Price Linkages in the North American Softwood Lumber Market. Jungho Baek 1

Transcription

1 Price Linkages in he Norh American Sofwood Lumber Marke Jungho Baek 1 1 Research Assisan Professor, Cener for Agriculural Policy and Trade Sudies, Deparmen of Agribusiness and Applied Economics, Norh Dakoa Sae Universiy, Fargo, ND 58105; Phone: (701) ; Fax: (701) ; jungho.baek@ndsu.nodak.edu. 68

2 Price Linkages in he Norh American Sofwood Lumber Marke Absrac This paper examines srucural changes and he dynamics of price relaionships in he U.S., Briish Columbia, Quebec and Onario lumber markes. Wih monhly price series from 1981 o 2002, we use Perron s mehod o idenify srucural shifs and he Johansen coinegraion analysis and vecor-error correcion (VEC) model o deermine boh shor-run and long-run price relaionships. We find ha, due o resricions on federal imber harvess in he Pacific Norhwes (PNW), price insabiliy experienced in 1992 has caused srucural shifs for he U.S. and Canadian lumber prices. We also find ha he Norh American lumber marke is indeed inegraed where he U.S. price significanly affecs Canadian prices in boh shor-run and longrun. This resul indicaes he price leadership role for he U.S. in he Norh American lumber marke where he Canadian prices respond o he U.S. price change, bu ha he reverse does no hold. Therefore, his finding may no suppor he claim of U.S. producers ha subsidized Canadian lumber has depressed he U.S. price and harmed he U.S. lumber indusry. Key Words: coinegraion analysis, srucural changes, vecor-error correcion 69

3 Inroducion The rade of sofwood lumber beween he U.S. and Canada is one of he major rade flows of fores producs in he world. These wo counries are no only he world s larges producers of sofwood lumber, bu also he world s larges imporer and exporer, respecively. For example, in 2002, he U.S. shared 45% of world impors for sofwood lumber, while Canada provided 48% of world lumber expors (FAO 2003). More imporanly, he U.S. and Canada are highly inerdependen on each oher s lumber marke. The U.S. depends on Canada for more han 90% of is lumber impors. Canada expors more han 60% of is lumber producion o he U.S. Given he economic imporance of lumber rade beween he wo counries, herefore, i is imporan o clearly undersand he behavior of sofwood lumber markes in Norh America. Several sudies have examined price relaionships in eiher he U.S. or Canadian lumber markes. Uri and Boyd (1990) use he concep of he Granger causaliy in order o deec he geographical exen of he U.S. lumber markes. They find ha he demand for sofwood lumber is indeed srongly conneced o prices, and ha here is a naional lumber marke in he U.S. Jung and Doroodian (1994) adop he Johansen coinegraion procedure o idenify he long-run equilibrium relaionships among four U.S. regional lumber markes. They discover ha, wih efficienly linked prices, here exiss a single long-run equilibrium price in he U.S. lumber marke. More recenly, wih he mos disaggregae daa and a large number of price combinaions for differen producs, Yin and Baek (2005) es he law of one price (LOP) hypohesis for he U.S. lumber markes. Afer exhausive invesigaions, hey find overwhelming evidence supporing he LOP for he enire U.S. marke. Similarly, a Canadian scholar uses he Johansen procedure o es he LOP hypohesis for five Canadian regional lumber markes (Nanang 2000). Wih he single coinegraion vecor idenified, he concludes ha here is no single marke for sofwood lumber in Canada. Previous sudies have undoubedly expanded our undersanding of he price relaionships in he U.S. and Canadian lumber markes. However, earlier sudies have examined eiher he long-run price relaionships based on he concep of coinegraion or he shor-run price dynamics based on he concep of Granger causaliy; herefore, lile aenion has been paid o conduc he rigorous sudy of long-run and shor-run price relaionships simulaneously. In oher words, no sudies have examined as o how equilibrium relaionships are resored and wha new equilibrium levels would be obained given policy shifs. Furher, no sudy so far has deal wih price relaionships in he U.S. and Canadian lumber markes ogeher. Wih he recen developmen of he lumber rade dispue, i is imely o explore his relaionship. 2 One objecive of his paper is o assess he dynamics of price relaionships in he Norh American lumber marke. To ha end, we examine shor-run and long-run price relaionships in hree 2 Since he early 1980s, a number of lumber rade dispues have arisen beween he U.S. and Canada. The very laes rade dispue beween he wo counries has come as a resul of he expiraion of he Sofwood Lumber Agreemen (SLA). In April 2001, U.S. producers filed counervailing and anidumping peiions, which claimed ha subsidized and below-cos Canadian lumber was being dumped on he U.S. marke, harming he U.S. lumber indusry. The Inernaional Trade Commission (ITC) issued is finding ha he U.S. lumber indusry is hreaened wih maerial injury by impors of Canadian lumber. As a resul, in May 2002, he U.S. governmen imposed he counervailing (18.79%) and anidumping (8.43%) duies on Canadian lumber expored o he U.S. 70

4 Canadian provincial and one naional U.S. lumber markes using he Johansen coinegraion analysis and vecor error-correcion (VEC) model. More specifically, previous sudies reveal ha here exiss a single naional marke in he U.S., since he LOP holds for he enire U.S. markes (Uri and Boyd 1990, Jung and Doroodian 1994, Yin and Baek 2005). As such, he U.S. marke is reaed as a single marke in our models. In conras, he Canadian provincial markes should be reaed as separae markes, since he LOP does no hold for he enire Canadian markes (Nanang 2000). We hus consider he Canadian markes as consising of hree segmened markes such as Briish Columbia (BC), Quebec, and Onario in our models. Since hese hree provinces accoun for approximaely 80% of oal Canadian producion and approximaely 85% of expors o he U.S., i seems reasonable o use hem as a represenaive of Canadian markes in our analysis. I is essenial o undersand price relaionships in U.S. and Canadian provincial lumber markes in order o address issues of marke srucure, price leadership, and marke modeling. For example, if we find evidence ha he Canadian prices respond o disequilibria induced by a shock shifing eiher U.S. or Canadian price levels, bu ha he U.S. price does no respond, i suggess ha U.S. acs as he price leader and imperfec compeiion exiss in he Norh American marke. On he oher hand, if U.S. and Canadian lumber prices are coinegraed, i indicaes ha hese prices end o drif in a similar fashion in he long-run, and he coinegraion relaionships should be included in modeling he Norh American lumber marke; oherwise, he economeric models could give a biased esimaion. More imporanly, i is imporan o assess he price relaionship o undersand he on-going lumber rade dispue beween he U.S. and Canada. For example, he finding of U.S price leadership indicaes ha he Canadian markes are influenced by he U.S. marke, bu ha he reverse does no hold. This furher suggess ha Canadian subsidies, if exiss, may no have an impac on price changes in he U.S. marke. As such, he U.S. claim ha subsidized Canadian lumber, paricularly coming from he hree provinces, has depressed he U.S. prices would no be suppored. A second objecive of his paper is o use he concep of srucural change o idenify srucural breaks in he U.S. and Canadian prices series. Srucural change is an imporan issue in imeseries analysis and affecs all he inferenial procedures associaed wih uni roos and coinegraion ess (Maddala and Kim 1998). Specifically, uni roo ess are prerequisie o consruc an appropriaely specified VAR model. However, assuming ha he deerminisic rend is correcly specified, he sandard augmened Dickey-Fuller (ADF) es is no able o deec a srucural break in he series (Maddala and Kim 1998). As such, if here is a break in he deerminisic rend, hen ADF es may have lower power and even could lead o a false conclusion ha here is a uni roo, when in fac here is no (Perron 1989). Hence, ess for srucural changes are performed o overcome he shorcomings of he sandard ADF procedure, as well as o examine wheher here is any evidence of srucural breaks in he lumber prices series. I is hoped ha his analysis will shed new ligh on he dynamics of price relaionships in boh U.S. and Canadian lumber markes and conribue o he lieraure of fores producs markes. The paper is organized in five secions. The nex secion describes he daa used for he analysis. The uni roo es under srucural change is hen discussed, followed by he main empirical 71

5 resuls of he sudy. A summary of principal findings and conclusions of he research are included in he final secion. Daa Monhly sofwood lumber prices for U.S. ( US ), Briish Columbia ( BC ), Quebec ( QE ), and Onario ( ON ) are colleced for he period of January 1981 o April All price series are quoed in indusry price indexes for sofwood lumber (1997=100), because acual lumber prices in Briish Columbia, Quebec, and Onario are no available. Price index for he U.S. is colleced from Bureau of Labor Saisics in he U.S. Deparmen of Labor. Price indexes for he hree Canadian provinces are aken from he CANSIM daabase (Indusry Price Indexes Table ) from Saisics Canada. Srucural Change and Uni Roo Tess Theoreical Framework To ake ino accoun srucural changes in he deerminisic rend funcion, Perron (1989) develops a modified augmened Dickey-Fuller (ADF) es for he presence of a uni roo wih hree alernaive models. Given a known srucural break, he approach is generalized o allow a one-ime change in he srucure occurring a a ime T B, referred o as he ime of break. The hree differen models are parameerized as follows: (1) Model (A): y = µ 0 + δ + µ 1DU + u where DU = 1 if > TB, and 0 oherwise. * (2) Model (B): y = µ + δ 0 + µ 1 DT + u where DT * = 1 if = T B + 1, and 0 oherwise. (3) Model (C): y = µ 0 + µ 1DU + δ 0 + δ1dt + u where DT = if > T, and 0 oherwise. B Model (A) is referred o as he crash model and allows for a one-ime change in he inercep of he rend funcion. Model (B) is known as he changing growh model and considers a change in he slope of he rend funcion wihou any sudden change in he inercep. Model (C) allows for boh effecs (slope and inercep) o ake place simulaneously. For empirical analysis, he hree differen models are reformulaed by nesing he corresponding models under he null and alernaive hypoheses as follows: A A A A A (4) Model (A): y = µ + β + θ DU + γ TB + α y 1 + ci y i + ε B B B B B (5) Model (B): y = µ + β + θ DU + δ DT + α y + c y i + ε C C C C C C (6) Model (C): y = µ + β + θ DU + γ TB + δ DT + α y + c y i + ε * 1 k i= 1 k i= 1 i 1 k i= 1 i 72

6 where TB = 1 if = TB, and 0 oherwise. The null hypohesis of a uni roo imposes he A A A resricions on he parameers of each model as follows: α = 1, β = 0, and θ = 0 in Model B B B C C C (A) ; α = 1, β = 0, γ = 0 in Model (B) ; and α = 1, β = 0, and γ = 0 in Model (C). A C B Finally, under he null hypohesis, γ, γ and θ are expeced o be significanly differen from zero. Idenifying Srucural Change To moivae he use of hree differen models developed by Perron (1989), we firs presen graphical invesigaion for he four price series (Figure 1). The graph of he U.S. price series shows ha here appears o be boh change in he inercep of he series in he early 1992 and he slope aferwards (firs Figure). The same feaure appears o hold for he BC and Quebec prices in he lae 1992 (second and hird Figures). Those hree price series hus behave in correspondence o Model C. On he oher hand, he Onario price series behaves according o Model A where here is no sharp change in he slope in he lae 1992 bu raher a change in he inercep (fourh Figure). To verify his graphical examinaion, we use ordinary leas squares (OLS) o esimae equaions (1) and (3) (Models A and C) for poenial break poins ( T B ) in he neighborhood of graphically inspeced break daes. 3 Given he OLS assumpion, he values of T B which minimize he sum of squared residuals are he maximum likelihood esimaes of he ime a which he srucural change occurs, referred o as grid search (Oehmke and Schimmelpfennig 2004). The resuling break poins are January 1992 for he U.S. price, November 1992 for he BC and Quebec prices, and December 1992 for he Onario price. 3 We es for a break in he hree-year neighborhood of a suspeced break. 73

7 LUS Fied 4.75 LBC Fied LQE Fied LON Fied Figure 1. Logarihm of U.S., BC, Quebec and Onario prices, acual values and modeled srucural shifs (fied values), Wih he maximum likelihood esimaes for break poins ( T ), we hen es for saisical significance of he parameers in equaions (1) and (3) (Table 1). The resuls show ha all regressions have high adjused R 2, above The coefficiens on he inercep, rend, and inercep- and rend shifs in he U.S., BC, and Quebec price series are significan a he 1% level. Addiionally, he coefficiens on he inercep, rend, and inercep shif in he Onario price are significan a leas a he 10% level. The OLS resuls hus indicae ha he incorporaion of DU and DT in he model is saisically imporan. For compleeness, we use he esimaed models o generae fied values (solid lines) of he dependen variables (Figure 1). These figures provide graphical validaion of he srucural changes obained from he regression resuls. The break poins found here coincided wih he federal imber harves reducions in he Pacific Norhwes (PNW), which creaed a dramaic price shock and hus has had a significan effec on he U.S. and Canadian lumber prices. * B 74

8 Table 1. OLS regression resuls on srucural shifs in U.S. and Canadian lumber prices Independen variable Dependen variable ( -saisic) ln ( US ) ln ( BC ) ln ( QE ) ln ( ON ) Inercep *** (284.0) *** (222.0) *** (212.0) *** (228.0) Inercep shif *** (17.9) *** (18.7) *** (14.1) *** (19.5) Trend *** *** *** * (9.44) (11.9) (8.11) (1.84) Trend shif *** *** *** (-5.77) (-7.27) (-4.39) - Time of shif 1992: : : :12 Observaion 2 Adjused R Noe: ***, **, and * denoe significance a he 1%, 5%, and 10% levels, respecively; Boh inercep and rend shifs occur in he U.S., BC, and Quebec prices, while only inercep shif occurs in he Onario price. Tesing for Uni Roos under Srucural Change To es for uni roos in he presence of srucural shifs, we esimae equaion (4) for he Onario price and equaion (6) for he oher hree series (Table 2). For comparison, we also esimae he sandard ADF saisics for he series. The resuls show ha he null hypohesis of nonsaionariy canno be rejeced for all four series wih he ADF es. In conras, when srucural shifs are included, he null hypohesis can be rejeced a leas a he 10% significance level for all he series. The resuls hus indicae ha he underlying process for he U.S. and hree Canadian prices can be characerized by saionary flucuaions around a deerminisic rend funcion. Given ha he null hypohesis of non-saionariy can be rejeced for all he series, i is no longer appropriae o use he full sample in our coinegraion analysis. We hen divide he full sample ino wo sub-samples according o he break poin (pre- and pos- 1992:12) in order o see if his feaure is sable in boh cases. 4 However, i is widely known ha when dealing wih finie samples, especially small numbers of observaions, he power of he sandard ADF es is nooriously low (Harris and Sollis 2003). In oher words, he ADF es has high probabiliy of acceping he null hypohesis of non-saionariy when he rue daa-generaing process is in fac saionary. Consequenly, we use more powerful ess for he wo sub-samples. 4 We spli he full sample a he 1992:12 break poin, since all he series have experienced srucural shifs beween 1992 and

9 Table 2. ADF and Perron ess for a uni roo # of lags ln ( US ) ln ( BC ) ln ( QE ) ln ( ON ) ADF Perron ADF Perron ADF Perron ADF Perron 2 lags *** *** *** *** 4 lags ** *** *** ** 6 lags * *** *** ** 8 lags * ** ** ** Noe: ***, **, and * denoe significance a he 1%, 5%, and 10% levels, respecively; The 1%, 5%, and 10% criical values for he ADF including a consan and a rend are -4.90, -4.24, and , respecively; The 1%, 5% and 10% criical values for he Perron es are -4.90, -4.24, and for Model C, and -4.45, -3.76, and for Model A. Criical values are obained from Tables 4B and 6B in Perron (1989). Ellio e al. (1996) develop a uni roo es which is well suied o our siuaion. They opimize he power of he ADF es using a form of derending, referred o as Dickey-Fuller generalized leas squares (DF-GLS) derended es. Mone Carlo experimens indicae ha he DF-GLS works well in small samples and has subsanially improved power when an unknown mean or rend is presen (Ellio e al. 1996, p. 813). Ng and Perron (2001) recenly have produced a esing procedure which incorporaes boh he new informaion crierion for seing he lag lengh and GLS derending. The resuls show ha, wih he pre-1992:12 sample, he rejecion of nonsaionariy for he BC and Quebec prices is consisen across differen lag lenghs a he 5% or beer significance level, indicaing ha hese wo prices are saionary (Table 3). In conras, he null hypohesis canno be rejeced for all he series in he pos-1992:12 sample. Kwiakowski e al. (KPSS) (1992) argue for he usefulness of performing ess of he null hypohesis of saionariy as well as ess of he null hypohesis of a uni roo, paricularly when using non-saionariy ess wih low power. Wih he null hypohesis of saionariy, eiher around a level or around a linear rend, he KPSS es hus can be used as a complemen o sandard uni roo ess. If he DF-GLS and KPSS ess provide differen resuls, he ess are inconclusive. We firs esimae he KPSS saisics for no rend models. The resuls show ha he KPSS es unambiguously rejecs he null hypohesis of saionariy for all he series in boh subsamples. We hen proceed o es he null hypohesis of rend saionariy. The resuls indicae ha he KPSS es fails o rejec he null for he BC and Quebec prices in he pre-1992:12 sample (Table 3). On he oher hand, wih he pos-1992:12 sample, he null hypohesis can be rejeced for all he series. From he findings of he DF-GLS and KPSS ess, we conclude ha he U.S. and Onario prices in he pre-1992:12 sample and all price series in he pos-1992:12 sample are non-saionary. However, since he BC and Quebec prices are consisenly found o be saionary in he pre- 1992:12 sample, hey canno be used for he coinegraion analysis. 5 Therefore, for furher imeseries analysis, we decide o focus our aenion on he pos-1992:12 sample. 5 Of course, we can use wo non-saionary variables such as he U.S. and Onario prices for our coinegraion analysis. However, only using wo price series is no sufficien and hus meaningful o our undersanding of he 76

10 Table 3. DF-GLS es for he null hypohesis of non-saionariy and KPSS es for he null hypohesis of rend saionariy. # of lags DF-GLS es Sub-sample І Sub-sample II (1981: :12) (1993: :04) ln ( US ) ln ( BC ) ln ( QE ) ln ( ON ) ln ( US ) ln ( BC ) ln ( QE ) ln ( ON ) 2 lags *** -4.83*** lags ** -4.39*** lags ** -3.30** lags ** -2.99** KPSS es Lag order Sub-sample І (1981: :12) Sub-sample II (1993: :04) ln ( US ) ln ( BC ) ln ( QE ) ln ( ON ) ln ( US ) ln ( BC ) ln ( QE ) ln ( ON ) *** 0.451*** 0.448*** 1.26*** 1.84*** 1.82*** 1.55*** 1.94*** *** 0.241*** 0.248*** 0.667*** 0.95*** 0.942*** 0.816*** 1.00*** 2 0.3*** 0.172** 0.186** 0.469*** 0.655*** 0.649*** 0.57*** 0.693*** *** 0.139* 0.158** 0.37*** 0.508*** 0.503*** 0.448*** 0.538*** ** 0.119* 0.142* 0.31*** 0.42*** 0.417*** 0.375*** 0.446*** ** * 0.269*** 0.362*** 0.359*** 0.326*** 0.384*** ** * 0.239*** 0.32*** 0.317*** 0.291*** 0.339*** ** * 0.216*** 0.288*** 0.286*** 0.264*** 0.305*** ** ** 0.264*** 0.262*** 0.243*** 0.279*** * ** 0.244*** 0.243*** 0.225*** 0.257*** * ** 0.228*** 0.227*** 0.211** 0.24*** * ** 0.215** 0.214** 0.2** 0.226*** * ** 0.204** 0.204** 0.19** 0.214** * * Noe: ***, **, and * denoe rejecion of he null hypohesis a he 1%, 5%, and 10% levels, respecively; The 1%, 5%, and 10% criical values for he DF-GLS es are -3.53, -2.99, and for sub-sample І, and -3.56, -3.02, and for sub-sample II; The 1%, 5%, and 10% criical values for he KPSS es of rend saionary are 0.216, 0.146, and for boh samples. To save space, he resuls for he hypohesis of level saionariy are no repored; The lag order for he KPSS es is chosen by Schwer crierion. Coinegraion Tes and Error-Correcion Model Theoreical Framework A long-run equilibrium price relaionship beween wo markes can be represened as follows: P = α + βp + u (7) i j ij price relaionships in he Norh American lumber marke. Hence, we decided o exclude he pre-1992:12 sample for coinegraion analysis. 77

11 where P i and P j are prices for marke i and j ; α and β are esimaed coefficiens; and u ij is a normally and independenly disribued error erm. The long-run equilibrium relaionship beween markes i and j can be deeced by esimaing β. In our case, price series are nonsaionary. The OLS regression beween such series hus leads o a spurious regression problem (Wooldridge 2000). To avoid his problem, we use he coinegraion procedure. Engle and Granger (1987) show ha even in he case ha all he variables in a model are non-saionary, i is possible for a linear combinaion of inegraed variables o be saionary. In his case, he variables are said o be coinegraed and he problem of spurious regression does no arise. The Johansen maximum likelihood esimaion mehod is used o deermine he number of coinegraion relaionships among he price series (Johansen and Juselius 1990, Johansen 1995). Following Johansen, he coinegraed vecor auo-regression (VAR) model can be defined as follows: (8) X = µ + Γ1 X Γk 1 X k ΠX k + u where X is a ( 1 n ) vecor of endogenous variable; i.e., X = [ US, BC, QE, ON ]; is he difference operaor; Γ1,..., Γk 1 are he coefficien marices of shor-erm dynamics, and Π = ( I Π Π k ) are he marix of long-run coefficiens; µ is a vecor of consan; and u is whie noise. Granger s represenaion heorem assers ha if he coefficien marix Π has reduced rank r < n, hen here exis ( n r ) marices of α and β, each wih rank r such ha Π = αβ' and β ' X k is saionary (Engle and Granger 1987). Here, r is he number of coinegraing relaions, α represens he speed of adjusmen o equilibrium, and β ' is a marix of long-run coefficiens. For n endogenous non-saionary variables, here can be 0 o n 1 linearly independen coinegraing relaions in he sysem. The number of coinegraion vecors, he rank of Π, in he model is deermined by he likelihood raio es (Johansen 1995). If all variables in a vecor of sochasic process X are coinegraed, an error-correcion represenaion capures he shor-run dynamics while resricing he long-run behavior of variables o converge o heir coinegraing relaionships (Engler and Granger 1987). This is accomplished by esimaing an error-correcion model in which residuals from he equilibrium coinegraing regression are used as an error-correcing regressor. For his purpose, equaion (8) can be reformulaed as a shor-run dynamic model as follows: (9) X = µ + Γ1 X Γk 1 X k α( β ' X 1 ) + u where β ' X 1 is a measure of he error or deviaion from he equilibrium, which is saionary since he series are coinegraed. Since variables are coinegraed, he VEC model incorporaes boh shor-run and long-run effecs. Tha is, if he long-run equilibrium holds, β ' X 1 = 0. During periods of disequilibrium, on he oher hand, his erm is non-zero and measures he disance of he sysem from equilibrium during ime ; hus, an esimae of α provides informaion on he speed-of-adjusmen, which implies how he variable X changes in response o disequilibrium. 78

12 Johansen Coinegraion Tes The Johansen coinegraion procedure is applied o deermine he number of coinegraing vecors using he pos-1992:12 sample. Prior o he coinegraion es, i is necessary o deermine he lag lengh o define a correcly specified VAR model, which ensures he residuals are approximaely whie noise. For his purpose, a number of VAR lag selecion crieria and diagnosic ess are used. The lag lenghs ( k ) of he VAR model are deermined by he Schwarz (SC), Hannan-Quinn (HQ), and Akaike (AIC) informaion crieria using likelihood raio ess (Doornik and Hendry 1994). For example, we sar from k = 8 and a reducion of he VAR from k =8 o k =7 is rejeced. This reducion sequence is hen conduced unil we find ha he reducion from k =5 o k =4 is acceped. Diagnosic ess on he residuals of each equaion and corresponding vecor es saisics suppor he VAR model wih four lags ( k =4; Table 4). In our serial correlaion es using he F -form of he Lagrange Muliplier (LM) es, he null hypohesis of no serial correlaion canno be rejeced a he 1% significance level. Heeroskedasiciy is esed using he F -form of he LM es and he null hypohesis of no heeroskedasiciy canno be rejeced a he 1% significance level. Normaliy of he residuals is esed wih he Doornik-Hansen (1994) mehod. The null hypohesis of normaliy canno be rejeced a he 1% significance level. Furhermore, he specificaion ess indicae ha a linear rend is necessary bu seasonal dummies are no. Table 4. Diagnosic ess wih he sub-sample II (1993: :04) Serial Correlaion F (7,86) AR Heeroskedasiciy F (7,79) ARCH Normaliy 2 χ (2) US 0.85 [0.55] 0.94 [0.49] 2.05 [0.36] BC 1.43 [0.21] 1.12 [0.36] 3.33 [0.26] QE 1.25 [0.29] 1.65 [0.13] 0.36 [0.83] ON 1.36 [0.23] 1.22 [0.16] 1.13 [0.57] Sysem 1.18 [0.15] 0.87 [0.93] [0.17] Noe: denoes he firs differences of he variables and parenheses are p -values; Serial correlaion of he residuals of individual equaions and a whole sysem is examined using he F - form of he Lagrange-Muliplier (LM) es, which is valid for sysems wih lagged independen variables; Heeroskedasiciy is esed using he F -form of he LM es; Normaliy of he residuals is esed wih he Doornik-Hansen es (Doornik and Hendry 1994). The resuls of coinegraion esimaion indicae hree coinegraion vecors ( r =3) in four price series (Table 5). Specifically, he race ess show ha he hypohesis of r =2 can be rejeced and r =3 is acceped. As a resul, hree coinegraion vecors are acceped a he 5% significance level. This suggess ha all of he four price series in he Norh American lumber marke are inegraed. 79

13 Table 5. Johansen coinegraion ess wih sub-sample II (1993: :04) Null hypohesis Eigenvalue Trace saisics 5% criical value H 0 : r = 0 H 0 : r 1 H 0 : r 2 H 0 : r ** 52.87** 27.97** Noe: ** denoes rejecion of he hypohesis a he 5% significance level. The es of long-run weak exogeneiy of each series in he model examines he absence of longrun levels of feed-back due o exogeneiy (Johansen and Juselius 1992). In oher words, a weakly exogenous variable is a driving variable, which pushes he oher variables away from adjusing o long-run equilibrium, bu is no influenced by he oher variables in he model. The long-run weak exogeneiy es is implemened by resricing parameer in speed-of-adjusmen (α ) o zero in he model. The resuls show ha he U.S. price is weakly exogenous a he 1% significance level (Table 6). This finding suggess ha he U.S. price is he driving variables in he sysem and significanly affecs he long-run movemens of Canadian prices, bu is no influenced by Canadian prices. Table 6. Weak exogeneiy es wih sub-sample II (1993: :04) Variable Weak exogeneiy H 0 : α i = 0 (LR es saic) US 5.57 [0.12] BC [0.00]*** QE [0.00]*** ON [0.02]** Noe: LR es saisic is based on he 2 χ disribuion and parenheses are p -values; *** and ** denoe he rejecion of weak exogeneiy a he 1% and 5% levels, respecively. I is now necessary o consider wheher coinegraion vecors are idenified, and hus wheher hey ell us anyhing abou he srucural economic relaionships underlying he long-run model (Johansen and Juselius 1994). For his purpose, we impose resricions on he coinegraing spaces, β (Table 7). The likelihood raio (LR) saisic is 1.38 ( p -value = 0.71), indicaing ha he resricions are accepable. The resuls show ha significan coefficiens on hree Canadian prices in α 1, α 2 and α 3 confirm hree coinegraion relaionships. This finding suggess ha join deviaions by he hree prices from he seady-sae posiion due o a specific shock in he Norh American lumber marke gradually disappear, and hey evenually reurn o an equilibrium 80

14 posiion. On he oher hand, he U.S. price is no significan in all of he hree relaions, indicaing ha his price do no adjus in he long-run, and hus weakly exogenous. Finally, he long-run coefficiens ( β ) explain he coinegraing relaionships among he price series (Table 7). For example, he firs error-correcion model, EC 1( β 1 ), which represens he BC price relaion, is wrien as follows: (10) EC1 : BC = 0.47ON + US rend Equaion (10) shows ha, in he long-run, he law of one price (LOP) holds beween he U.S. and BC. In addiion, he BC price increases as he Onario price rises. The shor-run adjusmen wihin EC 1 occurs primarily hrough he BC and Onario prices. The second and hird errorcorrecion models also show ha he LOP holds among he U.S., Quebec, and Onario prices. Table 7. Tess for he resricions on coinegraion vecors in U.S. and Canadian lumber price model wih sub-sample II (1993: :04) Eigenvecors Weighs β 1 β 2 β 3 α 1 α 2 α 3 BC -0.32** -0.48** -0.17** -0.30** (0.07) (0.17) (0.06) (0.12) QE -0.30** -0.16** -0.21* (0.13) (0.06) (-0.11) ON -0.47** -0.32** -0.11** -0.43** (0.07) (0.15) (0.05) (0.18) US (0.19) (0.13) (0.17) ** Trend (0.0002) Noe: ** denoes significance a he 5% level. Parenheses are sandard errors; LR es saisic is 2 χ (3) =1.38, p -value=0.71. VEC Model The VEC model is esimaed o find he shor-run adjusmen o long-run seady saes as well as he shor-run dynamics among price series. For his purpose, wih he idenified coinegraion relaionships, he VEC model in equaion (9) is esimaed. The mehodology used o find his represenaion follows a general-o-specific procedure (Hendry 1995). Specifically, since he U.S. price is found o be weakly exogenous o he sysem, he VEC model is firs esimaed condiional on he U.S. price. By eliminaing all he insignifican variables based on an F -es, he parsimonious VEC (PVEC) model is hen esimaed using full-informaion maximum likelihood (FIML, Harris and Sollis 2003). The number of lags included in he PVEC model is he same as in he coinegraion es. The mulivariae diagnosic ess on he esimaed model as 81

15 a sysem indicae no serious problems wih serial correlaion, heeroskedasiciy, and normaliy (Table 8). Hence, he model specificaion does no violae any of he sandard assumpions. Table 8. Parsimonious VEC model wih sub-sample II (1993: :04) BC 1 BC 3 QE 1 QE 3 QE 4 ON 3 ON 4 US 2 EC 1 EC 2 EC 3 Consan Mulivariae Tess BC QE ON 0.28 (3.99)*** 0.19 (2.22)*** 0.21 (3.70)*** 0.57 (3.07)*** (-2.12)** (-3.30)*** 0.21 (1.98)** 0.44 (2.49)** (-3.34)*** (-2.48)** 0.63 (4.08)*** (63,221) AR 2 χ (6) =4.03 [0.13] 0.66 (3.09)*** (-1.93)* (-3.86)*** 0.20 (2.01)** 0.50 (2.53)** (-2.30)** (-3.96)*** 0.55 (3.80)*** (228, (3.28)*** 0.60 (3.00)*** (-3.15)*** 0.57 (3.01)*** (-1.69)* (-3.14)*** 0.38 (2.74)*** F = 0.68 [0.96]; F ) =0.90 [0.81]; Noe: ***, **, and * indicae significance a he 1%, 5%, and 10% levels, respecively; EC1, EC2, and EC 3 represen error-correcion erms. Parenheses in mulivariae ess are p -values. The resuls of he PVEC models show ha he error-correcion erms for BC, Quebec, and Onario prices are negaively significan a he 10% or beer significance level (Table 8). The negaive coefficien of he error-correcion erm ensures ha he long-run equilibrium can be achieved. The absolue value of he error-correcion erm indicaes he speed of adjusmen o equilibrium. The resuls hus indicae ha when deviaing from equilibrium condiions, BC, Quebec, and Onario prices adjus o correc long-run disequilibria in he Norh American lumber marke. However, he adjusmen oward equilibrium is no insananeous. For example, BC price adjuss by 8% and 24% o he respecive long-run equilibria (EC2 and EC3) in one monh. These resuls imply ha i akes more han 12 monhs (1/0.08 = 12.5 monhs) and more han four monhs (1/0.24 = 4.2 monhs), respecively, o eliminae he disequilibria. I should be noed ha ARCH 82

16 he Sofwood Lumber Agreemen (SLA) during may resul in changes in U.S. and Canadian lumber prices. To capure such an effec, herefore, he dummy variable is included in he assessmens. However, due o insignifican coefficiens, he dummy for he SLA is dropped in he PVEC model. This indicaes ha he SLA had lile impac on U.S. and Canadian lumber prices. Finally, he coefficiens of he lagged variables in he PVEC models show ha he shor-run dynamics or causal linkage beween U.S. and Canadian lumber prices. Two period lagged U.S. price is saisically significan and posiively correlaed wih BC, Quebec, and Onario prices; for example, a 1% increase in he U.S. price causes a % increase in Canadian prices. The resul hus indicaes ha he U.S. price has a significan shor-run dynamic effec on he Canadian prices over he las decade. Summary and Conclusions This paper firs examines srucural changes in he U.S., Briish Columbia, Quebec, and Onario lumber prices and hen deermines he dynamics of price relaionships among hem. We uilize Perron s (1989) es o achieve he firs objecive and he Johansen coinegraion analysis and VEC model o deermine boh shor-run and long-run price relaionships. The resuls of uni roo ess under srucural change provide saisical evidence ha he price insabiliy winessed in 1992 has caused srucural shifs for he U.S. and Canadian lumber prices. The srucural shif coincides wih he period over which resricions on federal imber harvess in he PNW implemened. This finding furher suggess ha, when esimaing behavior relaionships wih hisorical daa, i is imporan o es for uni roos allowing for major policy shocks as srucural shifs. The resuls of he coinegraion analysis show ha he whole sofwood lumber marke in Norh America, including boh he U.S. and hree Canadian provinces, is indeed inegraed. The U.S. price is consisenly found o be weakly exogenous in he Norh American lumber marke, implying ha i influences he model o drif away from he long-run seady sae posiion, bu is no affeced by oher variables. The resuls of he VEC model indicae ha he shor-run dynamics are characerized by unidirecional causaion, wih he U.S. price significanly affecs he Canadian prices. Therefore, we conclude ha he U.S. price significanly affecs Canadian prices in boh shor-run and long-run in he inegraed Norh American lumber marke. In oher words, he U.S. acs as he price leader and he Canada as he follower in he Norh American lumber marke. Furhermore, he discovery of U.S. price leadership indicaes ha he Canadian prices respond o he U.S. price change bu U.S. does no respond o Canadian price changes. Hence, his finding may no suppor he claim of U.S. producers ha subsidized Canadian lumber has depressed he U.S. price and harmed he U.S. lumber indusry. References Doornik, J., and Hendry, D Ineracive economeric modeling of dynamic sysem (PcFiml 8.0). Inernaional Thomson Publishing, London, UK. 83

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