Mean reversion of real exchange rates in high-inflation countries.

• Author: Bleaney, Michael F.

1. Introduction

   Are exchange rate dynamics different in high inflation periods? Surprisingly, there has been relatively little work done on this issue. Yet there is a strong prima facie case for the proposition that the dynamics of real exchange rates are influenced by inflationary circumstances. First, at high rates of inflation, nominal shocks dominate real shocks, whereas at low rates the opposite is true. This suggests that mean-reverting tendencies in real exchange rates are likely to be more evident at higher inflation rates. Second, when inflation is high, demand for domestic money as an asset falls and it begins to be displaced by foreign currencies. This currency substitution implies flows across the exchanges, which are likely to affect both the short-run dynamics and the long-run equilibrium in real exchange rates.

   In the many empirical tests of purchasing power parity (PPP) reported in the literature, there is a clear pattern of greater support for PPP in episodes of high inflation. The classic example is the German hyperinflationary experience of 1922-1923, documented by Frenkel (1978), Edison (1985), and Taylor and McMahon (1988), but the same phenomenon is apparent for pegged exchange rates in Latin American countries in the postwar period (see McNown and Wallace 1989; Liu 1992). It is particularly striking that the estimated coefficients of cointegrating regressions between exchange rates and relative prices are much closer to the PPP-predicted value of unity in high inflation cases (e.g., compare Liu [1992] with Cheung and Lai [1993] for OECD countries).

   Empirical evidence from countries that have experienced varying inflation rates is, however, more ambiguous. Zhou (1997) cannot reject a unit root in the real exchange rate for five countries with episodes of high inflation but concludes in favor of stationarity after allowing for structural breaks that represent shifts in the level and/or the time trend of the estimated equilibrium real exchange rate. These shifts, the dates of which are estimated endogenously, appear to be associated with changes in the inflation regime. In this paper, we pursue this line of inquiry using monthly data from four economies that have experienced episodes of high inflation. We investigate fixed-parameter mean reversion models of the real exchange rate using the standard augmented Dickey-Fuller (ADF) unit root tests and compare these with the Leybourne-McCabe test, which takes stationarity as the null and has a unit root alternative. Further tests allow for a stochastic unit root and permit the deviations of the root from unity to follow a noise process or a random walk. We find possible evidence of both kinds of behavior and use a Kalman filter to estimate the root trajectories through time. These show that large spikes occur in the mean reversion process at times of high inflation.

   We conclude that a stochastic unit root model provides a more suitable econometric method to model mean reversion in real exchange rates than fixed coefficient unit root processes like ADF tests. Intuitively, the stochastic unit root process is preferred because it captures the spikes in the unit root often associated with jumps in the real exchange rate arising from episodes of high inflation, Since stochastic unit root models are able to allow for jumps in real exchange rates (which might otherwise cause standard unit root tests to spuriously reject the null of nonstationarity), they are to be preferred when assessing the evidence for purchasing power parity in high inflation countries.

2. Data Issues

   End of month data for the exchange rate and the wholesale price index were collected for Argentina, Brazil, Chile, and Israel for the period 1972(1)-1993(5) from International Financial Statistics. The countries chosen are similar to those covered by McNown and Wallace (1989); however, our data period is approximately twice as long as that used by McNown and Wallace. For reasons of comparison, we also analyze data from a Latin American country (Colombia) that has not experienced a high inflation episode. The inflation rate in the five countries is plotted in Figure 1, which shows the monthly change in the logarithm of the wholesale price index. Several features stand out.

   (1) There appears to be a positive association between the mean and the variance of inflation: Periods of high inflation are also characterized by high volatility of the inflation rate. This is a familiar finding.

   (2) Periods of very high inflation are not very persistent, Rather, they tend to appear as spikes in the data, and even when the average inflation rate is high for a relatively long period, there are months of quite moderate inflation rates within that period. Thus, the inflation rate has a highly skewed distribution, with below-average observations far more frequent than above-average ones.

   (3) The historical behavior of the inflation rate varies considerably from country to country. This is not surprising, but it is a useful reminder that high-inflation experiences are not necessarily identical to one another (as our empirical results confirm).

   We can identify certain historical features from the graphs since most of the major reforms have often been in response to inflationary circumstances getting out of hand. In the case of Argentina, the two most dramatic spikes occur in 1989 and 1990 as a result of two particularly traumatic hyperinflation episodes that resulted from 10 years of public finance problems. They were brought under control by two stabilization programs, the first of which...