Specification Testing for Transformation Models with an Application to Generalized Accelerated Failure-Time Models

Abstract

Consider a nonseparable model Y=R(X,U) where Y and X are observed, while U is unobserved and conditionally independent of X. This paper provides the first nonparametric test of whether R takes the form of a transformation model, meaning that Y is monotonic in the sum of a function of X plus a function of U. Transformation models of this form are commonly assumed in economics, including, e.g., standard specifications of duration models and hedonic pricing models. Our test statistic is asymptotically normal under local alternatives and consistent against nonparametric alternatives violating the implied restriction. Monte Carlo experiments show that our test performs well in finite samples. We apply our results to test for specifications of generalized accelerated failure-time (GAFT) models of the duration of strikes.

Keywords: additivity, control variable, endogenous variable, monotonicity, nonparametric nonseparable model, hazard model, specification test, transformation model, unobserved heterogeneity

JEL Classification: C12, C14