Endogenous Censoring in the Mixed Proportional Hazard Model with an Application to Optimal Unemployment Insurance

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 this paper 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. We provide a practical characterization 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. 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. We conclude that given the available data alone, one cannot credibly judge if the unemployment benefits in the US are close to the optimal level.