ANALYSIS OF TIMBER MARKETS IN THE U.S. SOUTH by HARRISON BARKSDALE HOOD (Under the Direction of Jacek Siry) ABSTRACT Timber markets in the U.S. South can be analyzed and evaluated in different ways and at multiple levels. These markets can be analyzed at a broad level to determine how markets for the same good interact with one another, in which case market integration can be studied. Traditional cointegration tests have been used to perform these analyses; however, these tests can only reveal the presence of stable or average long-term relationships. To evaluate market dynamics over time, a time-varying smooth transition autoregressive (TV-STAR) model has been modified to examine pine stumpage markets throughout this region. The proposed model incorporates an economic indicator and allows us to evaluate market integration as it changes throughout a specified time period. Timber markets can also be evaluated to observe how different components of the timber sale process effect prices. The sale of timber contains a number of different components unique to each specific sale, and includes items such as timber price, location of sale, total volume harvested, and sale size. The second aspect of this study evaluates pine sawtimber stumpage prices by modeling monthly prices using a seasonal autoregressive integrated moving-average (SARIMA) model. Previous studies have examined how timber prices are influenced by different sale characteristics; however, such studies have been confined to smaller market areas. The focus of this research is to observe which specific characteristics
Transcript
ANALYSIS OF TIMBER MARKETS IN THE U.S. SOUTH
by
HARRISON BARKSDALE HOOD
(Under the Direction of Jacek Siry)
ABSTRACT
Timber markets in the U.S. South can be analyzed and evaluated in different ways and at
multiple levels. These markets can be analyzed at a broad level to determine how markets for the
same good interact with one another, in which case market integration can be studied. Traditional
cointegration tests have been used to perform these analyses; however, these tests can only
reveal the presence of stable or average long-term relationships. To evaluate market dynamics
over time, a time-varying smooth transition autoregressive (TV-STAR) model has been modified
to examine pine stumpage markets throughout this region. The proposed model incorporates an
economic indicator and allows us to evaluate market integration as it changes throughout a
specified time period. Timber markets can also be evaluated to observe how different
components of the timber sale process effect prices. The sale of timber contains a number of
different components unique to each specific sale, and includes items such as timber price,
location of sale, total volume harvested, and sale size. The second aspect of this study evaluates
pine sawtimber stumpage prices by modeling monthly prices using a seasonal autoregressive
integrated moving-average (SARIMA) model. Previous studies have examined how timber
prices are influenced by different sale characteristics; however, such studies have been confined
to smaller market areas. The focus of this research is to observe which specific characteristics
influence stumpage prices on a much larger region-wide basis. Results indicate that three specific
factors significantly influence expected price: sale size, sale type, and competing hardwood
timber prices. Furthermore, we found evidence that stumpage prices have settled at a new level,
where prices will presumably remain in the immediate future. Mill location and demand
(capacity) are also know to influence market prices for different timber products, so the third
aspect of this study sought to determine the degree to which these two variables effect stumpage
prices for both pine sawtimber and pine pulpwood. Individual timber sales were converted into
panel data for this analysis, and results indicate that a timber sale’s location relative to
surrounding mills has a significant influence on expected stumpage price.
INDEX WORDS: market integration, smooth transition, timber markets, timber prices, sale
characteristics, time series, intervention, mill location, mill capacity
ANALYSIS OF TIMBER MARKETS IN THE U.S. SOUTH
by
HARRISON BARKSDALE HOOD
BBA, University of Mississippi, 2008
MFR, University of Georgia, 2012
A Dissertation Submitted to the Graduate Faculty of The University of Georgia in Partial
Major Professor: Jacek Siry Committee: Pete Bettinger Jeffrey Dorfman T. N. Sriram Electronic Version Approved: Julie Coffield Interim Dean of the Graduate School The University of Georgia December 2014
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DEDICATION
I’d like to dedicate this work to my wife, Jeannie. Thank you for all your encouragement
and support. Without you, this would not have been possible.
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ACKNOWLEDGEMENTS
I’d like to thank my major professor, Dr. Jacek Siry, and my committee members for
their guidance and assistance in writing my dissertation. More specifically, I’d like to thank Dr.
Dorfman for suggesting the topic of market integration and for all his help with the first paper,
and I’d also like to thank Dr. Sriram for all his direction and help with the second paper of my
dissertation.
I’d also like to Timber Mart-South for allowing me to work with their incredible dataset.
Furthermore, I’d like to thank the editors at Timber Mart-South, Tom Harris, Jonathan Smith,
and Sara Baldwin, for all of their support and the numerous research suggestions.
used by private companies, consultants, landowners, and others to assess market prices for
timber in the U.S. South, and it is with their extremely robust database of timber sales that all
results from this study are drawn. TMS quarterly reports are derived from individual timber sales
that are provided by numerous reporters across the region, and since 2000, over 120,000
individual sales have been reported. Using the TMS database of timber sales and prices, there are
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three primary topics that are evaluated: timber market linkages between sub-regional pine
sawtimber (PST) stumpage markets, the effect different sales characteristics have on stumpage
price, and the degree to which a mill’s location and capacity influence pine stumpage prices.
The first topic evaluated includes a study of PST market integration in the South. While
previous studies have tested spatial integration in forest product markets, these studies have
primarily implemented more popular and traditional tests to test for market integration
(Prestemon and Holmes 2000, Yin, Newman, and Siry 2002). While cointegration tests can be
used to examine how timber markets interact in the long-run, these tests are unable to show how
market interactions change over time. To evaluate market linkages between regional PST
stumpage markets, we propose a modified nonlinear model that includes an outside economic
indicator that drives the transitions in regional economic linkages. By including a transition
function in the model, market linkages can be observed in the short-run, or during specific
periods of time. This study seeks to understand timber markets by mapping when different
regional markets are linked, so that their price pairs are controlled by the law of one price.
The second research topic is focused on modeling PST stumpage prices using a variety of
different sale characteristics, such as harvest type, contract type, sale size (acres), and total
volume harvested. Previous studies have found some of these different sale characteristics to
significantly influence stumpage prices in specific markets (Niquidet and van Kooten 2006,
Sydor and Mendell 2008); however, this study examines a much larger south-wide region to
identify which sale characteristics significantly influence stumpage price in all submarkets. For
this study, a time series model is developed to test nearly 100 different sale characteristics in
order to identify which characteristics positively and negatively influence PST stumpage prices.
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The final topic evaluated in this comprehensive analysis is the effect both mill location
and mill capacity have on pine stumpage prices in the South. Analyses conducted by Puttock et
al. (1990) and Luppold and Baumgras (1995) have confirmed that haul distance and mill size
(capacity) significantly affect stumpage prices, but the aim of this study is to quantify the degree
to which both of the variables influence prices. For this analysis, PST and pine pulpwood (PPW)
stumpage sales are evaluated using linear models. The number of mills located within a specified
radius of a timber sale, and their cumulative capacity, are independent model variables that are
regressed on stumpage prices to estimate the degree to which both of these variables impact pine
stumpage prices. A secondary goal of this analysis is to develop a metric whereby all counties in
this region are ranked according to their locational relevance, which is based on the number of
mills, their cumulative capacity, and stumpage prices found within a specific proximity of each
county. Using this metric, counties and regions that have the strongest and weakest pine
stumpage markets can be identified.
This research in its totality is aimed at contributing to the literature by improving overall
understanding of how timber markets interact within this region and how different factors affect
timber prices. A variety of techniques and econometric models are utilized to perform the
comprehensive analysis, and each of the three topics introduced above and the results of their
analyses are detailed in the subsequent chapters.
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CHAPTER 2
EXAMINING DYNAMICALLY CHANGING TIMBER MARKET LINKAGES USING A
STAR MODEL WITH HOUSING START-CONTROLLED TRANSITIONS
The transportation of timber is limited to a degree greater than for many products by its
size and low value-to-weight ratio. However, the U.S. imports timber from Canada and
sometimes as far away as South America, proving that at times products move between markets
separated by large distances. To make transporting timber between regional markets economical,
demand must be strong. Thus, as demand for timber products changes we should expect to see
changes in the market linkages of the numerous, regional micro-markets. Gaining a better
understanding of how timber markets interact will improve economists’ ability to predict timber
price fluctuations and trends and should allow increased efficiency in these markets. Such
understanding begins with the concept of spatial equilibrium among geographically separated
markets.
The concept of spatial equilibrium imposes the existence of a long-run equilibrium
relationship among prices in geographically separated markets of a commodity. In the literature
this equilibrium has been examined with cointegration tests. Popular cointegration tests follow
either the procedure developed by Dickey and Fuller (1979 and 1981) or Johansen (1988). These
tests have been used extensively to study the law of one price (LOP) and purchasing power
parity (PPP) in numerous financial and agricultural markets.1 In the past, spatial integration in
forest product markets has been tested on a number of different forest products and commodities,
1 The law of one price has been tested in numerous markets, including the U.S. corn markets (Coleman, 2009), Chinese grain markets (Park, et al., 2002), international salmon markets (Asche, et al., 1999), and Chinese goods and services markets (Fan and Wei, 2006).
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such as lumber (Luppold and Prestemon, 2003, Shahi and Kant, 2009, Yin and Baek, 2005),
stumpage (Prestemon and Holmes, 2000), roundwood (Niquidet and Manley, 2011), oriented
strand board (Goodwin, Holt, and Prestemon, 2011), pulp and paper (Buongiorno and Uusivuori,
1992), and newsprint (Tang and Laaksonen-Craig, 2007). While traditional cointegration tests
have been used to examine how timber markets interact in the long-run, these tests are unable to
show changing market interactions over time. Econometric models have been developed to study
the extent to which spatially distinct markets are efficiently linked, and models such as these can
be modified to examine market linkages between timber markets.
While prior cointegration studies have focused primarily on lumber and other forest
products markets, very little research has focused on the spatial relationships between timber
markets. An exception is Yin, Newman, and Siry (2002) which examined spatial equilibrium of
softwood sawtimber and pulpwood stumpage markets across the U.S. South using both the
Dickey-Fuller and Johansen cointegration tests. Results indicated that the 11 sawtimber regions
were not fully cointegrated, instead they were segmented into four micro-regions, and the
pulpwood regions were more integrated than the sawtimber regions.
The LOP was tested in 21 delivered pine log and pine pulpwood markets across the U.S.
South (Bingham, et al., 2003). Results indicated that the LOP does not hold within either product
category. Sawlog prices in only about one-third of the price pairs tested were cointegrated at the
5% significance level and pulpwood prices in less than one-fifth of the price pairs were
cointegrated at the 5% significance level.
While previous studies of spatial integration in forest products markets have implemented
popular cointegration tests, to our knowledge, the work of Goodwin, Holt, and Prestemon (2011)
is the only one that has taken a more generalized and flexible approach by using a smooth
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transition autoregressive (STAR) model. This nonlinear time-series model allows for the
possibility of gradual adjustments among price linkages and structural change. The embedded
transition function within this model is of particular interest because it is the cornerstone on
which the model is built and shows us how market dynamics change over time. Numerous
variations of STAR-type model transition functions have been implemented in previous works,
but all of these functions rely on a lagged dependent variable to control the transition (Fan and
Wei, 2006, Jansen and Terasvirta, 1996, Kilian and Taylor, 2003, Paya and Peel, 2004, Taylor,
Peel, and Sarno, 2001). The primary difference between these past modeling efforts and our
proposed transition function is our use of an economic indicator as the transition function’s
control variable.
One possible choice of transition variable would be the volume of trade between regions.
Myers and Jayne (2012) tested maize price transmission between South Africa and Zambia and
found that spatial price linkage is likely to be sensitive to trade volume; however, results
indicated that no price transmission occurred in high import regimes. Since these results are
mixed with respect to trade volume being a good indicator of linkages and because the volume of
wood traded between states in the U.S. South is not readily available and can be difficult to
obtain, an alternative indicator is selected as the transition variable.
Extensive research and analysis of timber price indicators has occurred in previous years
and one of the economic variables known to be closely tied to timber prices is housing starts.
Since the primary building material used in home construction is lumber, it should come as no
surprise that housing starts and timber prices are strongly positively correlated. A linear
correlation test of these two variables verified this, so housing starts seems a strong candidate
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variable to control transitions in our timber market analysis.2 Specifically, we have selected
quarterly single-family housing starts as the basis of the transition function in our model of time-
varying market integration and separation.
As motivation for such a model, we refer to Sexton, Kling, and Carman (1990). They
tested integration in U.S. celery markets using a switching regression model with three regimes:
efficient arbitrage, shortage, and surplus. Their results indicated that, through a substitute
relationship, a surplus or shortage of celery in a terminal market could be corrected by an
adjustment in the supply from one of the competing supply markets. We suspect similar behavior
whereby an increase in home construction-driven demand in one market is filled by supply from
other markets also exists in the U.S. South timber market. When new home construction is high
is one region, surrounding markets should link together to provide the additional supply needed
to meet that increase in demand.
Thus, we modify a STAR model to examine roundwood market linkages throughout
eleven states in the U.S. South from 1976 through 2013 using quarterly pine sawtimber stumpage
prices as reported by Timber Mart-South.3 Our transition function accommodates two transition
variables that include information on housing starts from each region in a particular price pair.
This modified model makes a contribution to the literature by introducing an economically-
motivated transition function that allows for the evaluation of episodic market integration across
multiple regions, especially in the presence of excellent data. This type of model is particularly
2 Following the initial estimation, a subset of 25 region combinations were tested using two different transition variables to validate our choice of using housing starts as the transition variables. The first transition variable tested was personal income and the second transition variable tested was lagged values of the dependent variable. Based on the subset of 25 region combinations, housing starts was found to be the best transition variable selection. The models that contain housing starts as the transition variables produced the largest R-squared values in 48% of the models, compared to models that used personal income fitting the best in 32% of cases and lagged dependent variables being the best model in 20% of the cases. Subsample model results can be found in Appendix A. 3 Timber Mart-South is a quarterly forest products report produced by the Frank W. Norris Foundation and is housed at the University of Georgia’s Daniel B. Warnell School of Forestry and Natural Resources.
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useful for evaluating market equilibrium when future market conditions continually change and
evolve. We know timber markets do this, and a STAR model is able to capture those changing
conditions.
U.S. South Timber and Housing Markets
Timber Markets and Prices
The U.S. southeast is the world-leading producer of industrial roundwood. A common and well
know product that is made from industrial roundwood is dimensional lumber, a product used
predominately in construction. According to the most recent FAO Yearbook of Forest Products,
the United States produces roughly 20% of the world’s industrial roundwood, of which over 12%
of the world’s roundwood production comes from the U.S. South. One of the primary types of
industrial roundwood products that are produced in this region is softwood saw logs (pine
sawtimber).
There are two types of reported timber prices – stumpage and delivered prices. Stumpage
prices refer to those paid for standing timber, which would be paid to the landowner. Delivered
prices are those paid for timber that has been cut, hauled, and delivered – typically to a saw mill.
With the increased interest in timberland as an investment vehicle, we turned our focus to
studying stumpage price trends because these prices are used to determine investment returns on
timberland. We use quarterly pine sawtimber (PST) stumpage prices as reported by Timber Mart-
South for the fourth quarter of 1976 through the second quarter of 2013. Our data consists of
prices from 11 different states across the U.S. South, each of which is separated into two regions
– typically a northern and southern region. The 11 states include Alabama, Arkansas, Florida,
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Georgia, Louisiana, Mississippi, North Carolina, South Carolina, Tennessee, Texas, and
Virginia.
Over the time period for which we observe timber prices the market has experienced
large swings in PST stumpage prices. From the late 1970s until the early 1990s, PST stumpage
prices generally varied between $15 and $20 per ton. Following this period, prices increased
quite rapidly and by 1997 most regions saw prices over $50 per ton. Prices remained around $50
per ton through 2000 and then leveled off a bit, hovering between $35 and $45 per ton through
the fourth quarter of 2007. Starting in the first quarter of 2008, PST stumpage prices declined
rapidly and by the third quarter of 2011 the average price for PST in the U.S. South bottomed out
below $23 per ton – the lowest in nearly 20 years. Since then, the market for pine sawtimber has
begun to show signs of improvement and prices are currently over $25 per ton.
New Home Construction in the U.S. South
New home construction in the U.S. South, like in other regions of the country, is typically
concentrated in large metropolitan areas. In the most recent United States Environmental
Protection Agency (EPA) residential construction report, from 2000 through 2009 the
metropolitan areas with the greatest number of new homes constructed include Atlanta, GA
where t = (1, xt, yt-1), ψ1 = (0, , 0)´, ψ2 = ( , , , )´, and < 0 is required. We have
modified the transition function to accommodate transition variables that represent each region in
a respective price pair. Whereas the typical transition variable in the STAR model is defined as
some average value of the model’s dependent variable, we use an economic variable that is
strongly connected to timber prices to define the transition variable. Single-family housing starts
during each quarter of the observed time period are used as the foundation of the model’s
transition function.4 Our model uses single-family housing starts from each state represented in
the price pair relationship to define the two transition variables, st and vt.
(2.8) st = ∑ ,
(2.9) vt = ∑ ,
4 Quarterly housing start figures for each state have been reported since 1988; however, prior to this year only annual figures were reported. Quarterly housing starts as a percentage of total annual housing starts within each state have remained relatively stable and consistent over time, so quarterly housing start numbers prior to 1988 were interpolated based on these historical trends. The transition variable is a four-quarter moving average of that state’s housing starts, so the standard errors after averaging the estimated four quarters is minimal and does not affect final model results.
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where h1 and h2 denote housing starts from each state in the price pair and we use the
specification for the transition variables where Dmax= 4. In what we call the ECON-STAR model,
the resulting transition function is therefore given by:
(2.10) G(st, vt; , c, d) = 1 – exp
where (st – c) > 0 and (vt – d) > 0 are required. In equation (2.10), c and d are the minimum
transition variable values for each represented market (thus ensuring the required positivity), and
(st – c) and (vt – d) are normalized by and , respectively, to make the speed-of-adjustment
parameter unit free. When G(st, vt; , c, d) = 0, the model goes to ψ1, which is a random walk.
When G(st, vt; , c, d) = 1, the model goes to ψ2, which indicates cointegration.
The lag length was set to p=3 for all models based upon model diagnostic testing. The
speed-of-adjustment parameter, γ, is estimated to maximize the predictive strength of the final
model. To estimate this parameter, we scanned over a range of γ values. For each fixed value of
γ, the remaining parameters were estimated by maximum likelihood. The γ value that resulted in
the highest likelihood function value was chosen as the estimate. This is equivalent to joint
maximum likelihood of all the parameters. In our case, the speed-of-adjustment parameter value
that maximizes the likelihood function also maximizes the coefficient of determination (R2)
statistic, so we used this statistic to estimate the speed-of-adjustment parameter.
A maximum and minimum γ value constraint is imposed to restrict the speed-of-
adjustment parameter from going to zero or ∞. The minimum γ value is set to 0.05 and the
maximum γ value is set to 50. The smaller the parameter value the slower the two regions link
and unlink, and the larger the parameter value the quicker the two regions adjust between linked
and unlinked. The natural economic interpretation of the transition function is this: values equal
to one indicate linked markets and values equal to zero indicate unlinked markets.
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Interpretation of values between the two extremes is more subjective, especially for
intermediate values within this range, but observation of values not equal to zero or one is still
useful and allows us to observe how markets act during periods of transition. Further, note that
such a smooth transition model can be thought of as a multiple-regime model of market linkage
conditions with essentially an infinite number of possible regimes.
Estimation and Results
Final Model Results
Nearly 130 of the possible 231 region combinations were evaluated using the above described
model. Price pairs were selected based on proximity and include all markets three to four states
apart. The sample size is large enough to draw inference about market linkages among all
regions evaluated. Results indicate that strong growth in new home construction can cause
numerous regions and states to link together and function as one solitary market.5
We highlight six time periods (Figure 2.2) to show how timber market linkages changed
throughout the observed time period. We used G(st, vt; , c, d) 0.9 as the value required to
signify market linkage. Results indicate that in 1978 there were two distinct PST markets: 1) TX,
AR, LA, MS, AL, TN1, FL, GA, SC, and NC2 and 2) TN and VA. East Tennessee (TN1)6 is the
one commonality between the two markets while west North Carolina (NC1) was unlinked with
all other markets.
The early 1980s experienced two economic recessions, so we examined market linkages
in 1982 to learn how those recessions influenced timber markets. At this time we observe three
5 Full results can be found in Appendix B. 6 East Tennessee (denoted TN1) is composed of predominately hardwood forests, especially within the Appalachian Mountains that run through the eastern portion of this region. The western portion of TN1 is less mountainous and contains more pine forests, so, in essence, TN1 could be further subdivided into an eastern and western region.
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distinct PST markets: 1) TX and LA, 2) FL, and 3) GA. All other regions were unlinked. For the
entire time evaluated, this marked the period when the market was most fragmented and had the
fewest linkages.
During 1990 we observed three overlapping PST markets: 1) AR, MS, AL, TN1, FL, GA,
and SC2, 2) TN1, SC, and NC, and 3) TN and VA. Both regions in Texas and Louisiana were
unlinked with other markets at this time.
We found that during 2006 – at the peak of the housing bubble – the entire southeast
region was linked into a single pan-region market as stumpage prices in all regions approached
historic, all time highs.
During the most recent economic recession, new home construction in the overwhelming
majority of states fell to the lowest levels since the early 1980s, and as a result stumpage prices
for pine sawtimber fell to the lowest levels in nearly 20 years. In the US south, following the
most recent economic recession housing starts bottomed out in late 2010 and PST prices
bottomed out in the months following. Not surprisingly, in 2011 we observed only one distinct
linked market: TX, AR, LA, MS, and AL. All other regions were unlinked.
To better understand current market conditions, we examined market linkages in 2013
and observed two PST markets: 1) TX, AR, LA, MS, AL, TN1, FL, GA, SC, and NC and 2) TN
and VA1. East Tennessee (TN1) was the only region linked with both markets while eastern
Virginia (VA2) was the only region unlinked with all other markets. This suggests an ongoing
recovery in both the housing and stumpage markets in the South.
The U.S. South timber market is naturally divided by the Appalachian Mountain range,
which cuts through Virginia, North Carolina, South Carolina, and the northeast portion of
Georgia. Hardwood species are more prevalent in these mountainous regions and could explain
17
Note: Market linked regions are indicated by solid color, while a green striped pattern indicates unlinked regions in the maps above.
Figure 2.2: Regional Linkages Over Time.
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why these markets tend to be more weakly linked with other markets. The western half of
Tennessee (TN2) marks the bottom portion of a hardwood forest that covers a large part of the
central US, which helps explain why this market tends to link with the hardwood markets that
follow the Appalachian Mountains and be unlinked with regions covered predominately by
softwood species.
Transition Function Results
For the modeled price pairs, the speed-of-adjustment parameter values range from 0.05 to 50.
Figure 2.3 shows selected results for G(·). For γ ≤ 0.25, the transition function adjusts more
slowly between linked and unlinked and does not reach a value of 1.0 – which indicates
complete market linkage. For 0.25 ≤ γ ≤ 1.0, the transition function adjusts at a moderate rate
between zero and one. For γ ≥ 1.0, the transition function adjusts more rapidly and there are
extended periods of time in which the two markets are completely linked. The distribution of
these estimated parameters is heavily weighted at the top and bottom ends of this range (Figure
2.4).
Following the most recent economic recession which began in the last quarter of 2007,
the fewest number of market linkages occurred in the second quarter of 2011. Intuitively, one
would think this would occur shortly after the beginning of the recession; however, single-family
housing starts in the U.S. South bottomed out in the fourth quarter of 2010 and PST prices
bottomed out in the third quarter of 2011.
The distribution of the estimated speed-of-adjustment parameter, γ, for all models
evaluated is bimodal (Figure 2.4). Nearly 70% of all estimated γ values fell below 1.0 or above
35. Over 30% of observed γ values fell below 1.0 while just less than 40% fell above 35. These
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results tell us that observed market pairs tend to be either strongly linked and adjust quickly to
one another or weakly linked and adjust slowly to price movements within regions.
Note: Transition function values are bounded between 0 (unlinked) and 1 (linked). For the models represented above, the estimated speed-of-adjustment parameter value within the functions range from 0.05 to 50. The range of γ values by row: (1) 0.05 – 0.14, (2) 0.24 – 0.62, (3) 0.81 – 2.53, (4) 5.05 – 50.0.
Figure 2.3: Market Linkages of Select Price Pairs.
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Figure 2.4: Histogram of γ Values for All Price Pairs.
The γ values at the bounds (γ = 0.05 and γ = 50) account for roughly 44% of all possible
values. Over 10% of γ values lie at the lower bound, γ = 0.05, and nearly 34% of γ values lie at
the upper bound, γ = 50. Note that while a high percentage are at the constraints, allowing bigger
or smaller γ values would not change the speed-of-adjustment, G(·) shapes, or market linkages in
economically significant ways (i.e., models with γ = 50 and γ = 100 both look about the same).
Lastly, we performed a formal empirical test of the no cointegration hypothesis in the
high linkage regime. We calculated the variance of G(st, vt; , c, d) using the delta method, and
using this variance calculation we performed an asymptotic z-test on whether we could reject the
null hypothesis that G(st, vt; , c, d) = 1. Using the variance calculation, we also computed the
upper and lower bounds of 95% confidence intervals surrounding the estimated G(st, vt; , c, d)
functions. This visually shows whether we have statistical confidence in whether a pair is linked
or unlinked (Figure 2.5 displays four such confidence intervals).
0
5
10
15
20
25
30
35
40
45
50Fr
eque
ncy
γ Value
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Figure 2.5: Upper and Lower Confidence Interval of G(st, vt; , c, d) for Select Price Pairs.
Model Performance Results
In the ECON-STAR model where γ ≤ 1.0, markets link and unlink with high frequency and long-
run trends can be difficult to identify, but for models where γ > 3, market linkages are much
easier to identify. The Johansen cointegration test was performed on vector error-correction
models for price pairs whose corresponding ECON-STAR model contained γ ≤ 3, as we wanted
to evaluate the performance and ability of the ECON-STAR model to identify market linkages
and trends. Figure 2.5 shows a graph of the G(st, vt; , c, d) function for two different market
pairs – GA1/TN2 (γ = 0.38) and MS1/MS2 (γ = 0.62). Looking at Figure 2.6, it is difficult to
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determine whether the markets represented in each graph would be considered linked in the long-
run, but these graphs do give a good visual representation of how these markets interact over
time. However, according to the results of the Johansen cointegration test, we would say that the
GA1 and TN2 markets are not cointegrated, while the MS1 and MS2 markets are cointegrated.
We find that our approach has more nuance and flexibility in determining market linkages,
whereas traditional cointegration tests may not confirm market integration when in fact there are
extended periods of time when markets are linked. Further Johansen test results are provided in
Table 2.1.
Figure 2.6: Market Linkages of Select Price Pairs.
A total of 51 models containing γ values less than 3.0 were tested, and a number of these
market pairs are represented in Table 2.1. Results of the Johansen test based on both the trace
statistic, λtrace, and lambda-max statistic, λmax, reveal that cointegration could not always be
confirmed for market pairs where γ < 0.60, but cointegration was confirmed at the 5% and 1%
critical level for all market pairs whose corresponding γ value is greater than 0.60. These results
revealed that the ECON-STAR model does a fairly good job of indicating market linkages and
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that it is capable of identifying those markets where cointegrating relationships are not present.
The advantage of using the ECON-STAR model over traditional cointegration tests lies in its
ability to identify market linkages during a specific time period. Traditional cointegration tests
lack this flexibility and can only help make conclusions regarding spatial integration over the
long-run.
Table 2.1: Johansen Cointegration Test Results for Select Timber Regions.
Price Pair γ λtrace λtrace (max rank = 0) (max rank = 1) AR1/TX2 0.28 39.570 4.803 NC2/VA2 0.34 32.707 2.913 GA1/TN2 0.38 28.630 3.778 MS1/TN2 0.46 43.298 3.175 GA1/VA2 0.54 30.235 3.905 MS1/MS2 0.62 46.840 3.290 FL2/GA2 0.66 27.868 2.864 GA2/SC1 0.81 26.169 3.011 AR1/TN1 1.25 21.555 3.744 SC1/VA1 2.38 40.619 3.754 AL2/AR1 2.84 23.024 3.366 Note: 1. AR1 represents region 1 in Arkansas, other markets are similarly denoted; 2. The 5% critical value for the Johansen trace test is 15.41 at max rank=0 and 3.76 at max rank=1; 3. A bold figure indicates no cointegration.
Conclusions
We have modified a nonlinear STAR model to include an outside economic indicator that drives
the transitions in regional economic linkages to help us better understand pine sawtimber market
relationships in the southeastern U.S. region. The results with our ECON-STAR model indicate
that regions experiencing strong growth in new home construction can cause numerous regions
and states to link together and function as one solitary market. When this occurs, surrounding
24
timber markets strengthen which then leads to improved timber prices and increased trade
amongst these multiple markets. We found that during the mid 2000s – at the peak of the housing
bubble – the entire southeast region was linked, coinciding with stumpage prices in all regions
reaching historic highs.
Just the opposite effect occurs during recessionary periods, notably in the early 1980s and
late 2000s. During the most recent economic recession, new home construction in the
overwhelming majority of states fell to the lowest levels since the early 1980s, and, as a result,
stumpage prices for pine sawtimber fell to the lowest levels in nearly 20 years. During this
recessionary period essentially all regions became unlinked and exhibited no integrating
relationships. The only exceptions were those states that contain large metropolitan areas where
new home construction continued despite the economic conditions (i.e., Houston, TX).
The ECON-STAR model does not make assumptions regarding high or low demand,
rather the economic indicator transition variables allow us to determine when markets link and
unlink. The model decides which markets are linked and when, so it is possible for markets to be
linked when housing starts are low, or conversely, markets can be unlinked when housing starts
are high. This provides built-in flexibility similar to a generalization of Myers and Jayne (2012).
Our results provide somewhat of a updated mirror to those of Sexton, Kling, and Carman
(1990), with regional markets linking up when trade is needed to correct a supply-demand
imbalance in one or more regions. When new home construction is high is one region,
surrounding markets link together to provide the additional supply needed to meet that increase
in demand.
This paper makes a contribution to the theoretical literature by introducing a form of TV-
STAR model in which the transitions are controlled by related economic indicator variables.
25
When an economic indicator is found to be closely tied to the price of a specific good, it can
provide an alternative method of examining market interactions based on changing indicator
values. The paper also makes a contribution to the understanding of timber markets by mapping
when different regional markets are linked economically so that their price pairs are controlled
by the law of one price. Previous studies (Goodwin, Holt, and Prestemon, 2011, Stordal and
Nyrud, 2003) have examined larger market areas, but the sub-state regions examined here
provide a new level of geographic detail. The empirical results show how important economic
strength in the home building industry is for maintaining sufficient demand to ensure markets are
linked.
26
CHAPTER 3
FORECASTING PINE SAWTIMBER STUMPAGE PRICES IN THE SOUTHERN UNITED
STATES USING SALE CHARACTERISTICS
The U.S. South is considered to be one of the strongest and most competitive timber
markets in the world. There are a number of factors that contribute to the overall strength and
competitiveness of the region's timber market, such as tree species, climate, infrastructure, and
land ownership rights. According to the most recent United Nations FAO Forest Products
Yearbook, in terms of total world production, the US is responsible for nearly 20% of all
industrial roundwood, sawn wood, and wood pulp production. In fact, the southern region alone
is responsible for over 60% of the country's total production, which is over 12% of global
production of these products. Timber production and related industries are also economically
important in this region. According to the most recent figures released by the U.S. Bureau of
Economic Analysis, the forest industry in the U.S. South is roughly a $360 billion industry.
For many landowners, the production and sale of timber is an important component of
their income. While extensive research and new technology has allowed us to make significant
biological advances that have helped improved timber production, less is known about various
components of timber sales and how they affect the sale price. There are a variety of components
that encompass the sale of timber, such as harvest type, sale type, and total acreage harvested,
and a better understanding of these components will allow landowners to make more strategic
decisions regarding the harvest and sale of timber, which can ultimately lead to an improved
return on one's investment in timber production.
27
The effect of different sale characteristics on expected stumpage price has been studied in
the literature using a variety of different econometric and statistical models. Adams (1974)
studied the response of timber prices and output to alternative National Forest timber supply
policies in the Douglas-fir Region of western Oregon and Washington. His simulation results
indicated that price shifts are largely confined to the stumpage sector, with successively small
price changes at the log and secondary products levels. Empirical investigations of sealed bid
auctions and the effect of number of bidders on expected stumpage price are specific sale
characteristics that have received much attention over the years. Studies performed by Hansen
(1986), Athey and Levin (2001), and Brown et al. (2013) have evaluated sealed bid sales of
timber. Other studies performed by Brannman et al. (1987) and Haile (2001) have examined the
effect of number of bidders on expected stumpage price. All these findings confirmed that as the
number of bidders increases, so does expected stumpage price.
The effect of other specific sale characteristics on expected price has also been examined
in the past. Dennis (1989) performed an econometric analysis of harvest behavior in New
Hampshire stumpage markets. High per-acre volumes and the presence of commercially valuable
species were found to be key determinants of harvest behavior. Some studies suggest that factors
such as harvest volume (Niquidet and van Kooten 2006; Sydor and Mendell 2008) and sale area
(Buongiorno and Young 1984; Sydor and Mendell 2008) influence stumpage price. Puttock et al.
(1990) tested the effect of number of different characteristics on expected stumpage price in
southwestern Ontario. They estimated a hedonic model which indicated volume, species
composition, tree size, timber quality, and distance to purchasing mill all affect lump-sum
stumpage prices. Similar studies have also been conducted by Sendak (1991), Leefers and Potter-
Witter (2006), Brown et al. (2012), and Kolis et al. (2014), and these studies found sale
28
characteristics such as species composition, harvest volume, contract length, and haul distance to
significantly influence stumpage price.
Time series models are natural alternatives to study data collected over time because of
their ability to forecast future values. A variety of time series models has also been used in prior
research to forecast stumpage prices. Malaty et al. (2007) tested multiple time series models and
their ability to forecast Finnish pine sawlog stumpage prices. They used monthly prices from
January 1995 to June 2005, with the goal of developing a model that could accurately forecast
the price decrease that occurred from July through December of 2005. Based on their results,
they found it difficult to get precise estimates solely using the time-series approach, despite the
flexibility offered by their models with respect to structural changes. Mei et al. (2010) used
various time series techniques to model and forecast quarterly pine sawtimber stumpage prices in
12 timber regions in the U.S. South. They found that a number of different time series models
were able to forecast pine sawtimber prices with a fairly high degree of accuracy.
While most of the previous studies examined the effect of certain sale characteristics on
the expected timber price in a specific area or region, our study looks at these characteristics on a
market-wide basis. This research seeks to identify key characteristics found across all
submarkets that have a significant effect on expected price. We also focus on identifying how
changes in the way sales are conducted and characterized influence stumpage prices on a market-
wide basis. For this analysis we use a seasonal autoregressive integrated moving-average
(SARIMA) model to estimate and forecast south-wide pine sawtimber (PST) stumpage prices in
the U.S. South. The data used in the analysis are provided by Timber Mart-South, and it includes
nearly 26,000 individual timber sales from January of 2000 through December 2013. Prices and
other sale characteristic values are based on reported sales from all states within this region, and
29
the values reflect the overall trends associated with movements in price and the way stumpage
sales are conducted. Our primary goal is not to merely model the PST stumpage prices, but to
identify the key sale characteristics that both positively and negatively affect expected price on a
region-wide basis.
One important question often asked by landowners and sellers of timber is: When is the
best time during the year to sell timber? The common perception in the South is that the fourth
quarter is the best time to sell timber. Typically, in this region of the country, the summer and
fall months are characterized by large amounts of precipitation, and by the fourth quarter the soil
has become so saturated that logging operations may be extremely difficult to perform. This
would lead to a shortage in wood supply, and thus an increase in timber price, which supports the
idea that stumpage prices are highest during the fourth quarter. While this belief may hold true
and is supported in part by previous studies (Dunn and Dubois 2000; Dahal et al. 2014), we look
to draw our own conclusions based on the data and our statistical analysis; see Section 3.5 for
more details.
The Data
Timber Sale Characteristics
The data for this study consists of 25,986 individual timber sales across an 11-state region over
the period January 2000 through December 2013. The timber sales data was provided by Timber
Mart-South (TMS), which is a quarterly report of stumpage and delivered timber prices
throughout the U.S. South. The TMS reports prices of softwood and hardwood timber in 11
states (two regions per state), which include Alabama, Arkansas, Florida, Georgia, Louisiana,
30
Mississippi, North Carolina, South Carolina, Tennessee, Texas, and Virginia. See Figure 3.1 for
a map of the TMS regions.
Figure 3.1: Timber Mart-South Regional Map.
The information contained in reported timber sales include timber price, date of sale,
location of sale, and numerous other sale characteristics. Sales characteristics include Harvest
Volume by Product, Total Volume Harvested, Sale Type, Contract Type, Harvest Type, and Sale
Size. The Sale Type variable refers to whether the timber sale price was negotiated or based on a
sealed bid between multiple potential buyers. The Contract Type variable refers to the payment
method – Lump Sum Payment or Pay-as-Cut. The Harvest Type variable refers to whether the
timber stand is Clear Cut or Thinned.
TMS reports quarterly prices. However, monthly timber prices often exhibit seasonal
variations, which may be suppressed by performing a quarterly aggregation of the data.
Therefore, we decided to disaggregate the PST prices into monthly averages and use these to
build our time series models. Figure 3.2(a) shows both the monthly and quarterly south-wide
31
PST stumpage prices from 2000 through 2013. It is clear from Figure 3.2(a) that the monthly
PST series captures the seasonal variation much better than the quarterly PST series. Also, for
our analysis, we decided to evaluate the PST prices and other characteristics on a south-wide
basis. It should be mentioned that, using the time series modeling approach presented here, it is
possible to conduct similar statistical studies for specific states or sub-markets within this region.
We plan to pursue this elsewhere.
(a) (b)
Figure 3.2: (a): Monthly and Quarterly PST Stumpage Price (2000-2013) (b): Scatter Plot of PST Stumpage Prices and Mortgage Rates.
Note that Figure 3.2(a) also shows a significant downward trend in PST stumpage prices
beginning at or around the latter part of 2006. After the bursting of the housing bubble in 2008,
PST stumpage prices started declining steeply, reaching its lowest value in 2011; see Figure
3.2(a). To explain this downward shift in PST prices, we examined several economic variables
that may help explain the rapid decline in PST stumpage prices.
In particular, we examined the relationship between the PST prices and various economic
indicators, such as housing starts and mortgage interest rates, which presumably reacted to the
$20
$30
$40
$50
$60
Jan-
00Ja
n-01
Jan-
02Ja
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n-05
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n-07
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n-11
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12Ja
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page
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Quarterly PST
$20
$30
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3 4 5 6 7 8 9
PST
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ge ($
/ton)
Mortgage Rate (%)
32
bursting of the housing bubble. In fact, the plot of PST prices versus the mortgage rates (see
Figure 3.2(b)) exhibited a distinct break in PST prices when the mortgage rates are around 6%.
More specifically, when the mortgage rates are roughly below 6%, the PST prices range from
about $20 to $35 per ton, whereas when the mortgage rates are roughly above 6%, the prices are
generally much higher – ranging from $35 to over $50 per ton. This observation and a closer
inspection of the plot in Figure 3.2(a) indicated that the decline in PST prices may be associated
with the mortgage rates falling below 6%. In order to explain the sudden downward movement in
PST prices, we decided to incorporate a binary intervention variable in our time series analysis,
which indicates the time (January of 2008) when the mortgages rates started to fall below 6%.
The inclusion of an intervention variable is explained in detail in Section 3.3.
Preliminary analysis of the data also revealed that the monthly PST prices appear to be
strongly related to different aspects of a timber sale, such as the Sale Type, Harvest Type, Sale
Size, and Harvest Volume. The bar plots given in Figures 3.3 are based on 5-year average sale
prices from 2009 through 2013, where the categories PPW, CNS, HPW, and HST are defined in
Table 3.1.
To explain the variability in the monthly PST prices better, we strengthened our time
series modeling approach further by including different economic indicators, forest product
prices, and sale characteristics as covariates. This analysis is focused on evaluating region-wide
PST stumpage price movements over time, so inclusion of broader market indicators and sale
characteristics might help better explain price movements than by purely modeling prices using
autoregressive and moving-average parameters. These aspects of modeling are explained in the
subsequent sections. The monthly prices and values for the forest products and economic
33
indicators were provided by Random Lengths and the Federal Reserve Bank of St. Louis
economic database.
(a) (b)
(c) (d)
Figure 3.3. (a) Pine Sales by Acres, (b) Pine Sales by Harvest Type, (c) Pine Sales by Sale Type, and (d) Pine Sales by Volume (2009-2013). Sale Characteristic Variables
Based on our extensive preliminary analysis, we were able to gain a better understanding of how
the monthly PST prices related to some of the different sale characteristics. This prompted us to
group the variables we investigated in our analysis into three broad categories: Economic
Indicators, Forest Product Market Prices, and Sale Characteristics.
34
We considered the predictability of a variety of different economic indicators in our time
series models. These indicators include housing starts, construction expenditures, and spot prices
for crude oil, diesel, and natural gas. Forest product market prices that were investigated include
prices for lumber, 2x4s, structural panels, plywood, and oriented strand board. Finally, we also
considered over 80 different sale characteristic variables in our analysis. These variables relate to
Sale Type, Harvest Type, Harvest Volume, and Sale Size mentioned earlier. Table 3.1 contains
the complete list of all the different variables we considered in model building process along
with a brief description of what they are.
Table 3.1: List of All Model Variables Tested.
Variable Description Hstarts Number of housing starts in the U.S. South Construct U.S. construction spending ($ billions) Diesel Gulf Coast #2 diesel retail $/gallon Crude West Texas crude oil spot price FOB ($/barrel) Ngas Gulf Coast natural gas spot price ($/mmbtu) Lumber Framing lumber composite ($/mbf) Spcomp Southern pine lumber composite ($/mbf). 2x4 Southern pine 2x4s ($/mbf). Panel Structural panel composite ($/msf). Ply Southern pine plywood ($/msf) OSB Southern oriented strand board ($/msf). PST Pine sawtimber stumpage ($/ton). CNS Pine chip-n-saw stumpage ($/ton). PPW Pine pulpwood stumpage ($/ton). HST Hardwood sawtimber stumpage ($/ton). HPW Hardwood pulpwood stumpage ($/ton). STYPE Dummy variable representing sale type:
STYPE = 0 when a majority of sales are negotiated; and STYPE = 1 when a majority of sales are sold via sealed bid auction.
STYPEPRODUCT Weighted average ($/ton) by sale type. STYPEPRODUCT pct Percentage of sales sold via sealed bid auction, opposed to negotiated sales. HTYPE Dummy variable representing harvest type:
HTYPE = 0 when a majority of sales are clear cut; and HTYPE = 1 when a majority of sales are thinned.
HTYPEPRODUCT Weighted average ($/ton) by harvest type. HTYPEPRODUCT pct Percentage of sales that were thinned, as opposed to clear cut. ACRESTOTAL,1,2 Dummy variables representing total acres harvested:
ACRESTOTAL,1 = 1 when total acres harvested < 9,350 acres, 0 otherwise ACRESTOTAL,2 = 1 when total acres harvested > 13,950 acres, 0 otherwise
ACRESPPW = 1 when PPW acres harvested < 2,200 acres, 0 otherwise APSCC,1,2 Dummy variables representing average clear cut size:
APSCC,1 = 1 when average clear cut size < 90 acres, 0 otherwise APSCC,2 = 1 when average clear cut size > 105 acres, 0 otherwise
APSTHIN,1,2 Dummy variables representing the average thinning size: APSTHIN,1 = 1 when average thinning < 140 acres, 0 otherwise APSTHIN,2 = 1 when average thinning > 165 acres, 0 otherwise
APSNEG,1,2 Dummy variables representing average negotiated sale size: APSNEG,1 = 1 when average negotiated sale size < 115 acres, 0 otherwise APSNEG,2 = 1 when average negotiated sale size > 150 acres, 0 otherwise
APSSBID,1,2 Dummy variables representing the average sealed bid sale size: APSSBID,1 = 1 when average sealed bid sale < 100 acres, 0 otherwise APSSBID,2 = 1 when average sealed bid sale > 115 acres, 0 otherwise
APSTOTAL,1,2 Dummy variables representing average timber sale acreage: APSTOTAL,1 = 1 when average sale < 75 acres, 0 otherwise APSTOTAL,2 = 1 when average sale > 85 acres, 0 otherwise
APSPST,1,2 Dummy variables representing average PST sale acreage: APSPST,1 = 1 when average PST sale < 100 acres, 0 otherwise APSPST,2 = 1 when average PST sale > 115 acres, 0 otherwise
APSCNS,1,2 Dummy variables representing average CNS sale acreage: APSCNS,1 = 1 when average CNS sale < 70 acres, 0 otherwise APSCNS,2 = 1 when average CNS sale > 75 acres, 0 otherwise
APSPPW,1,2 Dummy variables representing average PPW sale acreage: APSPPW,1 = 1 when average PPW sale < 55 acres, 0 otherwise APSPPW,2 = 1 when average PPW sale > 65 acres, 0 otherwise
APSHST Average HST acres per sale. APSHPW Average HPW acres per sale. VPSTOTAL,1,2 Dummy variables representing average timber sale volume:
VPSTOTAL,1 = 1 when average volume < 1,350 tons, 0 otherwise VPSTOTAL,2 = 1 when average volume > 1,650 tons, 0 otherwise
NOTE: The subscript PRODUCT can refer to PST, CNS, PPW, HST, or HPW.
As observed in Figure 3.3, our extensive time series analysis revealed that Sale Type,
Harvest Type, and Sale Size appear to have a high degree of influence on expected monthly PST
prices. In our studies, we analyzed the variations of these three characteristics in a variety of
different ways for multiple timber products to determine whether and to what degree they impact
monthly PST prices. More specifically, we evaluated Sale Type in three different ways. First, we
identified Sale Type by how a majority of the sales were conducted each month. This was done
by including a dummy variable STYPE (see Table 3.1) in our model. Secondly, we evaluated
Sale Type by timber product; this variable is denoted by STYPEPRODUCT in Table 3.1, where
36
PRODUCT refers to PST, CNS, PPW, HST, or HPW (see Table 3.1). Here, each product is
evaluated on a price per ton weighted average basis, where the total numbers and average price
of both negotiated and sealed bid sales are used to weight the product's price. For example, sale
type price of pine pulpwood would be denoted STYPEPPW in our model below.
STYPEPRODUCT,Pct in Table 3.1 is defined similar to STYPEPRODUCT, except that the values are
percentages, where values below 0.5 indicate that a product was more frequently sold using a
negotiated price and values greater than 0.5 indicate that a product was sold more frequently via
sealed bid auction. For example, sale type percentage of chip-n-saw is STYPECNS, Pct in our
analysis. Harvest Type, which refers to whether a tract was clear cut or thinned, is defined in the
same three ways as that of Sale Type. Once again, we introduce three HTYPE variables; see
Table 3.1 for more information.
Lastly, we considered the total and average acreage of timber sales in our study. In Table
3.1, the total monthly acreage harvested is denoted by ACRES. Dummy variables were used to
identify whether the total number of acres harvested each month was low (bottom third of all
monthly values observed) or high (top third of all monthly values observed). Acreage was also
evaluated on an average per sale basis, denoted APS. Values were calculated for all products and
dummy variables were also used to identify when average per sale acreage was relatively low or
high for a given time period. For example, the average per sale acreage of timber sales
containing PST ranges from 70 to 150 acres. In Table 3.1, APSPST,1 is a dummy variable that
indicates when the average PST sale size is relatively low (70-100 acres), and APSPST,2 is a
dummy variable that indicates when the average PST sale size is relatively high (115-170 acres).
Other variables that are denoted APS are characterized similarly and are based on threshold
values.
37
Concepts and Procedures
After examining the overall and seasonal trend in the monthly PST stumpage price series over
the period January 2000 through December 2013, we modeled the PST series using seasonal
autoregressive integrated moving average (SARIMA) models. As discussed in Section 3.2, after
the bursting of the housing bubble in 2008, PST stumpage prices started declining steeply,
reaching their lowest value in 2011; see Figure 3.2(a). In order to quantify the (negative) effect
of 2008 housing crash on PST prices, we refined our SARIMA models by introducing a binary
intervention variable, It, which is a function of mortgage interest rates. More specifically,
(3.1) It = 1 if the mortgage interest rate 6%;0 if the mortgage interest rate 6%.
Finally, we used the intervention variable It and a host of other explanatory variables, X, listed in
Table 3.1 above to build our final time series model.
Models, Diagnostics, and Model Selection
The data under consideration is monthly PST stumpage prices, Yt, observed from January 2000
through December 2013, consisting of 168 observations. First, we addressed the overall and
seasonal trend in the data, respectively, by carrying out simple and seasonal differencing of Yt.
We then proceeded to build models for the de-trended PST series, Zt = (1-B12)(1-B)Yt, where B
is a back-shift operator defined by BpYt = Yt-p for p ≥ 1. In all our time series models, we
assumed that the associated (white noise) errors Wt are independent and normally distributed
with mean zero and constant variance, σ2. Subsequently, we examined the nature of the
autocorrelation function (ACF) and the partial autocorrelation function (PACF) of Zt, and fitted a
viable set of candidate ARMA models for Zt. We used SAS 9.3 to fit the candidate models,
38
where the model parameters were estimated using the method of maximum likelihood. Statistical
significance of the model parameters was determined at the 10% level.
In order to assess the adequacy of a fitted time series model, the literature offers a variety
of diagnostic and theoretical tools based on the residuals to test the assumptions made about the
errors Wt. We checked the normality assumption of Wt by examining the Q-Q plot of the
standardized residuals, which plots the sample quantiles of the standardized residuals against the
standard normal quantiles. If this scatter plot lies close the straight line through the origin with
slope 1, then it indicates that the assumption of normality of Wt is satisfied. In addition, we also
tested the normality assumption using the Shapiro-Wilk's test and the Anderson-Darling's test of
normality provided by SAS. In order to test the assumption of independence of the errors, we
performed the well-known Ljung-Box-Pierce (LBP) Chi-square test using the ACF of the
residuals up to lag 40. If the LBP Chi-square value is larger than the 95th percentile of a Chi-
square distribution, then the null hypothesis of independent error is rejected; otherwise the
assumption of independent errors is satisfied.
We formed a set of candidate SARIMA models for Yt, which only included models
where all the parameter estimates are statistically significant at the 10% level and the associated
residuals satisfy the assumption of normality and independence. Next, we focused on three
different model selection criteria in order to select the best SARIMA model from our set of
candidate models for the monthly PST price series. More specifically, we used the two well
known model selection criteria, namely the Akaike Information Criterion (AIC) and the Schwarz
Bayesian Information Criterion (SBC) to assess the goodness-of-fit of each model. Furthermore,
since we were also able to obtain an additional six months (January 2014 to June 2014) of PST
prices beyond the horizon (December 2013), we computed the (out-of-sample) forecast value, ,
39
for each of the six additional months from each of the models in our candidate set, and computed
the Mean Absolute Percentage Error (MAPE) using the formula
(3.2) MAPE = ∑ /
where Yi is the observed PST price and i is the forecasted value for each i = 169, …, 174,
which denote the six months, January 2014 through June 2014.
After carefully examining the results of residual analyses and the values of all the three
model selection criteria (AIC, SBC, and MAPE) for each SARIMA model in our candidate set,
we chose SARIMA (0,1,1) x (1,1,0)12 model (see equation below) as the best model. The model
equation for SARIMA (0,1,1) x (1,1,0)12 is given by
(3.3) (1 – ΦB12)(1 – B12)(1 – B)Yt = (1 – θB)Wt,
where B is he back-shift operator defined above, Wt are independent and having the N(0, σ2)
distribution, Φ is the autoregressive parameter associated with the lag value Yt-12 and θ is the
moving average parameter associated with the lag value Wt-1.
Next, based on the discussion presented in Section 3.2, we added the intervention
variable It defined in (3.1) in our SARIMA model in (3.3). After a thorough investigation a set of
candidate SARIMA models with It, we chose the following SARIMA model with intervention
model as the best model:
(3.4) (1 – ΦB12)(1 – B12)(1 – B)Yt = (1 – θB)Wt +
where is the parameter quantifying the initial effect of the intervention It and is the
parameter quantifying the effect of intervention, which increases/decreases gradually over time
40
to a limiting value. Note that in model (3.4), the intervention series It is also simple and
seasonally differenced.
Finally, we also added several different covariates listed in Table 3.1 to our SARIMA
model with intervention in (3.4) and, once again, thoroughly investigated a set of candidate
models, and selected the following SARIMA model with intervention and covariates as the best
model:
(3.5) (1 – ΦB12)(1 – B12)(1 – B)Yt = (1 – θB)Wt +
+ ∑ 1 1 , ,
where {Xk,t, k = 1, …, 25} are the 25 covariates we identified as being significant predictors of
PST prices (see Table 3.1 for a listing description) and Bk is coefficient associated with Xk,t.
Note once again that in the model (3.5), each covariate series Xk,t is also simple and seasonally
differenced. Since the fitted models progressively became better in terms of the three model
selection criteria, we only present the coefficient estimates corresponding to the final fitted
model (3.5), but also give some of the results corresponding to the models in (3.3) and (3.4) for
comparison purposes.
Results
Our final fitted SARIMA model with intervention and covariates (see model (3.5)) is given by
Although the coefficient estimate for the variable APSCC,1 that represents an average clear cut
size of less than 90 acres was not statistically significant at the 5% or 10% critical level, its
coefficient value was found to be positive. This could imply that more capital is required to buy
and harvest larger tracts of timber, so the pool of potential buyers is decreased thus reducing the
43
competition between buyers, which ultimately leads to lower stumpage prices. This reduction in
competition does not occur when tracts of timber are to be thinned.
Thinnings typically remove lower value products and the per acre volume of timber
removed is significantly less than the volume removed during a clear cut, so the total amount of
capital required to purchase the timber is lower. We found that at all levels, average thinning size
positively affects the expected PST price, which is supported by the statistical significance of the
coefficients corresponding to APSTHIN,1 and APSTHIN,2. Interestingly, in contrast to the
relationship between clear cut size and the PST prices, the coefficient estimate when the average
thin size is larger than 165 (falls within the top third of all observed values) is about 36% larger
than the estimated value corresponding to average thin size less than 140 (falls within the bottom
third of all observed values). This leads us to believe that buyer competition is strongest among
large tracts that are to be thinned and small tracts that are to be clear cut. With large thinning,
wood buyers can take advantage of economies of scale, while retaining more capital to invest in
subsequent timber purchases.
The second factor that was found to influence stumpage price is Sale Type. During
periods of time when a majority of timber sales were sealed bid sales, as opposed to negotiated
sales, expected price is increased, as indicated by the significance of the (positive) estimated
value of the coefficient corresponding to the variable STYPE. This strengthens the notion that
high levels of sealed bid sales indicate increased buyer competition, a higher willingness to pay
for the timber, and higher stumpage prices for the seller.
Lastly, we found that, in general, when hardwood timber prices increase, pine sawtimber
price decreases, as indicated by the (negative) coefficient estimates for HPW and HTYPEHST.
This indicates that a one dollar increase in hardwood price translates to a lower expected PST
44
price. From an economic perspective, the findings concerning hardwood timber prices can be
explained by way of consumer preference and substitute goods. When consumer preference
shifts from softwood (pine) to hardwood timber, the demand of hardwood timber products will
rise and, consequently, the demand and price of pine timber products will fall.
Table 3.4 provides a comparison of AIC, SBC, and MAPE values for the fitted versions
of models in (3.3), (3.4), and (3.5). From Table 3.3 it is clear that the inclusion of the
intervention It (see model in (3.4)) provided a slight improvement in AIC, SBC, and MAPE
values over the (initial) model in (3.3). However, the addition of It and the 25 covariates
significantly improved the overall performance of the final fitted model in (3.6), in terms of AIC,
SBC, and MAPE. We also fitted model (3.3) with the covariates only, whose AIC, SBC and
MAPE values are given in the last row of Table 3.3. This model will be discussed in the next
section.
Table 3.3: Model Comparison.
Model AIC SBC MAPE SARIMA(0,1,1)x(1,1,0)12 735.266 741.353 0.04979 SARIMA(0,1,1)x(1,1,0)12 + It 714.965 727.06 0.04658 SARIMA(0,1,1)x(1,1,0)12 + It + covariates 372.154 459.847 0.02955 SARIMA(0,1,1)x(1,1,0)12 + covariates 380.956 463.128 0.03122
Discussion
We developed a SARIMA model for monthly pine sawtimber stumpage prices from January
2000 through December 2013 that includes an intervention variable, It, defined in (3.1) and
numerous independent variables given in Table 3.1. The results provided interesting insight into
how other timber products and different aspects of a timber sale explain the dynamics of the PST
45
price series. Our final fitted model in (3.6) revealed the following three primary sale
characteristics that influence expected price: acreage, sale type, and hardwood prices.
The introduction of the intervention variable, It, allowed us to quantify the effect of the
housing market crash on the monthly PST prices. In Table 3.3, the estimate 0 (= 0.987)
represents the initial (positive) effect and 0 (= - 0.805) represents the long-term (negative) effect
(on PST prices) associated with the housing market crash and subsequent lower mortgage
interest rates. The (negative) 0 value in the factor in model (3.6) indicates that
the initial effect ( 0) of It is dampened over time, making the monthly PST prices settle down
around a new level, which is also evident from Figure 3.2(a). Beginning in 2008, PST stumpage
prices started to rapidly decline until they bottomed out in 2011. Over this three to four year
period, prices fell from about $40 per ton to less than $25 per ton, and since 2011, PST prices
have remained between $25 and $30 per ton.
To test whether there is an inherent mortgage rate threshold that helps explain PST
stumpage price levels, we refitted our final model (3.5) without the intervention variable, It. The
AIC, SBC, and MAPE for this model are given in the last row of Table 3.3. Note that these
values are substantially smaller than those of the basic SARIMA model (see first row of Table
3.3). However, these values were still larger than those of the final model that does include the
intervention variable, which indicates that the intervention helps provide a better explanation for
the downward shift in prices.
Initially, this analysis was aimed at determining how different sale characteristics affect
stumpage prices, but the results provided insight into what some would consider more important
– stumpage prices levels in the foreseeable future. From 2000 through 2007, PST prices fell in
the range of $40-$55 per ton and mortgage rates ranged from 6% to 8%. Since the housing
46
market crash, the PST prices have hovered between $25 and $30 per ton, while mortgage rates
have remained less than 5%. While no one can be certain of what mortgage rates will be in the
next 10-15 years, it is unlikely that the mortgage rates would return to the pre-recessionary levels
in the immediate future. We make no predictions regarding stumpage price levels in the next
five, ten, or 15 years, but the results of our analysis lead us to believe that the PST prices have
now reached a new level and that it is unlikely we will see prices back near $50 per ton anytime
soon.
In this study, we analyzed monthly PST prices and found some common trends for when
prices spike and are lowest during each calendar year. Our final model found the seasonal
autoregressive parameter at lag 12 to be statistically significant in explaining PST stumpage
price. If the PST price 12 months prior to it is significant in explaining the current price, then it is
reasonable to assume that prices will spike around the same time each year. Figure 3.2 (a)
supports this idea, so we decided to take a closer look at the price data to see which month these
spikes occurred each year. Our analysis covers a 14-year period, and we found that 100% of
price spikes occurred between November and February, and nearly 80% of price spikes occurred
between December and February. These findings partially support the common perception that
stumpage prices are highest during the fourth quarter, but we found prices to be typically highest
during the first two months of the calendar year. Similarly, we found prices to be lowest during
the summer months, with 86% of the price lows occurring between June and August.
Furthermore, this drop in price occurs each year 5-6 months following a price spike.
As previously mentioned, an area of focus for future studies includes performing similar
evaluations on specific states or sub-regions within this area. While this study was focused on
identifying the components of a timber sale that significantly affect expected pine sawtimber
47
stumpage price on a region-wide basis, timber sales within specific markets in the South are
undoubtedly characterized differently; however, such studies may be limited by data availability.
A few issues we experienced during our analysis include limited data points and series
that contain periods of high volatility. For this study, we evaluated a variety of sale
characteristics as they relate to different timber products, some of which had very few
observations. Related to the issue of data availability, some of the data series evaluated contained
high volatility, often times a direct result of values derived from a small sample. To account for
high volatility in some of these data series, future studies could incorporate models that account
for heteroscedasticity, such as ARCH/GARCH models.
This study identified a number of different timber sale characteristics that significantly
affect pine sawtimber stumpage prices on a region-wide basis, and to our knowledge, this study
evaluates the most exhaustive list of sale characteristics and includes the largest number of
individual timber sale observations. Furthermore, we were able to construct a model that is able
to forecast PST prices with a high degree of accuracy, with an overall MAPE reduction of nearly
50% compared to that of the original SARIMA model.
48
CHAPTER 4
THE EFFECT OF MILL LOCATION AND CAPACITY ON PINE STUMPAGE PRICES IN
THE U.S. SOUTH
Derived demand is a term used in economic analysis that describes the demand placed on
one good as a result of demand for another intermediate or finished good. Timber is the input
good used to create manufactured forest products, such as dimensional lumber and paper, and the
demand and value of timber is derived from the demand for these manufactured products. A
change in the demand for manufactured forest products leads to a change in demand for timber,
so one way to evaluate timber price is by observing mill demand (capacity). At the local level,
multiple mills often compete for wood and the larger the capacities of these competing mills, the
greater these mills capacities should influence stumpage prices. The stumpage value of timber is
also affected by the wood buyer’s cost to harvest and haul timber to the mill. The farther away a
mill is located from a timber sale location, the higher the costs associated with transporting the
wood to the mill. So, in theory, if competition exists among wood buyers, the closer a mill is
located to a sale location, the more the buyers would be willing to pay for the timber. This
analysis seeks to quantify the degree to which both mill locations and mill capacities influence
pine stumpage prices in the U.S. South.
Previous research has identified mill location as one of the variables that influence price.
Puttock et al. (1990) examined the effect specific timber sale characteristics have on expected
stumpage price in Southwestern Ontario. They found timber quality and hauling distance to the
purchasing mill to significantly affect the stumpage price for timber in a particular sale. Jackson
49
(1987) examined the differences in stumpage price between national forest timber and that sold
by other public agencies in the western U.S. from the fourth quarter of 1979 through the third
quarter of 1984. Numerous sale characteristics were evaluated and one variable that was found to
be statistically significant was haul distance. They concluded that total delivery distance and
stumpage price was inversely related – the farther the hauling distance, the lower the sale price.
Other studies have examined wood procurement for mills and how this is influenced by
sale location and delivery distance. May and LeDoux (1992) assessed timber availability in
hardwood forests in Tennessee and found that wood procurement zones for mills were limited
based on distance, such that wood from locations outside a specific radius could not be profitably
delivered to the mill site. Stier, Steele, and Engelhard (1986) assessed pulpwood procurement
practices in the Wisconsin-Upper Michigan pulp and paper industry. They found that mills had
reduced the average procurement distance. In 1966, 90% of the pulpwood supply was drawn
from within a distance of 225 miles, and in 1982, approximately 80% of the pulpwood supply
was drawn from within 125 miles.
Just as competition exists between wood buyers in the stumpage markets, so does it exist
among processing facilities that are supplied by the same timber market. Since the total volume
of available timber in a given market is limited by some degree, the economic theories of supply
and demand and competition suggest that the greater the capacities of these competing mills, the
higher price mills are willing to pay for delivered timber.
Luppold (1996) evaluated the sawmill capacity and concentration in the Central
Appalachian hardwood sawmilling industry between the mid-1970s and early 1990s. This
industry became more concentrated over time, and one could argue that large hardwood sawmills
could be a spatial monopsonists and could exercise market power, thus keeping stumpage prices
50
low; however, that behavior was not observed in this marketplace. Murray (1995) measured
market power in the U.S. sawlog and pulpwood markets for the years 1958 through 1988.
Murray found that sawlog processors, on average, possess less market power than pulpwood
processors, and that sawlog processors experienced a decline in market power over the observed
time period while pulpwood processors experienced a slight resurgence in market power during
the latter years.
Luppold and Baumgras (1993) examined Ohio hardwood stumpage markets between the
mid-1970s and early 1990s and found increasing capacity to be correlated with increased
competition in the stumpage market because larger mills needed to expand their procurement
area. Carter (1992) inspected the short-run effects of supply and demand on pulpwood stumpage
prices in Texas from 1964 to 1986. Results indicated that a sustained increase in mill capacity
would initially lead to an increase in stumpage price. Hetemaki and Kuuluvainen (1992) studied
the aggregate pulpwood market in Finland from 1960 to 1988. They found that stumpage price
had both a long-term and short-term effect on pulpwood demand. The long-term effect was
negative, while the short-term effect was positive – possibly related to export price or stumpage
price expectations. Haynes (1977) used a derived demand approach to evaluate the relationship
between the elasticity of demand in the product market and elasticity of demand in the factor
market. Results indicated that stumpage markets are more inelastic than lumber markets and that
stumpage prices react to shifts in total lumber demand.
An important topic that is closely related to our study is that of competition. One such
form of competition that has been explored in prior studies is competition between buyers of
timber, which in many cases refers to the number of bidders on a timber sale. Leefers and Potter-
Witter (2006) estimated hedonic pricing models to determine which sale and institutional
51
characteristics influenced stumpage prices in the Lake States. Sale characteristics that were
included in their model include sale size (hectares), total volume harvested, number of species
harvested, number of bids, and contract length, of which number of species harvested, number of
bids, and contract length were found to be statistically significant explanatory variables.
Brannman et al. (1987) examined the price effects of increased competition in different auction
markets, including bonds, oil, and timber, and found that the greater the number of bidders, the
higher the selling price.
While we seek to understand the degree to which a mill’s location and capacity affect
stumpage price, previous studies related to this topic have evaluated mill concentration and
factors that influence where mills choose to locate. Aguilar et al. (2009) examined spatial
clustering of primary wood products manufacturers in the U.S. South to determine location
preferences of mills and identify factors promoting industry clustering. They found that counties
with adequate transportation infrastructure and presence of related industries were most likely to
attract new primary forest products manufacturers. Aguilar (2009) examined the U.S. South
lumber industry and factors that drive the location of firms. Their results suggest that stumpage
prices, availability of labor, presence of a highway, local availability of forest resources, energy
costs, and land values were the main factors driving lumber industry location. Other studies have
evaluated forest products manufacturing and location drivers. Holley (1970) examined the
location of plywood and lumber industries across the U.S. South and West and found that the
South has a locational advantage in both the plywood and lumber manufacturing industries. The
South was found to have a comparative advantage in wages and timber availability.
For this analysis, instead of identifying locations where mills can take advantage of weak
competition and high local timber inventory levels, we seek to identify sub-regions within the
52
U.S. South that are positioned to take advantage of increased local mill competition. If mill
locations and capacities are know, a metric can be developed to identify specific areas within this
region that have a strong procurement influence, or an area that is saturated with numerous mills
with a large cumulative annual capacity. When we speak of competitive timber markets,
competition is defined in terms of the stumpage value of timber. If the stumpage price of a
particular product is high, relative to the price of a similar product in other areas of this region,
we make the assumption that the higher stumpage price is a function of higher competition
among wood buyers and processing facilities in that area. That procurement influence metric can
be further improved upon by including information related to stumpage values within a given
area. To our knowledge, no research has been performed to quantify an area’s locational
strength, relative to other areas, based on mill locations, local wood demand, and local stumpage
markets. One of the primary reasons this type of analysis has not been performed in the past is
data availability. Also, mills open and close on a relatively frequent basis, so it can be difficult to
maintain an accurate database of mills within such an expansive region.
This study evaluates stumpage prices for both pine sawtimber (PST) and pine pulpwood
(PPW) to determine the degree to which mill location and capacity affects price. Based on the
preliminary analysis of the price and mill data, we found that in the U.S. South, the number of
softwood lumber mills far exceeds the number of softwood pulpwood consuming mills. We
hypothesize that pulpwood mill location and capacity will have a larger (positive) effect on PPW
prices, compared to lumber mill location and capacity’s effect on PST prices. Also, lumber mill
capacities are highly variable from one mill to the next, while pulpwood mill capacities tend to
be more consistent, so we believe the results regarding PPW prices will be more consistent and
definitive than the results regarding PST prices.
53
The Data
Softwood Lumber and Pulpwood Mill Data
Mill types, locations, and annual capacity as reported by the University of Georgia’s Center for
Forest Business Wood Demand Report from the fourth quarter of 2010 through the second
quarter of 2014 (15 total quarters) were used for this analysis. The database of mills contains a
total of 1,472 mills across the 11-state Timber Mart-South region. For this study, we focus
specifically on softwood lumber mills and softwood pulpwood consuming mills, which include
pulp and paper, chip, and pellet mills. A total of 451 softwood lumber mills are used for this
analysis, and annual lumber mill capacities range from 10 thousand to 1.3 million tons of
roundwood per mill. A total of 277 softwood pulpwood consuming mills are used for this
analysis, and annual pulpwood capacities of those mills range from 20 thousand to 1.3 million
tons.
(a) (b)
Figure 4.1: (a): Pine Lumber Mill Locations and Annual Capacity (2014:Q2) (b): Pine Pulpwood Mill Locations and Annual Capacity (2014:Q2).
54
For each individual timber sale, the state and county of sale is reported. Distances from
location of sale to processing facilities is measured in miles from the center of the county of sale
to the physical location of the individual mills.7 The number of open mills and total combined
mill capacity, measured in ten million board feet for lumber mills and 100 thousand tons for
pulpwood mills, within a specified proximity of each timber sale location was calculated for all
individual timber sales and ranges from as far away as 150 miles to as close as 15 miles.
Timber Sale Data
Timber sale data was provided by Timber Mart-South (TMS), a quarterly report of stumpage and
delivered timber prices throughout the U.S. South. A total of 23,267 individual timber sales over
a 15-quarter period were used in the analysis, including 7,161 PST prices and 16,106 PPW
prices. These timber sales occurred within the 11-state TMS region (Figure 4.2), and while TMS
sales include both stumpage and delivered prices, for this study we only evaluate stumpage
prices.
Figure 4.2. Timber Mart-South Regional Map.
7 Latitude and longitude coordinates for each mill’s location are provided by the Wood Demand Report database. If exact coordinates were not provided for a mill, coordinates are given for the mill’s mailing address.
55
Concepts and Procedures
Model Estimation & Diagnostics
For this analysis, quarterly stumpage prices for both PST and PPW were transformed into panel
data to observe the degree to which mill presence and capacity affect price. The raw timber sale
data used for this analysis contains year and quarter of sale, along with the location of sale
(county), so we were able to convert the sales into panel data based on county of sale. Panel
prices were calculated as the average price of all sales within a particular county for a given
quarter and year. By converting the sales data into a panel data format, this helps solve the
problem of measurement error associated with the time component, quarter of sale.
A specific issue that may arise in such a model is omitted variable bias (OVB). There are
other factors that influence stumpage price, such as timber quality (Puttock et al. 1990), the
demand for forest products, and physiographic region, and these omitted factors could cause
omitted variable bias. Panel data lets us eliminate omitted variable bias when the omitted
variables are constant over time within a given county, so time-invariant variables could be
included in these models to mitigate possible bias. It may be difficult to determine a variable that
is uncorrelated with both stumpage price and the independent variables; however, inclusion of a
variable such as physiographic region may allow us to reduce possible bias. Following model
estimation, OVB will be tested using the Ramsey RESET test (Ramsey 1969).
Another possible issue that may arise amongst the model variables is heteroscedasticity.
Although heteroscedasticity does not cause OLS coefficient estimates to be biased, it can cause
OLS estimates of the variance of the estimated coefficients (and thus standard errors) to be
biased – above or below the true (population) variance. To test for the presence of
56
heteroscedasticity, we will use the Breusch-Pagan (Breusch and Pagan 1979) test of the null
hypothesis of constant variance.
Also, variance inflation factors (VIFs) will be examined to ensure multicolinearity is not
present in the estimated models. VIFs range from one to infinity, and values greater than ten are
generally seen as indicative of severe multicolinearity. Similarly, 1/VIF is the tolerance, which
ranges from zero to one, with a value of one being the absence of multicolinearity.
Individual models for both PST stumpage price and PPW stumpage price are estimated
using ordinary least squares (OLS) regression to determine the degree to which mill location
influences stumpage price. These models take the form:
where y denotes stumpage price, Mill denotes presence of a mill, i denotes county of sale, t
denotes the time period, and uit represents the errors. The variables denoted Physio2, Physio3,
and Physio4 are binary dummy variables that identify the physiographic region associated with
each location.8 Four primary physiographic regions are found in the U.S. South, and include the
Coastal Plain, Piedmont, Plateaus, and Valley/Ridge regions (see Figure 4.3). To avoid the
dummy variable trap, a scenario in which multicollinearity exists among the independent
(dummy) variables, the variable representing the Coastal Plain region has been excluded from
the model.
8 For each of the 22 individual TMS regions, the physiographic region, based on Figure 3.3, that is found within a majority of that TMS region was selected to characterize the region.
In
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57
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58
thinning), respectively. The variable Acres represents sale size, ProdVol represents the harvest
volume (tons) of the specific product, and TotalVol represents the total volume (tons) harvested.
A second set of models were constructed to evaluate the degree to which mill capacity
effects stumpage price. These models take the form:
The results indicate that for both pine sawtimber and pine pulpwood stumpage prices, sale
location has a significant effect on expected price. We examined both mill locations and their
cumulative capacity at a range of different distances from a timber sale location and were able to
quantify the degree to which both of these variables influence expected stumpage price. Our
analysis allowed us to draw two major conclusions related to mills’ locations and their
cumulative capacity’s influence on stumpage prices. First, the number of mills located within a
specified radius of a timber sale has a larger (positive) influence on both pine sawtimber and pine
pulpwood stumpage prices, and, secondly, pulpwood consuming mills have a greater (positive)
influence on PPW stumpage price than do lumber mills on PST stumpage prices.
As for the degree to which mill locations effect stumpage price, our results indicate that
each lumber mill located within a 100 to 150-mile radius of a timber sale increases expected PST
stumpage price by $0.02 per ton, by $0.08 per ton from an 85 to 100-mile radius, by $0.10 per
ton from a 40 to 85-mile radius, by $0.24 per ton from a 25 to 40-mile radius, by $0.33 per ton
73
from a 15 to 25 mile radius, and by $0.51 per ton within a 15-mile radius (see Figure 4.6(a)).
During the second quarter of 2014, on average, there were 51 softwood lumber mills located
within 150 miles of a given sale. Based on the model estimates, lumber mills increased PST
stumpage price by $4.00 per ton, or by roughly 14.8%, holding all other variables constant.
Pine pulpwood consuming mills were found to have an even larger (positive) effect on
PPW stumpage prices. Each pulpwood consuming mill located within an 85 to 100-mile radius
of a timber sale increases expected PPW stumpage price by $0.04 per ton, by $0.09 per ton from
a 50 to 85-mile radius, by $0.25 per ton from a 40 to 50-mile radius, by $0.43 per ton from a 30
to 40-mile radius, by $0.51 per ton from a 20 to 30-mile radius, and by $0.83 per ton within a 20-
mile radius (see Figure 4.6(b)). During the second quarter of 2014, on average, there were 26
softwood pulpwood consuming mills located within 90 miles of a given sale. Based on the model
estimates, pulpwood mills increased PPW stumpage price by $2.17 per ton, or by roughly 23.7%,
holding all other variables constant.
(a) (b)
Figure 4.6: (a): Lumber Mill Location’s Affect on PST Stumpage Price (b): Pulpwood Mill Location’s Affect on PPW Stumpage Price.
100-150 miles: $0.02
85-100 miles: $0.08
40-85 miles: $0.10
25-40 miles: $0.24
15-25 miles: $0.33
< 15 miles: $0.51
Radius $/ton ↑ per Mill Radius $/ton ↑ per Mill
85-100 miles: $0.04
50-85 miles: $0.09
40-50 miles: $0.25
30-40 miles: $0.43
20-30 miles: $0.51
< 20 miles: $0.83
74
Although mill capacities were found to have less influence than mill location on expected
stumpage price for both pine sawtimber and pine pulpwood, we are also able to draw conclusions
regarding the degree to with mill capacity influences stumpage price for both of these products.
Our results indicate that for every 100,000 ton increase in cumulative lumber mill capacity,
expected PST stumpage price increases by $0.05 per ton within a 40 to 75-mile radius, by $0.06
per ton within a 15 to 40-mile radius, and by $0.16 per ton at radiuses less than 15 miles around a
timber sale (see Figure 4.7(a)). Based on the most current mill data and timber sales from the
first and second quarters of 2014, on average, cumulative lumber mill capacity within 75 miles
of a sale location was approximately 3.85 million tons, which translates to a roughly $2.13 per
ton increase, or a 7.8% increase in PST stumpage price, holding all other variables constant.
(a) (b)
Figure 4.7: (a): Lumber Mill Capacity’s Affect on PST Stumpage Price (b): Pulpwood Mill Capacity’s Affect on PPW Stumpage Price.
Pine pulpwood mill capacity was found to have a larger (positive) effect on PPW
stumpage prices. For every 100,000 ton increase in cumulative pulpwood mill capacity, expected
PPW stumpage price increases by $0.01 per ton within a 50 to 100-mile radius, by $0.06 per ton
Radius $/ton ↑ per 100M tons
75-150 miles: $0.00
40-75 miles: $0.05
15-40 miles: $0.06
< 15 miles: $0.16
Radius $/ton ↑ per 100M tons
50-100 miles: $0.01
40-50 miles: $0.06
20-40 miles: $0.11
< 20 miles: $0.17
75
within a 40 to 50-mile radius, by $0.11 per ton within a 20 to 40-mile radius, and by $0.17 per
ton at radiuses less than 20 miles around a timber sale (see Figure 4.7(b)). Based on the most
current mill data and timber sales from the first and second quarters of 2014, on average,
cumulative softwood pulpwood mill capacity within 100miles of a sale location was
approximately 4.84 million tons, which translates to a roughly $1.73 per ton increase, or an
18.7% increase in PPW stumpage price, holding all other variables constant.
Our analysis also revealed some interesting findings regarding physiographic regions’
influence on stumpage prices. Dummy variables for physiographic region were included in the
estimated models to help mitigate estimation bias; however, the values associated with those
coefficient estimates indicate that physiographic region significantly effects stumpage price. The
four primary physiographic regions found within the U.S. South are Coastal Plain, Piedmont,
Plateaus, and Valley/Ridge regions, and stumpage prices are significantly (negatively) reduced in
Plateau and Valley/Ridge regions. These regions are found in northern Arkansas, throughout
Tennessee, and in large portions of Virginia – all areas that have traditionally had weak pine
markets compared to other areas in the South. One likely explanation is that these areas have
much stronger hardwood timber markets and that the demand for softwood timber in these areas
is relatively low. Also, the physiographic makeup of these areas may be such that softwood
timber quality is inferior to the quality of timber that can be grown in the coastal plain and
piedmont regions.
The components associated with a timber sale were also found to influence stumpage
price for both pine sawtimber and pine pulpwood. For both PST and PPW stumpage, sale type
and harvest type affect prices similarly. Sealed bid auction sales significantly increase stumpage
price, by an average of 5% for PST and 11% for PPW, while thinnings were found to
76
significantly reduce expected stumpage price, by an average of 6% for both PST and 12% for
PPW. One major difference found between PST and PPW prices is the effect contract type has
on expected price. For PST stumpage, pay-as-cut timber contracts reduce expected price by
approximately 5%, while pay-as-cut timber contracts for PPW were found to increase expected
price by roughly 6%.
Lastly, we sought to create a metric by which timber sale locations across this region
could be compared on a relative basis. These location values were calculated for each specific
county within the U.S. South as a means of identifying specific areas where stumpage markets
are relatively more competitive in terms of price and where high levels of wood demand exist, in
the form of mill capacity and competition. We were able to identify highly competitive markets
for both PST and PPW stumpage that are characterized by high prices, mill saturation, and large
mill capacities. We found that a number of smaller, highly competitive, markets for PST exist in
this region, while one relatively expansive PPW market exists. Also, physiographic region was
not considered in the calculation of a county’s location value. However, the location values
support the results of the PST and PPW models that indicated physiographic region significantly
influence these markets.
The analysis was limited by the strength and size of both the timber sale and mill data.
Although a significant number of individual timber sales were included in the analysis,
conversion of the sales into panel data reduced the total number of observations. Also, there were
a number of cases where stumpage prices were not reported during every time period for a given
county, so the final dataset was further reduced to balance the panel data. Limitations also
existed with the mill location and capacity data. The mill data used for this analysis comes from
a biannual report, so issue might exist from converting the biannual mill data into quarterly data.
77
We included a categorical variable and multiple sale characteristic variables in the estimated
models in order to mitigate potential bias in the coefficient estimates, and although bias was not
found to exist in all models, it could not be rejected in all cases. There are undoubtedly other
variables not included in our models that help explain changes in stumpage price, so future
studies can expand upon our research by testing and incorporating more independent model
variables.
This research was aimed at identifying the degree to which mill location and capacity
influence stumpage prices for both pine sawtimber and pine pulpwood in the U.S. South. Our
analysis found both of these variables to significantly affect price, and we were ultimately able to
quantify both mill location and mill capacity’s influence on stumpage price. We also developed a
metric by which sawtimber and pulpwood markets across this region can be compared against
one another on a relative basis so to identify specific areas where market competition is strongest
and weakest. This research contributes to the literature by providing further insight into how
different components of a timber sale influence stumpage prices and also by quantifying the
degree to which mill location and capacity influence expected price.
78
CHAPTER 5
CONCLUSIONS
The goal of this research in its entirety was to evaluate timber markets in the U.S. South
so to increase our overall understanding of the forest industry in this region. The conclusions
drawn on all of the evaluated topics are based results founded on robust data. This timber market
was examined at a broad south-wide level, as well as at sub-regional and micro levels. Certain
aspects of this research confirmed previous findings published in the literature. However, other
aspects explored new areas and provided new findings regarding timber markets in this region.
The first analysis evaluated market integration of pine sawtimber stumpage markets in
the South (Chapter 2). Although previous research has tested spatial integration of timber
markets, these studies have primarily implemented more traditional and less flexible tests to test
for market integration. The proposed model used in this analysis allows for more flexibility in
evaluating market linkages by introducing an economic indicator – housing starts – that drives
the transitions in regional timber market linkages. Housing starts were selected as the transition
variables because new home construction is a key indicator that is closely tied to PST stumpage
price movements.
The results of this analysis indicate that regions experiencing strong growth in new home
construction can cause numerous regions and states to link together and function as one solitary
market. When this occurs, surrounding timber markets strengthen which then leads to improved
timber prices and increased trade amongst these multiple markets. We found that during the mid
79
2000s – at the peak of the housing bubble – the entire southeast region was linked, coinciding
with stumpage prices in all regions reaching historic highs.
Just the opposite effect occurs during recessionary periods, notably in the early 1980s and
late 2000s. During the most recent economic recession, new home construction in the
overwhelming majority of states fell to the lowest levels since the early 1980s, and, as a result,
stumpage prices for pine sawtimber fell to the lowest levels in nearly 20 years. During this
recessionary period essentially all regions became unlinked and exhibited no integrating
relationships. This study makes a contribution to the theoretical literature by introducing a form
of TV-STAR model in which the transitions are controlled by related economic indicator
variables. When an economic indicator is found to be closely tied to the price of a specific good,
it can provide an alternative method of examining market interactions based on changing
indicator values.
The second analysis evaluated the ways timber sales are conducted and characterized
across the U.S. South to determine which sale characteristics significantly affect expected
stumpage price (Chapter 3). This study examined monthly PST stumpage prices and found a
strong seasonal component to exist and influence price. The results also revealed three primary
variables to significantly influence expected PST stumpage price: sale size (acres), sale type
(negotiated vs. sealed bid), and hardwood prices.
Most importantly, this research found a strong and significant relationship to exist
between PST stumpage prices and home mortgage rates. Since 2000, when mortgage rates were
above 6%, PST stumpage prices were relatively high ($35-$55 per ton), and when mortgage rates
were below 6%, PST stumpage prices were relatively low ($20-$35 per ton). This occurrence
was found to be directly related to the housing market crash and subsequent reduction in home
80
mortgage rates. The intervention variable that was introduced into the model allowed us to
quantify the effect of the housing market crash on monthly PST prices. The significance of the
coefficient estimates of the intervention variable leads us to believe that PST stumpage prices
have now settled at a new level and that prices are unlikely to return to pre-recessionary levels in
the immediate future.
The third and final analysis encompassed in this study evaluated PST and PPW stumpage
prices and markets at a micro level to assess the degree to which a mill’s location and annual
capacity influence prices (Chapter 4). The results of the study indicate that mill proximity and
mill capacity significantly (positively) affect stumpage prices, and that the closer in proximity a
mill is located from a timber sale, the greater (positive) affect it has on price.
As for the degree to which mill locations effect stumpage price, the results indicate that
each lumber mill located within a 100-mile radius of a timber sale increases expected PST
stumpage price by $0.07 per ton, and for every 10 miles closer in proximity a lumber mill is to
the sale location, price increases by an additional $0.03 per ton. Pine pulpwood consuming mills
were found to have an even larger (positive) effect on PPW stumpage prices. Each pulpwood
consuming mill located within a 100-mile radius of a timber sale increases expected PPW
stumpage price by $0.11 per ton, and every 10 miles closer in proximity a pulpwood mill is to
the sale location, price increases by an additional $0.09 per ton.
Although mill capacities were found to have less influence than mill location on expected
stumpage price for both pine sawtimber and pine pulpwood, we are also able to draw conclusions
regarding the degree to with mill capacity influences stumpage price for both of these products.
Our results indicate that for every 100,000 ton increase in cumulative lumber mill capacity,
expected PST stumpage price increases by $0.01 per ton within a 75 to 100-mile radius, $0.03
81
per ton within a 55 to 75-mile radius, $0.06 per ton within a 40 to 55-mile radius, and $0.09 per
ton at radiuses less than 40 miles around a timber sale. Pine pulpwood mill capacity was also
found to have a larger (positive) effect on PPW stumpage prices. For every 100,000 ton increase
in cumulative pulpwood mill capacity, expected PPW stumpage price increases by $0.03 per ton
within an 80 to 100-mile radius, $0.05 per ton within a 60 to 80-mile radius, $0.09 per ton within
a 40 to 60-mile radius, and $0.15 per ton at radiuses less than 40 miles around a timber sale.
Lastly, since the number of mills located within a given radius around a sale location and
their cumulative capacity were found to positively influence stumpage prices, a metric was
developed using these observed values by which individual counties across the region can be
compared against one another and ranked according to each county’s locational strength and
relevance.
One of the potential issues related to the first study, examining PST market linkages in
the U.S. South (Chapter 2), is the choice of model transition variable and its application. For this
analysis, housing start statistics were selected as the two variables that drive transitions between
markets being linked and unlinked. This economic indicator was selected because PST stumpage
price movements are highly correlated with housing starts. This study did consider two
additional transition variables and they were both found to be inferior to housing starts; however,
there are other possible transition variable candidates that may provide improved results, and
future studies may seek to identify alternative variables that more accurately drive market
transitions. Also, although each state was broken down into two regions, typically a north and
south region, housing starts for the entire state served as the transition variable for both regions
when represented in a market pair. Future studies may look to break down housing starts further
82
by state and region so that housing starts occurring specifically in each market, not the entire
state of each market, drive market linkages between those two regions.
Some issues arose with the analysis of PST stumpage prices and sale characteristics
(Chapter 3) and include limited data points and series that contain periods of high volatility. For
this study, we evaluated a variety of sale characteristics as they relate to different timber
products, some of which had very few observations. Related to the issue of data availability,
some of the data series evaluated contained high volatility, often times a direct result of values
derived from a small sample. To account for high volatility in some of these data series, future
studies could incorporate models that account for heteroscedasticity, such as ARCH/GARCH
models.
The third analysis, estimating the effect mill locations and capacity have on pine
stumpage prices (Chapter 4), was also limited by the strength of the data, especially after the
sales data was converted into panel data. The process of converting the individual sales into
panel data consisted of taking the average stumpage price of all sales that occurred within each
specific county during each time period. By converting the data into this format, the number of
observations was greatly reduced and price variations were reduced by the aggregation process.
When multiple sales are converted into a single average price, that stumpage price may not
accurately represent market conditions in that county during that specific time, especially when
the multiple reported stumpage prices varied significantly. If one of the reported stumpage prices
was low (high), while the others were high (low), that may have caused that market to appear
weaker (stronger) than it actually was, since that low (high) price reduced (increased) the
average price used to represent that county. This issue may be related to timber quality, which
was not specifically taken into account in this study. Since quality is an important aspect that is
83
known to directly influence the price buyers are willing to pay for timber, future studies could
breakdown the single panel data values into multiple values based on timber quality (i.e., below
average, average, and above average). This would not only increase the number of data points
included in the analysis, but could also possibly yield results regarding timber value’s influence
on stumpage prices.
This specific study was also limited by the available mill data. The mill database used to
perform this analysis does not include all small capacity mills (less than 10,000 tons per year),
which may have affect our results. Further studies may look to improve the accuracy and
completeness of the mill database, which would provide more accurate model estimates of the
effect mill locations and capacities have on stumpage prices. The Wood Demand Report mill
database also provides information on hardwood mills, so future analyses could also evaluate the
degree to which hardwood mills influence hardwood stumpage prices.
In conclusion, three separate but related topics were evaluated to examine U.S. South
timber markets and prices using a variety of statistical and econometric techniques and models.
Although each different study had its own set of issues and limitation, they have helped surface
new ideas that will lead to future research, and ultimately an improved understanding of timber
markets and price movements. This market was analyzed at both a broad and micro level, and
this comprehensive analysis adds to the literature by improving overall understanding of how
timber markets interact within this region and how different factors impact timber prices.
84
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Appendix A: STAR Model Results with Alternative Transition Variables.
Transition Variable = Lagged Dependent Variable Transition Variable = Personal Income Model Coefficient Estimates & Standard Errors Model Coefficient Estimates & Standard Errors Price Pair ψ1 ψ2 Γ θ γ R2 Price Pair ψ1 ψ2 Γ θ γ R2 AL1/AL2 -0.370 -0.155 -0.035 -0.241 50.000 0.275 AL1/AL2 -0.339 -0.129 -0.051 -0.552 0.370 0.286
Appendix C: Mill Location Model Estimates (Pine Sawtimber).
Radius Around Sale
Mill Physio2 Physio3 Physio4 Sale Type Contract Type Harvest Type Total Vol (1,000 tons) PST Vol (100 tons) Sale Size (10 acres) Intercept OVB-test Het-test Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Prob>F Prob>chi2
Appendix D: Mill Capacity Model Estimates (Pine Sawtimber).
Radius Around Sale
Capacity (100 M tons) Physio2 Physio3 Physio4 Sale Type Contract Type Harvest Type Total Vol (1,000 tons) PST Vol (100 tons) Sale Size (10 acres) Intercept OVB-test Het-test Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Prob>F Prob>chi2
Appendix E: Mill Location Model Estimates (Pine Pulpwood).
Radius Around Sale
Mill Physio2 Physio3 Physio4 Sale Type Contract Type Harvest Type Total Vol (1,000 tons) PPW Vol (100 tons) Sale Size (10 acres) Intercept OVB-test Het-test Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Prob>F Prob>chi2
Appendix F: Mill Capacity Model Estimates (Pine Pulpwood).
Radius Around Sale
Mill Physio2 Physio3 Physio4 Sale Type Contract Type Harvest Type Total Vol (1,000 tons) PPW Vol (100 tons) Sale Size (10 acres) Intercept OVB-test Het-test Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Coef. t Prob>F Prob>chi2
