The Credibility Revolution

Revisiting Event-Study Designs: Robust and Efficient Estimation

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Revisiting Event-Study Designs: Robust and Efficient Estimation

Causal Question / Estimand

How to estimate a researcher-chosen weighted sum of heterogeneous treatment effects in staggered-adoption event studies — including the ATT, ATTs at fixed event-time horizons (holding unit composition fixed), and effects heterogeneous by observed covariates (Causal-Estimand). The paper insists the target estimand be specified explicitly and separately from the identification assumptions.

Identification Strategy

Builds a framework that cleanly separates three things conventional TWFE regressions conflate: (i) the estimation target, (ii) the identifying assumptions (Parallel-Trends and No-Anticipation on untreated potential outcomes), and (iii) any auxiliary restriction on Treatment-Effect-Heterogeneity. The efficient robust estimator takes an intuitive imputation form when heterogeneity is unrestricted: fit unit and period fixed effects on untreated observations only, impute each treated observation’s untreated potential outcome Ŷit = α̂i + β̂t, form τ̂it = Yit − α̂i − β̂t, then take the target-defined weighted sum. Any unbiased linear estimator in this framework can be represented as an imputation estimator, so estimators differ only in how they impute and how they weight. Identifying assumptions are tested via OLS on untreated observations only, avoiding the heterogeneity contamination of lead-lag specifications.

Key Assumptions

Parallel-Trends and No-Anticipation on untreated potential outcomes, optional restrictions on Treatment-Effect-Heterogeneity, and SUTVA. Avoiding Negative-Weighting (“forbidden comparisons”) is the payoff of dropping the implicit homogeneity assumption embedded in TWFE.

Threats to Validity

Event-study designs assume a restrictive parametric model for untreated outcomes; the paper does not evaluate when parallel trends is ex-ante plausible (cf. RothSantAnna2023-WhatsTrendingInDiD) nor offer estimation robust to bounded violations (cf. RambachanRoth2023-MoreCredibleParallelTrends), though the framework can accommodate unit-specific trends and time-varying covariates. Under arbitrary heterogeneity, causal effects cannot be separated from errors, so only conservative standard errors are available (exact only in the random-sampling, cohort–period estimand case). Fully dynamic specifications with no never-treated units are under-identified — pre-trend testing must be separated from dynamic-effect estimation.

Setting / Data

Application: the marginal propensity for expenditure (MPX) out of 2001/2008 U.S. tax rebates. Notional first-quarter MPC of 8–11% — about half of benchmark estimates used to calibrate macro models — concentrated in the first month after the rebate. Also a simulation study.

Key Claims

  • Conventional TWFE/lead-lag event studies are biased under heterogeneous effects: they impose implicit homogeneity, produce “forbidden comparisons,” and can even spuriously identify long-run effects for which no valid DiD comparison exists.
  • The efficient robust estimator is an imputation estimator when heterogeneity is unrestricted; all unbiased estimators share this imputation structure.
  • Separating estimation from testing gives principled pre-trend and no-anticipation tests free of heterogeneity contamination and immune to Roth’s pre-testing inference problem (under spherical errors).
  • Extends to time-varying controls, triple-difference designs, and some non-binary treatments; provides consistent, asymptotically normal inference with conservative standard errors and a leave-one-out finite-sample refinement.

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Citation

Borusyak, K., Jaravel, X., & Spiess, J. (2024). Revisiting Event-Study Designs: Robust and Efficient Estimation. Review of Economic Studies, 91(6), 3253–3285.

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