Purchasing Power Parity, Productivity Differentials and Non-linearity Jyh-Lin Wu, Institute of Economics, NSYSU Pei-Fen Chen, D. of International Business Studies, NCNU Ching-Nun Lee, Institute of Economics, NSYSU The Manchester School, 77, 2009, 271-287 Institute of Finance and Information, KUAS 19, April, 2011

The validity of PPP Empirically, the validity of the PPP can be examined by testing the stationarity of real exchange rates. Conventional literature linear unit-root tests fails to reject the unit-root hypothesis for real exchange rates. The real exchange rate is defined as

Possible reasons not supporting PPP Standard unit root tests have low power The presence of transactions costs The presence of Harrod-Balassa-Samuelson effects (Harrod, 1939; Balassa, 1964; Samuelson, 1964). The HBS effects suggest that fast growing economies will experience a rising relative price of non-tradables and hence a real appreciation over time. In this case, deviations from the PPP will revert to an equilibrium trend instead of a constant equilibrium

The presence of transactions costs Sercu et. al, 1995; Coleman, 1995; Krugman, 1987; Froot and Klemperer, 1989 Implication: the speed of adjustment of deviations from PPP depends on the magnitude of the deviations Band-TAR process developed by Balke and Fomby (1997) is appropriate for the nonlinear real exchange rate adjustment with regard to the presence of transactions costs

The Econometric Model and its Estimation Methods (1)

The Econometric Models  

The Econometric Models  

The Econometric Models  

The Econometric Models  

The Econometric Models  

The Estimations  

Testing Hypotheses  

Generalized Impulse Response Function Analysis  

Data Data for the nominal pound-dollar rate and producer price indices over 1885-1994 are obtained from Engel and Kim (1999) and are extended to 2003 using IMF’s international financial statistics We extend Engel-Kim’s data from 1994 to 2003 using the data from IFS. 1995=100. Data for real per capita GDP for US and UK are obtained from Global Financial Data

3. Empirical Results

4. Conclusion We find that the unit root hypothesis of real exchange rates is rejected at the 5% level of significance if one approximates the non-constant equilibrium with either the differential of real GDP per capita or a non-linear trend. After removing the non-constant equilibrium of the real pound-dollar rate, we find that it is appropriate to model the real rate in a symmetric band-TAR model, in which it exhibits the property of non-linear mean reversion. the generalized impulse response analysis points out that the rate of adjustment for larger shocks is much faster than the rates previously reported by linear models.

Selected References Balassa, B. (1964). “The purchasing-power-parity doctrine: a reappraisal”. Journal of Political Economy, Vol. 72, No. 6, pp.584-596. Balke, N. S. and Fomby, T. B. (1997). “Threshold cointegration”, International Economic Review, Vol. 38, No. 3, pp. 627-645. Cheung, Y-W and Lai, K. S. (2000). “On the purchasing power parity puzzle”, Journal of International Economics, Vol 52, No. 2, pp. 321-330. Engle, C. and Kim, C. J. (1999). “The long-run U.S./U.K. real exchange rate,” Journal of Money, Credit, and Banking, Vol. 31, No. 3, pp. 335-356. Hansen, B. E. (1997). “Inference in TAR models.” Studies in Nonlinear Dynamics and Econometrics, Vol. 2, No. 1, pp. 1-14. Hansen, B. E. (1999). “Testing for linearity” Journal of Economic Survey, Vol. 13, No. 5, pp. 551-76.

Selected References Koop, G., Pesaran, M. H. and Potter, S. (1996). “Impulse response analysis in nonlinear multivariate models”. Journal of Econometrics, Vol. 74, No. 1, pp. 119-147. Lothian, J. R and Taylor, M. P. (2000) “Purchasing Power Parity Over Two Centuries: Strengthening the Case for Real Exchange Rate Stability”, Journal of International Money and Finance, Vol. 19, No. 5, pp. 759-764. O’Connell, P. G. J. (1998), “Market frictions and real exchange rates,” Journal of International Money and Finance, Vol. 17, No. 1, pp. 71-95. Rogoff, K. (1996). “The purchasing power parity puzzle,” Journal of Economic Literature, Vol. 34, No. 2, pp. 647-668. Samuelson, P. A. (1964). “Theoretical notes on trade problems,” Review of Economics and Statistics, Vol. 46, No. 2, pp. 145-154. Taylor, A. M. (2002). “A Century of Purchasing Power Parity”, Review of Economics and Statistics, Vol. 84, No. 1, pp. 139-150.