The behavior of real exchange rates during the post-Bretton Woods period

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Abstract

Since standard tests for mean reversion in real exchange rates may lack power with data spanning the recent float, researchers have employed more powerful multivariate tests. Such tests may, however, reject joint non-stationarity when just one of the processes is stationary. We suggest another test, easily constructed and with a known limiting distribution, whose null hypothesis is violated only when all of the processes in question are stationary. We investigate the finite-sample properties of both types of test by Monte Carlo simulation. Finally, we apply the tests to real exchange rates among the G5 over the recent float.

Introduction

The purchasing power parity (PPP) hypothesis states that national price levels expressed in a common currency should be equal. Equivalently, strict PPP implies that movements in the nominal exchange rate should be proportional to the ratio of national price levels or that the real exchange rate should be constant. PPP has variously been viewed as a theory of exchange rate determination, as a short-run or long-run equilibrium condition, and as an efficient arbitrage condition in either goods or asset markets (Officer, 1982, Dornbusch, 1987, Taylor, 1995, Froot and Rogoff, 1995, Rogoff, 1996).

The professional literature on PPP has a long history (Officer, 1982). Prior to the recent float, the professional consensus appeared to support the existence of a varying but fairly stable real exchange rate over long periods of time (e.g. Friedman and Schwartz, 1963, Gaillot, 1970). The prevailing orthodoxy of the early 1970s, however, assumed the much stronger proposition of continuous PPP (e.g. Frenkel, 1976, Frenkel and Johnson, 1978). In the mid to late 1970s, in the light of the very high variability of real exchange rates after the major exchange rates were allowed to float, this extreme position was largely abandoned (Frenkel, 1981). Subsequently, studies published mostly in the 1980s, which could not reject the hypothesis of random walk behavior in real exchange rates (e.g. Roll, 1979, Adler and Lehmann, 1983, Piggott and Sweeney, 1985), and related work which failed to find cointegration between nominal exchange rates and relative prices (e.g. Taylor, 1988, Corbae and Ouliaris, 1988, Enders, 1988, Mark, 1990) further reduced professional confidence in PPP and led to the widespread belief that it was of little or no use empirically (e.g. Dornbusch, 1988).1

A possible rationalisation of the widespread failure to reject non-stationarity of real exchange rates, suggested by a number of authors, is that the span of available data for the recent floating rate period alone may simply be too short to provide any reasonable degree of test power in the normal statistical tests for non-stationarity (Frankel, 1989, Lothian and Taylor, 1997, Hakkio and Rush, 1991). Accordingly, researchers have sought to remedy this by increasing the sample period under investigation, (e.g. Frankel, 1986Frankel, 1989Edison, 1987Abuaf and Jorion, 1990Kim, 1990Lothian, 1990Hakkio and Joines, 1990Diebold et al., 19912; Lothian and Taylor, 1996). As noted by Frankel and Rose (1996) and others, however, the long samples required to generate a reasonable level of statistical power with standard stationarity tests may be unavailable for many currencies and may potentially be inappropriate because of regime changes. While some authors, notably Lothian and Taylor (1996), have argued that reliable inferences can be drawn by extending the data across exchange rate regimes – at least concerning the stability of the first moments of real exchange rate series – others remain skeptical of this view. A number of authors, including Baxter and Stockman, 1989, Mussa, 1986, Frankel, 1989, Hegwood and Papell, 1998, argue that the statistical properties of the real exchange rate appear to vary strongly across nominal exchange rate regimes.3 To settle the issue of whether the real exchange rate has behaved in a mean-reverting fashion over the post-Bretton Woods period would therefore seem to require inference based on data for the recent float alone.

A second approach has therefore been taken by some researchers, involving the use of panel data on exchange rates over relatively shorter periods of time. Flood and Taylor (1996), for example, analyze a panel of annual data on 21 industrialized countries over the floating rate period and find strong support for mean reversion towards long-run purchasing power parity by regressing 5, 10 and 20 year average exchange rate movements on average inflation differentials with the US. Frankel and Rose (1996) analyze a very large panel of annual data on 150 countries in the post World War II period and also find evidence of mean reversion similar to that evident in studies of long time series. In an influential paper Abuaf and Jorion (1990) develop a multivariate unit root test based on systems estimation of autoregressive processes for a set of real exchange rate series, and use this to reject the joint null hypothesis of non-stationarity of a number of real exchange rates for the recent floating rate period. Panel data methods have also been applied to this issue by, inter alios, Wei and Parsley, 1995, Wu, 1996, Oh, 1996, O'Connell, 1998, Papell, 1998.

In the present paper, we seek to contribute to this literature in a number of ways. Firstly, we provide some further evidence on panel unit root tests of this kind, by calculating the finite sample empirical distribution of a multivariate augmented Dickey-Fuller (MADF) statistic while allowing for higher-order serial correlation in real exchange rates and relaxing the assumption that the sum of the autoregressive coefficients are identical across the panel under the alternative hypothesis.

Secondly, however, we point out and illustrate through Monte Carlo simulations an important potential pitfall in the interpretation of multivariate unit root tests of this kind. The pitfall is simply this: the null hypothesis in panel unit root tests is usually that all of the series under consideration are realizations of unit root processes. Thus, the null hypothesis will be violated even if only one of the real exchange rate series in the panel is in fact stationary. Hence, although such multivariate tests may be informative under certain conditions, they may also be relatively uninformative since rejection of the null hypothesis will in general not help the researcher in determining how many of the series under consideration are stationary. We show, inter alia, that multivariate unit root tests of this kind may lead to a very high probability of rejection of the joint null hypothesis of non-stationarity when there is a single stationary process among a system of otherwise unit root processes, even when the root of the single stationary process is close to the unit circle.

Thirdly, therefore, we investigate by Monte Carlo methods the finite-sample empirical performance of a multivariate test in which the null hypothesis is that at least one of the series in the panel is a realization of a unit root process. This null hypothesis is only violated if all of the series are in fact realizations of stationary processes.4 Moreover, the test procedure we suggest is now widely available to researchers since it simply involves a special application of Johansen's (Johansen, 1988) maximum likelihood procedure for testing for the number of cointegrating vectors in a system. A further attractive property of this test which we demonstrate is that, in the special case we examine – ie. under the null hypothesis that at least one of the series is a realization of a unit root process – it has a known limiting χ2(1) distribution. We compute finite-sample critical values for this test but we also show that the finite sample empirical distribution is quite close to the asymptotic distribution in sample sizes exceeding about 100, corresponding approximately to the number of quarterly observations currently available for the recent float.5

The remainder of the paper is set out as follows. In Section 2we briefly outline the PPP hypothesis and the long-run properties of real exchange rates which it implies. In Section 3we outline two multivariate unit root tests based on a generalization of the augmented Dickey-Fuller test statistic and of the Johansen maximum likelihood cointegration procedure respectively. In Section 4we discuss some preliminary data analysis and univariate unit root tests on four dollar real exchange rates over the floating rate period. In Section 5we report Monte Carlo evidence on the two multivariate tests described in Section 3. In Section 4we employ these tests on quarterly dollar real exchange rates constructed using nominal exchange rates and either relative consumer price indices or relative GDP deflators among the G5 countries over the recent floating rate period. In Section 7we report further empirical and Monte Carlo work based on real exchange rates among the same countries constructed using producer price indices; this section is designed as a check on the generality of the simulation results derived earlier as well as an investigation of real exchange rates constructed using price indices containing a smaller proportion of non-tradables. A final section summarizes and concludes.

Section snippets

Long-run purchasing power parity

PPP may be examined through the real exchange rate since the logarithm of the real exchange rate, qt, can be defined as the deviation from PPP:qtst+ptptwhere st denotes the logarithm of the nominal exchange rate (domestic price of foreign currency) observed at time t and pt and pt* are the logarithms of the domestic and foreign price levels respectively.

While qt may be subject to considerable short-run variation, a necessary condition for PPP to hold in the long run is that the real exchange

Multivariate unit root tests

In this section we outline two multivariate unit root tests. The first may be considered as an extension of previous work due to Abuaf and Jorion (1990). The second test we propose is an application of Johansen's maximum likelihood procedure for testing for the number of cointegrating vectors (Johansen, 1988Johansen, 1991) in the unusual case where the number of cointegrating vectors tested for is exactly equal to the number of time series in the system.

Preliminary data analysis and single-equation unit root tests

Quarterly data on bilateral real dollar exchange rates among the G5 countries (i.e. sterling–dollar, mark–dollar, franc–dollar and yen–dollar) for the period 1973i–1996ii were constructed from series obtained from the International Monetary Fund's International Financial Statistics (IFS) data bank.

Monte Carlo simulations

The Monte Carlo experiments were based on a data generation process consisting of one to four autoregressive models, each of order four. From the descriptive statistics reported in Table 1 (Panel B) we derive the average contemporaneous covariance matrix for the AR(4) residuals, averaged across the CPI and GDP deflator adjusted real exchange rate residual covariance matrices (Table 1 Panel C). We employ this average covariance matrix in executing the Monte Carlo simulations. For each

Empirical results for CPI-adjusted and GDP deflator-adjusted real exchange rates

In Table 4 we report the results of applying the MADF and JLR tests to the four real dollar exchange rates (dollar–sterling, dollar–mark, dollar–franc and dollar–yen) using quarterly data for the period 1973i through 1996ii, constructed using relative consumer price indices and relative GDP deflators. We used lag lengths of four for each of the autoregressions (in the construction of the MADF test statistic) and in the vector autoregression (in the construction of the JLR test statistic).

The

A Case Study: producer price indices29

As a check on the robustness of the simulation results discussed above to the specific data generating processes assumed, we also investigated the mean-reverting behavior of real dollar exchange rates among the G5 constructed using producer price indices (PPIs). Since PPIs cover a higher proportion of tradables goods prices than either CPIs or GDP deflators, one might also expect long-run PPP to hold more strongly using these indices to construct the real exchange rate series.

Conclusion

In this paper we have provided a number of insights into multivariate tests of long-run purchasing power parity. In particular, while we have shown that panel unit root tests may be quite powerful, they must be interpreted with caution since rejection of the null hypothesis of joint non-stationarity of a group of real exchange rates may be due to as few as one of the exchange rate series under investigation being generated by a stationary process. For a sample size of around 100, for example,

Acknowledgements

This paper was begun while Mark Taylor was on the staff of the International Monetary Fund. We are grateful to three anonymous referees and the managing editor, Andrew Rose, for helpful and constructive comments on an earlier version of this paper. The authors have also benefited from helpful comments from and discussions with Robert Flood, Alan Taylor, Hashem Pesaran, Richard Clarida, Ron Smith, Paul O'Connell, Nelson Mark, Martin Evans, Axel Weber and David Papell, as well as other conference

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