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Event Studies and Causal Measurement in Finance / Causal extensions

Instrumental Variables

The cross-sectional regression of an announcement CAR on a firm choice — shares issued, debt retired, a payout raised — estimates a slope. If the firm made that choice because of the same news that moved the price, the regressor is correlated with the regression error and ordinary least squares does not estimate the effect of the choice.

Wooldridge's instrumental-variables conditions say what would have to be true of a third variable before that slope is identified. This note maps those conditions onto the event-study regression.

It does not re-derive two-stage least squares.

Learning objectives. By the end of this note you should be able to:
  • point at the endogenous regressor in a CAR-on-choice regression;
  • state Wooldridge's exclusion condition and his partial-correlation condition;
  • say which of the two conditions a reduced-form regression can test;
  • write the just-identified IV formula as the sample version of his population moment, and stop there.

In this lesson

  1. Where the earnings design stops being enough
  2. Two conditions
  3. Identification, stated once
  4. Audit on the running announcement

Before you start

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

Read the full lesson

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