A Bayesian Semiparametric Competing Risk Model with Unobserved Heterogeneity

Abstract

This paper generalizes existing econometric models for censored competing risks by introducing a new flexible specification based on a piecewise linear baseline hazard, time‐varying regressors, and unobserved individual heterogeneity distributed as an infinite mixture of generalized inverse Gaussian (GIG) densities, nesting the gamma kernel as a special case. A common correlated latent time effect induces dependence among risks. Our model is based on underlying latent exit decisions in continuous time while only a time interval containing the exit time is observed, as is common in economic data. We do not make the simplifying assumption of discretizing exit decisions—our competing risk model setup allows for latent exit times of different risk types to be realized within the same time period. In this setting, we derive a tractable likelihood based on scaled GIG Laplace transforms and their higher‐order derivatives. We apply our approach to analyzing the determinants of unemployment duration with exits to jobs in the same industry or a different industry among unemployment insurance recipients on nationally representative individual‐level survey data from the US Department of Labor. Our approach allows us to conduct a counterfactual policy experiment by changing the replacement rate: we find that the impact of its change on the probability of exit from unemployment is inelastic. Copyright © 2014 John Wiley & Sons, Ltd.

Granger Causality and Structural Causality in Cross-Section and Panel Data

“…1 Browning and Carro (2007) provide some examples of such heterogeneity in micro-data. A similar question concerning distributional heterogeneity is also discussed in Hausman and Woutersen (2014) and Burda, Harding, and Hausman (2015) for duration models. The presence of either source of heterogeneity plays a central role in linking and testing G causality and structural causality.…”

Modelling Heaped Duration Data: An Application to Neonatal Mortality

“…While the gamma density choice might appear overly restrictive at first sight, we note that U(iii) can often be rationalised theoretically (Abbring and Van Den Berg, 2007) and findings by Han and Hausman (1990) as well as Meyer (1990) suggest that estimation results for discrete-time proportional hazard models where the baseline is left unspecified (as in our model) display little sensitivity to alternative distributional assumptions on v i . Finally, albeit beyond the scope of this paper, it might be possible to adopt other, more flexible approaches such as the one recently proposed by Burda, Harding, and Hausman (2014). Before stating our main identification result, we need to define some more notation, which will be used in the proof of Proposition 1 below.…”

“…However, as for identification of the baseline hazard, we do emphasize that the regularity conditions in Heckman and Singer (1984) would indeed suffice. Recently, Bierens (2008) suggests to approximate unobserved heterogeneity via Legendre polynomials, while Burda, Harding, Hausman (2014) suggest the use of an infinite mixture and, Hausman and Woutersen (2013) introduce a rank type estimator, which does not require the specification of unobserved heterogeneity. However, all these papers rule out incorrectly reported durations.…”

A hierarchical mixture cure model with unobserved heterogeneity for credit risk

“…Hanson et al (2008) find that ignoring heterogeneity in firm returns and default thresholds may lead to an underestimation of the expected loss and that there is an effect on portfolio risk too. Burda et al (2015) employ an approach to build a semiparametric competing risk model with unobserved heterogeneity for the analysis of unemployment in the US. Their Bayesian method does not involve the EM-algorithm, and introduces unobserved heterogeneity through an infinite mixture of generalized inverse Gaussian densities.…”