If one or more explanatory variables are not observed exactly in an ordered choice model, the parameters of interest cannot be point identified but are able to be partial identified. This paper is concerned with the identification and inference on regression in the ordered choice model when the interval data are available. We first develop an indistinguishable set for the parameter of interest after studying the structure of data. Then, a consistent estimator is proposed to trace the identified set which includes the indistinguishable set. It is an extension of Modified Maximum Score method in a binary choice model to the ordered alternatives case. This paper also provides insights of the relationship between the MMS estimator in 3-ordered choice model with interval data and the in...[ Read more ]

If one or more explanatory variables are not observed exactly in an ordered choice model, the parameters of interest cannot be point identified but are able to be partial identified. This paper is concerned with the identification and inference on regression in the ordered choice model when the interval data are available. We first develop an indistinguishable set for the parameter of interest after studying the structure of data. Then, a consistent estimator is proposed to trace the identified set which includes the indistinguishable set. It is an extension of Modified Maximum Score method in a binary choice model to the ordered alternatives case. This paper also provides insights of the relationship between the MMS estimator in 3-ordered choice model with interval data and the intersection of estimators in two binary choice models from the ordered choice model. It is found that they yield almost the same region. We carry out a series of Monte Carlo experiments, and their results provide evidence for our theoretical findings.

Keywords: interval data, ordered choice