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

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  • Massimiliano Bratti

    ()
    (Department of Economics, Business and Statistics, Universita degli Studi di Milano, Via Conservatorio~7, I-20122, Milan, Italy.)

  • Alfonso Miranda

    ()
    (Department of Quantitative Social Science, Institute of Education, University of London. 20 Bedford Way, London WC1H 0AL, UK.)

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.

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Bibliographic Info

Paper provided by Department of Quantitative Social Science - Institute of Education, University of London in its series DoQSS Working Papers with number 10-05.

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Length: 30 pages
Date of creation: 21 May 2010
Date of revision: 10 Dec 2010
Handle: RePEc:qss:dqsswp:1005

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Postal: Department of Quantitative Social Science. 20 Bedford Way London WC1H 0AL
Phone: (44) (0)20 7612 6654. Eliminate (44) and add (0) if calling from inside the UK. Add (44) and eliminate (0) if calling from abroad.
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Web page: http://www.ioe.ac.uk/study/departments/369.html
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Keywords: count data; drinking; endogenous participation; maximum simulated likelihood; sample selection; treatment effects;

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References

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  1. Frank Windmeijer & Joao Santos Silva, 1996. "Endogeneity in count data models; an application to demand for health care," IFS Working Papers W96/15, Institute for Fiscal Studies.
  2. 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.
  3. Adriaan S. Kalwij, 2000. "The effects of female employment status on the presence and number of children," Journal of Population Economics, Springer, vol. 13(2), pages 221-239.
  4. Heckman, James J, 1979. "Sample Selection Bias as a Specification Error," Econometrica, Econometric Society, vol. 47(1), pages 153-61, January.
  5. 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.
  6. James J. Heckman, 1977. "Dummy Endogenous Variables in a Simultaneous Equation System," NBER Working Papers 0177, National Bureau of Economic Research, Inc.
  7. Maria Melkersson & Dan-Olof Rooth, 2000. "Modeling female fertility using inflated count data models," Journal of Population Economics, Springer, vol. 13(2), pages 189-203.
  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. William Greene, 2009. "Models for count data with endogenous participation," Empirical Economics, Springer, vol. 36(1), pages 133-173, February.
  10. 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 829-44, September.
  11. Chamberlain, Gary, 1980. "Analysis of Covariance with Qualitative Data," Review of Economic Studies, Wiley Blackwell, vol. 47(1), pages 225-38, January.
  12. Alfonso Miranda, 2004. "FIML estimation of an endogenous switching model for count data," Stata Journal, StataCorp LP, vol. 4(1), pages 40-49, March.
  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. Terza, Joseph V., 1985. "A Tobit-type estimator for the censored Poisson regression model," Economics Letters, Elsevier, vol. 18(4), pages 361-365.
  15. R. Winkelmann, 1998. "Count data models with selectivity," Econometric Reviews, Taylor & Francis Journals, vol. 17(4), pages 339-359.
  16. 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.
  17. 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.
  18. 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.
  19. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
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