Post-Matching Two-Way Fixed Effects Estimation

2026-02-13

AI Summary

This study addresses the asymptotic bias and invalid standard errors of the conventional two-way fixed effects (2WFE) estimator following matching in settings with multiple, heterogeneous treatment cohorts. The authors propose an improved matched difference-in-differences strategy that compares each treatment cohort separately against the never-treated group, thereby avoiding bias induced by pooling heterogeneous cohorts and explicitly accounting for the variability inherent in the matching process. They provide the first systematic characterization of the sources of bias in post-matching 2WFE estimation, construct an unbiased estimator for the identifiable causal parameter, and derive valid standard errors that incorporate matching uncertainty. Theoretical analysis establishes the consistency of the proposed estimator under constant treatment effects, while simulations and empirical applications demonstrate its superior finite-sample performance and reliable inference.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

When estimating treatment effects with two-way fixed effects (2WFE) models, researchers often use matching as a pre-processing step when the parallel trends assumption is thought to hold conditionally on covariates. Specifically, in a first step, each treated unit is matched to one or more untreated units based on observed time-invariant covariates. In the second step, treatment effects are estimated with a 2WFE regression in the matched sample, reweighting the untreated units by the number of times they are matched. We formally analyze this common practice and highlight two problems. First, when different treatment cohorts enter treatment in different time periods, the post-matching 2WFE estimator that pools all treated cohorts has an asymptotic bias, even when the treatment effect is constant across units and over time. Second, failing to account for the variability introduced by the matching procedure yields invalid standard error estimators, which can be biased upwards or downwards depending on the data generating process. We propose simple post-matching difference-in-differences estimators that compare each treated cohort to the never-treated separately, instead of pooling all treated cohorts. We provide conditions under which these estimators are consistent for well-defined causal parameters, and derive valid standard errors that account for the matching step. We illustrate our results with simulations and with an empirical application.

Problem

• two-way fixed effects
• matching
• difference-in-differences
• treatment effect estimation
• standard errors

Innovation

• two-way fixed effects
• matching
• difference-in-differences
• treatment cohorts
• standard error correction