Semiparametric Estimation of a Regression Model with an Unknown Transformation of the Dependent Variable

This paper shows how to estimate a model in which an unknown transformation of the dependent variable is a linear function of explanatory variables plus an unobserved random variable, U, whose distribution is unknown. The model nests many familiar parametric and semiparametric models, including models with Box-Cox transformed dependent variables and proportional hazards models with and without unobserved heterogeneity. The paper develops root-n consistent, asymptotically normal estimators of the transformation function, coefficients of the explanatory variables, and distribution of U. The results of Monte Carlo experiments indicate that the estimators work well in samples of size one hundred. Copyright 1996 by The Econometric Society.