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Endogenous Treatment Effects for Count Data Models with Sample Selection or Endogenous Participation

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  • Bratti, M.
  • Miranda, A

Abstract

In this paper we propose a method to estimate models in which an endogenous dichotomous treatment affects a count outcome in the presence of either sample selection or endogenous participation using maximum simulated likelihood. We allow for the treatment to have an effect on both the sample selection or the participation rule and the main outcome. Applications of this model are frequent in many fields of economics, such as health, labor, and population economics. We show the performance of the model using data from Kenkel and Terza (2001), which investigates the effect of physician advice on the amount of alcohol consumption. Our estimates suggest that in these data (i) neglecting treatment endogeneity leads to a perversely signed effect of physician advice on drinking intensity, (ii) neglecting endogenous participation leads to an upward biased estimator of the treatment effect of physician advice on drinking intensity.

Suggested Citation

  • Bratti, M. & Miranda, A, 2010. "Endogenous Treatment Effects for Count Data Models with Sample Selection or Endogenous Participation," Health, Econometrics and Data Group (HEDG) Working Papers 10/19, HEDG, c/o Department of Economics, University of York.
  • Handle: RePEc:yor:hectdg:10/19
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    1. 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.
    2. Maria Melkersson & Dan-Olof Rooth, 2000. "Modeling female fertility using inflated count data models," Journal of Population Economics, Springer;European Society for Population Economics, vol. 13(2), pages 189-203.
    3. William Greene, 2009. "Models for count data with endogenous participation," Empirical Economics, Springer, vol. 36(1), pages 133-173, February.
    4. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-959, July.
    5. Andreas Million & Regina T. Riphahn & Achim Wambach, 2003. "Incentive effects in the demand for health care: a bivariate panel count data estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(4), pages 387-405.
    6. Cragg, John G, 1971. "Some Statistical Models for Limited Dependent Variables with Application to the Demand for Durable Goods," Econometrica, Econometric Society, vol. 39(5), pages 829-844, September.
    7. 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.
    8. Joseph V. Terza & Donald S. Kenkel & Tsui-Fang Lin & Shinichi Sakata, 2008. "Care-giver advice as a preventive measure for drinking during pregnancy: zeros, categorical outcome responses, and endogeneity," Health Economics, John Wiley & Sons, Ltd., vol. 17(1), pages 41-54.
    9. Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
    10. Terza, Joseph V., 1985. "A Tobit-type estimator for the censored Poisson regression model," Economics Letters, Elsevier, vol. 18(4), pages 361-365.
    11. 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.
    12. Alfonso Miranda, 2004. "FIML estimation of an endogenous switching model for count data," Stata Journal, StataCorp LP, pages 40-49.
    13. Alfonso Miranda & Sophia Rabe-Hesketh, 2006. "Maximum likelihood estimation of endogenous switching and sample selection models for binary, ordinal, and count variables," Stata Journal, StataCorp LP, vol. 6(3), pages 285-308, September.
    14. 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.
    15. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
    16. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Publishing House "SINERGIA PRESS", pages 129-137.
    17. R. Winkelmann, 1998. "Count data models with selectivity," Econometric Reviews, Taylor & Francis Journals, vol. 17(4), pages 339-359.
    18. Adriaan S. Kalwij, 2000. "The effects of female employment status on the presence and number of children," Journal of Population Economics, Springer;European Society for Population Economics, vol. 13(2), pages 221-239.
    19. Gary Chamberlain, 1980. "Analysis of Covariance with Qualitative Data," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 225-238.
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    Cited by:

    1. Rajendran, Srinivasulu & Afari-Sefa, Victor & Karanja, Daniel Kimani & Musebe, Richard & Romney, Dannie & Makaranga, Magesa A. & Samali, Silvest & Kessy, Radegunda Francis, 2016. "Farmer-Led Seed Enterprise Initiatives to Access Certified Seed for Traditional African Vegetables and its Effect on Incomes in Tanzania," International Food and Agribusiness Management Review, International Food and Agribusiness Management Association (IFAMA), vol. 19(1).

    More about this item

    Keywords

    count data; drinking; endogenous participation; maximum simulated likelihood; sample selection; treatment effects;

    JEL classification:

    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • I12 - Health, Education, and Welfare - - Health - - - Health Behavior
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education

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