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A Comparison of Alternative Methods to Model Endogeneity in Count Models. An Application to the Demand for Health Care and Health Insurance Choice

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  • Martin Schellhorn

Abstract

Several estimators have been suggested to tackle the problem of endogenous regressors and selectivity in count regression models. They differ in the structure and the degree of parametrization of the underlying models. The estimation of health services utilization conditional on the choice of different forms of health insurance provides a classical example of such problems. In Switzerland, basic health insurance is mandatory and each individual is insured separately. The insurance premium varies by region of residence but is independent of income and risk. The insured face a minimal annual deductible for ambulatory health services. Annually, they are given a choice of higher deductibles to reduce their insurance premium by a regulated percentage. The choice of a higher deductible sets incentives for a more cautious utilization of health services. Clearly, the choice is made based on expected health service utilization. The effect of the choice of a higher than the minimal deductible on the number of physician visits is analyzed. A matching estimator, a GMM estimator, two-stage method of moments estimators which account for selectivity and endogenous switching count regression models are applied to data from the 1997 Swiss Health Survey. Incentive-induced behavioral changes are disentangled from selection effects. The main finding is that most of the observed lower utilization for individuals with a high insurance deductible is caused by self- selection of individuals into the respective insurance contracts which either differ in their preferences or are healthier in unobserved aspects of their health status.

Suggested Citation

  • Martin Schellhorn, 2001. "A Comparison of Alternative Methods to Model Endogeneity in Count Models. An Application to the Demand for Health Care and Health Insurance Choice," Social and Economic Dimensions of an Aging Population Research Papers 40, McMaster University.
  • Handle: RePEc:mcm:sedapp:40
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    File URL: http://socserv.mcmaster.ca/sedap/p/sedap40.pdf
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    References listed on IDEAS

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    1. van Ophem, Hans, 2000. "Modeling Selectivity in Count-Data Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 503-511, October.
    2. Michael Gerfin & Michael Lechner, 2002. "A Microeconometric Evaluation of the Active Labour Market Policy in Switzerland," Economic Journal, Royal Economic Society, vol. 112(482), pages 854-893, October.
    3. John Mullahy, 1997. "Instrumental-Variable Estimation Of Count Data Models: Applications To Models Of Cigarette Smoking Behavior," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 586-593, November.
    4. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-959, July.
    5. Terza, Joseph V., 1998. "Estimating count data models with endogenous switching: Sample selection and endogenous treatment effects," Journal of Econometrics, Elsevier, vol. 84(1), pages 129-154, May.
    6. Holly, Alberto & Gardiol, Lucien & Domenighetti, Gianfranco & Brigitte Bisig, 1998. "An econometric model of health care utilization and health insurance in Switzerland," European Economic Review, Elsevier, vol. 42(3-5), pages 513-522, May.
    7. A. C. Cameron & P. K. Trivedi & Frank Milne & J. Piggott, 1988. "A Microeconometric Model of the Demand for Health Care and Health Insurance in Australia," Review of Economic Studies, Oxford University Press, vol. 55(1), pages 85-106.
    8. Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
    9. Windmeijer, F A G & Silva, J M C Santos, 1997. "Endogeneity in Count Data Models: An Application to Demand for Health Care," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(3), pages 281-294, May-June.
    10. James J. Heckman & Hidehiko Ichimura & Petra Todd, 1998. "Matching As An Econometric Evaluation Estimator," Review of Economic Studies, Oxford University Press, vol. 65(2), pages 261-294.
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    More about this item

    Keywords

    demand for health care and insurance; count models; endogenous regressors;

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

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