Are exchange rate fluctuations justified by changes in their “fundamental” determinants? In an efficient market with rational investors, exchange rates are forward-looking prices that reflect anticipated changes of the relative demand and supply of two moneys. Hence, their volatility should reflect investors’ expectations of changes in the determinants of money stocks, such as incomes and interest rates. Given a model of exchange rate determination, market efficiency places restrictions on the relative volatility of exchange rates and of their determinants, which can be tested to yield insight on the validity of the underlying model. We apply a family of such tests in this paper, to assess whether some popular exchange rate models are capable of matching observed patterns of exchange rate volatilities over the post-Bretton Woods period.
Our interest in exchange rate volatility is motivated by both analytical and policy concerns. Exhibit A in policy discussions of exchange rate volatility is often represented by a chart such as Figure 1, pointing to the dramatic increase in exchange rate volatility for major currencies since the breakdown of the Bretton Woods system. This evidence is often accompanied by an expression of concern that “private markets may not always anchor their behavior to economic fundamentals, thus making their responses susceptible to contagion and bandwagon effects that may be disruptive and detrimental to economic performance” (Mussa and others (1994), p. 18). Excessive exchange rate volatility is also often advocated as grounds for throwing sand in the wheels of currency markets (see, for instance, Eichengreen, Tobin, and Wyplosz (1995)).
Before policies to inhibit market response can be advocated, however, one ought to verify that the volatility of exchange rates does not simply reflect that of their underlying determinants. Also, as these tests are typically joint tests of market efficiency and of a specific exchange rate model, the results must be conditioned on the particular model that they are based on.
Given the prominence in research on exchange rates of the monetary model and of its variants, early studies of exchange rate volatility, including Huang (1981), Vander Kraats and Booth (1983), and Wadhwani (1987), followed Shiller’s (1981) work on stock price volatility to construct “variance bounds” tests of the monetary model of the exchange rate. Invariably, these studies found the volatility of exchange rates since the breakdown of the Bretton Woods system to exceed the model’s predictions, leading their authors and several commentators (see, for instance, Levich (1985)), to assert either the inefficiency of foreign exchange markets or the invalidity of the underlying model, or both.
Later studies, however, questioned those results. Diba (1987), for instance, showed that the tests of Huang (1981) and Vander Kraats and Booth (1983) were vitiated by an erroneous transformation of annual semi-elasticities of money demand to interest rates into their high-frequency counterparts. When correctly calibrated, those tests failed to reject the monetary model’s predictions, although that failure was likely to reflect the weak restrictions placed by those tests on the model. Early volatility tests of asset price models were also shown to suffer from serious statistical biases, leading them to reject the underlying model too often in finite samples (see, for instance, Kleidon (1986) and Marsh and Merton (1986)). To address some of these concerns, Gros (1989) used improved volatility inequalities to present new evidence of excessive exchange rate volatility. His analysis, however, was not based on a formal statistical test, was subject to the same calibration problems pointed out by Diba (1987), and involved measuring exchange rate volatility in a way that was likely to overstate his finding of excessive volatility. In summary, after 15 years of research, evidence on the ability of the most popular exchange rate models to match the observed variability of exchange rates rests largely on mis-specified and weak statistical tests. Not surprisingly, several authors have expressed a perception of futility when reviewing the inconclusive state of research on exchange rate volatility (see, for instance, Frankel and Meese (1987), pp. 134–6).
In this paper we use recent volatility-based tests of asset price models to provide new, clearer evidence on the ability of some popular exchange rate models to match observed patterns of exchange rate volatilities over the post-Bretton Woods period. We apply the methodology developed by Mankiw, Romer, and Shapiro (1991) in the context of stock price models, and use data for the eight major currencies from 1973 to 1994 to test the textbook flex-price version of the monetary model as well as more general models with sticky prices, sluggish adjustment of money stocks, and time-varying risk premiums.
Our tests show that these models are broadly rejected by the data, but that this rejection can—in general—be attributed not to excessive exchange rate volatility, but rather to the inconsistency of these models with the assumed efficiency of currency markets. Hence, our tests confirm the wisdom from standard regression-based tests of these models (see Hodrick (1987) for a survey). However, since our tests possess better statistical properties than previous regression-based tests (in particular, they are unbiased in small samples), they provide even stronger evidence against the joint hypotheses of the monetary model (or of its extensions) and of market efficiency. Furthermore, because they are explicitly constructed as volatility tests, our tests help clarify the role played by exchange rate volatility in the models’ rejection.
Specifically, our tests point to the importance of choosing an economically meaningful definition of exchange rate volatility as a basis for the tests, so as to avoid disguising a model’s rejection as evidence of excessive volatility. The tests show that when exchange rate volatility is defined—traditionally—as the average of conditional or unanticipated exchange rate changes, then there is no evidence that exchange rates may have been excessively volatile with respect to the predictions of even the most restrictive version of the monetary model. Evidence of excessive exchange rate volatility, however, may emerge on the basis of alternative definitions of volatility.
Our findings, we hope, will contribute to future research on exchange rate volatility being more clearly defined in its scope and perhaps encourage greater caution in making claims of “excessive” exchange rate volatility. Our imposition on the data of a monetary model straitjacket should strengthen our conclusions: if exchange rates do not appear to be excessively volatile even with respect to a framework predicting their close movement with money and income alone, the likelihood that evidence of excess volatility would be uncovered based on more flexible models appears even more remote.
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Research for this paper was conducted when Leonardo Bartolini was an Economist in, and Gordon Bodnar was visiting, the Research Department of the IMF. Leonardo Bartolini is now in the Research Department of the Federal Reserve Bank of New York. Gordon Bodnar is at the Wharton School of the University of Pennsylvania. Both authors hold a Ph.D. from Princeton University. They thank Eswar Prasad for providing them a Gauss code of the Hodrick-Prescott filter, Peter Isard, Peter Clark, Carol Osier, and participants in seminars at the IMF and at the Federal Reserve Bank of New York for comments, and Susanna Mursula for technical assistance.
Serial correlation is often a problem when using overlapping observations. In our case, in particular, observations overlap over the holding period h,
We limited our exploration of money demand equations to specifications with instantaneous or partial adjustment of money stocks. Recent literature has considered buffer-stock and error-correction models that imply even greater departure from the standard specification of the monetary model (see Boughton (1992) for a survey). These specifications are difficult to integrate in equilibrium exchange rate models because of their data-dependent parameterization and their tendency to involve lags of interest rates at different maturities and to predict long-run price non-homogeneity.
In particular, since we use all the model’s equations to obtain an ex post estimate of xt, the model would be identically satisfied (i.e.,
A more complete set of tests is available from the authors, together with the data and a copy of the GAUSS program used for the tests.
Given the existing econometric evidence on money demand equations, it is also not surprising that the data favor an extremely low value of λ. See the discussion of the calibration of λ above.
Exceptions included moving to quarterly data, which caused most tests to become insignificant, likely as a result of a drastic fall in the degrees of freedom; and increasing the holding period beyond six months and the lag