Microeconometrics: Methods and Applications A. Colin Cameron and Pravin K. Trivedi
MICROECONOMETRICS: Methods and Applications

Cambridge University Press, New York
May 2005

PART 4  (chapters 14-20)

Part 4, consisting of chapters 14 to 20, covers the core nonlinear limited dependent variable models for cross-section data, defined by the range of values taken by the dependent variable. Topics covered include models for binary and multinomial data, duration data and count data. The complications of censoring, truncation and sample selection are also studied.

Chapters 14-15 cover models for binary and multinomial data that are standard in the analysis of discrete choice and outcomes.  Maximum likelihood methods are dominant.  Different parameterizations for the conditional probabilities in these models lead to different models, notably logit and probit models, which are well-established  Recent literature has focused on less restrictive modeling with more flexible functional forms for conditional probabilities and on accommodating individual unobserved heterogeneity. These objectives motivate the use of  semiparametric methods and simulation-based estimation methods.

Censoring, truncation or sample selection generate empirically several important classes of models that are analyzed in Chapter 16. The long-established Tobit model is central to this literature, but its estimation and inference rely on strong distributional assumptions to permit consistent estimation. We also examine the newer semiparametric methods require weaker assumptions.

Chapters 17-19 consider duration models in which the focus is on either the determinants of spell lengths, such as length of an unemployment spell, or on modeling the hazard rate of transitions from one initial state to another. The relative importance of state dependence and unobserved heterogeneity as determinants of the average length of spell is a central issue, whose resolution raises fundamental questions about alternative modeling approaches. The analysis covers both discrete and continuous time models, and both parametric and semiparametric formulations, including the standard models like the exponential, the Weibull,  and the proportional hazards model.  Chapter 18 covers formulation and interpretation of richer models that incorporate unobserved heterogeneity. Chapter 19 deals with models with several types of events using the competing risks formulation and models of multiple spells.

Chapter 20 covers the analysis of event count of the kind very common in health economics. There are many strong connections and parallels between count data models and duration models because of their common foundation in stochastic processes. We analyze the widely-used Poisson and negative binomial regression models, together with important variants such as the two-part or hurdle model, zero-inflated models, latent class models, and endogenous regressor models, all of which accommodate different facets of the event processes.

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