Fixed Effects and the Generalized Mundlak Estimator

2023/09/07 by Dmitry Arkhangelsky, Guido W. Imbens · 1 voice
Mathematics · #Advanced Causal Inference Techniques #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · pdf · doi:10.1093/restud/rdad089

openalex publication_date 2023/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/26

Abstract

Abstract We develop a new approach for estimating average treatment effects in observational studies with unobserved group-level heterogeneity. We consider a general model with group-level unconfoundedness and provide conditions under which aggregate balancing statistics—group-level averages of functions of treatments and covariates—are sufficient to eliminate differences between groups. Building on these results, we re-interpret commonly used linear fixed-effect regression estimators by writing them in the Mundlak form as linear regression estimators without fixed effects but including group averages. We use this representation to develop Generalized Mundlak Estimators that capture group differences through group averages of (functions of) the unit-level variables and adjust for these group differences in flexible and robust ways in the spirit of the modern causal literature.

Citations

• On the Application of Probability Theory to Agricultural Experiments. Essay on Principles. Section 9
• On the adaptive elastic-net with a diverging number of parameters
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• Difference-in-differences with variation in treatment timing
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Discussions

• You could combine approaches as suggested here doi.org/10.1093/rest... If you put the group averages of the covariates (Mundlak device) into the propensity score estimator it captures idea that treatm [bsky, 1 points, 0 comments]

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