Selecting Inequalities for Sharp Identification in Models with Set-Valued Predictions.

• Econometrics

Date and Location

Monday, November 20, 2023, 3:40 PM - 5:00 PM
Blue Room, 1113 Social Sciences and Humanities

Abstract

One of the main challenges in partially identified models is obtaining a tractable characterization of the sharp identified set, which exhausts all information contained in the data and modeling assumptions. In a large class of models, sharp identified sets can be generally described using a special kind of conditional moment inequalities called Artstein’s inequalities. These inequalities verify that the distribution of the observed outcomes, conditional on covariates, could have been generated by the model for some parameter values. Typically, the total number of inequalities is very large or even infinite, but at the same time, many of them may be redundant in the sense that excluding them from the analysis does not change the identified set. Thus, some inequality selection is required. In this paper, I characterize the smallest possible set of inequalities that exhaust all information contained in the data and modeling assumptions. When the total number of inequalities is finite, I provide an efficient algorithm for computing such a set in practice. I apply the results to the models of entry games, discrete choice, selectively observed data, and English auctions and conduct a simulation study to demonstrate that the proposed method yields substantial improvements over ad hoc inequality selection.

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