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Event Studies and Causal Measurement in Finance / Dependence and robust inference

Difference-in-Differences

A market-model abnormal return subtracts a predicted return. That subtraction measures a firm's return relative to a chosen benchmark around its earnings date; causal attribution still needs assumptions about other news.

When a policy affects one group and leaves a credible comparison group untreated, difference-in-differences offers another design: a tax change in one city, or a compensation-cap change that binds only for high earners. The availability of a comparison group is a starting point, not evidence by itself that the comparison identifies a causal effect.

This note specialises Wooldridge's pooled-cross-section design to that policy event. Panel fixed effects, which remove a time-constant firm effect from a repeated panel, stay in the core panel lesson.

They are a different data structure: the same units observed twice, not a fresh cross section each period.

Learning objectives. By the end of this note you should be able to:
  • write the two-period, two-group regression and name the coefficient on the interaction;
  • express that coefficient as the four-cell contrast of sample means;
  • state what a pure time difference and a pure cross-section difference each fail to remove;
  • distinguish the four-cell contrast from a causal effect using parallel untreated trends, no anticipation and stable composition;
  • compute the contrast on a small fixture and read Wooldridge's workers'-compensation estimate as a textbook illustration.

In this lesson

  1. Two groups, two periods
  2. What this design is not
  3. Audit on the running announcement

Before you start

The full lesson, with worked examples and exercise solutions, is for members.

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