Yesterday at the Illinois Corporate Colloquium Jonathan Klick presented his important paper (co-authored by Jonah Gelbach and Eric Helland) Valid Inference in Single-Firm, Single-Event Studies.
The paper discusses single-firm event studies, which determine the existence of abnormal returns (compared to a model of expected returns such as the capital assets pricing model) around a disclosure or other event. Such studies are virtually mandatory in securities cases to demonstrate a causal link between an allegedly fraudulent statement and investor losses. They are also important in antitrust cases. Event studies generally are a staple of the finance literature. But how accurate are these studies?
Well, the paper shows that the current standard methodology for performing single-firm event studies is, in the authors' words, "fundamentally flawed," and that "existing securities litigation practices appear to be inappropriate as a matter of basic statistical practice."
Essentially what's happening is that single-firm event studies are determining the existence of abnormal returns against an assumption that the firm's returns are "normally" distributed under a bell-shaped curve. "Abnormal" refers to returns located around the "bell's" right and left sides. The problem is that returns are often not normally distributed, and you can't determine if the observed returns are abnormal if you don't know the shape of the curve. The paper proposes "a very simple but statistically sound alternative," the "SQ" test, which does not present the problem of assuming a normal distribution.
The paper concludes that "event studies as currently performed may be inadmissible on reliability grounds" under Daubert and Kumho Tire. Moreover, there is evidence that the flawed test is producing systematically anti-plaintiff results because it under-rejects the "null hypothesis" that the returns are normal. Specifically, it's mainly the more volatile stocks that are producing abnormal returns.
This already sounds pretty important. But the problem may touch not only single-firm event studies like those done in securities litigation, but multiple firm event studies such as those examining the effect of the passage of Sarbanes-Oxley. What's happening to the firms' returns may be correlated, again interfering with a normal distribution. Similar problems could infect even multiple-firm/multiple-event studies. In other words, it looks like a significant chunk of securities and antitrust cases and papers published in finance journals and law reviews are based on a fundamentally flawed test. This could be the finance equivalent of DNA evidence in criminal trials.
The discussion in the workshop and class touched on a wide range of issues:
- As a matter of policy, should we worry about the anti-plaintiff bias in securities cases? Behavioral finance suggests that investors may be over-reacting to disclosures of all sorts, true and false, which contributes to stock price volatility. Klick, et al, just provide more evidence of the unreliability of securities class actions by indicating that statistical fraud is a byproduct of volatility. My article Fraud on a Noisy Market suggests that we can minimize this problem by relying on a bright-line test of loss causation, as arguably supported by the Dura case. More broadly, maybe the anti-plaintiff bias just offsets more basic problems with fraud cases such as the circularity or "pocket-shifting" nature of fraud damages.
- The Klick et al paper raises basic questions about expert testimony. Judges and lawyers untrained in statistics have to rely on experts who are invested in their standard theories, or tied to one or the other side in particular types of litigation. Klick suggested that judges could appoint their own experts. But who?
- Can we do a better job of training lawyers and judges to deal with these problems? Require statistics in law school? Sounds like a good way to scare away applicants. Maybe require statistics in grammar school or high school. As Jon suggested, do the students really have to learn all the state capitals?
Anyway, this is important stuff. Start by reading the paper.
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