## 1 INTRODUCTION

In recent years, the half-life of deviations from purchasing power parity (PPP) has become a commonly used measure of the degree of mean reversion in real exchange rates.1 Understanding just how uncertain half-life estimates are is important for economists. For example, Rogoff (1996, p. 664, emphasis added) stresses that:

…it would seem hard to explain the short-term volatility [of real exchange rates] without a dominant role for shocks to money and financial markets. But given that such shocks should be largely neutral in the medium run, it is hard to see how this explanation is consistent with a

half-life for PPP deviations of three to five years

Rogoff's claim about the value of half-life is based on an informal reading of the empirical literature on the half-life under the recent float. In this paper, we present a Bayesian framework in which the uncertainty about the half-life can be quantified and alternative hypotheses about the half-life may be formally evaluated.

The literature on open economy macroeconomics concludes that different classes of theoretical models have different implications for the persistence of deviations from PPP. Models with purely nominal rigidities, for example, are unlikely to generate much persistence in deviations from PPP. In contrast, models with persistent differences in productivity growth across countries, intertemporal consumption smoothing or cross-country wealth redistribution effects are consistent with much slower mean reversion in real exchange rates. It is not surprising therefore that many economists are uncertain about what degree of mean reversion to expect in the real exchange rate. We set out to capture this prior uncertainty in the form of a prior distribution for the half-life. The starting point of our analysis is a survey study conducted by the authors in the summer of 1999, in which economists with an interest in the PPP debate were questioned about their subjective prior probability distribution for the half-life under the recent float. Based on the survey responses, we propose a prior probability distribution for the half-life intended to capture widely held views among economists. This *consensus prior* is used as a benchmark in our analysis and formally compared to a number of alternative views about the half-life. The use of economically informed priors in studying the uncertainty about the half-life has not been attempted before.

Our Bayesian framework allows us to incorporate formally such prior information. We first derive the posterior probability distribution of the half-life under the consensus prior. Our results confirm the presence of substantial uncertainty about the half-life of deviations from PPP, similar to the conclusion of a recent study by Murray and Papell (2000) based on classical confidence intervals for the half-life. On average, for the 17 countries analysed, the 68% (90%) posterior error bands cover values between about 2.4 (1.9) and 7.5 (15.1) years.

Our second finding is that the posterior is heavily influenced by the consensus prior. This fact makes it important to study the extent of the empirical support for the consensus prior relative to other plausible views about the half-life. Through the lens of our econometric model, we provide for the first time a comprehensive formal evaluation of several nonnested hypotheses of economic interest, including Rogoff's (1996) claim that the half-life is contained in the range of three to five years. These hypotheses are parameterized as priors about the half-life. Such nonnested comparisons have not been carried out in the existing PPP literature. We show that the data do not strongly favour Rogoff's claim nor any other of a number of hypotheses of economic interest including the consensus prior. These empirical results are new and would not have been readily apparent without formal analysis. They suggest that PPP studies of one country and one variable at a time are unlikely to shed light on the questions of economic interest, and they motivate the investigation of structural models of the real exchange rate that involve multiple equations, a task to which Bayesian methods seem eminently suited.

The remainder of the paper is organized as follows. In Section 2, we motivate the use of the half-life concept in assessing the evidence of long-run PPP. In Section 3, we describe the survey data underlying the consensus prior. In Section 4, we discuss the general econometric framework of our analysis. Section 5 contains the empirical results. Conclusions are presented in Section 6.