Palgrave Handbook of Econometrics: Applied Econometrics

1064 The Econometrics of Exchange Rates

but, as the horizon increases, the value ofR^2 becomes larger and reaches a maxi-

mum at a horizon of 44 quarters, whereR^244 =0.38. The authors argue that, in this
framework, panel estimation techniques may be useful in detecting predictability
by picking up a common element to the risk-premium across exchange rates.

22.6.4 Panels

Empirical studies based on country-by-country estimations are confronted with the
problem of low power and poor parameter estimates. The possibility of common
elements in the DGPs motivates the use of pooled time series estimation in order to
increase the power of predictability tests.^75 A number of recent studies using panel
datasets provide evidence in favor of a long-run relationship of the deviations of
the exchange rate from its fundamental value.^76
Mark and Sul (2001) investigate if panel estimation techniques are useful in fore-
casting exchanges rates by exploiting interdependencies of exchange rates with
the same numeraire, namely the US dollar, the Swiss franc and the Japanese
yen. The dataset includes 19 OECD countries and spans the period from 1973:1
through 1997:1. Their study centers on the panel version of the equation employed
in Mark (1995):

si,t+ 1 −si,t=βzi,t+ei,t+ 1 , (22.103)

ei,t+ 1 =γi+θt+ 1 +ui,t+ 1 , (22.104)

whereγiis a country-specific effect,θt+ 1 is a time-specific error andui,t+ 1 is an
idiosyncratic error. Before examining the out-of-sample performance of the multi-
country monetary model, Mark and Sul (2001) follow Berkowitz and Giorgianni
(2001) and test for cointegration. However, due to the fact that the standard least
squares dummy variable (LSDV) estimator suffers from second-order bias, caus-
ing thet-statistic to diverge asymptotically, the panel dynamic OLS estimator is
adopted. The system of equations for the changes in the exchange rates is:

si,t+ 1 −si,t=γi+θt+βzi,t− 1 +

∑pi

j=−pi

δijxi,t−j− 1 +ui,t. (22.105)

Although the correspondingt-ratio is asymptotically normally distributed, Mark
and Sul (2001) also use a bootstrap procedure to account for possible finite sample
bias. The null DGP for the bootstrap is a restricted VAR:

si,t = μis+εis,t, (22.106)

zi,t = μiz+

∑qi

j= 1

φi1,jsi,t−j+

∑qi

j= 1

φi2,jzi,t−j+εiz,t. (22.107)

The equations for zi,t are fitted by iterated seemingly unrelated regres-
sion (SUR).^77 For all three numeraire currencies, both the asymptotic and the