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Causal Inference under Mutual Information Restrictions

Abstract

Mutual information provides a general, model-free measure of statistical dependence between random variables and is a central concept in information theory. This paper introduces mutual information into the potential-outcome framework for causal inference. Rather than imposing unconfoundedness, we impose that conditioning on covariates reduces the dependence between potential outcomes and treatment assignment. This is formalized through a conditional mutual information (CMI) restriction. Even though this CMI restriction is not sufficient for identification of causal parameters it implies a specific structure on the generalized propensity score, i.e., the conditional treatment probability given potential outcomes and covariates. Borrowing from information theory, we show that under the CMI restriction the generalized propensity score (GPS) factorizes into a component depending only on the potential outcomes and a component depending only on covariates. We show that, building on this multiplicative structure, we can identify the average treatment effect (ATE) under a locally known covariate component of the GPS. This result even holds when the GPS is not identified from a conditional mean restriction but only satisfies a bridge condition. The identification results are constructive and yield ATE estimands based either on weighting with a generalized propensity score or on a conditional-mean representation. Finally, under identifying assumptions for the generalized propensity score, we derive the semiparametric efficient influence function.

About the speaker

Christoph Breunig is an econometrician, with a particular interest in microeconometrics, where he develops robust methods for causal inference. He obtained his doctoral degree from the 8xav¸£Àûµ¼º½ of Mannheim (Germany) in 2013. After a Postdoctoral Fellowship at the Cowles Foundation, Yale 8xav¸£Àûµ¼º½, he began as an Assistant Professor at Humboldt 8xav¸£Àûµ¼º½ of Berlin. In 2019, he moved to Emory 8xav¸£Àûµ¼º½ as an Assistant Professor, where he was tenured in 2023. On leave from Emory, Christoph Breunig started as an Associate Professor at the 8xav¸£Àûµ¼º½ of Bonn, where he was promoted to Full Professor in 2023. His research has been published in Economic Journal, Econometrica, Journal of Econometrics, and Quantitative Economics. Currently, he serves as Associate Editor for Journal of Econometrics and Journal of Business and Economic Statistics.

Language

English

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Supported by the Fond National de la Recherche,
Luxembourg (19441346)