Topics in identification and inference in duration models

In economic duration analysis, it is routinely assumed that the process which led to censoring of the observed duration is independent of unobserved characteristics. The objective of Chapters 1 and 2 is to examine the sensitivity of parameter estimates to this independence assumption in the context of an economic model of optimal unemployment insurance. We assume a parametric model for the duration of interest and leave the distribution of censoring unrestricted, allowing it to be correlated with both observed and unobserved characteristics. This leads to loss of point-identification. In Chapter 1 we provide a practical characterization of an outer set of the identified set with moment inequalities and suggest methods for estimating this set. In particular, we propose a profiled procedure that allows us to build a confidence set for a subvector of the model parameters. In Chapter 2 we apply this approach to estimate the elasticity of exit rate from unemployment with respect to unemployment benefit and find that both positive and negative values of this elasticity are supported by the data. When combined with the welfare formula in Chetty (2008), these estimates do not permit us to put an upper bound on the size of the welfare change due to an increase in the unemployment benefit.;In Chapter 3 we study specification testing in transformation models. Despite an abundance of semiparametric estimators of the transformation model, no procedure has been proposed yet to test the hypothesis that the transformation function belongs to a finite-dimensional parametric family against a nonparametric alternative. In this paper we introduce a bootstrap test based on integrated squared distance between a nonparametric estimator and a parametric null. As a special case, our procedure can be used to test the parametric specification of the integrated baseline hazard in a semiparametric mixed proportional hazard (MPH) model. We investigate the finite sample performance of our test in a Monte Carlo study. Finally, we apply the proposed test to Kennan's strike durations data.