Semiparametric duration analysis with an endogenous binary variable: An application to hospital stays

Background: In duration analysis, we find situations where covariates are simultaneously determined along with the duration variable. Moreover, although the models based on a hazard rate do not explicitly assume heterogeneity, in applied econometrics, the possibility of omitted variables is inevitable and controlling population heterogeneity alone is inadequate. It is important to consider both heterogeneity and endogeneity in duration analysis. Objectives and methods: Explicitly assuming semiparametric correlated heterogeneity, this paper proposes an alternative robust duration model with an endogenous binary variable that generalizes the heterogeneity of both duration and endogeneity using Hermite polynomials. Under these setups, we investigate the difference between the endogenous binary variable's coefficients of the parametric and semiparametric models using the Medical Expenditure Panel Survey (MEPS) data. Results: The parameter values of the endogenous binary variable (insurance choice) are statistically significant at the 1% level; however, the values differ among the parametric and semiparametric models and the any type of insurance choice increases the length of hospital stays by 104.010% in the censored parametric model, and 182.074% in the censored semiparametric model. Compared with the parametric model, the increase of hospital stays in the semiparametric model is large. Moreover, we find that the semiparametric model a twin-peak distribution and that the contour lines differ from the usual ellipsoids of the bivariate normal density. Conclusions: When applied to the duration of hospital stays of the MEPS data, the estimated results of the semiparametric model shows a good performance. The absolute values of the endogenous binary regressor coefficients of the semiparametric models are larger than that of the parametric model. The parametric model underestimates the effect of the individual's insurance choice in our example. Moreover, the estimated densities of the semiparametric models have twin peak distribution.