Endogenous censoring in the mixed proportional hazard model with an application to optimal unemployment insurance

Abstract

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 * I would like to thank Elie Tamer, Ivan Canay, Alex Torgovitsky for their guidance and support. I am grateful to Joel Horowitz for useful suggestions and discussions at the early stage of this project. I also benefited from comments by Agnieszka Szydłowska, Ryan Marsh, Shruti Sinha, Florian Hoffman, seminar participants at CERGE-EI and conversations with Tiago Pires. I would like to thank Raj Chetty for sharing his dataset and codes. This research used the ALICE High Performance Computing Facility at the University of Leicester and the Social Sciences Computing Cluster (SSCC) at Northwestern University. 1 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.

Founder's Human Capital and the Entrepreneurial Process Duration

“…Duration models are used to analyse the relationship between time spent in a particular state and the characteristics of interest (Szydłowski, 2019). The competing risks model is regarded as a suitable model to analyse duration data with multiple event types (Chao and Kobayashi, 2017).…”

“…As I mentioned at the start of this section, duration models are used to analyse the relationship between time spent in some state and observed characteristics (Szydłowski, 2019) and, therefore, the discrete and continuous time hazard models (i.e. Cox model, in this chapter) are considered to be best placed for estimating the effect of individual characteristics on the occurrence of an entrepreneurial outcome (Parker, 2018a).…”

Endogenously censored median regression with an application to benefit elasticity of US unemployment duration

“…We apply the profiled procedure of Gandhi et al (2013) (henceforth, GLS) to estimate confidence sets for the elasticity of unemployment duration with respect to unemployment benefit using SIPP data from the period 1985-2000. Similar inference procedure is used by Szydłowski (2017) to estimate the elasticity of unemployment hazard rate with respect to unemployment benefit using the same dataset but the MPH model for unemployment duration. 1…”

“…In application this will require discretizing the support of continuously distributed covariates. As shown bySzydłowski (2017), as long as the number of support points is relatively large, this should not have a significant effect on the size of the estimated confidence sets.…”

Modelling Heaped Duration Data: An Application to Neonatal Mortality

“…Szlydlowski (2013) allows for correlation between the censoring mechanism and unobserved heterogeneity, and, even in the absence of misreported durations, only achieves parameter set identification.…”