Pre-Event Trends in the Panel Event-Study Design

Causal Question / Estimand

The causal effect $\beta$ of a policy $z_{it}$ on an outcome $y_{it}$ in a linear panel event-study (Causal-Estimand) when a time-varying unobserved confound ${\eta }_{it}$ (e.g. labor demand, for minimum-wage studies of youth employment) drives both the policy and the outcome — i.e. exactly the setting where pre-trends appear and strict exogeneity fails.

Identification Strategy

Turns the pre-trends problem into an IV problem. Find a covariate $x_{it}$ that is affected by the confound but not by the policy (adult employment responds to labor demand, not to the minimum wage). Its event-time dynamics reveal the dynamics of the confound: rescale the covariate’s event-study path to match the outcome’s pre-event path, and the post-event gap between the two series is the causal effect. Formally, the model implies moment equations linear in parameters, and $\beta$ is estimated by 2SLS of $y$ on $z$ and $x$, with leads of the policy as excluded instruments (GMM in the general case with multiple confounds, unit fixed effects, and exogenous controls). Inference is valid whether or not pre-trends are detected — replacing the pass/fail pre-trend test with a magnitude-based correction.

Key Assumptions

Exclusion-Restriction — the covariate responds to the confound but is unaffected by the policy (and policy leads affect the outcome only through the confound); Weak-Instruments — identification strength requires the covariate to carry a real signal about the confound (a detectable pre-trend in $x$); strict exogeneity of the policy conditional on the confound; linear factor structure linking outcome, covariate, and confound; Parallel-Trends is what fails and gets repaired here.

Threats to Validity

Choosing an $x_{it}$ that is secretly affected by the policy violates exclusion; a covariate only weakly related to the confound yields weak identification (the estimator then adds noise rather than removing bias); more confounds than “unaffected covariates” leaves residual endogeneity; the linear, single-factor structure may be wrong. Simulations show controlling for $x$ directly is only adequate when $x$ is a near-perfect proxy, and linear-trend extrapolation and test-then-estimate both perform poorly.

Setting / Data

Monte Carlo experiments plus three applications: SNAP receipt and household spending (Hastings–Shapiro), newspaper entry and voter turnout (Gentzkow–Shapiro–Sinkinson), and minimum wage and youth employment (Neumark et al., Allegretto et al.) — spanning clear pre-trends, no pre-trends, and ambiguous cases.

Key Claims

• Pre-trend plots and tests are an incomplete response to endogeneity: absence of a detected pre-trend may just be low power, and a detected pre-trend gives no guidance on magnitude.
• An unaffected covariate identifies the confound’s dynamics; 2SLS with policy leads as instruments recovers the causal effect even with pre-trends in the outcome.
• The practical burden — finding a covariate related to the confound but not the policy — is comparable to finding a control variable, minus the perfect-proxy requirement.
• In simulations the estimator beats direct controlling, pre-event trend extrapolation, and pre-test-then-estimate.

Connections

• Complements: RothPretrends2022-PretestWithCaution — Roth documents the low power and pre-test distortion this design is built to avoid (Roth 2018 cited); RambachanRoth2023-MoreCredibleParallelTrends — an alternative repair (sensitivity analysis) where no unaffected covariate exists
• Same threat, classic instance: AshenfelterCard1985-LongitudinalEarnings — the Ashenfelter-Dip is an endogeneity-induced pre-trend of exactly this kind
• Event-study estimation context: SunAbraham2021-EventStudies, RothSantAnna2023-WhatsTrendingInDiD, BakerEtAl2025-DiDPractitionerGuide
• IV machinery and its fragilities: Murray2006-WeakAndInvalidInstruments, Imbens2014-IVEconometriciansPerspective
• See also: DiD, IV

Citation

Freyaldenhoven, S., Hansen, C., & Shapiro, J. M. (2019). Pre-Event Trends in the Panel Event-Study Design. American Economic Review, 109(9), 3307–3338. https://doi.org/10.1257/aer.20180609