474 Discrete Choice Modeling
11.4.3 Sample selection in a bivariate probit model 512
11.4.4 Multivariate binary choice and the panel probit model 513
11.4.5 Application 514
11.5 Ordered choice 515
11.5.1 Specification analysis 517
11.5.2 Bivariate ordered probit models 517
11.5.3 Panel data applications 519
11.5.3.1 Fixed effects 519
11.5.3.2 Random effects 520
11.5.4 Application 520
11.6 Models for counts 523
11.6.1 Heterogeneity and the negative binomial model 525
11.6.2 Extended models for counts: two-part, zero inflation, sample selection,
bivariate 527
11.6.2.1 Hurdle model 527
11.6.2.2 Zero inflation models 528
11.6.2.3 Sample selection 529
11.6.2.4 Bivariate Poisson model 530
11.6.3 Panel data models 531
11.6.4 Application 532
11.7 Multinomial unordered choices 536
11.7.1 Multinomial logit and multinomial probit models 538
11.7.1.1 Multinomial probit model 539
11.7.2 Nested logit models 540
11.7.3 Mixed logit and error component models 542
11.7.4 Application 544
11.8 Summary and conclusions 547
11.1 Introduction
This chapter will survey models for outcomes that arise through measurement
of discrete consumer choices, such as whether to vote for a particular candidate,
whether to purchase a car, how to get to work, whether to purchase insurance,
where to shop, or whether to rent or buy a home or a car. Traditional economic
theory for consumer choice – focused on utility maximization over bundles of con-
tinuous commodities – is relatively quiet on the subject of discrete choice among a
set of specific alternatives. Econometric theory and applications, in contrast, con-
tain a vast array of analyzes of discrete outcomes; discrete choice modeling has
been one of the most fruitful areas of study in econometrics for several decades.
There is a useful commonality in much of this. One can build an overview of mod-
els for discrete outcomes on a platform of individual maximizing behavior. Given
that the literature is as vast as it is, and we have but a small number of pages within
which to package it, this seems like a useful approach. In what follows, we will sur-
vey some of the techniques used to analyze individual random utility maximizing
behavior.