The single-firm event study design is a common one in the law and finance and securities litigation research literatures. One challenge to the standard t-statistic-based approach to inference involves a downward bias in asymptotic Type I errors. An interesting paper by Jonah Gelbach (Arizona), Eric Helland (Claremont McKenna College & RAND), and Jonathan Klick (Penn), Valid Inference in Single-Firm, Single-Event Studies, assesses this challenge and compares the standard approach to an alternative with the benefit of real-world data. An excerpted abstract summarizes the paper's findings.
"Our
results show that the standard approach is plagued by systematic,
downward bias in asymptotic Type I error rates relative to desired
significance levels. We then offer a very simple but statistically
sound alternative, called the SQ test. We show analytically that the SQ
test’s asymptotic Type I error rate always equals the desired
significance level. Using our CRSP data, we offer Monte Carlo evidence
that in event studies with 99 pre-event observations, the SQ test
performs very well at conventional significance levels. We then analyze
the asymptotic power of the SQ test and the standard approach. The SQ
test and the standard approach have the same size-corrected asymptotic
power, which means that even when the standard approach is appropriate,
there is no loss to using the SQ test. More relevant as an empirical
matter, we show that the standard approach’s downward bias in
asymptotic Type I error rates brings along severe power loss. As an
empirical matter, then, use of the standard approach can be expected to
lead to substantial anti-plaintiff bias in securities litigation,
though either pro- or anti-plaintiff bias is possible as an analytical
matter. By contrast, the SQ test has considerable asymptotic power,
even against moderately sized fixed alternatives."
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