An Algebraic Equivalence between Generalized Fixed Effects and a Generalized Mundlak Regression with Applications to Heterogeneous Trends and Difference-in-Differences

Jeffrey M. Wooldridge ()
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Jeffrey M. Wooldridge: Michigan State University

A chapter in Seven Decades of Econometrics and Beyond, 2025, pp 417-431 from Springer

Abstract: Abstract Using a modified version of the Frisch-Waugh-Lovell partialling out result, I show how the standard Mundlak regression for panel data can be extended to deliver ‘generalized fixed effects’ estimators, where coefficients on a subset of explanatory variables vary by cross-sectional unit. The characterization shows that only fitted values from individual specific regressions need to be controlled for—not the large set of interactions between unit-specific dummy variables and explanatory variables. In the special case of a single additive heterogeneity, the fitted values are simply the unit-specific time averages of the explanatory variables. The general results have practical applications, particularly when testing the standard fixed effects estimator against heterogeneous trend models. I derive a new, fully robust test that can be viewed as a regression-based Hausman test for choosing the level of heterogeneity. As an example, I reconsider some recently proposed difference-in-differences methods with staggered interventions and heterogeneous treatment effects when the parallel trends assumption is possibly violated.

Date: 2025
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DOI: 10.1007/978-3-031-92699-0_15

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