Improved estimators in the simultaneous equations model

Two stage least squares is a widely used method of estimating the parameters of a single structural equation in a system of simultaneous equations. The extension of the biased estimation procedures at both stages of the two stage least squares technique in simultaneous equations model is desirable so as to cope with the problem of multicollinearity. Such a two stage technique is applied with the help of ridge regression by Vinod and Ullah (1981). In a similar manner, three different kinds of Liu estimators which are named with regard to their implementation stages are proposed in this study. The mentioned estimators are compared theoretically and the results are supported by a numerical example. In addition, inequality restrictions are necessary to maintain structural consistency in a system of simultaneous equations. Therefore, the idea of inequality restrictions is applied to the two and three stage ridge regression estimation in the presence of multicollinearity by following Liew (1976a). Inequality constrained two stage and three stage ridge regression estimators are proposed by reducing the primal-dual relation to the fundamental problem of Dantzig-Cottle (1967, 1974) and solving with Lemke (1962) algorithm. Key Words: Biased estimators, Multicollinearity, Simultaneous equations model, Two stage estimation.