Distributional specification tests against semiparametric alternatives

Abstract

Score or Lagrange multiplier versions of a Hausman test for distributional specification are presented for limited dependent variable models. These tests are based on the first derivatives of semiparametric criterion functions associated with robust estimation of such models and only require the computation of the maximum likelihood estimator. Various regression forms of the statistic are also presented. Monte Carlo results for the Tobit model indicate that such tests may be efficacious in detecting situations in which the maximum likelihood estimator is seriously biased due to incorrect distributional specification. © 1991.