Bootstrap LM Test for the Box CoxTobit Model

Consistency of the maximum likelihood estimators for the parameters in the standard Tobit model rely heavily on the assumption of a normally distributed error term. The Box Cox transformation presents an obvious attempt to preserve normality when the data make this questionable. This paper sets o… ut an OPG version of an LM test for the null hypotheses of the standard Tobit model, against the alternative of a more general non-linear specification, as determined by the parameter of the Box Cox transformation. Monte Carlo estimates of the rejection probabilities using first order asymptotic and parametric bootstrap critical values are obtained, for sample sizes that are comparable to those used in practice. The results show that the LM-test using bootstrap critical values has practically no size distortion, whereas using asymptotic critical values, the empirical rejection probabilities are significantly larger than the nominal levels. A simple program which carries out this test using bootstrap critical values has also been written and can be run post the official Stata Tobit estimation command.