1. 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,
Institute of Finance and Information, KUAS
19, April, 2011

2. 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

3. 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

4. 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

5. The Econometric Model and its Estimation Methods
(1)

6. The Econometric Models

7. The Econometric Models

8. The Econometric Models

9. The Econometric Models

10. The Econometric Models

11. The Estimations

12. Testing Hypotheses

13. Generalized Impulse Response Function Analysis

14. Data
Data for the nominal pound-dollar rate and producer price indices over 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 =100.
Data for real per capita GDP for US and UK are obtained from Global Financial Data

15. 3. Empirical Results

20. 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.

21. Selected References
Balassa, B. (1964). “The purchasing-power-parity doctrine: a reappraisal”. Journal of Political Economy, Vol. 72, No. 6, pp
Balke, N. S. and Fomby, T. B. (1997). “Threshold cointegration”, International Economic Review, Vol. 38, No. 3, pp
Cheung, Y-W and Lai, K. S. (2000). “On the purchasing power parity puzzle”, Journal of International Economics, Vol 52, No. 2, pp
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
Hansen, B. E. (1997). “Inference in TAR models.” Studies in Nonlinear Dynamics and Econometrics, Vol. 2, No. 1, pp
Hansen, B. E. (1999). “Testing for linearity” Journal of Economic Survey, Vol. 13, No. 5, pp

22. 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
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
O’Connell, P. G. J. (1998), “Market frictions and real exchange rates,” Journal of International Money and Finance, Vol. 17, No. 1, pp
Rogoff, K. (1996). “The purchasing power parity puzzle,” Journal of Economic Literature, Vol. 34, No. 2, pp
Samuelson, P. A. (1964). “Theoretical notes on trade problems,” Review of Economics and Statistics, Vol. 46, No. 2, pp
Taylor, A. M. (2002). “A Century of Purchasing Power Parity”, Review of Economics and Statistics, Vol. 84, No. 1, pp