A Specification Test for Normality in the Generalized Censored Regression Models

Abstract

Based on the Pearson family of distributions, we have derived some Lagrangean multiplier tests for the normality and homoscedasticity assumptions in the censored regression models. The Lagrangean multiplier test statistic for the joint test of selectivity bias, homoscedasticity and normality is the sum of three components. Each component is shown to be a conditional Lagrangean multiplier test statistic. It has been shown that they can also be interpreted as tests of significance of coefficients in some linear models based on instrumental variable estimations. We have pointed out that for some very special cases, the Lagrange multiplier tests for selectivity have had no power, and are not equivalent, for large samples, to the likelihood ratio tests. This situation occurs as the likelihood evaluated at the constrained MLE is a stationary value of the unconstrained likelihood function. These . examples provide, probably, the first set of examples to confirm a conjecture in Silvey [1959, p. 399].