except the coefficients for own price in the hardwood pulp-
wood supply equation, which is significant at the 5 percent level, and for the price
of softwood sawtimber in the softwood pulpwood supply equation, which is insignif-
icant.1 All the signs are consistent with underlying theory (estimated coefficients of
pulpwood prices and lagged pulpwood quantities are positive, and the estimated co-
efficient of hardwood sawtimber price is negative), supporting the hypothesis about
substitution between pulpwood and sawtimber in hardwood pulpwood supply. Due
to the presence of lagged dependent variables in the supply equations, the elasticities
should be interpreted as short-run elasticities. The softwood pulpwood own price
1However, the coefficient of the price of softwood sawtimber price in the softwood pulpwood
supply equation becomes significant and has a sign indicating substitution when the two last two
years (2000, 2001) of the time series are removed.
25
elasticity is similar to elasticities estimated for the U.S. South by Newman (1987)
and Carter (1992).
3.5 Discussion and Conclusion
This study presents an econometric analysis of pulpwood supply and demand
for Alabama. It uses a two-stage least squares regression technique to estimate the
system of four supply and demand equations.
The price elasticity of softwood pulpwood supply was found to be relatively
low, but similar to those previously reported for the U.S. South (Newman 1987,
Carter 1992). The price elasticity of hardwood pulpwood supply was comparable
to the estimated price elasticity for softwood pulpwood. The substitution role of
sawtimber price found for hardwood pulpwood supply corresponds with findings for
Sweden and the U.S. South (Br?annlund et al. 1985, Newman 1987, Carter 1992).
This supports our hypothesis that, at least in hardwood pulpwood supply, sawtimber
could be considered as an alternative output, or a substitute in production.
The existence of a substitution effect between Alabama and Mississippi pulpwood
suggests that Alabama?s pulpwood market and the pulpwood markets in neighboring
states are tightly linked. This explains the approximate equality of absolute values
of the own and cross-price elasticities in both softwood and hardwood pulpwood
demands, as well as relatively high absolute values of own and cross-price elasticities in
softwood pulpwood demand. This phenomenon may be more general than anticipated
at the outset of this study, with imported pulpwood playing an important role in
satisfying pulp and paper industry demands in relatively small regions. Another
26
interesting finding is the complementary role of hardwood pulpwood in softwood
pulpwood demand.
27
Chapter 4
Modeling Pulpwood Trade within the U.S. South
4.1 Introduction
Despite the fact that it is often uneconomic to transport raw materials such as
wood long distances, significant volumes of roundwood products in the U.S. South
are transported across state boundaries. Nearly 25% of the pulpwood consumed by
the pulping industry and 12% of sawtimber consumed by the sawmilling industry of
the southern states are transported from other states in the region (while less than
1% is imported from outside the U.S. South). Most state level econometric studies
of supply and demand take trade into account as an exogenous variable. Creation of
a model capable of predicting timber supply and demand on a local level requires an
understanding of factors influencing trade of timber products between the states.
The main reason for the occurrence of cross-state roundwood trade is the pattern
of locations of timber harvest and roundwood consumption, which is determined by
the location of mills and location of inventory (for the pulpwood, see Figure 4.1).
Roundwood consumption and production in each state occurs not at a single point,
but in an area or group of points. Location of roundwood production areas (procure-
ment regions ) and concentrations of timber industry do not conform with state lines,
which in some cases cross areas of concentration of consumption and production. At
the same time, forest and industry statistics are aggregated by states. As a result we
28
Pulpmills Capacity, ton/24 hr50 - 500
501 - 10001001 - 1500
1501 - 20002001 - 3000
Pulpwood Production, mcf/sq mile< 3
4 -- 89 -- 14
15 -- 2223 -- 37
Figure 4.1: Pulpwood Production and Pulpmills Located in the South
observe trade across state boundaries (often in both directions ? ?cross-hauling?).
Most such trade takes place between neighboring states, but a significant amount is
traded between states that do not share a common border while the volume of trade
between neighboring states vary greatly.
Several methods exist for regional interdependence analysis. Among them are
fixed trade coefficient models (multiregional input-output models), gravity models,
and linear programming models.
Modeling interregional trade using linear programming requires knowledge of
a large number of parameters, including demand and supply prices and quantities
29
in each of the demand and supply regions, as well as the costs of transportation
between each pair of demand and supply regions. Under market conditions, prices
and quantities are determined simultaneously as the result of the interaction of supply
and demand in all regions, so the problem cannot easily be solved using a linear
programming procedure.
In contrast to linear programming, gravity model and fixed coefficient meth-
ods, utilize existing data on interregional or international trade to obtain information
about trading relationships between parties. This information could be used to pre-
dict future trade. In this study we will compare the forecasting performance regarding
the pulpwood trade between states of the U.S. South for various specifications of a
gravity model and a fixed gravity coefficient model, as well as discuss their possible
applications in interregional (subregional) timber inventory models. The study is re-
stricted to the analysis of pulpwood trade because of the greater amount of pulpwood
trade in comparison to trade of other roundwood products, and because of the data
availability.
4.2 Methods
4.2.1 Gravity Model
The general formulation of the standard gravity model is
Xgh = ?0Mg?1Mh?2Dgh?3, Xgh ? 0, g negationslash= h, ?0 > 0, ?1 > 0, ?2 > 0, ?3 < 0, (4.1)
where Xgh is the trade between exporting (g) and importing (h) regions, Mg is the size
of the economy of the exporting region, Mh is the size of the economy of the importing
30
region, Dgh is the distance between locations, and ?0 ...?3 are the parameters to be
estimated. Explanatory variables in this general gravity model could be viewed as
representing three groups of factors, which determine trade between two regions.
The size of the importing economy determines import demand (Tinbergen 1962). In
empirical studies of international trade, size of the economy is usually represented by
national income or income per capita. The size of the exporting economy represents
a group of factors determining export supply. For this purpose, national output
or output per capita is commonly used. The third group consist of factors that
inhibit or facilitate trade between two economies. Distance, serving as a proxy for
transportation costs, is the most common factor inhibiting trade (Tinbergen 1962).
Other variables used in empirical studies are common borders, tariffs, preferential
treatments, trade barriers or blocks, and language or cultural differences (Oguledo
and MacPhee 1994).
The use of national or per capita output or income as proxies for export supply
and import demand is understandable when aggregate trade is studied, especially in
the case of international trade. When the trade of a single product is analyzed, the
data on demand and supply of this product in individual regions could be readily
available. Import demand is a function of total demand and total supply in the
importing region. Export supply is a function of total supply and total demand in
the exporting region.
The gravity model for trade of each of roundwood products between the states
of the U.S. South in year t is specified in the following functional form:
Xght = e?0(Xgot)?1(Xogt)?2(Xoht)?3(Xhot)?4(Dgh)?5(e)?6Bgh +epsilon1ght, (4.2)
31
where Xgot is the supply (production) of a product in the exporting state, Xhot is the
supply (production) of a product in the importing state, Xogt and Xoht are demands
(consumptions) for a product in the exporting and importing states, and Dgh is the
distance between the states, and Bgh is the border dummy taking value of 1 if states
g and h share common border and 0 otherwise. Supply (production) and demand
(consumption) are calculated from known traded and retained amounts of products
for each of the states. Assuming that epsilon1ght is normally distributed with E [epsilon1ght] = 0,
the model could be estimated using Nonlinear Least Squares (NLS).
By taking logarithms of (4.2) and changing assumptions about the distribution
and effect of the error term, this model could be estimated using Ordinary Least
Squares (OLS), which is the most common way to estimate parameters of gravity
models:
lnXght = ?0 +?1 lnXgot+?2 lnXogt+?3 lnXoht+?4 lnXhot+?5 lnDgh+?6Bgh+epsilon1ght
(4.3)
While the vast majority of earlier applications of the gravity model used cross-
sectional data, many recent studies emphasize the advantages of a panel approach
(M?aty?as 1997, 1998, Egger 2000, Egger and Pfaffermayr 2003). A panel framework
allows to capture the relationships between the relevant variables over a longer period
and to reveal time invariant effects specific to the cross-sectional units (importing
region, exporting region and/or pairs of exporting and importing regions). Depending
on the assumptions about structure of the error component, panel data models can be
estimated using fixed effect and random effect models. According to the fixed effect
model, group (cross-sectional or time) effects are treated as fixed parameters. In other
32
words, groups have different intercepts. According to the random effect model, group
effects are treated as a sample of a random drawing from the larger population and
error component has different variation for different cross-sectional or time groups.
Using a fixed effect model is a reasonable approach when the differences between
units are viewed as parametric shifts of the regression function (Greene 2000), for
example when analyzing trade flows between a predetermined set of trading partners.
If the sample is randomly selected from the larger population of cross-sectional or
time-series units, more appropriate is the random effect model, which allows one to
extend inferences based on estimation results onto cross-sectional or time-series units
outside the sample. This reasoning clearly speaks for the use of a fixed effect model
to analyze roundwood products trade between states of the U.S. South, especially
when the goal is the prediction of trade between these particular states.
It has been argued that the proper specification of a gravity model with panel
data would include controls for time, importer, and exporter effects (M?aty?as 1997).
This is three-way panel specification containing two cross-sectional effects. The im-
porter and exporter effects capture observable and unobservable country or region
specific characteristics, while time effect captures common cyclical influences. Fur-
thermore, Egger and Pfaffermayr (2003) suggest that interaction effect between im-
porter and exporter main effects, which is the product of these two main effects,
should be included in the model. They show that omission of importer-exporter in-
teraction effect leads to bias in the estimates. From an economic point of view, the
interaction effect of importing and exporting regions could be interpreted as the time
invariant bilateral influences which lead to deviation from the ?normal? propensity
to trade for the pairs of regions (Egger and Pfaffermayr 2003).
33
The full set of dummy variables representing bilateral importer-exporter interac-
tion effect is collinear with the full set of dummies representing main cross-sectional
effects. In order to estimate regression, several dummies must be dropped. Because
of bilateral interaction effect is the product of main cross-sectional effects, it contains
all the information captured by both main cross-sectional effects. Thus, generalized
three-way specification with importer, exporter, time, and bilateral interaction effects
is identical to the two-way specification with time and bilateral effects only (Egger
and Pfaffermayr 2003). Therefore, both exporter and importer main effects could be
omitted. In addition to collinearity with main cross-sectional effects, bilateral interac-
tion effect is collinear with time invariant variables like distance and common border.
These variables should be also dropped from model. Thus, the panel specification for
the gravity model (4.3) becomes
lnXght = ?1 lnXgot +?2 lnXogt +?3 lnXoht +?4 lnXhot +?t +?gh +epsilon1ght (4.4)
where ?t are the time effects and ?gh are bilateral importer-exporter effects. The
corresponding specification without log-log transformation (to estimate the model
using NLS) will be
Xght = (Xgot)?1(Xogt)?2(Xoht)?3(Xhot)?4e?te?gh +epsilon1ght (4.5)
4.2.2 Fixed Trade Coefficient Models
Fixed trade coefficient models are based on the following principle: the total in-
terindustry demands (including the industry itself) and demands by final users equals
34
the industry?s output. These models were designed as rough and ready working tools
capable of making effective use of limited amounts of factual information (Leontief
and Strout 1963).
Interregional trade is accounted for using one of three models within the fixed
trade coefficient framework: a column coefficient model, row coefficient model, or a
gravity coefficient model.
The column coefficient model (Moses 1955, Polenske 1970) is based on the as-
sumption that shipments of a commodity between two regions are proportional to
total consumption of a commodity in the demand region. The row coefficient model
assumes that shipments of a commodity between two regions are proportional to the
total production of a commodity in the supply region. These models use a one way-
approach (Hua 1990), because they relate trade to one of two factors. According to
the gravity coefficient model (Leontief and Strout 1963), the amount of interregional
trade is directly proportional to the total production and total consumption of a com-
modity in the supply and demand regions, respectively, and is inversely proportional
to the total amount of a commodity produced in all regions. Because two orthogonal
factors are used, this model could be described as employing a two-way approach
(Hua 1990).
The amount of trade between the regions is expressed in the following ways
according to column, row, and gravity coefficient models, respectively:
Xigh = XiohCigh ? i,g,h; g negationslash= h (4.6)
Xigh = XigoRigh ? i,g,h; g negationslash= h (4.7)
Xigh = X
i
goX
i
oh
Xioo Q
i
gh ? i,g,h; g negationslash= h (4.8)
35
where i is the commodity; g is the supply region; h is the demand region; Xigh is
the amount of commodity i shipped from region g to region h; Xigo is the amount
of commodity produced in region g; Xioh is the amount of commodity consumed in
region h; Xioo is the total amount of commodity i produced in an economy; Cigh is the
column coefficient; Righ is the row coefficient; and Qigh is the gravity coefficient.
The empirical coefficients in the column and row coefficient models are calculated
directly from the base-year data. Depending on assumptions about the nature of
spatial interaction between supply and demand regions, gravity coefficients could be
either extracted from the base-year data or determined using exogenous variables, for
example, using one of the methods developed by Leontief and Strout (1963). In this
study we will investigate the temporal stability of empirical gravity coefficients.
4.3 Data
We analyze bilateral trades of softwood and hardwood pulpwood between 13
states of the United States South (Alabama, Arkansas, Florida, Georgia, Kentucky,
Louisiana, Mississippi, North Carolina, Oklahoma, South Carolina, Tennessee, Texas,
and Virginia) over the period 1994?2002. Roundwood pulpwood and wood chips
produced in the forest were taken into account, excluding pulpwood exported from the
country. The amount of annual softwood and hardwood pulpwood trade, production,
and consumption in cords were obtained from the annual reports ?Southern Pulpwood
Production? published by the Southern Research Station (Johnson and Steppleton
2003). The trade between each pair of states in both directions was accounted for
separately. The datasets could be viewed as two matrices (softwood and hardwood
pulpwood trade) with three dimensions: 13 exporting states, 13 importing states, and
36
9 years. Each of the matrices contain 1521 elements, of which 1404 elements represent
volumes of trade between states and 117 elements are volumes retained by the states.
Only the values representing trade between the states are used for modeling, however
retained volumes are used to obtain states? production and consumption of hardwood
and softwood pulpwood.
Euclidean distances in kilometers between exporting states? centers of inven-
tory and importing states? centers of consumption were determined using ArcGISR?
(geographic information system software from Environmental Systems Research In-
stitute). Exporting states? centers of inventory were calculated separately for hard-
woods and softwoods as centers of mass of counties for each of the states weighted,
respectively, by softwood or hardwood inventory from the latest Forest Inventory and
Analysis (FIA) data. Importing states? centers of consumption were calculated as
centers of mass of pulpmills for each of the states weighted by mills? daily pulping
capacity (Johnson and Steppleton 2003).
Descriptive statistics of the data used for the analysis of the pulpwood trade
between the states of U.S. South are presented in Table 4.1.
4.4 Empirical Results
4.4.1 Gravity Model
Pulpwood trade flows between states of the U.S. South were estimated using
several methodologies. First, for comparison purposes, the gravity models were esti-
mated without specific effects, that is, assuming that intercept terms are constant for
all 169 cross-sectional groups (which are importing-exporting pairs of states) and 9
37
Table 4.1: Descriptive statistics of the variables
Variables Units Mean Std. Dev. Minimum Maximum
Softwood pulpwood (n=1404)
Production cords 2410485 1691215 13894 6528057
Consumption cords 2404647 1749286 4271 6268474
Trade cords 46271 131861 0 950611
Distance kilometers 765 376 178 1676
Hardwood pulpwood (n=1404)
Production cords 1308856 918069 73111 4185204
Consumption cords 1318555 1124607 52338 5486348
Trade cords 33721 108824 0 1226806
Distance kilometers 755 364 186 1669
time periods. Models were estimated using linear and nonlinear least squares meth-
ods, however White?s test indicated severe heteroscedasticity problems. To obtain
robust variance-covariance matrix, models were re-estimated using the Generalized
Method of Moments (GMM) using Bartlett kernel with bandwidth parameter 1, which
corresponds to the White estimator (SAS Institute, Inc. 1999, p. 733). Estimation
results for the gravity equations using GMM are shown in Table 4.2.
All of the estimated regression coefficients have expected signs and most are
highlysignificant. The onlyones not significantlydifferent from zero are thecoefficient
of demand in the exporting state and the coefficient of supply in the importing state
in the log-linear model for hardwood pulpwood. Coefficients for the distance variable
between exporting and importing states in the nonlinear model are not significantly
different from ?2, which is consistent with underlying gravity law of physics.
The R2 values are higher for non-linear least squares models, however, these
statistics could not be compared directly, because nonlinear models fit the original
dependent variables, while log-linear models fit log-transformed dependent variables.
The goodness of fit of models could be compared using measures such as Root Mean
38
Table 4.2: Estimation results for bilateral pulpwood trade between states of the
U.S. South without specific effects (models (4.3) and (4.2))
Explanatory variables Softwood Hardwood
Log-linear Nonlinear Log-linear Nonlinear
Intercept 9.73??? ?2.64? 9.65??? 4.23???
(1.71) (1.48) (2.42) (1.29)
Demand in importing state 1.33??? 2.07??? 0.57?? 1.84???
(0.23) (0.20) (0.16) (0.15)
Supply in exporting state 0.98??? 1.88??? 0.69?? 0.80???
(0.23) (0.26) (0.20) (0.14)
Demand in exporting state ?0.52?? ?0.98??? ?0.24 ?0.33??
(0.22) (0.23) (0.16) (0.13)
Supply in importing state ?0.79??? ?1.43??? ?0.03 ?1.20???
(0.23) (0.20) (0.20) (0.13)
Distance ?3.42??? ?2.11??? ?3.30??? ?1.95???
(0.22) (0.18) (0.25) (0.17)
Border dummy 5.01??? 3.77??? 5.05??? 2.79???
(0.33) (0.28) (0.36) (0.24)
R2 0.71 0.77 0.66 0.86
RMSE 63753 41534
Adjusted RMSE 76366 58695
Log-linear stands for log-transformed model linear in parameters.
Standard errors are reported in parentheses.
??? significant at 1%, ?? significant at 5%, ? significant at 10%.
Square Error (RMSE):
RMSE =
?
? 1
N
Nsummationdisplay
i?1
(yi ? ?yi)2
?
?
1
2
(4.9)
where yi is the dependent variable and ?yi is predicted dependent variable.
To obtain comparable RMSE, predicted dependent variables of the log-linear
models ( hatwidestlnyi) should be reverse-transformed (?yi = ehatwidestlnyi). However, when used to
obtain mean response given values of the explanatory variables, reverse-transformed
fitted linear models sometimes produce severely biased models (Miller 1984). In order
39
for a detransformed estimator of a dependent variable to provide the mean response,
it should be adjusted in the following way (Miller 1984):
?yi = ehatwidestlnyie1/2??2 = e??primexie1/2??2 (4.10)
where hatwidestlnyi is the predicted transformed dependent variable, ?? is an estimator of the
coefficient vector, xi is a vector of explanatory variables, and ??2 is an estimator of
the regression variance.
For the log-linear models, we calculated adjusted Root Mean Square Error using a
detransformed predicted dependent variable adjusted as in (4.10). Despite elimination
of transformation bias, nonlinear models fit the data better than log-linear models.
The reason is the multiplicative nature of the error term in log-linear models versus
their additive nature in nonlinear models.
Next, we introduce individual bilateral and time effects into the models. Because
of the nature of the data and objectives of the study, we consider the fixed effect model
(FEM) appropriate as opposed to the random effect model (REM). The hypothesis
that individual importer-exporter bilateral effects are equal for all groups is appropri-
ately tested using an F ratio test. This test rejected equality of the individual effects
for both hardwood and softwood at 1% level of significance.1
Estimation results for the FEM for a log-transformed linear gravity model and
its nonlinear equivalent are presented in Table 4.3. A Breush-Pagan test indicated
1Because of introduction of fixed effects into the model, time-invariant variables were removed
from the model as collinear to the bilateral effects. Therefore, the use of F-test is not fully appro-
priate, need to use J-test (Davidson and MacKinnon 1981).
40
Table 4.3: Estimation results for bilateral pulpwood trade between states of the
U.S. South with fixed bilateral and time effects (models (4.4) and (4.5))
Explanatory variables Softwood Hardwood
Log-linear Nonlinear Log-linear Nonlinear
Demand in importing state 0.64??? 2.10??? 1.05??? 1.85???
(0.25) (0.31) (0.36) (0.26)
Supply in exporting state ?0.17 1.42??? 0.94?? 0.92???
(0.38) (0.31) (0.46) (0.30)
Demand in exporting state ?0.08 ?1.00??? ?0.26 ?0.50?
(0.19) (0.34) (0.33) (0.26)
Supply in importing state 0.09 ?1.73??? ?0.56 ?1.00???
(0.34) (0.40) (0.39) (0.22)
R2 0.89 0.96 0.84 0.98
RMSE 28144 17608
Adjusted RMSE 40114 30794
Log-linear stands for log-transformed model linear in parameters.
Bilateral and time effects are omitted from the table.
Standard errors are reported in parentheses.
??? significant at 1%, ?? significant at 5%, ? significant at 10%.
the presence of heteroscedasticity, therefore the models were estimated using the
Generalized Method of Moments.
Introduction of fixed bilateral and time effects improved the goodness of fit for
both the log-transformed linear model and the nonlinear model as indicated by R2
and RMSE measures. Similarly to the case without specific effects, nonlinear models
have better goodness of fit than log-transformed linear models. At the same time,
for log-transformed linear models, the introduction of fixed bilateral and time effects
made estimates of many explanatory variables not significantly different from zero
(supply in exporting state, demand in exporting state, supply in importing state
for softwood pulpwood trade), or significantly changed the estimates (demand in
importing state for both softwood and hardwood pulpwood trade). For nonlinear
41
models, all coefficient estimates remained significant and did not significantly change
due to introduction of the fixed bilateral and time effects.
4.4.2 Fixed Gravity Coefficient Model
The fundamental assumption of input-output and interregional input-output
analysis is the stability of technical input coefficients and trade coefficients. We will
test the stability of gravity coefficients calculated by the ?Point Estimate? procedure.
When actual trade data are available for the number of periods under study, we
can obtain a set of gravity coefficients for each period:
Qight = X
i
ootX
i
ght
XigotXioht ? i,g,h,t; g negationslash= h (4.11)
where t is time period.
Individual year gravity coefficients could be thought of as having variation in
three dimensions: exporter region, importer region, and time period (these are main
effects). Furthermore, interactions among the main effects allow us to specify three
additional dimensions of variation. The remaining variation is attributed to random
error. The individual gravity coefficients could be partitioned in the following way:
Qght = ?g +?h +?t + (??)gh + (??)gt + (??)ht +epsilon1ght (4.12)
where ?g, ?h, and ?t are main effects; (??)gh, (??)gt, and (??)ht are interaction effects;
and epsilon1ght is random error. Importer effect, exporter effect, and importer-exporter
interaction effect could be viewed as comprising time indifferent gravity coefficients
(Qgh = ?g + ?h + (??)gh). If gravity coefficients are stable, most variation of Qght
42
Table 4.4: Analysis of variance with main and bilateral interaction effects of the
fixed gravity coefficients for the pulpwood trade between states of the U.S. South
during period 1994?2002
Source Degrees of Partial Sum of Squares
Freedom Softwood Hardwood
Model 356 3937.6??? 1619.9???
(11.1) (20.4)
Exporter effect ?g 12 195.1??? 72.6???
(18.3) (27.0)
Importer effect ?h 12 226.4??? 73.1???
(21.2) (27.2)
Time effect ?t 8 9.7 2.7
(1.4) (1.5)
Exporter and Importer effect (??)gh 131 3329.9??? 1423.8???
(28.6) (48.5)
Exporter and Time effect (??)gt 96 85.0 19.3
(1.0) (0.9)
Importer and Time effect (??)ht 96 91.5 28.3??
(1.1) (1.3)
Residual 1048 931.1 234.7
Total 1404 4868.7 1854.6
F-values are reported in parentheses.
??? significant at 1%, ?? significant at 5%, ? significant at 10%.
should be explained by ?g, ?h, and (??)gh, while effect of ?t should be small and
statistically insignificant. Interpretation of (??)gt and (??)ht is not clear, however
their low significance would verify stability of gravity coefficients.
Table 4.4 presents results of the analysis of variance of gravity coefficients calcu-
lated for hardwood and softwood pulpwood trade between thirteen Southern states
during the period 1994?2002. The importer-exporter interaction effects explain the
largest part of variation of the gravity coefficients. The exporter effect, the importer
effect, and the interaction between two effects are highly significant explanatory vari-
ables, and account for more than 95% of explained variation in both softwood and
43
hardwood trade models. At the same time, time effect accounts for less than one-
quarter of one percent of the explained variations and is insignificant for both softwood
and hardwood trade gravity coefficients. Among time and importer or exporter in-
teraction effects, only the importer-time interaction effect for the hardwood gravity
coefficient is significant at 5% level. All this allows us to conclude that there is con-
siderable stability of fixed gravity coefficients for softwood and hardwood pulpwood
trade.
4.5 Simulation Results
To test the predictive capability of the models being studied, we performed sim-
ulations using existing data. Similarly to Bergkvist (2000), we randomly selected
approximately 80% of the observations into the training set, the remaining obser-
vations comprised the test set. Using the training set, we estimated coefficients for
each of four regression models and calculated average fixed gravity coefficients. Pulp-
wood trade quantities were predicted for the test set, and Root Mean Square Errors
(RMSE) were calculated. This procedure was repeated five times. RMSEs obtained
in simulation, as well as averages and standard deviations for each of the models are
presented in Table 4.5.
The nonlinear gravity equation with fixed effects has the lowest RMSE, followed
by the fixed gravity coefficient method and linear regression with fixed effects. Regres-
sions without fixed effects have significantly worse results, while results of methods
with fixed effects are overlapping, if standard deviations are taken into account.
44
Table 4.5: Root Mean Square Error (RMSE) for the different models and five
different training and learning sets
Test Products Models
OLS NLS OLS FEM NLS FEM FGCM
1 Hardwood 57761 38621 39218 23444 27806
Softwood 73659 61984 33076 22909 28675
2 Hardwood 77750 47191 26288 21633 23181
Softwood 83898 65453 34370 39005 33813
3 Hardwood 71919 44957 25143 17564 25371
Softwood 72157 60591 37871 32975 33070
4 Hardwood 57323 39071 31417 19315 21795
Softwood 60962 43180 29187 29294 31965
5 Hardwood 41874 34720 26681 16215 24839
Softwood 63095 52863 27980 27105 28032
Means Hardwood 61325 40912 29749 19634 24598
Softwood 70754 56814 32497 30258 31111
Standard Hardwood 14045 5069 5811 2941 2281
deviations Softwood 9189 8904 4003 6099 2612
4.6 Discussion and Conclusion
We have compared five different methods regarding their ability to predict trade
of roundwood pulpwood between thirteen states of the U.S. South. For the grav-
ity model, nonlinear estimation methods perform better than log-transformed OLS
because there is no transformation bias. Fixed effect estimation yields significantly
better results because distance and other observable variables are not capable of cap-
turing all factors influencing propensity to trade between two localities. Fixed gravity
coefficients are stable in time, and the method using fixed gravity coefficients pro-
vides the second best results. We would recommend the gravity model estimated
using non-linear least squares method with fixed importer-exporter interaction ef-
fects or the fixed gravity coefficient model to forecast interregional roundwood trade.
However, the fixed gravity coefficient method is much simpler and easier to use.
45
Chapter 5
Incorporating Interstate Trade in a Multi-region Timber Inventory
Projection System
5.1 Introduction
This chapter describes an interregional timber inventory projection model that
recognizes the importance of demand centers (centers of forest products manufactur-
ing activity), inventory dynamics, and trade flows in forecasting future harvests. The
model adapted work by Teeter et al. (1989), who modeled interindustry trade and
highlighted the interdependence of producing regions. Drawing from that work, a
gravity model was constructed that considers the relative position of each region vis-
?a-vis all others as a producer of stumpage and as a consumer of stumpage products.
As a result, the model allows for changes in the harvest levels among regions to accom-
modate imbalances in inventory, changes in production capacity, and transportation
costs from the source of the raw material to manufacturing facilities.
5.2 An Interregional DPSupply Model with Stochastic Prices
5.2.1 Overview of the Model
The Interregional DPSupply (IDPS) model utilizes a combination of normative
and positive approaches (Wear and Parks 1994) to modeling timber supply. It models
growth and optimal management decisions on the level of individual representative
46
stands (FIA sample plots). As the model progresses through time, stands are eval-
uated each year and, on the basis of maximizing land expectation value (LEV), a
recommendation is made to thin, conduct a final harvest, or leave the stand at a
given stumpage price level. Stands are evaluated over a range of stumpage price lev-
els and the stands recommended for harvest at any particular price level constitute
aggregated supply at that price level. The system models the supply of four round-
wood products: softwood pulpwood, softwood sawtimber, hardwood pulpwood, and
hardwood sawtimber. Demands for individual products within demand regions are
allocated to the supply regions using a modified gravity coefficient method. Within
supply regions, demands are allocated among the set of forest plots recommended for
harvesting using a linear programming procedure.
At the core of the IDPS model are three main components: a dynamic pro-
gramming (DP) model for determining optimal harvesting decisions, a linear pro-
gramming (LP) harvesting model, and an interregional trade model (see Figure 5.1).
These models depend on several auxiliary models, including growth models, product
distribution models, and information on area transition probabilities to account for
changes in forest area by type over time. Extending DPSupply (Teeter 1994, Zhou
and Teeter 1996, Zhou 1998) to incorporate the 13-state southern region requires
accounting for regional differences in growth, the anticipated products from represen-
tative stands and area change. To accomplish this goal, the region was delineated
according to physiographic regions (five) similar to those identified by Bailey (1995)
and included the coastal plain, the piedmont and mid-coastal plain, the mountains
and interior plateaus, the Mississippi alluvial basin, and the western piedmont and
mid-coastal plain regions. Using FIA data from the counties in each region, regional
47
DP
model
LP
harvesting
model
Interregional
trade
model
TimberMart South
stumpage prices
Forest Inventory Analysis
inventory data
Timber products
output (TPO) data
Stochastic
prices
model
Product
distribution
model
Final
demands
data
Growth
models
Inventory
at year t
Harvesting
levels
Harvesting
decision
rules
Figure 5.1: Interregional DPSupply system
growth models and product distribution models were constructed for each of 5 key
forest management types: planted pine, natural pine, oak-pine, lowland hardwood
and upland hardwood for each of the physiographic regions by owner class. The
growth models were constructed using methods similar to those used in Zhou (1998).
Product distribution models to allocate the projected volumes on each plot to each
potential product class were constructed following multinomial logit methods outlined
by Teeter and Zhou (1999).
5.2.2 Data
Development of an interregional DPSupply model for the U.S. South and per-
forming simulations requires the following data:
48
? Forest Inventory Analysis (FIA) inventory data by sample plot for each of
13 states. The data were obtained from the USDA Forest Service website
and included the following inventories: Alabama-2000, Arkansas-1995, Florida-
1995, Georgia-1997, Kentucky-1988, Louisiana-1991, Mississippi-1994, North
Carolina-1990, Oklahoma-1993, South Carolina-1993, Tennessee-1999, Texas-
1992, and Virginia-1992.
? Timber Product Output (TPO) data on production, consumption and trade
of major timber products for each of the U.S. South states. The data were
obtained from bulletins of the USDA Forest Service Southern Research Station
(e.g., Johnson and Steppleton 2001, Bentley et al. 2002, Johnson and Brown
2002), and from the TPO website.
? Stumpage price data, collected by Timber Mart-South (Norris Foundation 1977?
2001).
5.2.3 Modeling future trading activity in forest products
As an economy develops, goods produced in one region are often sold in another
region of the country. Several groups of methods exist for regional interdependence
analysis. One group includes fixed trade coefficient models (multiregional input-
output models), and another includes linear programming models.
Application of linear programming in the context of spatial models requires a
large number of parameters to support the analytical mechanisms of interregional
trade. These parameters include demand and supply prices and quantities in each
of the demand and supply regions, as well as the costs of transportation between
49
each pair of demand and supply regions. Unless prices and quantities in demand
and supply regions are exogenous to the model (e.g., Holley et al. 1975), the problem
cannot be solved using linear programming procedures. This difficulty was overcome
to an extent by using reactive programming, an iterative procedure that computes the
equilibrium solution using a series of successive approximations (Adams and Haynes
1980, 1996).
There are a few other obstacles to using linear programming for modeling inter-
regional trade. The trading regions are more or less extended areas, so the average
distances between them do not represent the actual diversity of trade flows (Leontief
and Strout 1963). Furthermore, the transportation distances of roundwood products
are of a similar order of magnitude as the size of the trading regions. As result,
transportation costs could not be determined with the accuracy necessary for the ap-
plication of linear programming procedures. Finally, yet importantly, cross-hauling,
or simultaneous shipment of a homogeneous commodity in both directions, is difficult
to incorporate into linear programming models (Polenske 1980).
Due to the above listed reasons we chose not to use a linear programming ap-
proach to model interregional trade. Instead, we base modelling of the roundwood
trade between the states of the U.S. South on fixed trade coefficient models, which
utilize empirical trade relationships between the industries and regions themselves.
These models are based on the assumption that the total output of interindustry
demands (including the industry itself), plus demands by final users plus exports
equal the industry?s output. Fixed trade coefficient models were designed as rough
50
and ready working tools capable of making effective use of limited amounts of infor-
mation (Leontief and Strout 1963). In forest economics, these models were used by
Teeter et al. (1989).
Interregional trade is accounted for using one of three models within the fixed
trade coefficient framework: a column coefficient model, row coefficient model (these
models use a one-way approach), or a gravity coefficient model (a two-way approach).
The column coefficient model (Moses 1955, Polenske 1970) is based on the as-
sumption that shipments of a commodity between two regions are proportional to
total consumption of the commodity in the demand region. The row coefficient model
assumes that shipments of a commodity between two regions are proportional to total
production of the commodity in the supply region. The assumptions behind one-way
approach models (trade is a function of demand or supply) seem very simplistic, how-
ever, the column coefficient model has been widely used due to its consistency with
the input-output framework.
According to the gravity coefficient model (Leontief and Strout 1963), the amount
of interregional trade is proportional to the total production and total consumption
of the commodity in, respectively, the supply and demand regions, and is inversely
proportional to the total amount of the commodity produced in all regions
Xigh = X
i
goX
i
oh
Xioo Q
i
gh (5.1)
where i, g, h are the product (i), production (g), and consumption regions (h); Xigo
is the amount of product i shipped from region g to h; Xioh is the amount of product
i shipped to region h from all regions; Xigo is the amount of product i shipped to
51
all regions from region g; Xioo is the total amount of commodity i produced in an
economy; and Qigh is the gravity coefficient. Depending on the assumptions about
the nature of spatial interaction between the supply and demand regions, gravity
coefficients could be either extracted from the base-year data or determined using
exogenous variables. Leontief and Strout (1963) developed four methods to derive
gravity coefficients within these two general approaches.
We selected the gravity coefficient method because it allows us to model trading
relationships more realistically by capturing interaction effects of the supply and
demand regions. The availability of data on the production, consumption and trade of
roundwood products between U.S. Southern states allows us to use the point estimate
procedure (Leontief and Strout 1963) to determine gravity coefficients from the base
year data. Direct application of the point estimate procedure, however would not
allow us to model the trade dynamics that result from changes in timber inventories
of producing states. An adaptation of the procedure was necessary.
Recall that the gravity coefficient method assumes that trade between two re-
gions is proportional to the total production of the commodity in the supply region.
However, the elasticity of roundwood supply with respect to the timber inventory is
commonly assumed equal to 1 (Binkley 1987, Abt et al. 2000), or, in other words,
roundwood supply is proportional to inventory. Consequently, it is reasonable to
assume that the shipments of roundwood product i from region g to region h are pro-
portional to the amount of wood available for harvest in region g. Now the amount
of timber product traded will be:
Xigh = I
i
gX
i
oh
Xioo
?Qigh (5.2)
52
where ?Qigh is the ?modified? gravity coefficient and Iig is the amount of timber product
i available in supply region g.
Assuming the ?modified? gravity coefficients remain stable (stability of tech-
nological and interregional coefficients is the basic assumption of input-output and
multiregional input-output models), the model allows prediction of harvest and trad-
ing levels in each forest product for future periods, based on the regional demands
and the amounts of wood available for harvesting each year of the prediction.
5.2.4 Harvest Decisions
The assumption of the dynamic programming component of the IDPS model is
that forest owners manage their forests in order to maximize net present value over an
infinite series of rotations. Although the importance of this objective for NIPF owners
has often been questioned, work by Newman and Wear (1993) supports the basic
assumption. Another assumption of IDPS is that forest owners bear replanting costs
at the beginning of the rotation and receive income when thinning occurs or at the end
of the rotation, when they sell stumpage. Because replanting is assumed only for pine
plantations, for all other forest types income at final harvest is the only component
of the cash flow. The immediate return from thinning or final harvest is evaluated
(using product distribution models) for each of the five levels of stumpage prices. The
range of possible price levels, as well as average ratios between the stumpage prices of
four roundwood products considered in the model, are calculated from Timber Mart-
South historical data (Norris Foundation 1977?2001). Stumpage prices fluctuate over
time, therefore expectations of future prices influence forest owners? decisions about
when to harvest. For this reason, a stochastic pricing element, similar to the one
53
developed by Teeter et al. (1993), was incorporated in the IDPS model to produce
more realistic outcomes, i.e., owners are more willing to offer timber for sale when
the price is higher because of the expectation that it will fall in the future.
The general backward recursive equation for the dynamic model can be expressed
as:
Vt = max
k
braceleftBig
?t (Pt,dt,vt,k,ol,fm,rn)
+ ?E[V?t+1 (Pt+1,dt+1(k),vt+1(k),ol,fm,rn)|Pt]
bracerightBig
? P,ol,fm,rn;l = 1,2;m = 1,...,5;n = 1,...,5 (5.3)
where V is the value function ($/acre), k is the decision variable ? management
decision at time t (clearcut, thinning, selective harvest, or no action); d is the stand?s
diameter at breast height (183 0.1 inch classes); v is the stand?s volume (209 25 cf/ac
classes), P is the level of the stumpage prices (5 levels from $1.70/cf to $4.10/cf); ol
is the ownership class (non-industrial private or industry); fm is the forest manage-
ment type (planted pine, natural pine, oak-pine, lowland or upland hardwood); rn is
the physiographic region (the coastal plain, the piedmont and mid-coastal plain, the
mountains and interior plateaus, the Mississippi alluvial basin, and the western pied-
mont and mid-coastal plain); ? is the immediate net return of management decision
k ($); ? is the discounting factor (we used 5% interest rate for NIPF and 7% for the
industry); and E is an expectations operator of random future prices Pt+1 conditional
on current prices Pt.
The output of the dynamic programming model is a matrix, which provides the
optimal management decision for each combination of dbh and volume within each
54
ownership class, forest management type and physiographic region, and at each of the
stumpage price levels. The lowest price level, at which the optimal decision for the
given stand would be harvesting or thinning, could be interpreted as the producer?s
(forest owner?s) reservation price.
The IDPS harvesting module provides an interface between the inventory data,
growth models, product distribution models, DP decision matrix and the interregional
forest products trade model. For each year of the projection period, the volumes of
timber products available for harvesting are generated using the initial inventory of
a given year, a matrix of optimal harvesting decisions obtained from the dynamic
program, and product distribution models derived from the region plot data. Harvest
levels for each product in each state are determined using available inventory, final
demands, and the interregional trade coefficients produced by the interregional trade
model. The linear programming model then allocates the harvest request (demand)
for each product in each state among the stands available for harvesting by choosing
those stands, which have an appropriate mix of products and could be harvested at
the lowest price:
mins
gj
Gsummationdisplay
g=1
Ngsummationdisplay
j=1
pgjsgj
s.t.
Ngsummationdisplay
j=1
vigjsgj =
Hsummationdisplay
h=1
XiohsummationtextNgj=1 vigjSgj
summationtextH
h=1 Xioh
?Qigh ? g,i
0 ? sgj ? Sgj ? g,i
(5.4)
where sgj is the area of stand j in the supply state g to be selected for harvesting
or thinning (decision variable); pgj is the reservation stumpage price ($/acre) for the
stand j in the supply state g; vigj is the volume of product i on the stand j (cubic
55
feet/acre); Xioh is the demand for product i in the demand state h; Sgj is the area
of stand j; and ?Qigh is the ?modified? gravity coefficient calculated from the base year
trade data.
5.2.5 Area Change
Area change in the projection system uses the method similar to one utilized
by Zhou et al. (2003) in their Scenario 1, which is to derive the changes of land use
and forest management type from the historical FIA data. The method has three
integrated components:
1. acres gained by each forest management type from non-timberland
2. acres lost by each forest management type to non-timber land
3. acres gained/lost by one management type through transition from/to another
management type
In order to model 1) and 2), all FIA plots were selected which had non-timber
land as the previous land use type and one of five forest management types as the
current land use type, or those having one of the five forest management types as the
old land use type and non-timber land as the current land use type. Plots represent-
ing public ownership were not included in this analysis. These plots were grouped
by forest inventory unit. For each forest inventory unit, loss and gain by forest man-
agement type were calculated. Based on the length of a unit?s survey period, annual
gain was calculated and future gain was modeled by annually adding the appropriate
proportion of acres to each forest management type by FIA unit. Net loss was mod-
eled by adjusting (decreasing) the area of timberland annually. Timberland area was
56
uniformly reduced across the region to reflect the effect of streamside management
zones based on the finding of Wu (1994).
To model transitions between forest management types, all FIA plots where har-
vesting took place during the survey period were selected. The probability of transi-
tion was modeled using a multinomial logit model. The probability of transition to
one of five forest management types (planted pine, natural pine, oak-pine, lowland
hardwood and upland hardwood) was assumed to be a function of the old (previous
survey) forest management type and the ownership class associated with the plot.
Transition probabilities were calculated for each forest management type by physio-
graphic region. During simulation, each harvested plot was partitioned into several
new plots of different management types depending on the plot?s pre-harvest forest
management type and ownership class, with new plot areas determined proportionally
according to the values of the transition probabilities.
5.3 Results
5.3.1 Inventory adjustment
As previously mentioned, the most recent FIA inventory data were collected in
different years for different states, ranging from 1988 (Kentucky) to 2000 (Alabama).
The consequence of using this kind of base data is that results of projections could
be biased (inventory could be underestimated) if those state inventories were used
as initial conditions for projections. One of the features of this study is that timber
inventory data were adjusted from the year of latest FIA to the base year, 2000 using
the IDPS model. We used Southern Pulpwood Production annual reports (Johnson
57
and Steppleton 2001) and interpolated data from Timber Product Output reports
(Johnson and Wells 1999) to determine annual harvest levels for these adjustments.
5.3.2 Inventory projections
We examined three different scenarios regarding future patterns of consumption
(by firms) of wood products in the southern region using the IDPS model. These
scenarios are: 1) no change in the level of forest products consumption from its level
in 2000, 2) a 0.5% annual increase in consumption of forest products, and 3) a 1%
annual increase in consumption. The first scenario was used to contrast the other
two. The 0.5% annual increase scenario, considered here as the base case scenario,
is consistent with the U.S. demand increase expected by Tr?mborg et al. (2000),
and with the EL (elastic demand, low increase of plantation growth rate) scenario of
the Southern Forest Resource Assessment (Wear and Greis 2002). In the last case,
despite an assumed 1.6% annual outward shift of timber demand, the removals level
during the period 2000?2025 increased 0.60% annually due to assumptions of elastic
timber demand. The 1.0% increase consumption scenario reflects trends similar to
those shown by the IH (inelastic demand, high plantation growth rate increase) of
the Southern Forest Resource Assessment (Wear and Greis 2002), which shows 1.03%
annual increase of removals during the period 2000?2025.
Figures 5.2 and 5.3 illustrate, respectively, softwood and hardwood inventory
projections for the entire southern region under three removals scenarios. The pro-
jections are shown by product (pulpwood and sawtimber). Total softwood inventory
is projected to increase 34%, 24%, and 15% under 0%, 0.5%, and 1.0% scenarios,
respectively, between 2000 and 2025 with pulpwood inventories peaking in 2004 and
58
20
40
60
80
100
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025
Pulpwood, + 0.0% scenarioSawtimber, + 0.0% scenario
Pulpwood, + 0.5% scenarioSawtimber, + 0.5% scenario
Pulpwood, + 1.0% scenarioSawtimber, + 1.0% scenario
Figure 5.2: Softwood inventory projections for the 13-state southern region under
three harvest increase scenarios, 2000-2025, billion cubic feet
ultimately declining about 10% below their 2000 levels under all of the scenarios.
Softwood sawtimber is generally expected to increase throughout the projection pe-
riod. Under 1.0% annual removals increase scenario, however, softwood sawtimber
trends downwards during the last four years of projection period.
Total hardwood inventories are projected to increase 14%, 11%, and 7% under
0%, 0.5%, and 1.0% scenarios. Pulpwood inventories are projected to remain approx-
imately unchanged over the period under the constant removals level scenario and
59
70
80
90
100
110
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025
Pulpwood, + 0.0% scenarioSawtimber, + 0.0% scenario
Pulpwood, + 0.5% scenarioSawtimber, + 0.5% scenario
Pulpwood, + 1.0% scenarioSawtimber, + 1.0% scenario
Figure 5.3: Softwood inventory projections for the 13-state southern region under
three harvest increase scenarios, 2000-2025, billion cubic feet
will decline about 3% and 4% under 0.5% and 1.0% annual removals increase scenar-
ios. Sawtimber inventories show net increases throughout the projection period, with
the increases slowing down under the 0% and 0.5% removals increase scenarios, and
declining during the last four years of the projection period under the 1.0% removals
increase scenario.
On an individual state basis however, a much different future is projected in some
cases. In Virginia and North Carolina, significant declines in softwood pulpwood in-
ventories are projected (?40% and ?34% respectively) for the Base Case. In North
60
Figure 5.4: Softwood inventory and harvest projections for North Carolina, Base
Case
Carolina, hardwood pulpwood inventories are also projected to decline (Figures 5.4
and 5.5). In general, most states show large softwood sawtimber increases and are
projected to have declining softwood pulpwood inventories under all scenarios. Hard-
wood pulpwood inventories are projected to decline 5% for the region under the Base
Case scenario, but a number of states including Alabama, Georgia, Louisiana, North
Carolina, South Carolina, and Virginia show projected declines of 14%?23% (mostly
due to trees migrating from the pulpwood to sawtimber size class over the period).
Reductions in harvest levels during the projection period have allowed inventories to
remain stable in some states.
61
Figure 5.5: Hardwood inventory and harvest projections for North Carolina, Base
Case
5.3.3 Interregional Trade
A key feature of the model developed for this study revolves around acknowledg-
ing the role of interregional trade in meeting regional demand for softwood and hard-
wood products. As was mentioned previously, harvest levels in some states dropped
over the projection period (Figure 5.6) while overall harvest for the region increased
over the projection period and met the demand levels for each state as they were rep-
resented by the scenarios. Trade among states allowed this to happen (see figures 5.8
and 5.9). Illustration of how these effects interact in the simulation model are best
62
understood by example. Consider Figure 5.6 and Figure 5.8 (below). Alabama and
Louisiana (Figure 5.6) are projected to reduce hardwood pulpwood harvest levels over
the projection period, while accommodating a 0.5% increase in demand in the Base
Case. In Figure 6 we see that this is accomplished by increasing imports of hardwood
pulpwood in each state. No state that is projected to increase hardwood pulpwood
harvest levels substantially is also projected to increase its imports of the product. A
similar connection between Figure 5.7 and Figure 5.8 can also be made. As hardwood
pulpwood harvest levels are projected to increase in several states, (e.g., Florida., Ten-
nessee, East Texas, Oklahoma, North Carolina) the exports of the product from those
states will increase to help meet demands in other states.
Trade matrices are recalculated for each year of the simulation to account for
changes in the relative ability of states to produce timber over and above the regional
(state level) demand. For example, a state that has 100,000 acres available for harvest
above those necessary to meet regional demand would be relatively more likely to
export to a state needing the product than another state that only has 50,000 acres
available above its regional demand. Acres available means they meet the economic
test of financial maturity. States with relatively more ?surplus? available acres are
more likely to be large exporters in a given period. States with a wider gap (deficit)
between the amount of a product available for harvest and its regional demand will
likely be a relatively larger importer of the product in any given year. Distance is also
a factor in establishing trading relationships with other states and that is evidenced
in the trading tables. Most states trade with neighboring states and possibly one
or two others. Table 5.1 illustrates trading relationships embedded in the model
for hardwood pulpwood. Georgia has export relationships with seven other regions
63
603245504837 6232504837
Figure 5.6: Relative changes in hardwood pulpwood inventory by state, 2000?2025
< 0% > 30%
Figure 5.7: Relative changes in hardwood pulpwood harvest by state, 2000?2025
64
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
Figure 5.8: Dynamics of hardwood pulpwood state-level imports, 2000?2025, Base
Scenario, MCF
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
0
50
100150
2000
2010
2020
Figure 5.9: Dynamics of hardwood pulpwood state-level exports, 2000?2025, Base
Scenario, MCF
65
(including Rest-of-the-World ? ROTW) and imports from four. Tennessee imports
hardwood pulpwood from seven states and exports to six. These trading relationships
are important for understanding the dynamics of inventory growth and removals
throughout the region and the ability of those relationships to help industries meet
regional demands.
5.4 Conclusions
IDPS is an interregional multi-product timber inventory projection system, which
models growth at the stand level, uses a net present value maximization framework
to model optimal harvesting decisions, and a gravity model for interregional trade. It
provides a framework for analyzing timber supply on regional and/or state levels.
The system was used to project timber inventories in thirteen Southern states
through 2025. The projections show a 24% increase in softwood inventory and 9%
increase in hardwood inventory given a base case scenario of 0.5% annual increase in
consumption. However, the pulpwood component of total inventory is predicted to
decline for both softwood and hardwood.
The IDPS model treats subregions (states) as interconnected markets. It recog-
nizes the mutual influence of states as supply and demand regions. It could also be
used to analyze regional demand or supply shocks such as new mill construction or
mill closures, urbanization, or natural disasters.
66
Ta
ble
5.1:
Example
tra
de
ma
trices
for
tw
oselected
years
for
hardw
oo
dpulp
wo
od,
20
00
and
20
25
,mcf
2000
To
From
AL
AR
FL
GA
KY
LA
MS
NC
OK
SC
TN
TX
VA
ROTW
Total
AL
196.6
14.2
5.0
0.7
0.1
2.6
219.2
AR
60.4
5.4
0.6
12.0
78.4
FL
1.5
27.3
10.8
39.6
GA
13.1
12.4
117.9
2.8
1.1
0.5
4.7
2.8
155.3
KY
0.6
12.4
0.2
0.6
2.5
16.3
LA
8.5
70.1
4.1
4.7
87.4
MS
59.1
6.6
0.1
20.
6
61.8
0.1
1.6
149.9
NC
4.3
53.1
25.4
0.3
15.5
4.3
102.9
OK
9.4
5.0
0.1
14.5
SC
14.9
4.5
62.9
82.3
TN
25.7
0.1
16.3
5.3
24.3
0.1
0.1
71.9
TX
16.7
7.6
21.3
45.6
VA
2.8
0.4
1.2
77.5
5.5
87.4
ROTW
3.4
0.2
1.2
14.8
19.6
Total
296.6
101.
6
54.0
148.7
39.2
103.7
67.2
67.0
5.0
89.6
36.5
38.1
107.9
15.2
1170.3
2025
To
From
AL
AR
FL
GA
KY
LA
MS
NC
OK
SC
TN
TX
VA
ROTW
Total
AL
185.9
10.3
5.9
0.5
0.1
1.7
204.4
AR
61.2
7.1
0.7
11.6
80.6
FL
3.2
43.1
27.4
0
73.7
GA
10.5
7.7
117
1.3
0
0.7
0.4
2.5
1.6
141.7
KY
1.6
18.2
0.1
0.5
1
4.4
25.8
LA
6.5
69.8
3.5
3.4
83.2
MS
86.0
6.8
0.1
27.
1
71.3
0.1
1.6
193
NC
0.1
3.8
60.6
38.4
0.3
16.1
4.6
123.9
OK
17.6
5.6
0.2
23.4
SC
18.0
3.3
61.1
82.4
TN
49.0
0.2
18.0
7.6
31.5
0.1
0.1
106.5
TX
22.9
13.5
27.9
64.3
VA
3.5
0.7
1.4
89.4
6.6
101.6
ROTW
3.2
0.1
0.4
1.4
16.6
21.7
Total
336.2
115
61.2
168.6
44.5
117.5
76.0
76.1
5.6
101.5
41.4
43.1
122.2
17.3
1326.2
67
References
Abt, R.C., F.W. Cubbage, and G. Pacheco. 2000. Southern forest resource as-
sessment using the subregional timber supply (SRTS) model. Forest Products
Journal 50(4):25?33. 1, 12, 14, 17, 52
Adams, D.M. 1975. A model of pulpwood production and trade in Wisconsin and
the Lake States. Forest Science 21(3):301?312. 3, 5, 6, 18
Adams, D.M., and R.W. Haynes. 1980. The 1980 softwood timber assessment
market model: structure, projections, and policy simulations, volume 22 of
Forest Science Monographs. 64 p. 12, 13, 50
Adams, D.M., and R.W. Haynes. 1996. The 1993 Timber Assessment Market
Model: Structure, Projections, and Policy Simulations. USDA FS Pacific
Northwest Research Station, Portland, OR, 58 p. 12, 13, 50
Anderson, J.E. 1979. A theoretical foundation for the gravity equation. American
Economic Review 69(1):106?116. 7
Bailey, R.G. 1995. Description of the ecoregions of the United States. Misc. publ.
1391, USDA, Washington, DC. 108 p. 47
Bentley, J.W., T.G. Johnson, and C.W. Becker. 2002. Virginia?s timber
industry?an assessment of timber product output and use, 1999. USDA FS
Southern Research Station, Asheville, NC. 49
Bergkvist, E. 2000. Forecasting interregional freight flows by gravity models.
Jahrbuch f?ur Regionalwissenschaft 20(2):133?148. 44
Bergstrand, J.H. 1985. The Gravity Equation in international trade: Some mi-
croeconomic foundations and empirical evidence. Review of Economics &
Statistics 67(3):474?481. 7
Binkley, C.S. 1987. Economic models of timber supply. P. 109?136 in The global
forest sector: an analytical perspective. Kallio, M., D.P. Dykstra, and C.S.
Binkley (eds.). John Wiley & Sons, Chichester, UK. 52
Br?annlund, R., P.O. Johansson, and K.G. L?ofgren. 1985. An economet-
ric analysis of aggregate sawtimber and pulpwood supply in Sweden. Forest
Science 31(3):595?606. iv, 3, 4, 5, 17, 18, 20, 26
68
Breuss, F., and P. Egger. 1999. How reliable are estimations of East-West trade
potentials based on cross-section gravity analyses? Empirica 26(2):81?94. 7
Carter, D.R. 1992. Effects of supply and demand determinants on pulpwood
stumpage quantity and price in Texas. Forest Science 38(3):652?660. iv,
3, 5, 6, 18, 20, 26
Cubbage, F.W., T.G. Harris, jr, R.J. Alig, D.W. Hogg, and J.A.
Burgess. 1991. Projecting State and Substate Timber Inventories: The Geor-
gia Regional Timber Supply Model. Research Bulletin 398. The University of
Georgia, Athens, GA, 32 p. 12
Daniels, B.J., and W.F. Hyde. 1986. Estimation of supply and demand for North
Carolina?s timber. Forest Ecology & Management 14(1):59?67. 3, 18
Davidson, R., and J. MacKinnon. 1981. Several tests for model specification in
presence of alternative hypotheses. Econometrica 49(3):781?793. 40
Egger, P. 2000. A note on the proper econometric specification of the Gravity
Equation. Economics Letters 66(1):25?31. 7, 32
Egger, P., and M. Pfaffermayr. 2003. The proper panel econometric specifi-
cation of the gravity equation: A three-way model with bilateral interaction
effects. Empirical Economics 28(3):571?580. 8, 32, 33, 34
Egger, P., and M. Pfaffermayr. 2004. Distance, trade and FDI: a Hausman?
Taylor SUR approach. Journal of Applied Econometrics 19(2):227?246. 8
Greene, W.H. 2000. Econometric Analysis. Prentice-Hall, NJ, 1004 p. 23, 33
Gregory, G.R. 1960. A statistical investigation of factors affecting hardwood floor-
ing. Forest Science 6(2):123?134. 3
Gujarati, D.N.1988. Basic Econometrics. Second edition. McGraw-Hill, New York,
706 p. 22
Hausman, J.A., and W.E. Taylor. 1981. Panel data and unobservable individual
effects. Econometrica 49(6):1377?1398. 8
Haynes, R.W., and D.M. Adams. 1985. Simulations of the effects of alternative
assumptions on demand-supply determinants of the timber situation in the
United States. USDA Forest Service, For. Res. Econ. Res., Washinton, DC,
113 p. 1, 3, 18
Haynes, R.W., D.M. Adams, R. Alig, et al. 2003. An analysis of the timber
situation in the United States: 1952 to 2050 Gen. Tech. Rep. PNW-GTR-
560. USDA, Forest Service, Pacific Northwest Research Station, Portland,
OR, 254 p. 1
69
Hetem?aki, L., and J. Kuuluvainen. 1992. Incorporating data and theory in
roundwood supply and demand estimation. American Journal of Agricultural
Economics 74(4):1010?18. 3, 17
Holley, D.L., R.W. Haynes, and H.F. Kaiser. 1975. An interregional timber
model for simulating change in the softwood forest economy. Technical Re-
port 54, School of Forest Resources, NC State University, Raleigh, NC. 70 p.
13, 50
Howard, J.L.1999. U.S. TimberProduction, Trade, Consumption, and Price Statis-
tics 1965?1997. Gen. Tech. Rep. FPL?GTR?116. USDA Forest Service, Madi-
son, WI, 76 p. 1
Howard, J.L.2001. U.S. TimberProduction, Trade, Consumption, and Price Statis-
tics 1965?1999. Gen. Tech. Rep. FPL?RP?595. USDA Forest Service, Madison,
WI, 90 p. 17
Hua, C. 1990. A flexible and consistent system for modeling interregional trade
flows. Environment and Planning A 22(4):439?457. 8, 35
Isard, W. 1960. Methods of Regional Analysis, chapter 11: Gravity, Potential, and
Spatial Interaction Models, p. 493?598. Massachusetts Institute of Technology,
Cambridge, Massachusetts. 6
Johnson, T.G., and D.R. Brown. 2002. North Carolina?s timber industry?
an assessment of timber product output and use, 1999. USDA FS Southern
Research Station, Asheville, NC. 49
Johnson, T.G., and C.D. Steppleton. 2001. Southern Pulpwood Produc-
tion, 1999. Resource Bulletin SRS?57. USDA FS Southern Research Station,
Asheville, NC, 34 p. 49, 57
Johnson, T.G., and C.D. Steppleton. 2003. Southern Pulpwood Produc-
tion, 2001. Resource Bulletin SRS?84. USDA FS Southern Research Station,
Asheville, NC, 40 p. 17, 36, 37
Johnson, T.G., and J.L. Wells. 1999. Georgia?s timber industry?an assessment
of timber product output and use, 1997. USDA FS Southern Research Station,
Asheville, NC, 36 p. 58
Kang, M. 2003. United States wood products and regional trade: A gravity model
approach. Ph.D. dissertation, Auburn University, Auburn, AL. 103 p. 7
Kangas, K., and A. Niskanen. 2003. Trade in forest products between European
Union and the Central and Eastern European access candidates. Forest Policy
and Economics 5(3):297?304. 7
70
Larson, R.W., and M.H. Goforth. 1970. TRAS: a computer program for the
projection of timber volume. Agriculture handbook ; no. 377. USDA Forest
Service, Washington, DC, 24 p. 13
Leontief, W., and A. Strout. 1963. Multiregional input-output analysis. P.
119?150 in Structural Interdependence and Economic Development. Barna,
T. (ed.). St. Martin?s Press, New York. 9, 35, 36, 50, 51, 52
Leuschner, W.A. 1973. An econometric analysis of the Wisconsin aspen pulpwood
market. Forest Science 19(1):41?46. 3, 4, 5, 18, 19, 21
M?aty?as, L. 1997. Proper econometric specification of the gravity model. World
Economy 20(3):363?368. 7, 32, 33
M?aty?as, L. 1998. The gravity model: Some econometric considerations. World
Economy 21(3):397?401. 7, 32
McKillop, W.M. 1967. Supply and demand for forest products?an econometric
study. Hilgardia 38(1):1?132. 3
Merz, T.E. 1984. An econometric analyis of the market for pulpwood harvested in
Michigan?s Upper Peninsula. Forest Science 30(1):107?113. 6
Miller, D.M. 1984. Reducing transformation bias in curve fitting. American Statis-
tician 38(2):124?126. 39, 40
Moses, L.N. 1955. The stability of interregional trading patterns and input-output
analysis. American Economic Review 45(5):803?826. 9, 10, 35, 51
Nagubadi, V., I.A. Munn, and A. Tahai. 2001. Integration of hardwood
stumpage markets in the Southcentral United States. Journal of Forest Eco-
nomics 7(1):69?98. 5, 18
Newman, D., and D. Wear. 1993. Production economics of private forestry: a
comparison of industrial and nonindustrial forest owners. Am J Agric Econ
75(3):674?684. 53
Newman, D.H. 1987. An econometric analysis of the Southern softwood stumpage
market: 1950?1980. Forest Science 33(4):932?945. iv, 3, 4, 5, 18, 20, 23, 26
Newman, D.H. 1990. Shifting Southern softwood stumpage supply: implications
for welfare estimation from technical change. Forest Science 36(3):705?718. 3
Norris Foundation. 1977?2001. Timber Mart-South. The Daniel B. Warnell
School of Forest Resources, University of Georgia, Athens. 22, 49, 53
71
Oguledo, V.I., and C.R. MacPhee. 1994. Gravity models: a reformulation
and an application to discriminatory trade arrangements. Applied Economics
26(2):107?120. 31
Polenske, K.R. 1970. An empirical test of interregional input-output models: Esti-
mation of 1963 Japanese production. American Economic Review 60(2):76?82.
9, 10, 35, 51
Polenske, K.R. 1980. The U.S. multiregional input-output accounts and model.
D. C. Heath and Company, Lexington, 360 p. 50
P?oyh?onen, P. 1963. A tentative model for the volume of trade between countries.
Weltwirtschaftliches Archiv 90(1):93?99. 6
SAS Institute, Inc. 1999. SAS/ETS User?s Guide, Version 8. SAS Institute Inc.,
Carry, NC, 1546 p. 38
Serlenga, L., and Y. Shin. 2004. Gravity models of intra-EU trade: Application
of the Hausman-Taylor estimation in panels with heterogeneous time-specific
common factors. Working paper, School of Economics, University of Edin-
burgh. 35 p. 8
Teeter, L. 1994. Methods for predicting change in timber inventories and product
markets over time: A dynamic programming approach for modeling change in
timber inventories. Final rep. to the USDA For. Serv. Coop. Agree. USFS?
29?749, Auburn University. 27 p. v, 12, 15, 47
Teeter, L., G.S. Alward, and W.A. Flick. 1989. Interregional impacts of
forest-based economic activity. Forest Science 35(2):515?531. 46, 51
Teeter, L., G. Somers, and J. Sullivan. 1993. Optimal harvest decisions: A
stochastic dynamic programming approach. Agricultural Systems 42(1?2):73?
84. 54
Teeter, L., and X. Zhou. 1999. Projecting timber inventory at the product level.
Forest Science 45(2):226?231. 15, 48
Tinbergen, J. 1962. Shaping the world economy; suggestions for an international
economic policy. Twentieth Century Fund, New York, 330 p. 6, 31
Tr?mborg, E., J. Buongiorno, and B. Solberg. 2000. The global timber
market: implications of changes in economic growth, timber supply, and tech-
nological trends. Forest Policy and Economics 1(1):53?69. 17, 58
Wear, D.N., and J.G. Greis (eds.). 2002. Southern forest resource assessment.
General technical report SRS?53. Southern Research Station, Asheville, NC,
635 p. 1, 58
72
Wear, D.N., and P.J. Parks. 1994. The economics of timber supply: an analytical
synthesis of modeling approaches. Natural Resources Modeling 8(3):199?223.
46
White, H. 1980. A heteroskedasticity-consistent covariance matrix estimator and a
direct test for heteroskedasticity. Econometrica 48(4):817?838. 23
Wu, C.S. 1994. Assessing the economic effect of streamside management zones on
the forestry sector. Ph.D. dissertation, Auburn University, Auburn, AL. 165 p.
57
Zhou, X. 1998. Methods for improving timber inventory projections in Alabama.
Ph.D. dissertation, Auburn University, Auburn, AL. 114 p. v, 12, 15, 47, 48
Zhou, X., J.R. Mills, and L.D. Teeter. 2003. Modeling forest type transitions
in the South-Central region: results from three methods. Southern Journal of
Applied Forestry 27(3):190?197. 56
Zhou, X., and L. Teeter. 1996. DPSupply: a new approach to timber inven-
tory projection in the Southeast. P. 293?298 in Proceedings of the 25th an-
nual Southern Forest Economics Workshop; 5 April 17?19; New Orleans, LA.
Caulfield, J.P., and S.H. Bullard (eds.). Mississippi State University, Depart-
ment of Forestry, Mississippi State, MS. v, 47
73