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1 50-71 APEC PPP (Asia-Pacific Economic Cooperation) (World Trade Organization) Can PPP Predict the Exchange rate? -An Empirical Study on the Exchange Rate of NTD and USD Abstract This study serves one of the first papers to adopt the nonlinear Markovswitching model (hereafter MS model) to examine the performance of purchasing power parity (hereafter PPP) theory in predicting the exchange rate. Specifically, Li, Ming-yuan 1 / Gi, Yen-lin / Markov-switching MSthe theory of purchasing power parity PPP MS PPP MS MS PPP PPP PPP MS PPP MS PPPMS we use the MS model to identify the high- or the low-volatility regime of the exchange rate, establish a model incorporating MS and PPP, and improve the performance in predicting exchange rate of the traditional PPP or MS model. Our empirical findings are consistent with the following notions. First, the two-mean regime and the two-volatility regime setting of the exchange rate of USD and NTD are significant. Second, The explanation performance of PPP in exchange rate is significant (insignificant) in the low- (high-) volatility regime. Third, the prediction performance of the model incorporating MS and PPP outstands the random walk, the MS and the linear PPP model. This study also contributes to practices in Taiwan exchange market, since Taiwan serves one member of APEC (Asia-Pacific Economic Cooperation), and a new comer of WTO (World Trade Organization). Its research design and test results add to the tasks of predication and analysis system of exchange rate. Keywords: purchasing power parity (PPP), Markov-switching model, exchange rate, volatility, Asia-Pacific Economic Cooperation 1 Tel: (049) ext 4984, Fax: (049) , lmy@ncnu.edu.tw

2 purchasing power parity hypothesis PPP 1920 Gustav Cassel arbitrage law of one price PPP PPP PPPPPP Meesse and Rogoff 1983 random walk RMSE MAE ME PPP PPP PPP Edsion 1991 PPP J J MacDonald and Marsh 1997 PPP PPP PPP PPP PPP PPP unit root test stationarity Roll 1979 Mark ( ) post-bretton-woods PPP Frankel 1986 post-bretton-woods Frankel 1990 PPP post-bretton-woods O Engle and Granger 1987 cointegration test PPP Panel PPP Frankel and Rose 1996 Oh 1996 Wu and Chen 1999 Panel Boothe and Glassman 1987 Hsieh 1988 leptokurtic Hsieh 1989 Steurer 1995 BDS 2 Brock Dechert Scheinkman Engel and Hamilton 1990 Klaassen 1999 MS random walk Baum et al exponential smooth transition autoregressive ESTAR PPP 2001 Threshold Model 96 panel PPP PPP (unexpected) (surprise) Hamilton (1989) MS 3 PPP MS PPP PPP PPP MS 2 Brock,W. W. Dechert and J. Scheinkman (regime) 52 53

3 (Asia-Pacific Economic Cooperation Apec) World Trade Organization WTO MS PPP PPP R t st MS 4 5 0<q,p<1 st =-1+p+q CPI TEJ (no switching in mean and variance) R t = u e t R t V 0 0 R t e t (return shock) (Gaussian distribution) (Linear Model) (switching in mean) R t = u st + st. e t st=0,1 R t u0 u1 Rt MS 1 A B (switching in variance) R t = u 0 + st. e t Rt 0 1 Rt (switching in mean and variance) R t = u st + st. e t Rt u0 u1 Rt st 5 st 0 1 (transition probability) p=p(st=1 st-1=1) q=p(st=0 st=0) st (strictly stationary process) 0 p,q 1 St (first order autoregressive) st=(1-q)+ st-1+vt, =-1+p+q vt st Hamilton (1989)

4 MS st t Hamilton (1989) smoothed regime probabilities % , (B) ** (A) MS (0.082) (0.073) (0.045) (0.254) ** (0.647) (0.235) q 0.648** 0.815** 0.821** (0.250) (0.065) (0.063) p 0.993** 0.908** 0.912** (0.006) (0.035) (0.034) ** 1.123** 0.525** 0.530** (0.256) (0.053) (0.054) (0.053) ** 2.044** (0.202) (0.200) Log-likelihood Likelihood ratio ** ** ** (0.216) (0.388) (0.231) (0.402) ** (1.006) (0.619) q ** 0.747** (0.183) (0.068) (0.190) p 0.842** 0.841** 0.473** (0.065) (0.214) (0.125) ** 2.755** 2.052** 1.750* (0.455) (0.233) (0.531) (0.665) ** 3.914** (0.273) (0.276) Log-likelihood Likelihood ratio regime standard error 2. Hansen 1992, TEJ 5. ** * Garcia 1992 MS Hansen Hamilton

5 PPP PPP PPP MS PPP PPP CPI WPI CPI 11 absolute purchasing power parity relative purchasing power parity MS PPP PPP Z t-1 PPP p Z t-1 = S t-1 S t-1 St-1 t-1 S p t-1 PPP t-1 S t-1 p = S 0 p t-1 p f t-1 S p t-1 t-1 S 0 P t-1 P f t-1 t-1 Z t-1 Z t-1 t-1ppp t-1 PPP t MS PPP MS PPP PPP PPP MS R t = u st + st (z t-1 ) + st. e t 1 PPP Z t-1 st PPP st PPP R t = u 0 + st (z t-1 ) + st. e t 2 PPP R t = u st + st (z t-1 ) + st. e t 3 PPP R t = u st + 0. e t p(s t = 0 s t = 0) = q(z t-1 ), p(s t = 1 s t = 1) = p(z t-1 ) 58 59

6 where q(z t ) exp(q 0+q 1 *z t ) (1+exp(q 0 +q 1 *z t )) p(z t ) exp(p0+p1*z t) (1+exp(p0+p1*z t )) 4 PPP Zt-1 PPP Zt-1 0 PPP PPP 0 0 PPP 0 PPP MS PPP 12 PPP 13 MS PPP MS PPP PPP u0 u , PPP CPI WPI CPI WPI 12 R t = R t e t, E (et) = 0 1 E (e i. e t) =0 for t s 13 PPPR t = u ( z t-1 ) l i PPP MS * 0.175* * (0.112) (0.082) (0.090) (0.417) ** (2.052) (0.401) (0.104) * * * (0.599) (0.381) (0.407) ** (8.646) (1.355) (2.222) p ** (1.609) q (1.409) p (6.021) q (8.300) p 0.888** 0.831** 0.832** (0.107) (0.059) (0.059) q 0.993** 0.915** 0.915** (0.006) (0.031) (0.031) ** 0.519** 0.519** 1.133** (0.052) (0.048) (0.047) (0.157) ** 2.012** (0.187) (0.186) Log-likelihood ** * PPP PPP

7 PPP PPP PPP PPP PPP Hamilton (1989) PPP PPP PPP MS PPP 8 7 PPP TVTP-MS PPP PPP PPP PPP MS MS MAE mean absolute error 1 t=s ŷt-y t T t=1 MSE mean squared prediction error 1 t=s (ŷt-y t ) 2 1 t=s E t E t 14 T t=1 T t= ~ ŷ-y ~ bias proportion 2 ŷ1-y 1 T ~ ~ ~ variance proportion 2 (S ˆy -S y ) 2 ŷ1-y 1 T ~

8 PPP MS MS Mathews Diamantopoulos 1994 ratio accuracy volume accuracy bias fit MAE MSE bias proportion variance proportion MAE MSE PPP MS MAE MSE PPP MS PPP MS MAE (0.63%) (1.38%) (2.14%) MSE (0.50%) (1.01%) (2.08%) (0) (-5.24%) (4.01%) Hamilton 1989 MS PPP MS PPP PPP PPP MS PPP PPP PPP PPP PPP PPP MS PPP PPP MS PPP MS PPP MS PPP PPP * * , "Inflation Thresholds and the Purchasing Power Parity: Evidence from Panel Data",2001. Brock, W., W. Dechert and J. Scheinkman 1987, "A test for independence based on the 64 65

9 correlation dimension ", University of Wisconsin, Madison, University of Houston, and University of Chicago. Christopher F. Baum, John T. " Barkoulas, Mustafa Caglayan 2001, Nonlinear adjustment to purchasing power parity in the post-bretton woods era", Journal of International Money and Finance, 20, Edison 1991, H.J., Fishier, E.O. 1991, "A long-run view of the European monetary system", Journal of International Money and Financ, 10, Engel, C. and J.D. Hamilton 1990," Long Swings in Dollar: Are They in the Data and Do Markets Know It? ", American Economic Review, 80, Engel, C. 1994,"Can the Markov Switching Model Forecast Exchange Rates? ", Journal of International Economics, 36, Engle, R. and C. Granger 1987, "Cointegration and Error Correction: Representation, Estimation and Testing", Econometric, 36, Franc, K. 1999, "Purchasing Power Parity: Evidence from a New Test", working paper, Frankel, J.A. 1986,"International Capital Mobility and Crowding-out in the U.S. Economy: Imperfect Integration of Financial Markets or Goods Markets? ", How Open is The U.S. Economy? Lexington: Lexington Books, Frankel, J.A. 1990,"Zen and the Art of Modern Macroeconomics: A Commentary, Monetary Policy for a Volatile Global Economy", Washington DC: American Enterprise Institute for Public Policy Research, Frankel, J.A., A.K. Rose 1996,"A Panel Project on Purchasing Power Parity :Mean Reversion Between and Within Countries", Journal of International Economics,40, Garica, R. 1992," Asymptotic null distribution of likelihood ratio test in Markov switching models", Manuscript, University of Montreal. Harberger, Arnold 1986,"Economic Adjustment and the Real Exchanges Rate, In Developing Countries, ed.",sebastizn Edwards and Liaquat Ahamed, University of Chicago Press, Chicago, Hamilton, J.D. 1990,"Specification testing in Markov-Switching times series models", Journal of Econometrics,70, Hamilton, J.D. 1989,"A new approach to the economic analysis of nonstationary time series and the business cycle", Econometrica,57, Hansen, B. E. 1992, "The likelihood ratio test under nonstandard condition: testing the Markov switching model of GNP", Journal of Applied Econometric, 7, S61-S82. Hansen, B.E. 1993,"Inference when a nuisance parameter is not identified under the null hypothesis", Mimeo, University of Rochester. Hsieh, D.A. 1989,"Testing for nonlinear dependence in daily foreign exchange rates," Journal of business,62, Klaassen, F.J.G.M 1999, "Long swings in Exchange Rates: Are They Really in the Data?", Center for Economic Reseach,Tilburg University, Discussion Paper No Mathews B. P. and A. Diamantopoulos 1994, "Towards a taxonomy of forecast error measures: A factor-comparative investigation of forecast error dimensions", Journal of Forecasting, 13 4, MacDonald, R. and I. W. Marsh 1997, "On fundamentals and exchange rate: A Casselian perspective", The Review of Economics and Statistics. Mark, N. 1990," Real and nominal Exchange Rates in the Long Run: An Empirical Investigation", Journal of International Economics, 28, Messe, R A. and K. D. Rogoff, 1983, "The out-of-sample failure of empirical exchange rate models: sampling error or misspecification? ", in Exchange Rates and International Macroeconomics, Frenkel, J.A. eds Oh, K.Y. 1996, "Purchasing Power Parity and Unit Root Tests Using Panel Data", Journal of International Money and Financ, 15, Roll, R. 1979,"Violations of Purchasing Power Parity and their Implications for Efficient International Commodity Markets", In Marshall Sarnat and Giorgio Szego,eds., International Finance and Trade. Turner, C. M., Startz, R. and Nelson, C.R. 1989,"A Markov model of heteroscedasticity, risk and learning in stock market", Journal of Financial Economics, 25, Steurer, Elmar 1995," Nonlinear modeling of the DEM/USD exchange rates, in Neural 66 67

10 Networks in The Capital Markets", ,John Wiley & Sons. Wu, J.L. and S. L. Chen 1999, "Are Real Exchange Rates Stationary Based on Panel Unit Root Test? Evidence from Pacific Basin Countries", International Journal of Finance and Economics, 4, MS MS 68 69

11 5 MS 7 PPP MS 2 6 PPP MS 1 8 PPP MS

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