William Greene 475We emphasize that we have chosen to focus on models for discretechoice, rather
than models for discretedependent variables. This provides us with several oppor-
tunities to focus and narrow this review. First, it allows us to limit the scope of
the survey to a reasonably manageable few types of models. As noted, the liter-
ature on this topic is vast. We will use this framework to select a few classes of
models that are used by analysts of individual choice. It also gives us license to
make a few major omissions that might otherwise fall under the umbrella of dis-
crete outcomes. One conspicuous case will be models for counts. Event counts are
obviously discrete – models for them are used to study, e.g., traffic incidents, inci-
dence of disease, health care system utilization, credit and financial markets, and
an array of other settings. Models for counts can occupy an entire library of its own
in this area – two excellent references are Cameron and Trivedi (1998) and Winkel-
mann (2003) – but this area will extend far beyond our reach. On the other hand,
applications in health economics (system utilization) and industrial organization
(patents and innovations) do lead to some settings in which individual or firm
choice produces a count response. We will briefly consider models for counts from
this standpoint. The reader will no doubt note other areas of discrete response anal-
ysis that are certainly important. Space limitations force us to consider a fairly small
number of cases.
This chapter proceeds as follows. Section 11.2 details the estimation and infer-
ence tools used throughout the remainder of the survey, including the basic results
in maximum likelihood estimation. Section 11.3 analyzes in detail the fundamen-
tal pillar of analysis of discrete choice, the model for binary choice – the choice
between two alternatives. Most of the applications that follow are obtained by
extending or building on the basic binary choice model. Thus we examine the
binary choice model in greater detail than the others, as it also provides a con-
venient setting in which to develop the estimation and inferential concepts that
carry over to the other models. Section 11.4 considers the immediate extension of
the binary choice, bivariate and multivariate binary choice models. Section 11.5
returns to the single choice setting and examines ordered choice models. Models
for count data are examined in section 11.6. Finally, section 11.7 turns to an area
of literature in its own right, multinomial choice modeling. As before, but even
more so here, we face the problem of surveying a huge literature in a few pages. We
therefore describe the most fundamental elements of multinomial choice analysis,
and point the reader toward more detailed sources in the literature. Section 11.8
concludes.
11.2 Specification, estimation and inference for
discrete choice models
The classical theory of consumer behavior provides the departure point for eco-
nomic models of discrete individual choice.^1 A representative consumer with
preferences represented by a utility function defined over the consumption of a
vector of goods,U
(
d)
, is assumed to maximize this utility subject to a budget