Previous methodological research has shown that hidden heterogeneity in hazard rate regression models—in the form of systematic differences between sample members in the risk or hazard of making a transition due to unobserved variables not accounted for by the measured covariates—can produce biased parameter estimates and erroneous inferences. However, few empirical applications of hazard regression do more than pay lip service to the complications of hidden heterogeneity. In part, this is due to the relative inaccessibility of the mathematical apparatus of continuous-time hazard regression methodology with flexible nonparametric specifications on the hidden heterogeneity. This article presents new methods for incorporating nonparametric specifications of hidden heterogeneity into hazard regressions by developing discrete-time Poisson rate/complementary log-log hazard regression models with nonparametric hidden heterogeneity that are analogous to the continuous-time models of Heckman and Singer. Maximum-likelihood estimators and associated hypothesis tests are described. An empirical application to data on criminal careers, which illustrates the utility of models that explicitly incorporate hidden heterogeneity, is presented.
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