In this paper, we propose a test for bivariate normality in imperfectly observed models, based on the information matrix test for censored models with bootstrap critical values. In order to evaluate its properties, we run a comprehensive Monte Carlo experiment, in which we use the bivariate probit model and Heckman sample selection model as examples. We find that, while asymptotic critical values can be seriously misleading, the use of bootstrap critical values results in a test that has excellent size and power properties even in small samples. Since this procedure is relatively inexpensive from a computational viewpoint and is easy to generalise to models with arbitrary censoring schemes, we recommend it as an important and valuable testing tool.
A test for bivariate normality with applications in microeconometric models / Lucchetti, Riccardo; Pigini, Claudia. - In: STATISTICAL METHODS & APPLICATIONS. - ISSN 1618-2510. - 22:4(2013), pp. 535-572. [10.1007/s10260-013-0236-5]