Discrete Factor Approximations in Simultaneous Equation Models: Estimating the Impact of a Dummy Endogenous Variable on a
Continuous Outcome
Continuous Outcome
This paper contains a Monte Carlo evaluation of estimators used to control for the endogeneity of dummy explanatory variables in continuous outcome regression models. It highlights the use of discrete approximations to model the unobserved factors that give rise to endogeneity. The experiments vary sample sizes, distributions, error correlations, R2 's , and exclusions restrictions. When the true underlying model has joint normal disturbances, estimators using discrete approximations compare favorably to the efficient normal maximum likelihood estimator in terms of bias and precision. When the true disturbances are non-normal, the discrete factor estimators outperform estimators incorrectly assuming joint normality. The Monte Carlo results also indicate that one should use liberal criteria for deciding whether to add additional points of support to the discrete factor distribution. The paper concludes with an application of the discrete factor approach to the estimation of the impact of marriage on younger men’s wages.
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