Conditional Moment Tests for Normality in Bivariate Limited Dependent Variable Models: a Monte Carlo Study

In this paper, we run a Monte Carlo analysis of the finite-sample performance of an Information Matrix Test put forward by Smith (1985) for bivariate censored models. We use the bivariate probit model and Heckman selection model as examples.;Approximating the finite-sample distribution of this test statistic by its asymptotic distribution can lead to very misleading results: its size is severely distorted even in samples that common practice would judge to be perfectly adequate for asymptotics. This is especially true when the correlation coefficient is far from zero.;Power properties of the test statistic are investigated by using bivariate t(6) and x2(1) alternatives. The test has very low power against leptokurtosis, especially in the bivariate probit case, while power against asymmetry appears to be much more satisfactory.;In general, the performance of the Information Matrix test seems to be related to the amount of information on the latent variables which survives the censoring mechanism. A somewhat improved version of the test can be obtained, in some cases, by a careful choice of the moment conditions to employ.