Review of Economic Studies (1990) 517, 167-182 © 1990 The Review of Economic Studies Limited 0034-6527/90/00100167 $02.00 , The Non-Parametric Identification of Generalized Accelerated Failure-Time Models GEERT RIDDER Rijksuniuersiteit Groningen First uersion received August 1988; final version accepted November 1989 i Eds.) We consider a class of models that generalizes the popular Mixed Proportional Hazard (MPH) model for duration data: the Generalized Accelerated Failure-Time (GAFT) model. We show that the GAFf model is non-parametrically identified (up to a normalization). We then reconsider the non-parametric identification of the MPH model. We show that the class of MPH models is not closed under normalization. This implies that a finite mean of the mixing distribution is a necessary condition for (non-parametric) identification of the MPH model. It is impossible to test this hypothesis without imposing arbitrary restrictions on the base-line hazard and/ or the regression function. 1. INTRODUCTION An econometric model usually characterizes the (conditional) distribution of some vari- able(s) of interest by specifying the mean and variance of that distribution. The obvious example is the linear regression model and its extensions. Even econometric models for limited dependent variables are derived from latent regression models which specify the (conditional) mean and variance of some latent variable. In contrast, econometric models for duration data start from a specification of the hazard rate of the duration distribution. There are several reasons for this. First, empirical distributions of duration data are usually skewed, and their mean and standard deviation are of the same order of magnitude. The simplest model that has been used to describe such data, the exponential distribution, has a constant hazard rate. Second, economists are often interested in the variation of the hazard rate with the elapsed duration and with explanatory variables. Economic theories, e.g. job search theory, provide testable restrictions on the duration dependence of the hazard rate. Third, time-varying explanatory variables can be easily included in a specification of the hazard rate. However, particularly in biomedical and life-testing applications, duration data have been analysed with standard regression methods. The resulting duration models are called Accelerated Failure-Time (AFT) models. Of course, regression methods have a strong attraction to econometricians. If durations can be modelled by (non)linear regression models, duration analysis becomes a part of "mainstream" econometrics, and simultaneity, measurement error etc. can be studied in a more traditional way. In this paper we discuss a class of duration models that can be seen as a generalization of the Accelerated Failure-Time models. This class of models, the Generalized Accelerated Failure-Time (GAFT) models, contains as special cases the popular Proportional Hazards (PH) and the Mixed Proportional Hazards (MPH) models that have been used extensively in economic research. 167 Downloaded from https://academic.oup.com/restud/article/57/2/167/1551576 by guest on 14 October 2021