A Monte Carlo comparison of two-square least squares and ridge estimators in a simultaneous equation model
Quigley, Michael Regan
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Consider a model of the form shown below: Y = X*B + e where Y is a vector of dependent variables, X a matrix containing exogenous variables and e is a vector of independently and identically distributed (iid) white noise random variables. To estimate the parameters in B, the commonly used method is ordinary least squares (OLS). The OLS estimator is the best linear unbiased estimator (BLUE) of B. If, however, the vectors which make up the X matrix are collinear, then the OLS estimator while still unbiased may not be optimal under a mean square error (MSE) criterion. One potentially better estimator reviewed extensively in the literature are ridge estimators. But most of the literature deals with single equation models and very few papers have been written on the use of ridge regression in the context of a simultaneous equation model (SEM). Now one of the most popular techniques for estimating SEM is two-stage least squares (2SLS). But 2SLS is just OLS applied twice. Therefore, since ridge estimators have proved themselves to be superior to OLS in certain circumstances, we would expect that 2SLS estimators might be improved by applying ridge estimation techniques to it. We studied finite sample properties of 2SLS estimators obtained using ridge techniques. Our results indicated that unaltered 2SLS estimators were superior to the ridge alternatives.