The foregoing has surveyed nearly all of the literature on ordered choice modeling. We have, of course, listed only a small fraction of the received applications. However, the full range of methodological developments has been presented, with a single remaining exception. As in many other areas of econometrics, a thread of the contemporary literature has explored the boundaries of the model that are circumscribed by the distributional assumptions. We have limited ourselves to ordered logit and probit models, while relaxing certain assumptions such as homoscedasticity, all within the boundaries of the parametric model. The last strand of literature to be examined is the development of estimators that extend beyond the parametric distributional assumptions. It is useful to organize the overview around a few features of the model: scaling, the distribution of the disturbance, the functional form of the regression, and so on. In each of these cases, we can focus on applications that broaden the reach of the ordered choice model to less tightly specified settings.

There is a long, rich history of semiparametric and nonparametric analysis of binary choice modeling (far too long and rich to examine in depth in this already long survey) that begins in the 1970s, only a few years after analysis of individual binary data became a standard technique. The binary choice literature has two focal points, maximum score estimation (Manski (1975, 1985), Manski and Thompson (1985), and Horowitz (1992)) and the Klein and Spady (1993) kernel-based semiparametric estimator for binary choice. (As noted, there is a huge number of other papers on the subject. We are making no attempt to survey this literature.)