Reading Event-Study Plots: Beyond the Lines

Event-study plots visualize estimated treatment effects $\theta_k$ across event time $k$. But interpreting these lines requires care—especially in the presence of treatment effect heterogeneity and changing cohort composition.

What the Plot Shows (and What It Hides)

  • Each point: An estimated $\theta_k$ (or bin) relative to the omitted reference period (usually $k = -1$).
  • Confidence intervals: Reflect statistical uncertainty, but not bias from model misspecification or compositional shifts.
  • Pre-trend check: Flat, near-zero pre-treatment coefficients ($k < 0$) support parallel trends, but sparse support or binning can mask violations.

Cohort Composition: The Hidden Axis

At each event time $k$, the set of units contributing to the estimate changes. Early post-treatment periods include all treated cohorts; later periods include only early adopters. If treatment effects differ by cohort, the plot can mislead:

  • Apparent dynamics may reflect changing cohort mix, not true effect evolution.
  • Support tables/figures: Always report the number of units and cohorts contributing to each $k$; plot effective sample size alongside $\theta_k$.
  • Cohort-specific plots: Plot $\theta_{g,k}$ for major cohorts to reveal heterogeneity.

Common Pitfalls and Diagnostic Tools

  • Sparse support at tails: Wide confidence intervals and unstable estimates. Use binning and report support.
  • Over-interpreting late $k$: Later event times reflect only early adopters—do not generalize.
  • Ignoring anticipation or contamination: If $k=0$ is contaminated, interpret $k \geq 1$ with caution.
  • Neglecting pre-trend diagnostics: Always check for credible pre-treatment flatness.

Best Practices

  • Always accompany event-study plots with support tables/figures.
  • Use binning for sparse event times, but be transparent about bin definitions.
  • Interpret late post-treatment effects as cohort-specific, not average.
  • When possible, estimate and plot cohort-specific effects.

Summary

Event-study plots are powerful, but their interpretation is subtle. Always check support, cohort composition, and pre-trends before drawing causal conclusions. Use diagnostic tools to distinguish genuine effect dynamics from artifacts of the data structure.