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A smooth mixture of Tobits model for healthcare expenditure

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  • Michael Keane
  • Olena Stavrunova

Abstract

This paper develops a smooth mixture of Tobits (SMTobit) model for healthcare expenditure. The model is a generalization of the smoothly mixing regressions framework of Geweke and Keane (J Econometrics 2007; 138: 257–290) to the case of a Tobit‐type limited dependent variable. A Markov chain Monte Carlo algorithm with data augmentation is developed to obtain the posterior distribution of model parameters. The model is applied to the US Medicare Current Beneficiary Survey data on total medical expenditure. The results suggest that the model can capture the overall shape of the expenditure distribution very well, and also provide a good fit to a number of characteristics of the conditional (on covariates) distribution of expenditure, such as the conditional mean, variance and probability of extreme outcomes, as well as the 50th, 90th, and 95th, percentiles. We find that healthier individuals face an expenditure distribution with lower mean, variance and probability of extreme outcomes, compared with their counterparts in a worse state of health. Males have an expenditure distribution with higher mean, variance and probability of an extreme outcome, compared with their female counterparts. The results also suggest that heart and cardiovascular diseases affect the expenditure of males more than that of females. Copyright © 2011 John Wiley & Sons, Ltd.

Suggested Citation

  • Michael Keane & Olena Stavrunova, 2011. "A smooth mixture of Tobits model for healthcare expenditure," Health Economics, John Wiley & Sons, Ltd., vol. 20(9), pages 1126-1153, September.
  • Handle: RePEc:wly:hlthec:v:20:y:2011:i:9:p:1126-1153
    DOI: 10.1002/hec.1777
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    References listed on IDEAS

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    1. John Geweke, 2004. "Getting It Right: Joint Distribution Tests of Posterior Simulators," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 799-804, January.
    2. John Mullahy, 1998. "Much Ado About Two: Reconsidering Retransformation and the Two-Part Model in Health Economics," NBER Technical Working Papers 0228, National Bureau of Economic Research, Inc.
    3. Manning, Willard G. & Basu, Anirban & Mullahy, John, 2005. "Generalized modeling approaches to risk adjustment of skewed outcomes data," Journal of Health Economics, Elsevier, vol. 24(3), pages 465-488, May.
    4. Meliyanni Johar & Glenn Jones & Michael Keane & Elizabeth Savage & Olena Stavrunova, 2011. "Waiting times for elective surgery and the decision to buy private health insurance," Health Economics, John Wiley & Sons, Ltd., vol. 20(S1), pages 68-86, September.
    5. Geweke, John & Keane, Michael, 2007. "Smoothly mixing regressions," Journal of Econometrics, Elsevier, vol. 138(1), pages 252-290, May.
    6. Keane, Michael & Stavrunova, Olena, 2016. "Adverse selection, moral hazard and the demand for Medigap insurance," Journal of Econometrics, Elsevier, vol. 190(1), pages 62-78.
    7. Partha Deb & Murat K. Munkin & Pravin K. Trivedi, 2006. "Bayesian analysis of the two‐part model with endogeneity: application to health care expenditure," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(7), pages 1081-1099, November.
    8. Mullahy, John, 1998. "Much ado about two: reconsidering retransformation and the two-part model in health econometrics," Journal of Health Economics, Elsevier, vol. 17(3), pages 247-281, June.
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    10. Buntin, Melinda Beeuwkes & Zaslavsky, Alan M., 2004. "Too much ado about two-part models and transformation?: Comparing methods of modeling Medicare expenditures," Journal of Health Economics, Elsevier, vol. 23(3), pages 525-542, May.
    11. Blough, David K. & Madden, Carolyn W. & Hornbrook, Mark C., 1999. "Modeling risk using generalized linear models," Journal of Health Economics, Elsevier, vol. 18(2), pages 153-171, April.
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    Cited by:

    1. Laura Liu & Hyungsik Roger Moon & Frank Schorfheide, 2023. "Forecasting with a panel Tobit model," Quantitative Economics, Econometric Society, vol. 14(1), pages 117-159, January.
    2. Keane, Michael & Stavrunova, Olena, 2016. "Adverse selection, moral hazard and the demand for Medigap insurance," Journal of Econometrics, Elsevier, vol. 190(1), pages 62-78.
    3. Keane, Michael & Stavrunova, Olena, 2016. "Adverse selection, moral hazard and the demand for Medigap insurance," Journal of Econometrics, Elsevier, vol. 190(1), pages 62-78.

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    1. Keane, Michael & Stavrunova, Olena, 2016. "Adverse selection, moral hazard and the demand for Medigap insurance," Journal of Econometrics, Elsevier, vol. 190(1), pages 62-78.
    2. Keane, Michael & Stavrunova, Olena, 2016. "Adverse selection, moral hazard and the demand for Medigap insurance," Journal of Econometrics, Elsevier, vol. 190(1), pages 62-78.

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