Specication Testing for Transformation Models with an Application to Generalized Accelerated Failure-time Models

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 …rst 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 speci…cations of duration models and hedonic pricing models. Our test statistic is asymptotically normal under local alternatives and consistent against nonparametric alternatives. Monte Carlo experiments show that our test performs well in …nite samples. We apply our results to test for speci…cations of generalized accelerated failure-time (GAFT) models of the duration of strikes and of marriages. Keywords: additivity, control variable, endogenous variable, monotonicity, nonparametric nonseparable model, hazard model, speci…cation test, transformation model, unobserved heterogeneity JEL Classi…cation: C12, C14 Acknowledgements: Halbert White inspired this project, brought us together to work on it, and provided substantial advice, discussion, and enthusiasm. We deeply mourn his passing. We also want to thank Songnian Chen for helpful comments and suggestions.