The reduced form of recursive models: Small sample properties Original Research Article

The reduced form of a recursive multiequation model can be estimated either directly by ordinary least squares (OLS) or indirectly by first estimating the structural form, equation by equation, by OLS and then solving for the endogenous variables. Under certain conditions on the inclusion of variables in the hierarchically ordered equations, the direct estimator is uniformly inferior to the indirect estimator in the sense that the difference of the covariance matrices of the two estimators is always nonnegative definite. Necessary and sufficient conditions are given for the equality of the covariance matrices.