Derived Short-Run and Long-Run Softwood Lumber Demand and Supply

Transcription

1 Derived Shor-Run and Long-Run Sofwood Lumber Demand and Supply Nianfu Song and Sun Joseph Chang School of Renewable Naural Resources Louisiana Sae Universiy

2 Ouline Shor-run run and long-run implied by dynamic models. Daa frequency and is implicaion on shor-run and long-run. Condiions for a consisen esimae of dynamic model. A single equaion sofwood lumber demand model. A single equaion sofwood lumber supply model.

3 Long-Run and Shor-Run by Microeconomics Wih quasi-fixed facors Shor-run run model Quasi-fixed variables achieves heir equilibrium Long-run run model. Examples: Wear and Newman (1991) and Newman and Wear (1993)

4 More Examples Some lumber model include capaciy Bernard e al.1997, Adams and Haynes, 1996 Adams e al Y = f(p, X, K(P)) = f(p, X) They are shor-run models by microeconomics.

5 Challenge I is unknown how many periods he shor run implies. How fas a long-run equilibrium can be achieved?

6 Pas Research on Transforming a Dynamic Equaion ino a Long-Run Equaion Buongiorno, J., J. Chou, and R.N. Sone derived a long-run relaion from a dynamic model. Assumpion: saionary variables Simple single equaion model

7 ECM Example: Long-Run and Shor-Run Relaions by ECM Shor run relaion li Δ Y = ΔX 0. 18Z + ε Where Z and Y is 1 ( X ( 1) ) = Y 1 1 = X 1 + he long run relaion ( 1)

8 ECM as a Represenaion of Coinegraion Ad dynamic model Γ(L)y + B(L)x = ε The long-run model from i Γ(1)y + B(1)x = ε The ECM ransformed from he dynamic model Γ*(L)y + B*(L)x +Γ(1)y -1 + B(1)x -1 = ε Esimae eiher ECM or dynamic model

9 To Ensure Coinegraion Γ(L) mus be inverible for an auoregressive model o represen a coinegraion. and ε is assumed o be saionary. Tes is available (e.g. Johansen s MLE), bu no applicable in our case (explained ed laer).

10 DW and Coinegraion For a single equaion model, a large Durbin- Wason saisics means ha here is lile chance ha he residual is nonsaionary. DW approach zero if residual is nonsaionary (Engle and Granger 1987). Durbin-h may no improve very much. Or ploing he residual o check, ofen used by saisicians.

11 Example Esimae Esimae ECM Successful ECM example Toppinen (1998) esimaed a simulaneous equaions demand and supply model for he Finnish sawlog marke. Johansen s Maximum likelihood mehod Nonsaionary daa Srucural model Simulaneous equaion

12 Johansen Maximum Likelihood Mehod Esimaes ECM direcly Designed for esing he exisence of coinegraion. Bu ignores he relaion beween shor-run and dlong-run. Because here may be more han one ECMs for one coinegraion relaion (Maddala and Kim 1998). Two ses of condiions for idenificaion of he model.

13 Mehod for Esimaing Single Equaion Models Γ(L)y + B(L)x = ε Engle-Granger s wo-sep mehod (ignores he relaion beween he long-run and shor-run run coefficiens). Fully modified OLS (Phillips and Hansen 1990) Oher modified LS mehod (Saikkonen 1991, Sock and Wason 1993, Philips and Lorean 1991) wih differenced variables o mop up he dynamic (Maddala and Kim 1998).

14 Fully Modified Leas Squares Assumes ha he error erm is saionary. Correcs boh auocorrelaion and endogeneiy so ha dynamic models can be esimaed wih i. Even if here are endogenous variables on boh side, he mehod can be used. Tes saisics i i can be used in classical l Wald ess. Used o esimae single equaion model wih nonsaionary ime series.

15 Simulaed Annual Daa wih Lagged Response 62 Dada generaed by oupu=0.3price+0.5(lagged oupu)+random 37 Price upu O Year 30

16 Oupu Agains Price The slope of he firs segmen represen he shor-run 38 coefficien of price The verical line shows he lagged effecs The equilibrium is achieved in laer years upu O Fi wih lagged oupu Price

17 Long-Run Relaion upu The righ end of he segmen is he Long-run relaion equilibrium poin The slope of he 36 segmen represens Ohe long-run coefficien of price If here are no lag Price effecs he equilibrium poin is achieved in he firs year.

18 Frequency, Shor-Run and Long-Run Wih monhly daa he slope of he firs segmen may be differen so ha he shor-run run resuls may be differen. The equilibrium poin should be he same so ha he long-run relaion esimaed should be he same.

19 Auocorrelaion and Uni-Roos Price Raios Year Wage/Plum Pele/Plum

20 U.S Sofwood Lumber Supply Supply equaion is derived from Generalized Leonief profi funcion of sawmill indusry (see Wear and Newman 1991, Newman and Wear 1993, Williamson e al for such profi funcions) Le Y is he sofwood lumber oupu. m for maerial (logs), w for wage, k for capial, e for elecriciy. Y 1/ 2 P i = α ll + αli + βα l + γαl 2 i= m,w,k,e P l 2

21 Dynamic Supply Equaion Add a lagged lumber producion o represen he delayed response. Y 1/ 2 P i 2 = α + α + α + α + ηy + 0 i i m,w,k,e P 2 1 = l ε

22 Resuls Esimaed wih FMLS P e has an insignifican coefficien and is excluded. Re-esimaed resuls wih adjused R 2 = 0.79, DW=2.17 Y 1/ 2 1/ 2 1/ 2 P P P m, k, w, Y P + l, P l, P ε l, ( ) ( ) ( ) ( ) ( ) ( ) =

23 Excludes Insignifican Variables The adjused R 2 = 0.81, and DW=2.05 Y 1/ / 2 P m, Y P l, ( ) ( ) ( ) ( ) = + ε

24 Derived ECM and Shor-Run Elasiciy Shor-run run price elasiciy Each year 18% of he equilibrium error is adjused. ΔY P = Δ P m, l, 1/ Y P m P l 1 1/ ε

25 Long-run Relaion and Price Elasiciy y of Supply The long-run price elasiciy of supply is / 2 P m Y = P l

26 Elasiciies of Sofwood Lumber Supply Range from o in Pas Sudies Supply equaion 1. From profi funcion Bernard e al.1997, Norheas SPF 0.27 (K) 2. Linear form Adams and Haynes, 1996; o (K) for differen regions Lewandrowski e al. 1994, (shipmen), 0.35 o 0.44(producion)) Myneni e al. 1994; 0.27 Adams e al (Operaing margin), o 0.510(K) 3. Mill uiliy Cardellichio, o 0.7

27 Sofwood Lumber Demand Model Sofwood Lumber Demand Model Derived from Generalized Leonief cos funcion of housing indusry Lagged dependen variable is included and lagged housing consrucion area H -1 is included because housing consrucions ofen cross wo calendar years. y D is he sofwood lumber demand. me is for meal producs such as meal door, sash and rim, c is for concree, wc is for wage rae of consrucion workers. / i v D H H P D = γ β β β β β β H H me,c,wc,e,k i l i v H H H P H = γ β β β β β β

28 Esimaed Coefficiens Esimaed value P-values β <0.01 β me <0.01 β c <0.01 Adjused R 2 = 0.9 DW = 1.8 All P-values <= β wc β e < β k <0.01 β H < β H <0.01 R DW 1.8

29 Esimaed Elasiciies Variables Means Shor-run elasiciies Long-run elasiciies Pl P me P c P wc P e P k H Two years 0.78 The long-run coefficien of H is -1.12, he sum of he esimaed values for β H and β H1. Long-run housing elasiciy is 0.78 D

30 Collineariy and Explanaion of he Esimaed ddemand dequaion Despie high correlaions among price raios, he inflaed esimaed variances of he coefficien are small enough o obain significan coefficiens. However we do no expec he price raios o However, we do no expec he price raios o change independenly.

31 Collineariy and Explanaion of he Esimaed ddemand dequaion They change simulaneously, and hus heir subsiuion and complemenary effecs ogeher have small effec on lumber demand. The lumber price elasiciy is 032in boh long The lumber price elasiciy is in boh long run and shor run.

32 Price Elasiciies of Demand for he U.S. Marke (1) of Pas Sudies Adams e al. 1986; Adams e al (Kalman Filer esimaes) residenial: shor-run -0.13, long-run -0.55, nonresidenial: 3-4 ime larger (long-run -1.15) Adams and Haynes, 1996, -0.07(1985); Speler, 1985, -0.11(1980)

33 Price Elasiciies of Demand for he U.S. Marke (2) Rockel and Buongiorno, 1982, Rao e al. 2004, o for differen kinds of lumber Bernard e al for U.S. Norheas Spruce-Pine- Fir Lewandrowski e al. 1994, SP , DF , Canadian Lumber, Myneni e al. 1994, -0.10

34 Conclusions-Mehod (1) Shor-run and long-run demand and supply can be esimaed wih dynamic model. The esimaed dynamic model can be ransformed ino ECM. Shor-run implies one period by ECM.

35 Conclusions-Special Aenion (2) Dynamic model mus be able o represen a coinegraion relaion when ime series have uni roos Inveribiliy and high DW are used o ensure assumpion for a FMLS Oher mehods such as residual plo possible

36 Conclusion-Supply (3) The esimaed sofwood lumber supply of he U.S. marke has an elasiciy 004in 0.04 he shor run and 0.23 in he long run, i l dj f h suggesing a very slow adjusmen of he supply o he marke price.

37 Conclusion-Demand (4) The esimae sofwood lumber demand of he U.S. marke is driven by he housing consrucion area. Each percen change in housing area resul in 0.51percen of change (shif of he curve given prices) in sofwood lumber demand in one year bu 078percen 0.78 of change (shif of he curve given prices) in wo years.

38 Conclusions-Implicaion of Collineariy (5) The prices usually change simulaneously, despie heir large elasiciies, heir oal effec on lumber demand is no very large. The esimaed lumber price elasiciy of demand is only in boh he long run and he shor run.

39 Quesions/Commens