Qualitative Response. Models
This chapter deals with regression models when the dependent variable is qualitative. There are many situations in economics where the dependent variable takes discrete values, due to the qualitative nature of many behavioral responses. For instance, consider a worker deciding whether or not to participate in the labor force, a consumer deciding whether or not to buy a good, etc.
There are good reviews of qualitative response models (QRM) in the literature (Amemiya, 1981; McFadden, 1981, 1984; Maddala, 1983, chs. 2-5). Here we focus on some basic concepts about QRM, some topics not covered in the above reviews, and on some recent work in this area. We discuss binary and multinomial response models, specification tests, panel data with qualitative variables, semiparametric estimation, and simulation methods.
Section 2 introduces some basic concepts about QRM, with an emphasis on univariate QRM and, in particular, on the estimation of binary and multinomial logit and probit models. A more in-depth review of all types of QRM, both univariate and multivariate, can be found in Maddala (1983, chs. 2-5).
Some concepts about specification tests in QRM are discussed in Section 3. Pagan and Vella (1989) argued that the use of specification tests in qualitative response models is not common since they are difficult to compute, but that has changed as computationally simpler specification tests have become available.
Sections 4 to 6 review some further topics in QRM. Panel data with qualitative variables (Section 4) has been an intensive area of research, both theoretical and applied, since the early reviews by Heckman (1981) and Chamberlain (1980, 1984). The principal issue in this literature is on controling for heterogeneity and state dependence.
The other two topics, semiparametric estimation (Section 5) and simulation methods (Section 6), correspond to two specific problems in qualitative response models: the inconsistency of estimators when the distributional assumption of the model is incorrect, and the computational problem of evaluating higher order integrals in multinomial qualitative response models.