Abstract

We analyze tests for long-run abnormal returns and document that two approaches yield well-specified test statistics in random samples. The first uses a traditional event study framework and buy-and-hold abnormal returns calculated using carefully constructed reference portfolios. Inference is based on either a skewnessadjusted t-statistic or the empirically generated distribution of long-run abnormal returns. The second approach is based on calculation of mean monthly abnormal returns using calendar-time portfolios and a time-series t-statistic. Though both approaches perform well in random samples, misspecification in nonrandom samples is pervasive. Thus, analysis of long-run abnormal returns is treacherous. COMMONLY USED METHODS TO TEST for long-run abnormal stock returns yield misspecified test statistics, as documented by Barber and Lyon ~1997a! and Kothari and Warner ~1997!. 1 Simulations reveal that empirical rejection levels routinely exceed theoretical rejection levels in these tests. In combination, these papers highlight three causes for this misspecification. First, the

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