A Specification Test for Normality Assumption for the Truncated and Censored Tobit Models

Abstract

Some specification tests for the normality assumption for the truncated and censored Tobit models are derived. The tests are Lagrangean multiplier tests based on the Pearson family of distributions. For the truncated case, the test compares the estimated differences between the third- and fourth-order sample moments and the corresponding hypothesized moments of the disturbances. For the censored case, the likelihood. function is a product of the likelihood function of the noncensored sample observations and the likelihood function of the dichotomous indicators. As each component can be used to derive a test for the normality assumption, the Lagrangean multiplier test combines the two sources of information in a simple way.