Price Indices and Nonlinear Mean-Reversion of Real Exchange Rates

Abstract

[Author Affiliation]Jyh-Lin Wu, Institute of Economics, National Sun Yat-sen University, Kaohsiung, 804, Taiwan; jlwu2@mail.nsysu.edu.tw and the Department of Economics, National Chung-Cheng University, Chia-Yi, 106, Taiwan; ecdjlw@ccu.edu.tw; corresponding authorPei-Fen Chen, Department of International Business and Trade, Shu-Te University, Kaohsiung, Taiwan; cpf@mail.stu.edu.tw[Acknowledgment]We thank two anonymous referees for interesting and constructive comments on an earlier version of the paper. Any remaining errors are ours.1. Introduction Are price indices crucial for the existence of a nonlinear mean reversion of real exchange rates? Do prices or exchange-rate adjustments dominate when deviations from purchasing power parity (PPP) occur? Is the half-life implied by a nonlinear model reasonable? The purpose of this article is to address the above three questions for the UK and New Zealand over the period of recent float.The PPP hypothesis has been one of the most intensive research issues in empirical international finance over the past two decades. The rationale behind it is a simple arbitrage hypothesis, which results in a linear adjustment of deviations from PPP and the stationarity of real exchange rates. Empirically, existing evidence based on unit-root tests provide mixed results for PPP (Abuaf and Jorion 1990; Mark 1990; O'Connell 1998a).Theoretically there are several reasons for the nonlinear adjustment of deviations from PPP, such as the existence of market frictions or transaction costs (Sercu, Uppal, and Van Hulle 1995). In addition, models of pricing to market and exchange rate pass-through give rise to impediments to goods' arbitrage (Krugman 1987; Froot and Klemperer 1989). The implication is that the speed of adjustment of deviations from PPP depends on the magnitude of the deviations.On the other hand, the adoption of a price index is crucial in examining PPP. Several authors have argued that the consumer and producer price indices (CPI and PPI, respectively) do not correspond to their theoretical counterparts and contain measurement errors and aggregation biases (Cheung and Lai 1993; Imbs et al. 2005). In addition, the commodity basket for CPI and PPI includes nontradable goods, which impart a nonstationary component to real CPI or PPI exchange rates (Engel 1999). Recently, Xu (2003) argues that the price index of traded goods (TPI) is the appropriate one for PPP since it reflects the behavior of arbitrage better than the CPI or PPI.The purpose of this article, therefore, is to examine the nonlinear dynamics of TPI-based real exchange rates. Several authors have applied a smooth transition autoregressive (STAR) model to capture the nonlinear dynamics of real exchange rates, as it allows for a smooth adjustment between regimes (Michael, Nobay, and Peel 1997; Taylor, Peel, and Sarno 2001). There are several reasons for us to apply a band-threshold autoregressive (TAR) instead of a STAR-type model in our empirical analysis. First, our empirical evidence fails to reject the unit-root hypothesis against the hypothesis of a nonlinear STAR stationary process based on the test provided by Kapetanios, Shin, and Snell (2003).1 Second, the plots of CPI-, PPI-, and TPI-based real exchange rates in Figure 1 show that the TPI-based real rate has the largest variation among these three real rates. Third, our empirical evidence rejects the null hypothesis of linearity against TAR-type nonlinearity and supports the hypothesis that real exchange rates are TAR-type stationary.Figure 1 Plots of Real Exchange Rates for the UK and New Zealand (Figure omitted. See article image.)Several empirical studies have applied a threshold-type process to examine the nonlinear mean-reversion of real exchange rates (Obstfeld and Taylor 1997; O'Connell 1998b; Taylor 2001; Sarno, Taylor, and Chowdhury 2004). …