Alternative covariance estimators of the standard Tobit model

Abstract

A number of alternative estimators for the coefficients of a Tobit model have been proposed in the literature. The covariance matrix of ML estimates is typically associated with the algorithm applied to maximize the likelihood. Covariance estimators used in practice are derived by: (1) the Hessian (observed information), (2) the matrix of outer products of the first derivatives of the log-likelihood (OPG version), (3) the expected Hessian (estimated information), (4) a mixture of (1) and (2) (White's QML covariance matrix). Significant differences among estimates are usually interpreted as an indication of misspecification. From our Monte Carlo study this seems not to be true, unless the sample size is really very large. Even in the absence of misspecification, large differences are encountered in small samples, and the sign of the differences is almost systematic. This suggests that the choice of the covariance estimator is not neutral and the results of hypotheses testing may be strongly affected by such a choice.