An Analysis Of Purchasing Power Parity Based On Nonlinear Dynamics Of Real Exchange Rate

Purchasing Power Parity is one of the fundamental theories describing the behavior of the exchange rate.Previous empirical studies focus on the validity of the theory by examining exchange rates.Researchers find that it is difficult to reject the unit root null hypothesis of the real exchange rate data under a linear framework.Although the unit root hypothesis can be rejected by using long span data or panel data,the speed of adjustment towards the long run equilibrium is quite slow,which could take three to five years for half-life shock adjustment.Nonlinearity is found to be more suitable for explaining this PPP puzzle while nonlinear models such as the TAR and STAR models have become popular over the last decades.Whether the PPP theory applies for RMB real exchange rate,the results are inconclusive.In the early empirical studies,linear unit root test and cointegration test cannot provide solid evidence for the validity of PPP.Therefore,some scholars argue that due to the specialty of the capital market in China,PPP is not proper to fit and forecast the RMB exchange rate.Many of them try to explain the deviations from PPP.Others try to build nonlinear frameworks to capture the volatility of the RMB exchange rate.In this study,the ESTAR model is employed to capture the nonlinearity in the adjustment process for sterling-dollar,mark-dollar,franc-dollar and RMB-dollar real exchange rates.After analyze the movement of RMB-dollar real exchange rate,the article tries to shed light on the validity of the PPP in China and offer some suggestions based on the empirical results.There are some innovations in this study.First,since the conditional heteroscedasticity is seldom considered in the existing studies,the model ESTAR is augmented into ESTAR-GARCH based on the properties of the residuals.In addition,the regime alteration is also included in the model specification.Second,there are few articles based on RMB exchange rate advocate the PPP theory.I hope this study which based on the nonlinear ESTAR can provide further evidence for PPP.Third,for the sterling-dollar,mark-dollar and franc-dollar,the out of sample period covers the post-Bretton Woods era.And for RMB-dollar real exchange rate,the out of sample forecast starts after the reform of the RMB exchange rate regime taken place in July 2005.Based on the out of sample forecasts,random walk model,linear AR model,ESTAR model and ESTAR-GARCH model are compared based on the forecast evaluation tests.After analysis the four real exchange rates,the results provide further support for PPP theory,ESTAR and ESTAR-GARCH modelling.Furthermore,the forecast accuracy tests and forecast encompassing tests are employed for pair comparison between Random Walk,linear AR model,nonlinear ESTAR and ESTAR-GARCH models.The results show that ESTAR and ESTAR-GRACH model outperform the Random Walk model.In terms of the RMB-dollar real exchange rate,the results show that PPP theory fits for the current RMB-dollar real exchange rate and the RMB is over-valued in recent years.In addition,the real exchange rate follows a typical nonlinear mean reversion process among four cases,which is caused by the intervention of the government.When a shock strikes,the RMB-dollar adjusts to the long-run equilibrium with the fastest speed in four cases reflecting that the reform of the exchange rate regime has achieved great success.However,since the capital market in China is still under development and the internationalization of RMB is a long-term goal,the revolution of the exchange rate regime is highly required.Therefore,it is vital to improve the elasticity of the RMB exchange rate and deepen the development of the macro supervision system,in order to tackle the destructive capital outflow and stabilize the RMB exchange rate.