All the topics dealt with in this chapter are treated at greater length and depth in Cameron and Trivedi (1998) which also provides a comprehensive bibliography. Winkelmann (1997) also provides a fairly complete treatment of the econometric literature on counts. The statistics literature generally analyzes counts in the context of generalized linear models (GLM). The standard reference is McCullagh and Nelder (1989). The econometrics literature generally fails to appreciate the contributions of the GLM literature on generalized linear models. Fahrmeir and Tutz (1994) provide a recent and more econometric exposition of GLMs.
The material in Section 2 is very standard and appears in many places. A similar observation applies to the negative binomial model in Section 3.1. Cameron and Trivedi (1986) provide an early presentation and application. For the finite mixture approach of Section 3.2 see Deb and Trivedi (1997). Applications of the hurdle model in Section 3.3 include Mullahy (1986), who first proposed the model, Pohlmeier and Ulrich (1995), and Gurmu and Trivedi (1996). The quasi-MLE of Section 4.1 is presented in detail by Gourieroux ef al. (1984a, 1984b) and by Cameron and Trivedi (1986).
Regression models for the types of data discussed in Section 5 are in their infancy. The notable exception is that (static) panel data count models are well established, with the standard reference being Hausman ef al. (1984). See also Brannas and Johansson (1996). For reviews of the various time series models see MacDonald and Zucchini (1997, ch. 2) and Cameron and Trivedi (1998, ch. 7). Developing adequate regression models for multivariate count data is currently an active area. For dynamic count panel data models there are several recent references, including Blundell ef al. (1995).
For further discussion of diagnostic testing, only briefly mentioned in Section 6, see Cameron and Trivedi (1998, ch. 5).
Blundell, R., R. Griffith, and J. Van Reenen (1995). Dynamic count data models of technological innovation. Economic Journal 105, 333-44.
Brannas, K., and P. Johansson (1996). Panel data regression for counts. Statistical Papers 37, 191-213.
Cameron, A. C., and P. K. Trivedi (1986). Econometric models based on count data: Comparisons and applications of some estimators. Journal of Applied Econometrics 1, 29-53.
Cameron, A. C., and P. K. Trivedi (1998). Regression Analysis of Count Data. New York: Cambridge University Press.
Cameron, A. C., P. K. Trivedi, F. Milne, and J. Piggott (1988). A microeconometric model of the demand for health care and health insurance in Australia. Review of Economic Studies 55, 85-106.
Cameron, A. C., and F. A.G. Windmeijer (1996). R-squared measures for count data regression models with applications to health care utilization. Journal of Business and Economic Statistics 14, 209-20.
Davutyan, N. (1989). Bank failures as Poisson variates. Economic Letters 29, 333-8.
Deb, P., and P. K. Trivedi (1997). Demand for medical care by the elderly: A finite mixture approach. Journal of Applied Econometrics 12, 313-26.
Delgado, M. A., and T. J. Kniesner (1997). Count data models with variance of unknown form: An application to a hedonic model of worker absenteeism. Review of Economics and Statistics 79, 41-9.
Fahrmeir, L., and G. T. Tutz (1994). Multivariate Statistical Modelling Based on Generalized Linear Models. New York: Springer-Verlag.
Gourieroux, C., and A. Monfort (1997). Simulation Based Econometric Methods. Oxford: Oxford University Press.
Gourieroux, C., A. Monfort, and A. Trognon (1984a). Pseudo maximum likelihood methods: Theory. Econometrica 52, 681-700.
Gourieroux, C., A. Monfort, and A. Trognon (1984b). Pseudo maximum likelihood methods: Applications to Poisson models. Econometrica 52, 701-20.
Gurmu, S., and P. K. Trivedi (1996). Excess zeros in count models for recreational trips. Journal of Business and Economic Statistics 14, 469-77.
Harvey, A. C., and C. Fernandes (1989). Time series models for count or qualitative observations (with discussion). Journal of Business and Economic Statistics 7, 407-17.
Hausman, J. A., B. H. Hall, and Z. Griliches (1984). Econometric models for count data with an application to the patents-R and D relationship. Econometrica 52, 909-38.
Johnson, N. L., S. Kotz, and A. W. Kemp (1992). Univariate Distributions, 2nd edn. New York: John Wiley.
MacDonald, I. L., and W. Zucchini (1997). Hidden Markov and other Models for Discretevalued Time Series. London: Chapman and Hall.
McCullagh, P., and J. A. Nelder (1989). Generalized Linear Models, 2nd edn. London: Chapman and Hall.
Mullahy, J. (1986). Specification and testing of some modified count data models. Journal of Econometrics 33, 341-65.
Nelder, J. A., and R. W.M. Wedderburn (1972). Generalized linear models. Journal of the Royal Statistical Society A 135, 370-84.
Pohlmeier, W., and V. Ulrich (1995). An econometric model of the two-part decisionmaking process in the demand for health care. Journal of Human Resources 30, 339-61.
Rose, N. (1990). Profitability and product quality: Economic determinants of airline safety performance. Journal of Political Economy 98, 944-64.
Terza, J. (1998). Estimating count data models with endogenous switching: Sample selection and endogenous switching effects. Journal of Econometrics 84, 129-39.
Winkelmann, R. (1995). Duration dependence and dispersion in count-data models. Journal of Business and Economic Statistics 13, 467-74.
Winkelmann, R. (1997). Econometric Analysis of Count Data. Berlin: Springer-Verlag.
Zeger, S. L. (1988). A regression model for time series of counts. Biometrika 75, 621-9.