Course outline

The course will cover regression methods for count data, such as number of doctor visits, where the dependent variable is a nonnegative integer.  While the focus is on count data, most of the methods are applicable to nonlinear regression models in general , and the relevant general frameworks will be presented ahead of specialization to counts. We will cover methods, theory, and applications. All methods will be carefully illustrated in full detail by applications to cross-section and panel count data examples.

Day 1: Cross-section data models. The first lecture will focus on standard regression models for count data: quasi-ML estimation of the Poisson model, the closely related generalized linear models framework, and maximum likelihood estimation of the negative binomial model. Various marginal effects from these nonlinear models will be presented.  Inference using heteroskedastic-robust and cluster-robust standard errors and appropriate bootstraps will be presented.

Day 2: Cross-section data models continued. The second lecture continues with more specialized models. Two-part models and with-zeros models control for excess zeros commonly-observed with count data. Finite mixture or latent class models are also more flexible parametric models. The lecture concludes with nonlinear two-stage least squares or generalized method of moments estimation of count models with endogenous regressors.

Day 3: Panel data models. The third lecture will focus on short panel data models where the number of cross-sectional units is large. We begin with random effects and fixed effects models for count data. We then present estimation of dynamic count data models that is a generalization of Arellano-Bond methods for linear models.

Day 4: Estimation by simulation methods. The fourth lecture will present maximum simulated likelihood estimation and Bayesian estimation (using Markov chain Monte Carlo) of parametric models for count data.

Day 5: Semiparametric  methods. The final lecture will introduce semiparametric methods such as single-index models for count data.

Practical lab sessions

The afternoon sessions will illustrate the various methods using Stata, and Stata programs and datasets will be provided. Additionally the final day will use R. No prior experience with Stata or R is assumed, though prior exposure to Stata will be beneficial.

Reading list

Virtually all the material is covered in A. Colin Cameron and Pravin K. Trivedi (2013), Regression Analysis of Count Data, Second Edition, Cambridge University Press. (See especially chapters 1-4 and 9-12.)