Tests for Symmetric and Asymmetric Nonlinear Mean Reversion in Real Exchange Rates

Robert Sollis · Stephen J. Leybourne · Paul Newbold

105 citations0/0 files storedJournal of money credit and banking

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Abstract

New tests, based on smooth transition autoregressive models, for mean reversion in time series of real exchange rates are proposed.One test forces mean reversion to be symmetric about the integrated process central case, while the other permits asymmetry.The tests are applied to monthly series of seventeen real exchange rates against the U.S. dollar and fourteen against the deutsche mark.They reveal stronger evidence against the unit root null hypothesis than does the usual Dickey-Fuller test.THE THEORETICAL IDEA of purchasing power parity, grounded in the "law of one price," is discussed by Rogoff (1996).This law states that, for any good «, P, = EP^, where P-is the domestic currency price of the good, F, is the foreign currency price, and E is the nominal exchange rate as the home currency price of foreign currency.Tariffs, nontariff barriers, and transportation costs can all mitigate against the law of one price, preventing purchasing power parity from holding.However, Rogoff (1996) notes that most economists have an "instinctive belief" in the purchasing power parity hypothesis in the long run, implying mean reversion in time series of real exchange rates.Early analyses of this mean reversion hypothesis, including Meese and Rogoff (1988), Enders (1988), Taylor (1988), and Mark (1990), were based on augmented Dickey-Fuller tests, and generally failed to find strong evidence against the unit root null hypothesis-that is, of mean reversion.Similarly, Edison, Gagnon, and Melick (1994) found only weak evidence of cointegration between nominal exchange rates and relative prices.Frankel (1986) and Lothian and Taylor (1996), arguing that failure to reject the unit root hypothesis could reflect the low power of the test, extended tbe data sets to cover periods of over one hundred years, then finding apparently The authors would like to thank an anonymous referee, whose suggestions significantly improved the initial draft of this paper.

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References

2002Unit root tests in panel data: asymptotic and finite-sample properties 1996The Purchasing Power Parity Puzzle 1998The overvaluation of purchasing power parity 1998Unit-Root Tests and Asymmetric Adjustment With an Example Using the Term Structure of Interest Rates 1984Are Economic Time Series Asymmetric over the Business Cycle?1996Real Exchange Rate Behavior: The Recent Float from the Perspective of the Past Two Centuries 1988Was It Real? The Exchange Rate‐Interest Differential Relation over the Modern Floating‐Rate Period 1990Purchasing Power Parity in the Long Run

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