Finite sample properties of the partially restricted reduced form estimator

Abstract

The paper considers the exact density of a linear function of the PRRF estimator under the same set of assumptions as in Nagar and Sahay (l978). We obtain the general expression for the exact moments of such a linear function, which can be used to obtain expressions for moments of arbitrary order. Using this result the explicit formulae for the first four integer moments are given. We will then extend the results to the case where the matrix of exogenous variables is only assumed to have full column rank, and the covariance matrix of the endogenous variables has to be only positive definite. The analytical tool used to work out these results is the technique of fractional calculus first applied to econometrics by Phillips (l984).