le - timber restrictions, financial crisis and price transmission in north american lumber markets

8/20/2019 LE - Timber Restrictions, Financial Crisis and Price Transmission in North American Lumber Markets

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Changyou Sun, Zhuo Ning

Land Economics, Volume 90, Number 2, May 2014, pp. 306-323 (Article)

DOI: 10.1353/lde.2014.0013

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Timber Restrictions, Financial Crisis, and PriceTransmission in North American Softwood

Lumber MarketsChangyou Sun and Zhuo Ning

ABSTRACT. Competition among the South, the West,and Canada as major softwood lumber productionregions has been affected by timber resource endow-ments, public land policies, and the general economy.To assess spatial price linkages, a threshold vector error correction model is applied on softwood lumber

prices from 1978 to 2011. Price transmission is found to be nonlinear and asymmetric. The South is moreadaptive to price disequilibrium. Short-term price ad-

justments are more sophisticated over the period of 1991 to 1993 related to the federal timber restrictionsthan over the period of 2008 to 2009 related to theglobal financial crisis. (JEL C32, Q23)

I. INTRODUCTION

Softwood lumber in North America is pro-duced mainly in three regions: the southernUnited States (South), the western UnitedStates (West), and Canada.1 Price transmis-

1 The United States of America can be divided into sev-eral regions. Three references with slightly different classi-fications are cited in this study. For forest inventory assess-ment, Smith et al. (2009) divided the 50 states into severalregions and subregions: the North (North Central, North-east), South (South Central, Southeast), Rocky Mountain(Great Plains, Intermountain), and Pacific Coast (PacificNorthwest, Pacific Southwest). For annual statistics of forestproducts (e.g., lumber), Howard (2007) used three regions:the North, South, and West, where the West mostly corre-sponds to the Pacific Coast of Smith et al. (2009). Formonthly prices of forest products, Random Lengths (2012)reported data mainly by species. These species generallycorrespond to a particular region, but with a less clearlydefined geographical boundary than these for forest inven-tory assessment (e.g., southern yellow pine is producedmainly in the southern United States). In this study, lumberprices by species are used in the analyses, and the UnitedStates is divided into three lumber production regions (i.e.,the North, South, and West), following the classification inHoward (2007).

Land Economics • May 2014 • 90 (2): 306–323

ISSN 0023-7639; E-ISSN 1543-8325 2014 by the Board of Regents of theUniversity of Wisconsin System

sion of softwood lumber products amongthese supplying regions or subregions hasbeen an important issue for at least two rea-sons. First, the softwood lumber industry is amajor sector of the forest products industrywhose value of shipments was 6.1% of total

manufacturing outputs in 2010 (U.S. CensusBureau 2012). The value of annual softwoodlumber consumption in the United Statesalone has reached about $20 billion in recentyears (Howard 2007; Random Lengths 2012).More than 70% of softwood lumber productsare linked to residential construction throughvarious end uses (Shook, Plesha, and Nalle2009). Second, unlike many market goods(e.g., computers or toys), softwood lumberproducts have been greatly affected by publicpolicies for land use and natural resources. In

particular, protection of the spotted owl in theWest since the 1990s has resulted in severetimber harvesting restrictions on public land.At the same time, the South and Canada haveproduced an increasing amount of softwoodlumber to meet market demand. Thus, spatialprice transmission of softwood lumber prod-ucts has received widespread attention overtime because of the economic status of theindustry and the close relation between re-source policies and lumber products.

A number of studies have investigated the

market integration and price linkage of soft-wood lumber among the major supplyingregions in North America.2 For instance,

2 A number of studies have used linear cointegrationmodels to analyze market integration of forest products inother countries (e.g., Hänninen, Toppinen, and Toivonen2007; Nyrud 2002). However, to our knowledge, no spatialintegration study on lumber markets out of North Americahas been published.

The authors are, respectively, associate professor andresearch assistant, Department of Forestry, Missis-sippi State University, Mississippi State.


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90(2) Sun and Ning: Timber Restrictions and Softwood Markets 307

Murray and Wear (1998) applied the Engle-Granger cointegration test on monthly pricesfrom 1983 to 1993 to investigate the impactof federal timber restrictions on the integra-

tion of softwood lumber markets in the Westand South. A structural break was found inthe relationship, and the restrictions led tomore integrated markets. Other similar studieshave been conducted with different coverageof period and species (Nanang 2000; Shook,Plesha, and Nalle 2009; Yin and Baek 2005).Each of these studies used linear time serieseconometric models, including linear cointe-gration analyses and vector error correctionmodels. However, among the competing re-

gions of softwood lumber production, the ac-tual price dynamics may be nonlinear andasymmetric, as explicitly but only briefly dis-cussed in the literature (Murray and Wear1998; Spelter 2006). Therefore, there has beena need to investigate the integration of re-gional softwood lumber markets with appro-priate nonlinear time series econometrics.

In recent years, nonlinear time series mod-els have been rapidly developed and exten-sively applied for price analyses. Particularly,

asymmetric price transmission has emerged asa main research issue because price transmis-sion may differ according to whether pricesare increasing or decreasing (Meyer and vonCramon-Taubadel 2004). Asymmetric pricetransmission can be positive or negative andcan occur along a vertical value chain or be-tween spatially separated markets. Positiveasymmetric price transmission between twoprices arises when price movements thatsqueeze their margin are transmitted morerapidly or completely than the equivalentmovements that stretch the margin. Con-versely, the transmission is negative whenprice movements that stretch the margin aretransmitted more rapidly or completely thanmovements that squeeze it. Furthermore, anumber of econometric models have been de-veloped to assess the nature and magnitude of price transmission (Frey and Manera 2007).These include the specification of split priceterms (Kinnucan and Forker 1987), thresholdcointegration (Enders and Granger 1998), andthreshold vector error correction models(Goodwin and Piggott 2001).

The objective of this study is to assess thespatial price linkage among three regionalsoftwood lumber markets in the South, theWest, and Canada through a threshold vector

error correction model and generalized im-pulse response function. Monthly softwoodlumber prices between 1978 and 2011 for studgrade are defined by region and used in theanalyses. This study makes several contribu-tions to the literature of softwood lumber mar-kets and relevant natural resource policies. Toour best knowledge, nonlinear threshold mod-els have not been utilized to analyze softwoodlumber price linkages before. The analyses inthe present study provide new insights into thenonlinear relation among the three major soft-wood lumber production regions. Further-more, a nonlinear impulse response functionis used to analyze the impact of two selectedhistories on price adjustment among the re-gions. The first history is related to the pro-tection of the northern spotted owl, as man-dated by the Endangered Species Act and thesharp decline of timber supply between 1991and 1993. The second history is related to theglobal financial crisis and the resultant largereduction of softwood lumber demand be-

tween 2008 and 2009. The results from thisstudy can help us understand the competitionamong the major lumber supplying regionswhen public policies for natural resourceschange or the general economy fluctuates.

II. SOFTWOOD LUMBER MARKET INNORTH AMERICA

Regional Production Patterns andContributing Factors

The geographic supply sources of the soft-wood lumber market in North America can bedivided into several regions: the South, theWest, the North, and Canada (Howard 2007).In the United States, the South and the Westhave been the two major softwood lumberproduction regions, and the production in theNorth is generally less than 5%. Canadian im-ports have been a major source of supply tothe U.S. market. The West was the dominant

producing region before 1985. However, inrecent decades, the production in the West hasdropped to a level similar to the southern pro-


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May 2014 Land Economics308

FIGURE 1

Annual Quantity of Softwood Lumber Production in the South, West, and North in the United States, andImports from Canada between 1965 and 2010

duction and Canadian import. As a result,softwood from each of the three major sup-plying regions, namely, the South, the West,and Canada, has accounted for about one-third of the U.S. market shares since 1993

(Figure 1).More specifically, the West supplied an av-

erage of 58% of the softwood lumber con-sumed in the United States between 1965 and1975 (Howard 2007; recent unpublished datacollected from Howard through personal com-munication). The share from the Westdropped after 1975, recovered to 47% in1989, and then dropped gradually and con-verged with that from the South and Canadaat the 33% level. This trend has been attrib-

uted to several factors. The most cited factoris the timber harvesting restrictions on federallands in the West (Murray and Wear 1998).The restrictions were driven by efforts sincethe late 1980s to protect the habitat of thenorthern spotted owl on federal lands, as man-dated by the Endangered Species Act. Thenorthern spotted owl was proposed as an en-dangered species in June 1989, and timberharvesting restrictions have been formally im-plemented since 1993. In addition, federal

legislation, such as the National Forest Man-agement Act of 1976, requires that forest out-puts other than timber be given due consid-

eration in the management of national forests(Wear and Murray 2004). In aggregate, allthese factors are related to the distinctive for-estland ownership in the West: 66% of for-estlands in the West are owned by the public,

22% by industrial firms, and 11% by nonin-dustrial private landowners (Smith et al.2009). Therefore, public policies have af-fected softwood lumber production in the re-gion considerably. Private ownership of for-ests is relatively small in the West, but it hascontributed more to timber production in re-cent years. At present, the West as a wholestill plays a large role in the national market.

The South has been gaining softwood mar-ket share steadily, from 21% between 1965

and 1975 to more than 31% since 1993. Thisregion is unique in that the land ownershippattern is dominated by private owners: about70% by millions of small nonindustrial pri-vate landowners, 20% by industrial or insti-tutional landowners, and 10% by the public(Smith et al. 2009). In the South, harvests aremore frequent and increasingly derived fromagricultural forestry, with forests growing onshorter rotations. As a result, the harvestingdecisions are distributed among many small

landowners, timber supply is more sensitiveto market information, and the overall pro-duction is less likely to be affected by dra-


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matic changes in environmental and forestpolicies. As pine plantations have steadily es-tablished in the South, this region can be ex-pected to maintain its status as an active and

stable supplier in the national market.Canada has a strong comparative advan-tage in the production of softwood lumber(Wear and Murray 2004). It is rich in forestresources, has a small population relative tothe size of its timber resource, and is geo-graphically close to the large U.S. softwoodlumber market. Thus, Canada is naturally po-sitioned as an exporter of forest products, with80% of its lumber products exported to theUnited States. As shown in Figure 1, Canadahas been gaining market share in the UnitedStates, from 18% (1965–1975) to 33% (1993–2010). However, there has been a long, bitterhistory between the two countries about thesoftwood lumber trade (Zhang 2007). Thecentral issue of the trade dispute has beenwhether Canadian lumber is subsidizedthrough provincial stumpage systems, and if it is, whether the lumber industry in theUnited States is injured. The dispute startedin October 1982 when a group of lumber pro-ducers in the United States filed a petition to

the Department of Commerce. Since then,there have been numerous negotiations, law-suits, and actions. Major periodic outputsfrom the dispute include the 1986 Memoran-dum of Understanding, and the 1996 and 2006Softwood Lumber Agreements.

A common factor that can impact all timberproduction regions is the status of the generaleconomy. As softwood lumber consumptionis closely related to the housing market, eco-nomic declines can, ultimately, influence the

demand for softwood lumber products (Zhang2007). For example, the economic recessionand change in macroeconomic policy in theearly 1980s resulted in a decline in softwoodconsumption. The more recent global finan-cial crisis in 2008 also created a lasting neg-ative impact on the softwood lumber market.

Analyses of Spatial Price Linkages

Numerous studies have analyzed various

issues related to the softwood lumber marketin the United States, Canada, or both. An issuethat has attracted plentiful efforts is the price

linkage in these markets. In an early study, Uriand Boyd (1990) used a causality test and an-nual softwood lumber prices between 1950and 1985 to determine the market integration

in four regions of the United States. The re-sults confirmed that there was a national mar-ket for softwood lumber. Applying the Johan-sen cointegration test on the same dataset,Jung and Doroodian (1994) supported the hy-pothesis of the “law of one price.” More re-cently, Yin and Baek (2005) conducted an ex-tensive investigation to assess the marketintegration in the United States with the Jo-hansen cointegration test and 36 monthly soft-wood lumber prices between 1991 and 1999.Their conclusion was that the law of one priceheld for the entire softwood lumber market inthe United States.

Furthermore, Shahi, Kant, and Yang (2006)used monthly data between 1996 and 2004 toassess market integration in 10 regional NorthAmerican markets. The regional markets of homogeneous softwood products in theUnited States and Canada were found to becointegrated. Shook, Plesha, and Nalle (2009)used the Engle-Granger cointegration analysisto examine the correlation among 11 soft-

wood lumber products (either stud or panel)in North America. With monthly data from1995 to 2001, long-term cointegration existedamong the different regions, but no clear evi-dence was found to support perfect substitut-ability. Finally, Shahi and Kant (2009) usederror correction models and generalized im-pulse response functions to assess price dy-namics by species in the North American soft-wood lumber market. With monthly data from1994 to 2004, the long-run price equilibrium

and degree of market integration were foundto be different by species.In total, this cohort of studies possesses

several common features, which can becomethe basis for further studies. Most studies usedmonthly data for approximately 10 years toaddress a specific objective. The major meth-ods employed were the linear Engle-Grangeror Johansen cointegration test. Possible non-linear or asymmetric relation was briefly dis-cussed by Murray and Wear (1998) and Spel-

ter (2006), but no rigorous analyses wereoffered. All of these motivate us to constructa longer softwood price series and conduct a


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dedicated examination of spatial price lumberlinkages, with special attention to the periodswhen timber supply or lumber demandchanges dramatically. A set of nonlinear time

series techniques is adopted in the analyses,as detailed next.

III. METHODOLOGY

Threshold vector error correction modelsand the related techniques are employed to in-vestigate the softwood lumber price dynamicsin North America. This model has an intuitiveeconomic explanation of spatial price relation,as transaction costs can affect the trade be-tween regions (Goodwin and Piggott 2001). Itis usually applied to a pair of prices becauseestimation and inference methods have beenbetter developed for bivariate cases than forthree variables or more. In this study, monthlytime series data are collected to represent lum-ber prices in the South, the West, and Canada,and then three price pairs among these regionsare formed. Major steps are to analyze timeseries properties of data, evaluate the long-term cointegration relation, estimate the linearand threshold error correction models, select

the best model through nonlinearity tests, andfinally, assess the short-term dynamicsthrough impulse response analyses at severalcritical histories.

Linear and Threshold Vector ErrorCorrection Model

Consider a standard linear cointegrationrelationship between a vector of pricesWt = ( yt , x t )′ as

y = α + α x + ξ , [1]t 0 1 t t

where α 0 and α 1 are parameters, and ξ t rep-resents the residual of the equilibrium rela-tion. Cointegration between the two pricesrequires the residual to be stationary, whichcan be evaluated by applying the augmentedDickey-Fuller (ADF) test on the residual withspecial critical values (Engle and Granger1987). Given that the cointegration relation

exists, the Granger representation theoremstates that a linear vector error correctionmodel can be developed as

p

∆W = β +ϕ ξ + λ ∆W + u , [2]t t −1 i t − i t i = 1

where , , and are parameters; isβ ϕ λ ξ i t −1

the lagged residual from the cointegration re-lation (also referred to as the error correctionterm); p is the number of lags; and is theut disturbance term.

The above linear analysis can be extendedto the case where the residual of the long-termequilibrium relation follows a threshold au-toregression (Balke and Fomby 1997). Athree-regime vector error correction represen-tation of the threshold model can be specifiedas

p1 1 1 1β +ϕ ξ + λ ∆W + u ,t −1 i t −1 t

i = 1

if −∞


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threshold model with one threshold value γ only, can be similarly defined.

If the threshold values are known, equation[4] can be estimated easily. However, the

threshold values are usually unknown andmust be estimated along with other parame-ters. In practice, the model is estimated withsequential iterated regressions in severalsteps. First, determine the possible range of threshold values. For the threshold values( and ) to be meaningful and create re-γ γ 1 2gimes, they must be one of the values of thethreshold variable (Enders 2010). In ad-ξ t −k dition, to estimate the parameters, each re-gime needs to have a minimum number of ob-

servations. In this study, the first threshold inthe three-regime model is searched between2.5% and 95% of the largest absolute valuesof the negative lagged error correction term.The second threshold is searched between2.5% and 95% of the largest positive laggederror correction term. Next, for each pair of threshold values, estimate the threshold modeland save the covariance matrix ( ) of the re- Σ̂siduals. Finally, select the pair of thresholdvalues that minimizes the log determinants of

, that is, ( = arg min(ln . ˆ ˆˆ ̂ ˆ ˆ Σ γ , γ ) Σ(γ ,γ ))1 2 1 2With the selected threshold values, estimate

the model again and generate the final param-eter estimates.

Tests for Nonlinearity and Model Selection

Once linear and threshold vector error cor-rection models are estimated, tests are neededto evaluate whether the dynamic behavior andadjustment toward the long-run equilibriumrelationship is linear or exhibits threshold

nonlinearity. Lo and Zivot (2001) extendedthe method adopted by Hansen (1999) fortesting linearity in univariate threshold auto-regressive models to multivariate thresholdmodels. They proposed a set of sup-likelihoodratio (LR) tests as follows:

ˆ ˆ ˆ LR = T (lnΣ − lnΣ (γ )),1,2 1 2 ˆ ˆ ˆ ˆ LR = T (lnΣ − lnΣ (γ ,γ )),1,3 1 3 1 2 ˆ ˆˆ ˆ ˆ LR = T (lnΣ (γ )− lnΣ (γ ,γ )), [5]2,3 2 3 1 2

where (k = 1, 2, 3) are the estimated resid- Σ̂k ual covariance matrices of the linear, two-re-

gime, and three-regime vector error correctionmodels, respectively. The first two tests eval-uate the null hypothesis of a linear modelagainst the alternative hypothesis of either a

two-regime or three-regime model. If thepresence of the threshold effect is confirmed,the third test is to select a better-fitted modelbetween the two- and three-regime models forthe data.

The above statistics suffer from the prob-lem of unidentified nuisance parameters underthe null hypothesis (Hansen 1999; Hansen andSeo 2002). Thus, the algorithm of parametricresidual bootstrap is adopted to compute the p-value for these statistics. A random sample

of is first generated by sampling with re-∗

ut placement from the residuals of the linear er-ror correction model. Then, using the fixedinitial conditions (Wt , t = 1,. .. ,1+ p) and theparameters from the linear error correctionmodel recursively generates a simulated sam-ple . Apply the methods described for the∗Wt original data on the simulated sample to cal-culate the test statistics. After repeating theprocedure 500 times, the bootstrap p-value foreach test statistic is the percentage of simu-

lated statistics that exceed the statistic fromthe original data.

Generalized Impulse Response Analysis

The generalized impulse response functionfrom Potter (1995) and Koop, Pesaran, andPotter (1996) is used to compute the impulseresponse function for the nonlinear thresholdmodel. Mathematically, the response I for aspecific shock and history can be ex-δ Ωt −1

pressed as

I (h,δ ,Ω ) =t −1

E [W (u = δ ,u = u , . . . ,u = u ,Ω )]−t + h t t +1 t +1 t + H t + H t −1

E [W (u = u ,u = u , . . . ,u = u ,Ω )], [6]t + h t t t +1 t +1 t + H t + H t −1

where h = 1, . . . , and H is the forecasting timehorizon. As both shocks and histories are re-alizations of random variables, the responsesare also realizations of random variables as

I (h,δ ,Ω ) =t −1

E [W (δ ,Ω )]− E [W (Ω )]. [7]t + h t −1 t + h t −1


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In this study, the responses of each price ina pair are evaluated for a horizon of two years(i.e., H = 24). Both positive and negativeshocks are included, and their magnitudes are

two times the standard error of the residualsof the source price from the threshold model.Furthermore, hypothetical shocks are initiatedover two particular histories. The northernspotted owl was listed as an endangered spe-cies in the early 1990s, resulting in a hike of softwood lumber price at that time. Thus, re-lated to the Endangered Species Act and fed-eral timber restrictions, the period betweenJanuary 1991 and December 1993 is selectedas the first history. In addition, the global fi-

nancial crisis in 2008 also caused a low de-mand of softwood lumber and a falling price.The period between October 2008 and De-cember 2009 is selected as the second history.

The specific estimation steps are as fol-lows. For each time point in a history, collectWt (t = i−1− p, . . . ,i−1) from the series ashistory , where i is the location of theΩt −1time point in the price series. For a given ho-rizon, randomly sample a matrix from the es-timated residuals with the dimension of

( H + 1)×

2. Use one exogenous positive shock (two times the standard error of the residual),the first H random shocks, the history ,Ωt −1and the parameters from the fitted vector errorcorrection model to recursively calculate therealizations of the prices. Repeat the abovecalculation with ( H +1) random shocks only.Calculate the difference from the previous twocalibrations. Repeat the procedure 1,000 timesfor each selected time point in a history, andtake the average differences to form the esti-

mates of impulse responses over the ( H + 1)horizon. When the history contains more thanone time point, averages are taken over all theestimates. Whether an average estimate is sig-nificantly different from zero can be evaluatedby calculating the 90% confidence intervalfrom the 1,000 simulations, and then examineif the interval includes zero or not. If zero isnot within the confidence interval, then the av-erage estimate is significantly different fromzero. The whole process can be repeated by

history, different shock sign, and differentshock size, and the resulting responses can beplotted.

IV. DATA AND PRELIMINARYANALYSES

Monthly lumber prices for various forest

products by dimension, species, and regionhave been reported by Random Lengths(2012). In this study, the price of kiln-driedlumber with stud grade and dimensions of 2inches by 4 inches by 8 feet (precision endtrimmed) is selected because it is a typicallumber product in North America. Three spe-cies are involved: southern yellow pine for theSouth, Douglas-fir for the West, and spruce-pine-fir for Canada. In the South and Canada,several time series have been reported fortheir subregions, and the one with consistentreporting over time is selected. This results inthe selection of the Westside price series forthe South, the Coast price series for the West,and the Eastern/Great Lakes price series forCanada (Random Lengths 2012). The substi-tutability among forest products made fromdifferent species and regions has been inves-tigated in a number of studies (e.g., Nagubadiet al. 2004). Given the similar dimensions of forest products and the leading role of thesespecies in the corresponding regions, the se-

lected prices are deemed appropriate for thestudy purpose. This is also consistent with thedata treatment in previous lumber price stud-ies (e.g., Shook, Plesha, and Nalle 2009). Thebeginning period is January 1978, which is theearliest date for which consistent data can becollected across the regions. The end date of December 2011 reflects the data availabilitywhen the study was conducted. In total, thethree lumber price series cover the period be-tween January 1978 and December 2011, with

408 monthly observations. The unit is dollarsper thousand board feet.The price series are deflated by the pro-

ducer price index of all commodities, pub-lished by the U.S. Bureau of Labor Statistics(index value of 100 at 1982). All the series arealso expressed in natural logarithms. The log-arithmic transformation mitigates fluctuationsof individual series and allows us to interpretthe results by percentage change. As the dataare monthly, seasonality is investigated by im-

plementing seasonal unit root tests, followingthe procedure of Hylleberg et al. (1990). Re-sults from the seasonal unit root tests reveal


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FIGURE 2

Monthly Nominal and Logarithmic Real Lumber Prices in the South, the West, and Canada between January1978 and December 2011

that only the null of the unit root at the regularfrequency cannot be rejected, and a seasonalcomponent is not significant. Alternatively,the systematic component of seasonality iscaptured by a second-order Fourier approxi-mation (Ben-Kaabia and Gil 2007), whichturns out to be small relative to the overallmagnitude of the series. Removing this sys-tematic component from the series does not

qualitatively change the results. Therefore, thefinal price series used in the nonlinear modelare real lumber prices in logarithm withoutfurther adjustment. A comparison of the nom-inal and transformed prices among the threeregions is demonstrated in Figure 2.

V. EMPRICAL RESULTS

Basic Statistics and Cointegration Results

The nominal price in the South has the low-est mean at $258.086 per thousand board feet,followed by the West at 271.887, and Canada

at 306.936 (Table 1). The West has the largeststandard error at 84.333, which is related tothe relatively large price surges in the early1990s and drops since 2008. The South-Westpair has the lowest linear correlation at 0.900,followed by the Canada-South pair at 0.933,and the Canada-West pair at 0.946. The logreal prices display similar trends as the nom-inal prices. Furthermore, two graphs for each

pair are created to further reveal the price re-lationship (Figure 33). Nominal prices are util-ized in drawing the graphs to have a moreintuitive explanation. The first one is the rela-tive margin, which is defined as mt = ( yt − x t )/ x t ×100% for the price pair Wt = ( yt , x t )′(t = 1,. . . ,408). The average of all relative

3 For each price pair , the relative margin isW = ( y , x )′t t t defined as . For the four asymmetricm = ( y − x )/ x ×100%t t t t response values, 1 refers to the average price change in y

when , 2 refers to the average price change in x ∆m >0t when , and 3 and 4 are similarly defined for the∆m >0t subsamples when .∆m ≤ 0t


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TABLE 1

Basic Statistics and Properties of Softwood Lumber Prices

Nominal Price Log Real Price

Item South West Canada South West Canada

BasicMean 258.086 271.887 306.936 5.308 5.349 5.491Std. error 70.998 84.833 72.961 0.269 0.314 0.240Minimum 155 137 175 4.681 4.450 4.833Maximum 429 520 542 5.863 6.071 6.125Observations 408 408 408 408 408 408

CorrelationSouth 1.000 0.900 0.933 1.000 0.902 0.932West 0.900 1.000 0.946 0.902 1.000 0.946

ADF test statisticLevel — — — −2.007 −1.681 −2.264Difference — — — −11.878*** −11.291*** −11.607***

Note: The unit of the price is dollars per thousand board feet. The augmented Dickey-Fuller (ADF) test examines the null hypothesis of nonstationarity. The lag lengths selected are six.

*** Significance of the estimates at the 1% level.

FIGURE 3

Margin Changes in Percentage and Asymmetric Responses of Nominal Lumber Prices by Pair

margins is 5.2% for West-South, 16.0% for

Canada-West, and 20.7% for Canada-South,and the corresponding standard error is14.5%, 13.6%, and 11.8%. Thus, the relative

margin for the West-South pair has the small-

est mean and the largest volatility.The second graph is created to show thedegree of asymmetric price response. The


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TABLE 2

Estimates of Cointegration Vectors and Results of the Engle-Granger Cointegration Test

West-South Canada-West Canada-South

Item Coefficients t -Ratio Coefficients t -Ratio Coefficients t -Ratio

Constant −0.242* −1.821 1.627*** 24.637 1.079*** 12.671 x 1.053*** 42.156 0.722*** 58.594 0.831*** 51.886 R2 0.814 — 0.894 — 0.869 —ADF test 5.805*** — −5.675*** — −6.335*** —

Note: The lag length selected for the augmented Dickey-Fuller (ADF) test is six. x is the second variable in each pair (e.g., the southern pricein the pair of West-South).

*, *** Significance of the estimates at the 10% and 1% levels, respectively.

whole sample is divided into two groups, de-pending on whether the relative margin in one

period over that in the previous period is in-creasing (∆mt >0) or decreasing (∆mt ≤ 0).Then, within each group, the monthly averagepercentage changes in prices are calculated,

for example, for the first price in

T 1

( ∆ y )/ T t 1i = 1

a group with T 1 observations. This results ina vector of four numbers for each pair (i.e.,two average price changes by two groups),and they are shown as bar charts in Figure 3.For example, the four values in the West-

South pair are −1.68%, 4.39%, 2.02%, and−3.27%; the first two are the changes inprices when the margin increases, and the lasttwo are the changes in prices when the margindecreases. Two observations can be drawn incomparing these values. First, positivechanges in each price are slightly larger thanthe negative changes in magnitude (i.e.,4.39>3.27 and 2.02>1.68). This is an indi-cation of asymmetric response of these pricesto the disequilibrium in the margin. Second,

changes in the relative margin are primarilydue to the changes in the second variable (i.e.,4.39>1.68 and 3.27>2.02). Thus, the firstprice is stickier than the second price. By pair,the South is more active than the West andCanada, and the West is more active than Can-ada. This observation motivates us to followthis order in normalizing on the first variablewhen later evaluating the cointegration rela-tion.

The nonstationarity property of the price

series is assessed by the ADF test. The teststatistics are not significant for the individualprice series but are significant for the first-dif-

ferenced price series. Thus, all the price seriesare nonstationary with an integration order of

one. Furthermore, the long-term relation is es-timated through the Engle-Granger two-stepcointegration test (Table 2). All the coeffi-cients are highly significant at the 1% level orbetter, with the exception that the intercept forthe West-South pair is significant at the 10%level only. The coefficient for the price vari-able on the right side is 1.053 for the West-South pair, 0.722 for the Canada-West pair,and 0.831 for the Canada-South pair. This in-dicates that the first pair for domestic prices

may have a different dynamic relation than theother two pairs with Canadian prices in-volved. Finally, the ADF test on the residualfrom the long-run relation reveals that the re-sidual is stationary and each pair is cointe-grated.

Results of Nonlinearity Tests and ModelSelection

Three types of models are estimated for

each price pair: linear, two-regime, and three-regime vector error correction models (Table3). Based on the Akaike information criterion,the lag used is three for the West-South andCanada-West pairs, and one for the Canada-South pair. For the sup-likelihood ratio test of linear versus two-regime or three-regimemodels, the statistic is significant at the 5%level or better for each pair; the exception isthe insignificant LR1,2 for the Canada-Westpair. Thus, nonlinearity is present in the pricerelationship. In deciding on the number of re-gimes, the test statistics select the three-re-gime model. Misspecification tests, including


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TABLE 3

Nonlinearity Diagnostic Tests and Threshold Estimates of Three-Regime Model byRegional Pair

Item West-South Canada-West Canada-South

Sup-likelihood ratio test LR1,2 24.954 [0.02] 15.216 [0.18] 23.716 [0.00] LR1,3 50.222 [0.00] 35.130 [0.02] 37.051 [0.00] LR2,3 25.268 [0.01] 19.914 [0.04] 13.335 [0.06]

Threshold estimatesγ 1 −0.196 −0.055 −0.143γ 2 0.215 0.027 0.146

Observations (share)Regime I (lower) 31 (7.7%) 78 (19.3%) 21 (5.2%)Regime II (middle) 351 (86.9%) 162 (40.1%) 363 (89.4%)Regime III (upper) 22 (5.4%) 164 (40.6%) 22 (5.4%)

Note: LR1,2 tests the hypothesis of linear against two-regime vector error correction models. LR1,3 tests the

hypothesis of linear against three-regime models. LR2,3 tests the hypothesis of two-regime against three-regimemodels. Numbers in brackets are p-values from the parametric residual bootstrapping. Threshold estimates andobservation numbers are from the three-regime model.

ARCH Lagrange multiplier and Ljung-Boxstatistics, are used to assess the properties of the residuals from the three-regime thresholdmodel. The results are satisfactory with theonly exception of slight heteroskedasticity forlags larger than 12 months. Therefore, the

three-regime threshold error correction modelis selected and estimated for all the three pricepairs.

The threshold estimates from the three-re-gime threshold models are reported in Table3, and their relation to the residual values fromthe long-term cointegration is presented inFigure 4. The residual values from the Can-ada-West pair have less dispersion, and thethreshold estimates divide the samples intomore evenly distributed regimes. Specifically,

for the Canada-West pair, the share of the ob-servations is 19.3% for the lower regime,40.1% for the middle regime, and 40.6% forthe upper regime. For the West-South pair, thethree shares are 7.7%, 86.9%, and 5.4%. Forthe Canada-South pair, the shares are 5.2%,89.4%, and 5.4%. Regime switching occursmainly at the beginning and end periods forthe West-South and Canada-South pair. Incontrast, for the Canada-West pair, regimeswitching occurs more frequently; lower re-

gimes are mainly in the early period before1995; and upper regimes are mainly in morerecent years after 2000.

Results from Linear and Threshold Models

To facilitate comparison, the results fromthe linear vector error correction model arereported in Table 4, and the results from thethreshold model are reported in Table 5 by

pair. In the linear model, all the error correc-tion terms have the expected signs and are sig-nificant, with only one exception in the Can-ada-West pair. For example, in the West-Southpair, the response to one positive unit of dis-equilibrium is −0.059 by the western priceand 0.102 by the southern price. The magni-tude of the response is bigger for the southernprice, which confirms the finding in Figure 3that the southern price is more active than thewestern price.

The results from the threshold models aresimilar to those from the linear model, butthey also provide additional insights. For theWest-South pair, the only significant estimatefor the error correction term is the response of the western price in the middle regime (i.e.,−0.097), which is slightly larger in magni-tude than the corresponding estimate in thelinear model (i.e., −0.059). For the southernprice, the estimates in all three regimes aresignificant at the 15% level only. The values

in the lower regime (0.386) and upper regime(0.382) are especially large. Both prices havemore significant lagged variables in the sys-


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FIGURE 4

Residual Values from the Long-Term Cointegration, Threshold Estimates, and Time of Regime Switching

from Three-Regime Threshold Vector Error Correction Model by Pair

TABLE 4

Results from Linear Vector Error Correction Models by Pair

y = West, x = South y = Canada, x = West y = Canada, x = South

Variable ∆ yt ∆ x t ∆ yt ∆ x t ∆ yt ∆ x t

ξ t −1 −0.059**(−2.071)

0.102***(3.137)

−0.147***(−2.944)

0.024(0.485)

−0.133***(−3.224)

0.143***(3.055)

Constant −0.002(−0.555)

−0.002(−0.544)

−0.002(−0.593)

−0.002(−0.570)

−0.002(−0.533)

−0.002(−0.418)

∆ yt −1 0.197***(3.211)

0.024(0.345)

0.277***(3.255)

0.214**(2.505)

0.143**(2.175)

0.119(1.595)

∆ x t −1 0.079(1.466)

0.294***(4.774)

−0.103(−1.237)

0.080(0.965)

0.037(0.655)

0.214***(3.362)

∆ yt −2 −0.133**(−2.220)

−0.071(−1.042)

−0.051(−0.602)

0.014(0.171)

— —

∆ x t −2 0.132**(2.432)

0.009(0.149)

0.010(0.122)

−0.049(−0.583)

— —

∆ yt −3 −0.013(−0.221)

−0.097(−1.440)

0.094(1.136)

0.044(0.528)

— —

∆ x t −3 −0.044(−0.805)

−0.030(−0.477)

−0.113(−1.425)

−0.070(−0.878)

— —

Note: The error correction term ξ t −1 is the lagged residual from the cointegration regression.**, *** Significance of the estimates at the 5% and 1% levels, respectively.


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FIGURE 5Generalized Impulse Responses over the Period 1991–1993 Related to the History of the Endangered Species

Act (ESA)

Act are plotted in Figure 5,4 and those relatedto the history of global financial crisis areplotted in Figure 6.5 For all three pairs, theresponses are highly consistent with long-runmarket integration. Isolated shocks in one re-gion provoke responses in the other regionthat eventually lead to a tendency for prices

to equalize. For example, a positive shock tothe western price evokes an equilibratingpositive response in the southern price thateventually leads to price convergence. In most

4 There are four lines in each panel: y(+) stands for theresponse of series y to a positive shock, x (+) for x to apositive shock, y(− ) for y to a negative shock, and x (− )for x to a negative shock. y and x are the first and secondprice in each pair, respectively. The size of the shock is twotimes the residual standard error. The shock occurs at timezero, and the forecasting horizon is 24 months. The dots on

the lines indicate that the responses are significant at the 10%level.

5 See the notations for Figure 5.

cases, the shocks result in permanent shifts inthe price series, reflecting the nonstationarynature of the price data. Thus, positive shocksoften lead to permanent price increases, whilenegative shocks lead to permanent price de-creases. The responses suggest that after someshort-term dynamic adjustments, prices con-verge on one another in the long run.

By history, over the period of 1991 to 1993related to federal timber restrictions, sophis-ticated and fluctuating responses are observedduring the first half year, especially when theshock is initiated on the western price. Thismay reflect that the disputes over the spottedowl were controversial and long lasting, andthe responses are calculated as the averagesover the period of three years. A market dis-equilibrium or shock on the Canadian priceover the same period related to the Endan-gered Species Act generates smoother curves.


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Canada-West and Canada-South pairs. In con-trast, the West-South pair shows some posi-tive asymmetry.

VI. SUMMARY AND POLICYIMPLICATIONS

After several decades’ evolution, the soft-wood lumber market in North America hasbecome the battlefield of lumber producersfrom three major regions with similar marketshares: the southern United States, the westernUnited States, and Canada. The competitionamong these regions has been affected bymany factors, including timber resource en-dowments, forestland ownership, environ-mental protection and public land policies,trade disputes between the two countries, andthe status of the general economy. Followingprevious market integration studies, a thresh-old vector error correction model is developedin this study to investigate nonlinear pricetransmission in the softwood lumber marketamong these regions. The time span includes34 years between 1978 and 2011 and is longerthan those used in previous studies. The majorconclusion is that price transmission among

lumber production regions in North Americais nonlinear and asymmetric. As the first studythat utilizes a nonlinear time series model toanalyze softwood lumber price dynamics andthe impact of resource policies, the new find-ings from this study have several policy andmanagement implications.

The lumber price in the South shows themost flexibility and the largest magnitude inresponding to price disequilibrium with otherregions. Forestlands in both the West and

Canada are mostly publicly owned, whereasabout 90% of forestlands in the South are pri-vately owned, including nonindustrial forestlandowners, industrial firms, and institutionalinvestors. The dominance of the market mech-anism in the South may be largely responsiblefor the active behavior of the southern lumberprice in regional competition. This finding hasimportant implications for forest policy de-sign and implementation. In general, policymakers utilize instruments of coercion and

regulations, financial aids, technical service,and public land ownership in achieving forestpolicy goals (Cubbage, O’Laughlin, and Bul-

lock 1993). In particular, government man-agement of public forestlands is expected toproduce more nonmarket goods and demon-strate public preferences of natural resource

management to private forest landowners.The new finding reveals that when the shareof lumber production from privately ownedforests is sufficiently large, the interaction be-tween public and private forestland ownershipcan be modified substantially. Feedbacks fromthe southern market can disclose the prefer-ences of private landowners and other marketparticipants in the face of evolving environ-mental regulations and market competition.These timely feedbacks provide valuable in-formation to the general public and policymakers for policy design, implementation,and evaluation.

The nonlinear price transmission differsamong regions. The domestic pair betweenthe West and the South in the United Stateshas the lowest correlation, the smallest aver-age of price margins, but the highest volatilityof price margins. Some positive asymmetricprice transmission is identified between thewestern and southern prices. In contrast, theother two pairs with the Canadian price in-

volved have larger correlation coefficients andare more prone to negative asymmetry. Thissuggests that producers in the West and Southare slow in responding to an enlarged pricemargin between the two regions, but fast inresponding to a reduced price margin. In con-trast, both the western and southern priceshave reacted to any price disequilibrium rela-tive to the Canadian price in a way that theseprices follow each other as closely as possible.These differences among regional price pairs

may be attributed to product differentiationand varying degrees of substitution betweenimported and domestic softwood products(Nagubadi et al. 2004). Given the differencebetween the two countries (e.g., forestlandownership), softwood lumber trade disputesbetween Canada and the United States willlikely continue. Incorporating nonlinearityand asymmetry in welfare analyses may re-veal different impacts on market participantsacross regions and, thus, improve the existing

assessments in this area (e.g., Zhang 2001).From a policy perspective, the finding fromthe present study highlights the need to con-


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sider nonlinear price transmission among re-gional prices in pursuing a better trade remedyfor the softwood lumber dispute in NorthAmerica.

Different events can generate very diverseand nonlinear price adjustments. The gener-alized impulse response analyses reveal thatbetween 1991 and 1993, related to the federaltimber restrictions, short-term price responsesare more sophisticated with varying durationand magnitudes, especially when the priceshock is initiated on the western price. This isconsistent with the fact that the contentiousdisputes over the spotted owl lasted for sev-eral years in the 1990s. The global financial

crisis that started in 2008 has been more prev-alent over all the regions under consideration,and the responses over this period are morebalanced among the three price pairs. In gen-eral, when nonlinear price transmission exists,the effect of a shock depends on the historyof the time series when the shock occurs, thesign of the shock, and the magnitude of theshock. The implication of this finding is thatin adopting a specific forest policy or evalu-ating its effectiveness, individual assessments

should be conducted to examine the nonlinearand asymmetric impacts that are unique to thepolicy under consideration.

In recent years, the consumption of soft-wood lumber in the United States has expe-rienced one of its lowest levels in history,which is largely due to the economic recessionthat began in 2008. As the economy has beenon the way toward recovery, the housing mar-ket has improved and the demand of softwoodlumber products has gradually increased, es-pecially since 2012. Nonetheless, other un-certainties such as environmental protectionand trade disputes between the United Statesand Canada can still affect the comparativeadvantages of lumber producers in differentregions. Thus, the competition among themain supplying regions will likely developfurther, and regional price dynamics can be-come even more sophisticated. As public pol-icies for natural resources continue to evolveto meet the diverse demand from the public,further studies are needed to closely monitorthese interactions among regional softwoodlumber markets.

Acknowledgments

The authors wish to thank Randall C. Campbell andIan A. Munn for valuable comments on earlier drafts.

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le - timber restrictions, financial crisis and price transmission in north american lumber markets

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