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Event Studies and Causal Measurement in Finance / Causal extensions

Robust Inference

The cross-sectional regression of a CAR on a surprise, and the difference-in-differences interaction, both produce a slope and a standard error. The classical standard error assumes spherical residuals.

Earnings residuals are heteroscedastic across firms, repeated quarters of one firm are dependent, and a policy date is shared. This note assigns each of those facts to a covariance Wooldridge or Brooks actually states: White, the cluster sandwich in equation (7.26), or Newey–West.

The algebra of OLS under classical assumptions stays in regression diagnostics. A robust covariance does not fix an endogenous regressor; that is the previous lesson.
Learning objectives. By the end of this note you should be able to:
  • match White, cluster-robust, and Newey–West standard errors to the dependence they allow;
  • write the cluster sandwich with one residual vector per cluster;
  • state Wooldridge's requirement that the number of clusters be large relative to cluster size;
  • refuse a robust standard error as a repair for instrument failure.

In this lesson

  1. Three covariances
  2. How many clusters
  3. Audit on the running announcement

Before you start

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