Partial Identification and Estimation of Semiparametric Ordered Response Models with Interval Regressor Data

In many micro‐data studies, the dependent variable often involves ordered categories and at least one regressor is measured by the interval rather than the precise value. This paper considers partial identification of such an ordered response model when point identification fails. We show the identified set of non‐intercept coefficients is the intersection of those for composite binary response models. We also propose a generalized modified maximum score set (GMMS) estimator. A practical implication of our finding is researchers can shrink the identified set and obtain more precise inference by designing as many as categories of response in a questionnaire during data collection. Another advantage is our theoretical finding can be used to infer the identified region in the multinomial choice model. A Monte Carlo study is conducted to illustrate the main finding in a finite sample. Finally, we apply GMMS estimator to a job satisfaction study using US data with the interval income.