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

Abstract

Widely used test statistics for non-zero mean abnormal returns in short-horizon event studies ignore cross-firm variation in event effects. Cross-sectional regression analyses of abnormal returns often either ignore heteroskedasticity in model disturbances or ignore plausible implications of unexplained variation in effects for the structure of heteroskedasticity. We use a simple model of event effects and simulations patterned after Brown and Warner (1980, 1985) and Boehmer, Musumeci, and Poulsen (BMP, 1991) to highlight the resulting biases and the importance of using test procedures that appropriately allow for cross-sectional variation. We demonstrate analytically how cross-sectional variation produces event-induced variance increases and biases popular tests for non-zero mean abnormal returns. Our simulations provide evidence of that bias and of test power for several theoretically robust tests for non-zero means, including the standardized cross-sectional test statistic suggested by BMP, which we show equals the mean standardized prediction error divided by a heteroskedasticity-consistent standard error, and cross-sectional regression tests that condition on relevant regressors. We also analyze and provide evidence of bias and power for alternative tests for non-zero slopes in abnormal return regression models with heteroskedastic errors attributable to cross-firm variation in event effects and market model disturbance variances. Neither OLS nor WLS has good properties. WLS with robust standard errors and maximum likelihood estimation assuming non-proportional heteroskedasticity may represent useful supplements to OLS with robust standard errors.