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


  • Masuhara, Hiroaki


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.

Suggested Citation

  • Masuhara, Hiroaki, 2013. "Semiparametric duration analysis with an endogenous binary variable: An application to hospital stays," CIS Discussion paper series 597, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
  • Handle: RePEc:hit:cisdps:597

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    References listed on IDEAS

    1. Hajivassiliou, V A, 1994. "A Simulation Estimation Analysis of the External Debt Crises of Developing Countries," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 9(2), pages 109-131, April-Jun.
    2. Bhat, Chandra R., 2001. "Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 677-693, August.
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    4. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, March.
    5. Donald S. Kenkel & Joseph V. Terza, 2001. "The effect of physician advice on alcohol consumption: count regression with an endogenous treatment effect," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(2), pages 165-184.
    6. van der Klaauw, Bas & Koning, Ruud H, 2003. "Testing the Normality Assumption in the Sample Selection Model with an Application to Travel Demand," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 31-42, January.
    7. Bijwaard, Govert E. & Ridder, Geert, 2005. "Correcting for selective compliance in a re-employment bonus experiment," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 77-111.
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    9. Hiroaki Masuhara, 2007. "Semi-nonparametric estimation of regression-based survival models," Economics Bulletin, AccessEcon, vol. 3(61), pages 1-12.
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    More about this item


    Endogenous switching; duration analysis; probit; semi-nonparametric model; heterogeneity;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models

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