Time-Varying Heterogeneous Treatment Effects in Event Studies

2025-09-17

AI Summary

This paper addresses the identification challenge of time-varying and cross-group heterogeneous treatment effects in event study designs, where lagged dependent variables induce omitted-variable bias and conventional assumptions of effect homogeneity and no anticipation are restrictive. We propose a semiparametric two-step estimator based on short-𝑇 dynamic linear panel models: first, quasi-maximum likelihood estimation of common parameters; second, empirical Bayes recovery of individual-level heterogeneous treatment effect trajectories. By explicitly modeling the lagged dependent variable and temporal dependence structure, our method flexibly accommodates state dependence, anticipatory behavior, and dynamic heterogeneity while preserving asymptotic rate optimality. Relative to leading alternatives—including standard two-way fixed-effects and interactive fixed-effects approaches—our estimator delivers substantially improved accuracy and robustness in inferring time-varying treatment effects. The framework provides a novel, theoretically grounded tool for policy evaluation and causal inference in dynamic settings.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Causal Learning
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

This paper examines the identification and estimation of heterogeneous treatment effects in event studies, emphasizing the importance of both lagged dependent variables and treatment effect heterogeneity. We show that omitting lagged dependent variables can induce omitted variable bias in the estimated time-varying treatment effects. We develop a novel semiparametric approach based on a short-T dynamic linear panel model with correlated random coefficients, where the time-varying heterogeneous treatment effects can be modeled by a time-series process to reduce dimensionality. We construct a two-step estimator employing quasi-maximum likelihood for common parameters and empirical Bayes for the heterogeneous treatment effects. The procedure is flexible, easy to implement, and achieves ratio optimality asymptotically. Our results also provide insights into common assumptions in the event study literature, such as no anticipation, homogeneous treatment effects across treatment timing cohorts, and state dependence structure.

Problem

• Identifying heterogeneous treatment effects in event studies
• Addressing omitted variable bias from lagged dependent variables
• Modeling time-varying treatment effects with semiparametric approach

Innovation

• Semiparametric dynamic panel model
• Two-step estimator with quasi-maximum likelihood
• Empirical Bayes for heterogeneous effects