(DP 1979-23) Large Sample Asymptotic Expansions for General Linear Simultaneous Systems Under Misspecification

Based on large-sample stochastic approximations, we obtain asymptotic bias and mean squared error for the k-class estimators of an identified but misspecified equation with an arbitrary number of endogenous variables in linear simultaneous-equations model. The specification error considered here is the omission of appropriate exogenous variables from the equation being estimated. This paper extends existing results in various respects. It treats not only consistent estimators but also inconsistent ones, like ordinary least squares, and it provides conditions under which ordinary least squares will be preferred among those estimators under study. It covers cases where the estimated equation contains three or more endogenous variables. It includes the limited-information maximum likelihood as one of the estimators under analysis. It also contains a rigorous argument for the propriety of the stochastic approximations from which asymptotic moments of estimators are calculated.