Functional Form and Heterogeneity in Models for Count Data
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.
(This abstract was borrowed from another version of this item.)
|Date of creation:||2007|
|Date of revision:|
|Contact details of provider:|| Postal: New York University, Leonard N. Stern School of Business, Department of Economics, 44 West 4th Street, New York, NY 10012-1126|
Phone: (212) 998-0860
Fax: (212) 995-4218
Web page: http://w4.stern.nyu.edu/economics/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Terza, Joseph V., 1985. "A Tobit-type estimator for the censored Poisson regression model," Economics Letters, Elsevier, vol. 18(4), pages 361-365.
- Asplund, Marcus & Sandin, Rickard, 1999. "The Number of Firms and Production Capacity in Relation to Market Size," Journal of Industrial Economics, Wiley Blackwell, vol. 47(1), pages 69-85, March.
- Krinsky, Itzhak & Robb, A Leslie, 1986. "On Approximating the Statistical Properties of Elasticities," The Review of Economics and Statistics, MIT Press, vol. 68(4), pages 715-19, November.
- Cameron,A. Colin & Trivedi,Pravin K., 2005. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9780521848053.
- Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
- Lancaster, Tony, 2000. "The incidental parameter problem since 1948," Journal of Econometrics, Elsevier, vol. 95(2), pages 391-413, April.
- 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.
- Cameron, A. Colin & Trivedi, Pravin K., 1990. "Regression-based tests for overdispersion in the Poisson model," Journal of Econometrics, Elsevier, vol. 46(3), pages 347-364, December.
- Murat K. Munkin & Pravin K. Trivedi, 1999. "Simulated maximum likelihood estimation of multivariate mixed-Poisson regression models, with application," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 29-48.
- 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.
- Joseph Hilbe, 1994. "Negative binomial regression," Stata Technical Bulletin, StataCorp LP, vol. 3(18).
- Jung, Robert C & Winkelmann, Rainer, 1993. "Two Aspects of Labor Mobility: A Bivariate Poisson Regression Approach," Empirical Economics, Springer, vol. 18(3), pages 543-56.
- Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
When requesting a correction, please mention this item's handle: RePEc:ste:nystbu:07-9. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Viveca Licata)
If references are entirely missing, you can add them using this form.