Comments on “Unobservable Selection and Coefficient Stability: Theory and Evidence” and “Poorly Measured Confounders are More Useful on the Left Than on the Right”

Abstract–

We establish a link between the approaches proposed by Oster (2019) and Pei, Pischke, and Schwandt (2019) which contribute to the development of inferential procedures for causal effects in the challenging and empirically relevant situation where the unknown data-generation process is not included in the set of models considered by the investigator. We use the general misspecification framework recently proposed by De Luca, Magnus, and Peracchi (2018) to analyze and understand the implications of the restrictions imposed by the two approaches.

ACKNOWLEDGMENTS

We thank the editor, an associate editor, and two anonymous referees for their extremely valuable comments. We also thank Josh Angrist, Arik Levinson and Salvatore Modica for useful discussions.

Additional information

Funding

Giuseppe De Luca and Franco Peracchi acknowledge financial support from MIUR PRIN 2015FMRE5X.