1054 The Econometrics of Exchange Rates
A general “prediction” equation that nests all models under examination is:st+k=a0,k+a1,k(mt−m∗t)+a2,k(wt−w∗t)+a3,k(it−i∗t)
+a4,k(πte−πte∗)+a5,ktbt+a6,ktb∗t+ut, (22.78)wherest+kdenotes the log exchange rate (domestic price of foreign currency),mt
is the log of the money supply,wtis the log of real income,itis the short-term
interest rate,πtedenotes expected inflation,tbtis the cumulated trade balance,utis
a possibly serially correlated error term, and theaks are parameters corresponding
to thekth forecast horizon, withk=1, 3, 6, 12 months. An asterisk denotes foreign
quantities. Meese and Rogoff (1983a) estimated the above regression by OLS, as
well as GLS and instrumental variables (IVs) (Fair, 1970) so as to deal with the
presence of serial correlation in the residuals and simultaneous equation bias due
to the endogeneity of the variables. Surprisingly, on the basis of root mean squared
error (RMSE), none of these models outperformed the naive RW model for horizons
up to a year, even though realized values of the forcing variables were used.
The poor forecasting performance of the considered models can be attributed
to a number of factors. First, the fact that the variables are highly persistent
may lead to biased estimates of the coefficients (Rossi, 2005). If the error term
is non-stationary (i.e., the exchange rate is not cointegrated with fundamentals),
the coefficients will be inconsistent and forecasting will be meaningless. Second,
equation dynamics (MacDonald and Taylor, 1994) are omitted from the regres-
sion equation and the case of a nonlinear DGP is not considered (see Taylor and
Peel, 2000; Meese and Rose, 1990). Further, parameter instability may character-
ize empirical exchange rate models (Wolff, 1987; Rossi, 2006) and simultaneous
equation bias may not have been properly accounted for. As far as the latter expla-
nation is concerned, Meese and Rogoff (1983b) impose coefficient restrictions based
on the theoretical and empirical literature on money demand and the rate at which
shocks to the real exchange rate appear to damp out. This enables the examination
of longer forecasting periods. Their findings indicate that, for horizons greater than
a year, there are cases where the RMSE of the RW is larger than that of structural
models, suggesting the presence of simultaneous equation bias and that the per-
formance of structural models may improve at longer horizons (Meese and Rogoff,
1983b; Rogoff, 1999). These findings support the estimation of long-horizon regres-
sions and the application of advanced inference procedures (see, e.g., Mark, 1995;
Chinn and Meese, 1995).
22.6.1 Long-horizon regressions
Consider the monetary model (22.66) and let the fundamental term,ft, follow a
driftless RW. Then equation (22.66) reduces tost=ft. The relationship between the
exchange rate and the monetary fundamentals motivates Mark (1995) to examine
whether current deviations of the exchange rate from its fundamental value,zt≡
ft−st, contain predictive power for future movements in the exchange rate, as well
as the horizon at which the predictive power of the deviations becomes apparent.
Obviously, this contrasts with the view that exchange rates are best characterized