Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2506.17729

Efficient Difference-in-Differences and Event Study Estimators

Xiaohong Chen·Pedro H. C. Sant'Anna·Haitian Xie
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper investigates efficient Difference-in-Differences (DiD) and Event Study (ES) estimation using short panel data sets within the heterogeneous treatment effect framework, free from parametric functional form assumptions and allowing for variation in treatment timing. We provide an equivalent characterization of the DiD potential outcome model using sequential conditional moment restrictions on observables, which shows that the DiD identification assumptions typically imply nonparametric overidentification restrictions. We derive the semiparametric efficient influence function (EIF) in closed form for DiD and ES causal parameters under commonly imposed parallel trends assumptions. The EIF is automatically Neyman orthogonal and yields the smallest variance among all asymptotically normal, regular estimators of the DiD and ES parameters. Leveraging the EIF, we propose simple-to-compute efficient estimators. Our results highlight how to optimally explore different pre-treatment periods and comparison groups to obtain the tightest (asymptotic) confidence intervals, offering practical tools for improving inference in modern DiD and ES applications even in small samples. Calibrated simulations and an empirical application demonstrate substantial precision gains of our efficient estimators in finite samples.

Explore related subjects

econ.EMmath.STstat.TH

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Xiaohong Chen, Pedro H. C. Sant'Anna, Haitian Xie. 2025-06-21. Efficient Difference-in-Differences and Event Study Estimators. https://arxiv.org/abs/2506.17729

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Conditional-Moment Estimation and Inference in the BLP Model

The random-coefficient demand model of Berry, Levinsohn, and Pakes (1995) is commonly estimated by the generalized method of moments (GMM), using an unconditional moment restriction with a fixed set of instruments. Identification of the model, however, rests on a conditional moment restriction. The two are not equivalent: the unconditional restriction may admit additional parameter values. We construct a counterexample in which the model is identified by the conditional restriction yet standard GMM is not, even with the optimal instrument. Building directly on the identifying restriction, we propose a two-step estimator, following Ai and Chen (2003), that first estimates the relevant conditional expectations nonparametrically and then selects the structural parameters by a conditional-variance-weighted minimum-distance criterion; standard GMM is recovered as the special case of a linear projection onto finitely many instruments. We establish root-T asymptotic normality for the proposed estimator, and we develop the theory for both kernel and series implementations of the first stage. The two implementations share a common limiting distribution, attaining the semiparametric efficiency bound. Simulation evidence illustrates the consequences of the identification gap and demonstrates that the proposed estimator outperforms standard GMM in finite samples.

econ.EM↗
arXiv2026

Generic Covariate Adjustment for Regression Discontinuity Designs

It is standard practice to include covariates in regression discontinuity designs (RDDs) and regression kink designs (RKDs), but the theoretical justification for doing so does not generally extend beyond linear estimands. This paper proposes a novel entropy balancing reweighting approach for covariate adjustment within a general framework of RDDs and RKDs. While conventional regression-based covariate adjustment methods generally fail to deliver consistent estimation for nonlinear estimands such as quantile treatment effects, our reweighting approach achieves consistency while improving efficiency. Moreover, even in settings where the regression-based covariate adjustment method already improves efficiency, our approach can deliver additional efficiency gains. Simulation studies corroborate these theoretical findings. We present an empirical application in which our covariate adjustment yields statistically significant results that would not be obtained without covariate adjustment.

econ.EM↗
arXiv2026

Kernel Balancing in Tree-based Methods

Studying heterogeneous treatment effects has become essential in experimental and observational studies. A critical assumption for obtaining reliable treatment effect estimates is overlap, which requires that treated and control units have sufficiently similar covariate distributions. Poor overlap may limit the effectiveness of estimators, especially those based on propensity scores, potentially leading to unreliable results. We investigate the effectiveness of kernel balancing (KBal) (Hazlett, 2020) as an alternative to propensity score methods for conditional average treatment effect (CATE) estimation, particularly in settings with overlap violations. Building on optimization-based balancing approaches, we integrate KBal weights into tree-based methods, specifically, causal forests (Athey et al., 2019) and the X-Learner (XRF) (Künzel et al., 2019), to assess their impact on bias reduction and estimation precision. Monte Carlo evidence shows that KBal achieves near-exact balance in a transformed feature space, thereby improving treatment effect estimation in cases where traditional reweighting methods struggle due to extreme weights, finite-sample bias, or insufficient removal of pre-existing confounding bias. We apply the proposed methods to the semi-synthetic IHDP benchmark dataset. Overall, the results indicate that KBal leads to performance improvements, especially in settings with nonlinear treatment effects and limited overlap, making it a useful alternative to propensity score methods.

econ.EM↗