James R. Lothian Mark P. Taylor*
Irish Management Institute Centre for Economic
Policy Research, London

When the current float began, it appeared to offer an ideal laboratory for the study of exchange-rate behavior. After two decades of experience with floating rates, researchers, however, stand divided on many of the most basic issues of exchange-rate economics.

Real exchange rates are hard to distinguish from random walks (or at least martingales). Asset models, including monetary models, have poor predictive power. Nominal exchange rates show much greater variability than fundamental macroeconomic variables. Real exchange rates are more variable under floating rates than under fixed (see MacDonald and Taylor (1992) for a recent survey and discussion).

These are among the important stylized facts of the recent float. They are not, however, characteristic of all exchange-rate data. Using a variety of statistical techniques and much broader data samples than the floating-rate period alone, researchers have now begun to reject the random-walk hypothesis. They find instead that real exchange rates revert to equilibrium values over the long run and correspondingly that nominal exchange rates and relative price levels converge (see, for example, Abuaf and Jorion (1990), Lothian (1990), Diebold, Husted and Rush (1992)).

What accounts for the disparity in results across data samples? One possible explanation is that the regime itself matters, that the current float is indeed fundamentally quite different from earlier regimes. Another is that the shocks impinging on exchange rates have been different in this episode. A third explanation is statistical. The behavior of real exchange rates under the float may in fact be similar to behavior in other periods and the relative incidence of different types of shocks also largely the same, but researchers may not be able to tell. With less than twenty annual data points, the float may simply contain too few meaningful degrees of freedom for researchers to detect mean-reverting real exchange rate behavior using conventional statistical tests. (See Shiller and Perron (1985) and Hakkio and Rush (1992) on this issue).

Our purpose in this paper is to distinguish among these potential explanations. In particular, we investigate whether the salient characteristics of exchange-rate behavior have shifted significantly during the post-World War II period and, more particularly, during the recent float. To do so, we have assembled exchange-rate and price-level data for the United States, the United Kingdom, France and Japan for a sample period that at its longest (UK-US) spans two centuries in length and its shortest (UK-Japan) somewhat more than a century. This data set has the distinct advantage of exceptional variability in the "other" (non-monetary) factors affecting exchange rates. It thus allows us to subject the theory to a more rigorous set of tests than would be possible with data for the float, or even the entire post-WWII period, alone.

We find that, in very broad terms, the behavior of exchange rates has not altered significantly during the recent float. Purchasing-power-parity relation, with its long tradition in monetary history and the history of economic thought, continued to hold during the float. We conclude that the difficulty in detecting mean reversion in real exchange rates for this period in earlier studies may very well be due to a statistical lack of power in the traditional tests.

Overview of the Data

We define the real exchange rate in terms of the logarithmic deviation from purchasing power parity (PPP):

qt = st -(pt* -ptUK) (1)

where q is the logarithm of the real exchange rate, s is the logarithm of the nominal rate (the price in foreign currency of a pound sterling), p* and pUK are logarithms of the other-country (French or Japanese) and UK price indexes, respectively, and t is a time subscript. If (relative) PPP held continuously, q would be a constant reflecting differences in the units of measurement of s and p*-pUK. There is, however, little evidence of this being the case.

The important question empirically, therefore, is the extent to which PPP holds in the long run. In dealing with this question, we find it useful conceptually to view qt as made up of two components, a long-run equilibrium real exchange rate, qt, and the deviation of qt from qt:

qt = qt + (qt -qt) (2)

where qt = st - (pt* -ptUK), and a bar over a variable denotes a long-run equilibrium value.

If (relative) PPP holds in this long-run context, qt will be a constant, and qt will ultimately converge to this value, which in turn implies convergence of et, pt, and pt* to their equilibrium values. Over the short run, however, qt need not, and empirically generally will not, equal qt. Divergences will exist so long as et, pt, and p*t diverge from their long-run equilibria. As a result, tests of long-run PPP have increasingly focused on the error process followed by qt, and in particular whether qt contains a unit root, or does in fact show convergence to some stable value. This is the approach that we employ.

In each instance, our data are for actual exchange rates, as opposed to gold parity values, and for wholesale price indices, both for as far back in time as we could get meaningful figures for each of the country pairs. For the United States and Great Britain this is 1791, for France, 1805, and for Japan, 1874. These data came from a variety of sources and more often than not, particularly for the price data, involved our interpolating and splicing together series. Rather obviously this adds to the potential for measurement-error effects. and thus increases the likelihood of non-stationarity in the data. Potentially even more important in this regard are the substantial changes in political institutions, the outright political disruptions associated with wars, the considerable differences in exchange-rate regimes and in domestic monetary arrangements, and the substantial variations in real economic variables that took place over this long historical span.

Despite all of these factors, however, we observe a surprising degree of long-run stability in real exchange rates when we simply look at the data. This is most striking in the case of the real franc-sterling exchange rate plotted immediately below. It is also, however, characteristic of the data for the other two countries. The standard deviation of the logarithmic index plotted here is .122, in contrast to 1.582 for the standard deviation of

Fig 1. Index of Franc-Sterling Real Exchange Rate

the log nominal franc-sterling exchange rate. Comparable figures for yen-sterling are .188 and 2.102, respectively, and for dollar-sterling .133 and .334, respectively. Translated into coefficients of determination for a simple PPP model in which the mean of the actual log real exchange rate is used as a estimator of the equilibrium rate, these imply over 99% predictability for the logarithm of the nominal franc-sterling rate, 98% predictability for the logarithm of the nominal yen-sterling rate, and 84% predictability for the logarithm of the nominal dollar-sterling rate.

Mean Reversion of the Real Exchange Rate

To determine further if there was a tendency in the data towards long-run purchasing power parity in the form of mean reversion of the real exchange rate, we applied two sets of unit root tests to the data, both standard Dickey-Fuller tests and the Phillips-Perron modifications of those tests as developed in Perron (1988).

For dollar-sterling and franc-sterling for the full sample periods (1791-1990 and 1805-1990 respectively), the unit root hypothesis is rejected at standard significance levels. This is also true when the sample period is truncated at 1945. For the subperiod following World War II (1945-1990), however, we are unable to reject the unit root hypothesis at even the 10╩percent level for either exchange rate. The only difference between the test results for dollar-sterling and franc-sterling, in fact, is that the test statistics are further from the critical values for dollar-sterling than for franc-sterling.

For yen-sterling, however, the unit root hypothesis is rejected for both the full sample period and for each of the subperiods -- including the post-WWII subperiod. For this exchange rate, however, we find evidence of stationarity around a deterministic trend in mean rather than absolute stationarity as in the other two cases. We are inclined, as in Marston (1986), Lothian (1990, 1991) and Yoshikawa (1990), to attribute this trend to faster growth in productivity of tradable goods in Japan than in the UK.

Error Correction Models

The next stage of the investigation involved estimating short-run, dynamic equations for the nominal exchange rate. Since we found the real exchange rate to be stationary (for at least some periods), this implies, in effect, cointegration of the nominal exchange rate and British and foreign prices. In turn, by the Granger Representation Theorem (Engle and Granger (1987)), cointegration implies the existence of a dynamic error correction form for exchange rates and prices.

In each case, the estimated error correction equations were encouraging. The estimated coefficients in all instances were strongly significantly different from zero and of the expected signs and magnitudes. The estimated equations were also satisfactory in providing adequate regression diagnostics. For the nominal exchange rate, a surprisingly simple error correction form appeared adequately to characterize the data:

Ăst = -r(s + pUK - p*)t-1 - aĂptUK + bĂp*t + d .(3)

A priori, we should expect a and b to lie between zero and unity, with values less than one indicating less than full within-year accommodation of the exchange rate to movements in British and foreign prices. The presence of the error correction term (-r(s + pUK - pÁ*)t-1) implies that (for positive values of r), deviations from purchasing power will have a feedback on the current percentage change in the nominal exchange rate. Thus, in long-run equilibrium at constant, steady-state rates of inflation (╣UK and ╣*), equation (3) reduces to:

st = p* -pUK+(b╣t* -a╣tUK)/r, (4)

which, subject to scaling factors in the price indices, is consistent with long-run purchasing power parity.

It is also interesting to compare the magnitude of the estimated error correction coefficients for each of the exchange rates. For dollar-sterling, the point estimate is -0.087. Holding British and foreign prices constant, this implies an adjustment of the nominal exchange rate of about 9% per annum of the deviation from long-run PPP (although with less than perfectly rigid prices, adjustment in the real exchange rate would be faster than this). For franc-sterling the comparable figure is some 22% while for yen-sterling it is near to 50% per annum. These differences in the speed of adjustment may explain the different results obtained in our unit root tests for the real exchange rate for the post-WWII period. The case in which we were unable to reject the unit root hypothesis for this period (i.e. dollar-sterling) corresponds to the case with the slowest speed of adjustment.

Out-of-Sample Forecasts

We concluded by conducting a series of out-of-sample forecasting exercises with these equations. These equations performed remarkably well in forecasting the path of nominal exchange rates during the float. In each case, we estimated the equations initially with data through 1973. Using a rolling regression estimation technique for the period 1974-1990 like that of Meese and Rogoff (1983), we found that the error correction forms easily outperformed real- and nominal-exchange-rate random-walk models in terms of the root mean square error from dynamic forecasts up to five years ahead. The implication is therefore that, in very broad terms, the behavior of exchange rates has not altered significantly during the recent float, and that difficulty in detecting mean reversion in real exchange rates for this period may indeed be due to a lack of statistical power in the traditional tests.

In Sum

Viewed from the perspective of the past two centuries of exchange rate behavior the current float does not appear terribly aberrant.

For two of the three annual exchange rate series that we examine, we cannot reject the hypothesis of a unit root for the years since World War╩II. For the third, we can reject a unit root, but only after allowance for a deterministic trend. Thus, the persistence in real exchange rate movements that others have found in higher-frequency data for the recent float rate, not surprisingly, is common to these data too. For real exchange rates under the float, the random-walk model, therefore, contains a strong element of truth.

But that is as far as it goes. The same tests applied to the three real exchange rates for the full periods for which we have data allow us to reject the null hypothesis of a unit root in each instance. Since these findings imply the existence of cointegrating relationship between the three nominal exchanges and relative price levels we go on to estimate the corresponding error-correction models for the three exchange rates. Not only do these take on relatively simple forms that are themselves consistent with long-run PPP, but when re-estimated for the periods up to the current float, they perform remarkably well in mimicking the behavior of nominal exchange rates under the float.

We conclude that as a long-run equilibrium relationship -- as a monetary equilibrium condition linking the nominal exchange rate and relative price levels and as a guide to long-term movements in nominal exchange rates -- purchasing-power parity is alive, and as well as it ever was.