Quantitative Economics

Journal Of The Econometric Society

Edited by: Stéphane Bonhomme • Print ISSN: 1759-7323 • Online ISSN: 1759-7331

Quantitative Economics: May, 2024, Volume 15, Issue 2

Discordant Relaxations of Misspecified Models

p. 331-379

Lixiong Li, Désiré Kédagni, Ismaël Mourifié

In many set‐identified models, it is difficult to obtain a tractable characterization of the identified set. Therefore, researchers often rely on nonsharp identification conditions, and empirical results are often based on an outer set of the identified set. This practice is often viewed as conservative yet valid because an outer set is always a superset of the identified set. However, this paper shows that when the model is refuted by the data, two sets of nonsharp identification conditions derived from the same model could lead to disjoint outer sets and conflicting empirical results. We provide a sufficient condition for the existence of such discordancy, which covers models characterized by conditional moment inequalities and the Artstein (1983) inequalities. We also derive sufficient conditions for the nonexistence 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 (2021) 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 that restores data consistency. We find that the union of the identified sets of these minimum relaxations is robust to detectable misspecifications and has an intuitive empirical interpretation.

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Supplemental Material

Supplement to "Discordant Relaxations of Misspecified Models"

Lixiong Li, Désiré Kédagni, and Ismaël Mourifié

The replication package for this paper is available at https://doi.org/10.5281/zenodo.10641299. The Journal checked the data and codes included in the package for their ability to reproduce the results in the paper and approved online appendices.