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A Monte Carlo Study of Alternative Simultaneous Equation Estimators

A. L. Nagar

Abstract

We study the small sample properties of the simultaneous equation estimators by a Monte Carlo approach. The four methods of estimation considered are: least squares, two-stage least squares, unbiased and minimum-second-moment. The last of these four methods possesses the smallest second order sampling moments about the true parameter value in a majority of cases, while two-stage least squares shows the smallest bias in all cases. It is also found that the usual asymptotic standard errors of two-stage least squares give a rather satisfactory picture of the variability of the estimates about the true value. This is not true for the least squares method in all cases considered. Instead, it seems that the classical least squares standard errors measure the variability of the estimates about the biased expectation, not about the true value. In some cases this makes a very large difference.