Fixed Effects and Causal Inference

Abstract

Across many disciplines, the fixed effects estimator of linear panel data models is the default method to estimate causal effects with nonexperimental data that are not confounded by time-invariant, unit-specific heterogeneity. One feature of the fixed effects estimator, however, is often overlooked in practice: With data over time t ∈ {1,...,T} for each unit of observation i ∈ {1,...,N}, the amount of unobserved heterogeneity the researcher can remove with unit fixed effects is weakly decreasing in T. Put differently, the set of attributes that are time-invariant is not invariant to the length of the panel. We consider several alternatives to the fixed effects estimator with T > 2 when relevant unit-specific heterogeneity is not time-invariant, including existing estimators such as the first-difference, twice first-differenced, and interactive fixed effects estimators. We also introduce several novel algorithms based on rolling estimators. In the situations considered here, there is little to be gained and much to lose by using the fixed effects estimator. We recommend reporting the results from multiple linear panel data estimators in applied research.

Keywords: panel data, fixed effects, first-differences, interactive fixed effects, unobserved heterogeneity, time-varying individual effects

JEL Classification: C23, C51, C52