Exchange Rate Economics: Theories and Evidence

142 Empirical evidence on the monetary approach
Ever since the publication of the Meese and Rogoff paper the ability of an exchange
rate model to beat a random walk has become something of an acid test,indeed,the
acid test of how successful an exchange rate model is. It has become the equivalent
of the R squared metric by which an exchange rate model is judged.
In sum,Meese and Rogoff (1983) take the FLMA and RID model,and variants
of these models (the Hooper–Morton variant of the monetary model which is discussed
in Chapter 7),and estimate these models for the dollar–mark,dollar–pound,
dollar–yen and the trade weighted dollar. The sample period studied was March
1973 to November 1980,with the out-of-sample forecasts conducted over the
sub-period December 1976 to November 1980. In particular,the models were
estimated from March 1973 to November 1976 and 1- to 12-step ahead forecasts
were conducted. The observation for December 1976 was then added in and the
process repeated up to November 1980. Rather than forecast all of the right-handside
variables from a particular exchange rate relationship simultaneously with the
exchange rate,to produce real time forecasts (i.e. forecasts which could potentially
have been used at the time),Meese and Rogoff gave the monetary class of models
an unfair advantage by including actual data outcomes of the right-hand-side
variables. Data on the latter variables were available to them due to the historical
nature of their study,but of course they would not have been available at the time
of forecasting to a forecaster producing ‘real time’ forecasts. To produce the latter
all of the right-hand-side variables would have had to be forecast simultaneously
with the exchange rate. Out-of-sample forecasting accuracy was determined using
the mean bias,mean absolute bias and the root mean square error criteria. The
benchmark comparison is,as we have noted,a simple random walk with drift:
s t = s t−1 + κ + ε t ,(6.15)
where κ is a constant (drift) term and ε t is a random disturbance. Since the RMSE
criterion has become the measure that most subsequent researchers have focussed
on we note it here as:
√ ∑ (Ft − A t ) 2
RMSE =
n
,
where F is the forecast and A is an actual outcome. By taking the ratio of the
RMSE obtained from the model under scrutiny,to the RMSE of the random walk
process,a summary measure of the forecasting performance can be obtained as:
RMSE r = RMSEm
RMSErw ,(6.16)
where RMSE r is the root mean square error ratio (this is equivalent to the Theil
statistic).
In sum,Meese and Rogoff were unable to outperform a random walk at horizons
of between 1 and 12 months ahead,although in 4 instances (out of a possible 224)
the VAR model produced a ranking which was above the random walk at longer