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1 c 2003 FAO WTO OLS 2SLS 3SLS OLS 1. WTO 1992 Gallagher 1980 McKillop

2 Yukutake et al Koopmans-Hitchkock Labys 1989 JAFSEM Japanese Forest Sector Model JAFSEMII Yoshimoto and Yukutake 2002 IIASA International Institute for Applied Systems Analysis GTM Global Trade Model Kallio et al GTM Perez-Garcia 1993 CGTM CINTRAFOR Global Trade Model Zhu et al FAO GFPM Global Forest Product Model FAO 4 FAOSTAT Database FAO

3 FAO OLS 2SLS 3SLS A B X A 1 a DaDa SaSa X p a x a B X 1 c DbDb SbSb B A B p b x b A B X p a <p b (2.1) q = sa da = db sb p A B ABE A B E A CDE B C D E 1 b A B E GFPM FAO A B 1.

4 GFPM 1 b ED MD ES MS FAOSTAT Database 1 1 FAOSTAT b p q A A B B p q B A a 1.2 a 1.3 a 1.4 (2.2) log(q S i,t) =a a 1.2 (+) log(p i,t)+a 1.3 log(wag i,t) ( ) + a 1.4 log(exr i,t)(or + a 1.5 log(q S i,t 1)) (+) (2.3) log(q D i,t) =a a 2.2 ( ) log(p i,t)+a 2.3 log(gdp i,t) (+) + a 2.4 log(exr i,t)(or + a 2.5 log(q D i,t 1)) ( ) (2.4) log(q S i,t) =log(q D i,t) Q i,t P i,t WAG i,t EXR i,t t i GDP i,t t i GDP S D GDP 2.2

5 FAO OLS (2.5) log(q S i,t) =b (2.6) log(q D i,t) =b X k=0 6X k=0 b 1.2,k log(p i,t k )+b 1.3 log(wag i,t)+b 1.4 log(exr i,t) b 2.2,k log(p i,t k )+b 2.3 log(gdp i,t)+b 2.4 log(exr i,t) FAOSTAT Database International Financial Statistic Yearbook 2000 SDR IMF special drawing right Michie and Kin GDP v j,t q j,t prdp j,t j t m =100 Exr j,t Gdp j,t Wag j,t GDP i n i 1.

6 p j,t = v j,t/q j,t 2 rp j,t = p j,t/prdp j,t 3 P i,t = 4 EXR i,t = 1 n i n X i j=1 n X i Exr j,t j=1 5 GDP GDP i,t = 1 n i 6 WAG i,t = 1 n i (rp j,t q j,t) n X i j=1 n i X j=1, ni X j=1 (Gdp j,t/prdp j,t) (Wag j,t/prdp j,t) GDP i,t GDP WAG i,t GDP 3.2 t spurious regression Dickey and Fuller 1979 unit root Johansen 1988, Johansen and Juselius 1990, 1992 co-integration TSP Hall 1999 TSP Dickey and Fuller t Johansen trace 30 Johansen DF 1 ADF 2 10 GDP GDP q j,t

7 FAO

8 p- r H : r =0 H : r 1 H : r H : r

9 FAO

11 FAO P/Wag 6 4 4

12 SLS 3SLS GDP OLS 2SLS 3SLS OLS OLS GDP GDP GDP t-

13 FAO 159 P/Gdp 5 t OLS 2SLS 3SLS OLS OLS Engle and Granger

15 FAO

16 FAOSTAT SLS 3SLS OLS OLS OLS

17 FAO 163 OLS Dickey, D. A. and Fuller, W. A Distribution of the estimators for autoregressive time-series with a unit root, J. Amer. Statist. Assoc., 74, Engle, R. F. and Granger, C. W. J Co-integration and error corrections representation, estimation and testing, Econometrica, 55, FAO FAOSTAT DATABASE: Forestry, FAO, Rome. Gallagher, P An analysis of the softwood log trade between the United States and Japan, Technical Bulletin 330 Forestry Series, No. 34, 2 19, Agricultural Experiment Station, University of Minnesota, Minnesota. Hall, B. H Time Series Processor Version4.5, User s Reference Manual, TSP International, California. Johansen, S Statistical analysis of cointegrating vectors, J. Econom. Dynam. Control, 12, Johansen, S. and Juselius, K Maximum likelihood estimation and inference on cointegrationwith application to the demand for money, Oxford Bulletin of Economics and Statistics, 55, Johansen, S. and Juselius, K Testing structural hypotheses in multivariate cointegration

18 analysis of the PPP and the UIP for UK, Journal of Econometrics, 53, Kallio, M., Dykstra, D. P. and Binkley, C. S The Global Forest Sector: An Analytical Perspective, Wiley, New York. Labys, W. C Spatial and temporal price and allocation models of mineral and energy markets, Quantitative Methods for Market-oriented Economic Analysis over Space and Time eds. W. C. Labys, T. Takayama and N. D. Uri, 14 47, Avebury, Vermont. McKillop, W. L. M Structural analysis of Japan-North America trade in forest products, Forest Science, 19 (1), Michie, B. and Kin, S A Global Study of Regional Trade Flows of Five Groups of Forest Products, World Forests, Society and Environment Research Program, Helsinki II 103, Perez-Garcia, J. M Global forestry impacts of producing softwood supplies from North America, CINTRAFOR Working Paper 43, Center for International Trade in Forest Products, College of Forest Resources, University of Washington, Seattle , TSP 2 p Yoshimoto, A. and Yukutake, K Japanese forest sector modeling through a partial equilibrium market model, Journal of Forestry Research, 7, Yukutake, K., Yoshimoto, A., Nagata, S. and Tachibana, S Forest sector modeling in Japan, Proceeding of Project Group P.6.11 FORESEA Meeting at the 20 th IUFRO World Congress, CINTRAFOR, SP22, , Centor for International Trade in Forest Products, College of Forest Resources, University of Washington, Seattle II OLS 109, 1 4. Zhu, S., Tomberlin, D. and Buongiorno, J Global forest products consumption, production, trade, and prices: GFPM model projections to 2010, Forestry Policy and Planning Division, Forestry Department, FAO, Rome.

19 Proceedings of the Institute of Statistical Mathematics Vol. 51, No. 1, (2003) 165 Derivation of Export/Import Functions for Forest Products Trade Using FAO Data Kiyoshi Yukutake (Department of Agriculture, Miyazaki University) Atsushi Yoshimoto (The Institute of Statistical Mathematics) Hiroe Hamada (Department of Agriculture, Miyazaki University) The problem of environmental conservation and timber products trade has been one of the major issues in international meetings, e.g., WTO, where quantitative analysis using trade models has been playing an important role in negotiations. In constructing the trade models, it is necessary to have the export/import functions of the target products in the target regions. These functions are derived by applying the price elasticity of the corresponding export and import of the products. In this study, we estimate the price elasticity of the export and import of timber products, where the sign test of the derived elasticity is mainly implemented. There are ten target regions: Japan, developing countries in Asia, North America, Central America, South America, East Europe, West Europe, Oceania, Russia, and Africa. The target products are industrial logs, lumber, wooden panels, chips and particles. The data source is the FAO statistics data on a monthly basis from 1970 to We apply OLS, 2SLS, and 3SLS estimation methods to the logtransformed linear functions. Furthermore, considering the effect of time-lagged variables, the Almon lag model is also estimated. Our experiments show that if the results from OLS are unsatisfactory for the sign test, none of the others, i.e., 2SLS, 3SLS and Almon lag could outperform it. The supply side estimation would not be satisfactory in terms of the sign test in most cases. Key words: Trade structure of forest products, function of exports & imports, price elasticity, econometric analysis.

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main.dvi FORMATH Vol. 8 (2009): 63 91 63 FAO, The Reporting Status of FAO Statistics on the Forest Resources and Forest Products Oka, Hiroyasu : : Abstract:,,, FAO (2005 ) (2006 ). FRA2005 7, 9. 99%,, FAO. 3/4,.,