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Functional Form and Heterogeneity in Models for Count Data

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  • William Greene

Abstract

This study presents several extensions of the most familiar models for count data, the Poisson and negative binomial models. We develop an encompassing model for two well-known variants of the negative binomial model (the NB1 and NB2 forms). We then analyze some alternative approaches to the standard log gamma model for introducing heterogeneity into the loglinear conditional means for these models. The lognormal model provides a versatile alternative specification that is more flexible (and more natural) than the log gamma form, and provides a platform for several "two part" extensions, including zero inflation, hurdle, and sample selection models. (We briefly present some alternative approaches to modeling heterogeneity.) We also resolve some features in Hausman, Hall and Griliches (1984, Economic models for count data with an application to the patents–R&D relationship, Econometrica 52 , 909–938) widely used panel data treatments for the Poisson and negative binomial models that appear to conflict with more familiar models of fixed and random effects. Finally, we consider a bivariate Poisson model that is also based on the lognormal heterogeneity model. Two recent applications have used this model. We suggest that the correlation estimated in their model frameworks is an ambiguous measure of the correlation of the variables of interest, and may substantially overstate it. We conclude with a detailed application of the proposed methods using the data employed in one of the two aforementioned bivariate Poisson studies.
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  • William Greene, 2007. "Functional Form and Heterogeneity in Models for Count Data," Working Papers 07-9, New York University, Leonard N. Stern School of Business, Department of Economics.
  • Handle: RePEc:ste:nystbu:07-9
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    14. William H. Greene & Mark N. Harris & Bruce Hollingworth & Pushkar Maitra, 2008. "A Bivariate Latent Class Correlated Generalized Ordered Probit Model with an Application to Modeling Observed Obesity Levels," Working Papers 08-18, New York University, Leonard N. Stern School of Business, Department of Economics.
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    1. repec:jss:jstsof:v:074:i10 is not listed on IDEAS
    2. Kirui, Oliver K., 2013. "Drivers of Collective Action and the Welfare Gains of such Initiatives among smallholder farmers: Experiences from Kenya," 2013 AAAE Fourth International Conference, September 22-25, 2013, Hammamet, Tunisia 161619, African Association of Agricultural Economists (AAAE).
    3. Niklas Elert, 2014. "What determines entry? Evidence from Sweden," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 53(1), pages 55-92, August.
    4. William Greene, 2007. "Correlation in Bivariate Poisson Regression Model," Working Papers 07-14, New York University, Leonard N. Stern School of Business, Department of Economics.
    5. Iezzi, Elisa & Lippi Bruni, Matteo & Ugolini, Cristina, 2014. "The role of GP's compensation schemes in diabetes care: Evidence from panel data," Journal of Health Economics, Elsevier, vol. 34(C), pages 104-120.
    6. repec:eme:jepppp:jepp-02-2016-0004 is not listed on IDEAS
    7. repec:eee:jiaata:v:30:y:2018:i:c:p:69-84 is not listed on IDEAS
    8. Sardana, Kavita & Bowker, James Michael & Bergstrom, John C. & Starbuck, C. Meghan & English, Donald B.K., 2008. "Accounting for Geographic Heterogeneity in Recreation Demand Models," 2008 Annual Meeting, July 27-29, 2008, Orlando, Florida 6437, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    9. repec:eee:tefoso:v:122:y:2017:i:c:p:49-62 is not listed on IDEAS
    10. Tsagris, Michail & Elmatzoglou, Ioannis & C. Frangos, Christos, 2012. "Assessment of Performance of Correlation Estimates in Discrete Bivariate Distributions using Bootstrap Methodology," MPRA Paper 68057, University Library of Munich, Germany.
    11. William Greene, 2009. "Models for count data with endogenous participation," Empirical Economics, Springer, vol. 36(1), pages 133-173, February.
    12. Burda, Martin & Harding, Matthew & Hausman, Jerry, 2012. "A Poisson mixture model of discrete choice," Journal of Econometrics, Elsevier, vol. 166(2), pages 184-203.
    13. William Greene, 2007. "Discrete Choice Modeling," Working Papers 07-6, New York University, Leonard N. Stern School of Business, Department of Economics.
    14. Lippi Bruni, Matteo & Mammi, Irene & Ugolini, Cristina, 2016. "Does the extension of primary care practice opening hours reduce the use of emergency services?," Journal of Health Economics, Elsevier, vol. 50(C), pages 144-155.
    15. repec:spr:sjecst:v:153:y:2017:i:2:d:10.1007_bf03399437 is not listed on IDEAS

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