Title:  Discordant Relaxations of Misspecified Models

Speaker: Lixiong Li, Johns Hopkins University

Time: Dec.20, 9:00 -10:30 am (Beijing Time)

On Zoom

About the Speaker:

Lixiong Li is an Assistant Professor of Economics at Johns Hopkins University. He obtained his Ph.D. in Economics from the Pennsylvania State University. His research interests are mainly in microeconometrics and applied industrial organization. In particular, he is interested in partial identification and moment inequality models.

Abstract：

In many set-identified models, it is difficult to obtain a tractable characterization of the identified set. Therefore, empirical works often construct confidence regions based on an outer set of the identified set. Because an outer set is always a superset of the identified set, this practice is often viewed as conservative yet valid. However, this paper shows that, when the model is refuted by the data, a nonempty outer set could deliver conflicting results with another outer set derived from the same underlying model structure, so that the results of outer sets could be misleading in the presence of misspecification. We provide a sufficient condition for the existence of discordant outer sets which covers models characterized by intersection bounds and the Artstein (1983) inequalities. We also derive sufficient conditions for the non-existence of discordant submodels, therefore providing a class of models for which constructing outer sets cannot lead to misleading interpretations. In the case of discordancy, we follow Masten and Poirier (2020) by developing a method to salvage misspecified models, but unlike them we focus on discrete relaxations. We consider all minimum relaxations of a refuted model which restores data-consistency. We find that the union of the identified sets of these minimum relaxations is misspecification-robust and has a new and intuitive empirical interpretation.