Is there a viable alternative to ordinary least squares regression when security abnormal returns are the dependent variable?

Abstract

Regression analysis is often used to estimate a linear relationship between security abnormal returns and firm-specific variables. If the abnormal returns are caused by a common event (i.e., there is “event clustering”) the error term of the cross-sectional regression will be heteroskedastic and correlated across observations. The size and power of alternative test statistics for the event clustering case has been evaluated under ideal conditions (Monte Carlo experiments using normally distributed synthetic security returns) by Chandra and Balachandran (J Finance 47:2055–2070, 1992) and Karafiath (J Financ Quant Anal 29(2):279–300, 1994). Harrington and Shrider (J Financ Quant Anal 42(1):229–256, 2007) evaluate cross-sectional regressions using actual (not simulated) stock returns only for the case of cross-sectional independence, i.e., in the absence of clustering. In order to evaluate the event clustering case, random samples of security returns are drawn from the data set provided by the Center for Research in Security Prices (CRSP) and the empirical distributions of alternative test statistics compared. These simulations include a comparison of OLS, WLS, GLS, two heteroskedastic-consistent estimators, and a bootstrap test for GLS. In addition, the Sefcik and Thompson (J Accounting Res 24(2):316–334, 1986) portfolio counterparts to OLS, WLS, and GLS, are evaluated. The main result from these simulations is none of the other estimator shows clear advantages over OLS or WLS. Researchers should be aware, however, that in these simulations the variance of the error term in the cross-sectional regression is unrelated to the explanatory variable.