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

Cross-Sectional Dependence

Overlapping windows are a design fact. This note is the inference that follows: the variance of an average cumulative abnormal return, the cross-sectional estimator that allows the earnings date to change residual variance, and the sign and rank checks that do not lean on normality.

The Dow day-0 ratios in the CAR lesson used the no-clustering variance. A researcher who publishes those ratios for a week in which many firms report together is using a formula the overlap has already invalidated.

Learning objectives. By the end of this note you should be able to:
  • write the large-L1L_1 variance of AR‾t\overline{AR}_t and say which covariance it drops;
  • estimate the variance of CAR‾\overline{CAR} from the cross section of CARs, and state the condition for consistency;
  • separate a null that forbids a variance shift from a null that allows one;
  • state the sign test's null proportion and the rank test's expected event-day rank.

In this lesson

  1. The variance that drops covariances
  2. A variance taken from the cross section
  3. Sign test and rank test
  4. Audit on the running announcement

Before you start

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

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