Efficient Predictive Regressions
Authors: Faust, Jon; Wright, Jonathan H.
Source: Manuscript, 2005
Abstract: It is well known that augmenting a standard linear regression model with
variables that are correlated with the error term, but uncorrelated with
the original regressors, leaves the estimates of coeffcients on the
original regressors consistent, but will in- crease the asymptotic efficiency of the estimates. In a forecasting regression, ex post measures
of an unforecastable component of the forecasted variable can play this
role: such measures are uncorrelated with variables one might use to
forecast but are correlated with the error in any forecast regression.
Augmenting the regression with these variables may increase the
precision of estimates of coefficients on the original regressors and
hence produce better forecasts. It may be that this is approach is
seldom used because of difficulty finding variables satisfying these
conditions. We argue that in some canonical predictive regressions in
finance, there are good reasons to believe that the assumptions will be
satisfied. Ex-post survey forecast errors, and surprise components of
macroeconomic news announcements are good candidate augmenting
variables. In pseudo-out-of-sample prediction exercises, we find that
augmenting standard excess return regressions using these variables
nearly uniformly reduces mean square prediction errors. In some cases,
the improvement is quite substantial.
