A Monte Carlo Study of Small-Sample Properties of Simultaneous Equation Estimators With Normal and Nonnormal Disturbances

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Abstract
In this paper we consider four alternative forms of two-parameter normal and nonnormal error distributions and report on a Monte Carlo study of the small-sample properties of least squares, two-stage least squares, three-stage least squares and full information maximum likelihood estimators. On the basis of 1,000 replications of sample size 20 in two experiments on an overidentified model, we found that the small-sample rankings of econometric estimators of both structural coefficients and forecasts of endogenous variables, according to parametric and nonparametric measures of bias, dispersion, and dispersion including bias, do not change for any of the four error distributions. Further, least squares is the most biased and maintains the Gauss-Markov property of minimum variance. The large bias of least squares, however, more than offsets the small variance, so that least squares exhibits the largest mean squares of the four estimators. Maximum likelihood is least biased and most efficient, except as an estimator of structural coefficients on the parametric measure of mean squared error.

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