All Events Induce Variance: Analyzing Abnormal Returns When Effects Vary Across Firms

Abstract

We demonstrate analytically that cross-sectional variation in the effects of events, i.e., in true abnormal returns, necessarily produces "event-induced" variance increases, biasing popular tests for mean abnormal returns in short-horizon event studies. We show that unexplained cross-sectional variation in true abnormal returns plausibly produces non-proportional heteroskedasticity in cross-sectional regressions, biasing coefficient standard errors for both ordinary least squares and weighted least squares. Simulations highlight the resulting biases, the necessity of using tests robust to cross-sectional variation, and the power of robust tests, including regression-based tests for non-zero mean abnormal returns, which may increase power by conditioning on relevant explanatory variables.

Keywords: abnormal returns, event-induced variance, event study methodology, heteroskedasticity

JEL Classification: G10, G14