A Note on the Variance of Ex-Post Forecasts in Econometric Models

Abstract

IT IS WELL KNOWN that in an econometric model, under general assumptions, the ex-post forecast error (conditional on predetermined variables) can be decomposed into the sum of two independent terms; the former is the component due to error in estimated coefficients, while the latter depends on the random error terms. The asymptotic covariance matrix of the first component can be analytically derived through intermediate computation of the covariance matrix of restricted reduced form coefficients. However, in the case of overidentified models, this may lead to a great increase in the problem's dimensions, the number of reduced form parameters being larger (often much larger) than the number of structural parameters. This intermediate step is, however, unnecessary; this note discusses a straightforward analytic derivation of the desired matrix directly from the estimated structural parameters, without any increase in the dimensions of the problem, thus facilitating the computation even for medium to large econometric models. Let