Expert Testimony In Securities Litigation.
This section is excerpted and adapted from the written materials for a CLE program entitled “The Law, Science and Economics of Expert Testimony in Business Litigation” presented in Miami in November 1999.
Virtually all credible economics, as practiced outside of the courtroom, routinely meets the test articulated in Daubert. This would seem to leave little room to argue against requiring that economics based expert testimony be tested by the Daubert factors, and most courts seem to come to this conclusion, as the citations of this draft indicate. There is, however, a contrasting view, and it is discussed here as well, infra, in the discussion of Executive Telcard in section 3.c and more extensively in the discussion of Harcross v. Tuscaloosa in the Antitrust section.
Not only does virtually all credible non-forensic economics research meet the Daubert criteria, but examples of whole classes of testimony that apparently meet the Daubert criteria abound in both pre- and post-Daubert era litigation. See Finkelstein & Levenbach, Regression Estimates of Damages in Price-Fixing Cases; Vol 46, no. 4, L. and Contemp. Problems 146 (1983) and the cases cited therein; Rubinfeld & Steiner, Quantitative Methods in Antitrust Litigation, Vol 46, No 4, L. & Contemp. Problems 69 (1984), and the cases cited therein; Proving Antitrust Damages, Section of Antitrust Law, ABA, 1996, and the cases cited therein; Alexander, Rethinking Damages in Securities Class Actions, 48 Stan. L. Rev. 1487 (1996) and Lempert, Symposium on Law and Economics: Statistics in the Courtroom: Building on Rubenfeld, 85 Colum. L. Rev. 1098 (1985) (applying regression to employment discrimination).
a. Statistical Strict Scrutiny
Courts are holding in limine Daubert hearings to determine if proffered economics expert testimony is reliable and they are applying increasingly sophisticated and detailed econometric analysis in making their reliability determinations. The court in In Re: Polypropylene Carpet Antitrust Litigation, 966 F. Supp. 18 (1997, N.D. Ga.), held an in limine hearing on the reliability of economics expert testimony, and while reserving judgment on admissibility of the economists testimony, agreed that the economists “multiple regression analysis is a scientific endeavor whose admissibility . . . must be determined using the test set forth in Daubert. . . ,” ) In Estate of Bud Hill v. ConAgra, 1997 U.S. Dist. Lexis (1997, N.D.Ga.), the same court identifies and discusses some of the particular shortcomings that can cause regression-based testimony to fail a Daubert test, and discusses heteroskedasticity and regression specification error. Addressing a similar issue, Judge Posner provides an accessible and informative discussion of specification error in Sheehan v. Daily Racing Form, Inc. 104 F.3d 940 (7th Cir. 1997), an employment discrimination case that is discussed in that section. This chapter cites repeatedly to the growing literature on the use of regression in legal proceedings, and is premised on the assumption that it is well settled that any technique that uses regression or other statistical analysis must be assessed for reliability by the application of the Daubert test as announced in In Re: Polypropylene Carpet Antitrust Litigation, supra, at 26. However, note again that there is contra authority. Note also that this case was pre-Kumho and hence was written before the distinction between Daubert and the Daubert factors was in vogue. Finally, note that, in virtually all instances, regression analysis, when carried out in non-litigation settings, not only meets the Daubert criteria very well, but indeed, when evaluated by peer-researchers is evaluated using a set of criteria that is very similar to Daubert's.
b. Aside: Regression's Impact On Daubert
Indeed, a good case can be made that regression is a member of the broad class of analysis that was the model for Daubert. One of the well reasoned amicus briefs filed in Daubert was submitted by a group of "eighteen scientists, scholars and teachers of science." This group of amici includes a Nobel Laureate in economics, a discipline where regression is a primary research tool. The balance of this chapter applies the concepts developed supra to an investigation of the admissibility of expert testimony techniques that economists employ in a range of litigation settings. The first of these will be economics testimony as to damages suffered by a plaintiff in a 10b-5 matter.
c. Introduction to Regression in 10b-5 litigation
The use of regression in securities litigation in concentrated in a well defined area of damage calculation and the controlling law is fairly well settled. While this law has been settled outside of the 11th Circuit, a quick browse through the South Florida Business press illustrates the presence of securities fraud litigation in Florida. Because such matters so often settle before the end of trial, it seems not surprising that there are few published opinions. That notwithstanding, there is securities fraud litigated to settlement here and the law articulated in this area by the other circuits comports so well with the existing non-litigation scientific research that one would expect it to be persuasive. In brief, the law regarding damages in securities fraud requires that experts calculate damages by the use of a very highly intuitive regression technique known as an event study. The event study is technical but very intuitive. See Romano, The Genius of American Corporation Law 17 (1993). (explaining that event study techniques “examine whether particular information events .. . . significantly affect the firm’s stock price (technically , they examine whether the average residuals of a regression of observed stock prices on predicted prices are statistically different from zero). If an information event . . . is considered beneficial for shareholders then stock prices will rise significantly above their expected value on the public announcement of the event. If the event is perceived as detrimental to shareholder wealth, then stock prices will significantly decline. Given the regression methodology, such stock price effects are referred to as average residuals or abnormal returns.” In short, event studies are used to measure the impact, on a company’s market value, of the release into the market of some significant news about the company.
d. Generalizing The Securities Litigation Techniques To Antitrust and Employment Law.
The statistical concepts developed here generalize immediately to areas of antitrust, employment and discrimination, and an array of other practice areas that rely on statistical evidence and proof.
2. Non-Forensic Economics And A Scientific View Of Daubert
One of Daubert's central statement is that "[s]cientific methodology today is based on generating hypotheses and testing them to see if they can be falsified” Daubert at 593. This sentiment is well ingrained among economists. During the first year of my doctoral program in economics one of my professors said to me that 'the only interesting hypothesis in economics is one that can be rejected.' This simple statement summarizes how non-forensic economics research is done. Economists test hypotheses. They test them at fairly strict rates of error. Their prestige and financial rewards are tied to publishing the results of their research in well-regarded peer-reviewed journals. The hypothesis testing is part, and often the core, of virtually every empirical article published. If the published work withstands the broader scrutiny to which publication exposes the work, and if other scientists replicate and extend the work, the work begins to be generally accepted. In brief, non-forensic economists test hypotheses using proper techniques and specify the error rates of those hypotheses in attempts to gain publication in peer reviewed journals. As the published work stands the test of time and the broader scrutiny to which publication exposes it, the work moves toward general acceptance in the research community. It is not coincidence that this rings of Daubert.
3. An Intuitive Introduction To Event Studies in Legal Proceedings
a. In Re: Oracle Securities Litigation
In an opinion that came down six weeks after Daubert and does not cite it, the Northern District of California generally disparaged the proffer of a damage estimate that was calculated using a “value line” approach and opined that the “use of an event study or similar analysis is necessary more accurately to isolate” damages. “As a result of his failure to employ such a study,” the court said that the expert’s results “cannot be evaluated by standard measures of statistical significance” making his results “unreliable.” In Re: Oracle Securities Litigation, 829 F. Supp. 1176, 1181 (N.D.Cal. 1993).
Event studies are widely used by economists in non-litigation settings to investigate the impact of the release of a variety of kinds of new information on the price of a stock that is actively traded in an efficient market. A properly executed event study apparently meets all of the Daubert criteria. Studies based on the technique have been peer reviewed and published hundreds of times and the technique is, as much as any, generally accepted in the relevant scientific community. There are well established standards that govern its use and these standards point to proper hypothesis tests and the error rates of those tests as the proper instruments of investigation, assuming that the tests are conducted in ways that satisfy the assumptions of the underlying regression model. Interesting for legal purposes is the fact that event studies use regression analysis and since the reliability of regression analysis rests on several assumptions, when those assumptions can be shown to be violated, the admissibility of the event study is put into doubt. This is because when the basis of an expert’s testimony loses its scientific reliability it apparently loses it its evidentiary reliability and must be excluded. Because regression is susceptible to successful challenge, when confronted with the proffer of event study damages, the prudent attorney may wish to inquire as to whether the regression assumptions, discussed supra are met.
b. Prototype Securities Litigation Expert Testimony In Florida.
Current events provide an example of the use of an event study in a securities fraud matter whose fact pattern is strikingly similar to that of Oracle. Several Florida companies have recently been in the news because of allegations that their financial statements reported exaggerated sales figures. Each company’s stock fell sharply following the release of this information and several pending lawsuits allege that a class of each corporation’s stockholders has been damaged by purchasing stock whose price was inflated by the alleged overstatements. If this litigation proceeds, economists will likely estimate the damages that were alleged to have been suffered by this class of stockholders. They will likely use an event study for this purpose.
c. Event Study Cases
In Re: Executive Telcard Securities Litigation, 979 F.Supp 1021 (S.D.N.Y. 1997) cites Oracle for the proposition that an event study is required to distinguish between fraud related and non-fraud related influences on the company’s stock price, and excludes expert testimony that fails adequately to account for non-fraud related bad news. Note that the failure to account for non-fraud related bad news is a form of the model specification problem discussed in section V.A. This case contains several interesting types of analysis that somewhat defie easy description. The court recounts Daubert’s basics and then goes on to opine that “damages in a securities class action such as this does not appear to be the sort of ‘hard science’ that requires application of the specific factors set forth in Daubert.” In Re: Executive Telcard Securities Litigation, 979 F.Supp 1021 (S.D.N.Y. 1997), at 1026. The court instead requires that ”an expert’s opinion should at least ‘have a reliable basis in the knowledge and experience’ of the particular ‘discipline’ involved.” Id. The court here raises several interesting issues. First, Daubert propoposed the specific factors as suggestions for proceeding with a flexible inquiry, so none of them have ever been "required," as is underscored by Kumho. Second, it is notable that Daubert makes no distinction between “hard” and “not-hard” sciences, relying instead on the scientific method to define science, and the various disciplines to establish by the use (or non-use) of the scientific method in their non-litigation research to sort out the scientific disciplines from the non-scientific. Third, other courts have come to precisely the opposite conclusion expressed in Executive Telcard on whether regression based expert testimony falls under Daubert's purview.
In particular, recall the discussion of In Re: Polypropylene Carpet Antitrust Litigation, in section V.B.1.a (“multiple regression analysis is a scientific endeavor whose admissibility . . . must be determined using the test set forth in Daubert. . . ,”) and the prodding of the 11th Circuit in Tuscaloosa v. Harcros, 158 F.3d 548 (11th Cir. 1998), that the District court should have held a Daubert Hearing (n.21) to decide issues of admissibility of proffered expert testimony, because it would have avoided subsequent problems. Tuscaloosa is a complex ruling that is discussed further in section V.C. In Rebel Oil 146 F.3d 1088 (9th Cir. 1998), the ninth circuit discusses with approval the lower court’s Daubert-based admissibility decision on expert economics testimony in a petroleum antitrust case.
Where regression based testimony is being evaluated and the discipline involved is economics, requiring that ”an expert’s opinion should at least ‘have a reliable basis in the knowledge and experience’ of the particular ‘discipline’ involved,” as In Re: Executive Telcard Securities Litigation does is tantamount to requiring precisely that the testimony be evaluated using Daubert's factors. See V.B.1.a. We shall see that this is a theme that is repeated in section VI on expert testimony in Florida State Courts.
d. The Economics of Event Studies
Event study logic flows from economists' belief that the current value of a security is equal to the present value of all of the payments that the security is expected make to its owners throughout its life. An immediate implication of this is the belief that the value of the security changes when new information is released into the market that changes the market’s assessment of the future payments that the security will make to its holder. When information comes into the market that is hypothesized to affect the value of a particular stock, economists test that hypothesis by comparing how that particular stock performed right after the release of the information to how the stock would have been expected to have performed in the absence of the release of the new information.
1. Aside: The Intuition of How Information Changes Price
To see how information changes securities prices we start with a day when no information is released into the marketplace that alters the market’s perception of the value of any stock: no Federal Reserve announcements of actual or potential interest rate movements, no big contracts awarded, no lawsuits filed, won or lost, no new inventions or patents. On such a day, every publicly traded stock would close essentially where it had opened. Now imagine a similar day where only one piece of new information is released into the market, and that this information affects the value of only one stock. If the news is good, the price of that one stock will rise, but assuming that the information has no secondary effects on any other stock and that the stock is not part of the Dow Jones Industrial average, the Dow will not move. One could then calculate the impact of the newly released information upon the value of a share of the stock. If the stock opens at $100 and closes at $103 while no other stock moves, economists would say that the information raised the value of the stock by three dollars.
Of course, such no-news days do not exist, so estimating the impact of the release of new information on the value of a stock is a little more complicated, but still involves comparing the return on the particular stock with the return to an index of stocks that have not been affected by the information. For example, if the days news, including some news about Stock A, caused the market to rise by 4%, while the days news, including the news about Stock A caused Stock A to rise by 3%, then the economist would conclude that the news about Stock A was not good, since, on that news, the value of Stock A fell by 1% relative to the market.
The event study technique ascribes this change in the stock’s value to the event that the information disclosed. In the case of the Florida corporations mentioned here, this information is the release of allegations that reported sales figures were inflated. The event study is the financial economist’s standard technique for determining the impact of mergers, dividend and earnings announcements, management changes, and a host of other phenomena, upon the value of the subject firm’s stock, so it has well established non-litigation uses. The heart of the technique is a test of the null hypothesis that the information had no impact upon the price of the stock. The economist will reject this null hypothesis if and only if the hypothesis test yields both an estimate of the change in the stock’s value that is non-zero, and an error rate of the test that convinces the economist that sampling error has not caused the non-zero estimate of the change in the stock’s value. This technique meets all of the Daubert criteria: it poses and tests a hypothesis, reports the pertinent error rates, and is based upon peer reviewed and published techniques that are so pervasively used within the relevant scientific community that they are the generally accepted tool for evaluating the impact of the release of new information upon the value of a publicly traded security.
2. Aside: Damage Ribbons
It is interesting to compare, very briefly, this technique that is actually used by economists to the set of techniques that forensic economists refer to variously as damage ribbons and value lines and that Oracle dismissed in favor of event studies. These techniques, which were routinely admitted in many federal courts prior to Daubert are apparently no longer admissible because they seem to meet none of the Daubert criteria. One interesting aspect of the comparison is that virtually all of the computer programs that a forensic economist would use to calculate a damage ribbon would also calculate everything necessary to perform the hypothesis tests and error rates required by Daubert. See Bradford Cornell & R. Gregory Morgan, Using Finance Theory to Measure Damages in Fraud on the Market Cases, 37 UCLA L. Rev. 883, 899 (1990) (providing a thorough description of the techniques).
3. The Econometrics of Event Studies: Applied Regression Analysis.
The event study is intuitively straightforward. To determine how much a security's price moves as new information (about an event that affects the security) enters the market, one need only compare the return on the security over the time that the market receives the news, called the observed return, to the return on the security that would be expected during that time period in the absence of any news, called the expected return. See e.g. Brown & Warner, Measuring Security Price Performance, 8 J. Fin. Econ. 205 (1980) (developing the event study technique); See also Brown & Warner, Using Daily Stock Returns: The Case of Event Studies, 14 J. Fin. Econ. 3 (1985) (continuing development of the event study technique). The first routinely cited event study was in Fama et al., The Adjustment of Stock Prices to New Information, 10 Int'l. Econ. R. 1 (1969).
The period during which the news is thought to affect the security's return is called the "event window." Researchers typically use an event window that begins just before the news is publicly announced to capture the price effects that are associated with pre-announcement information leakage. An event window of one day before the announcement to one day after the announcement is a very popular choice among financial economists, but the event window specified tends to vary depending upon the particular circumstance. See Black, Bidder Overpayment in Takeovers, 41 Stan. L. Rev. 597, 602 (collecting event study results for "narrow (one to four day) 'window' periods"). For example, if a security is thinly traded, it may take longer for information to be fully incorporated, requiring a longer event window. The longer is the event window, the more certain is the analyst that the full effect of the announcement has been measured. However, the longer is the event window, the more likely it is that other value-affecting information will enter the market during the event window, with the undesirable result that the analyst’s estimates of the impact of the news of the event under consideration will actually reflect the impact of more than one event on the security.
a. Practice Pointer
One choice of the expert witnesses that can immediately be seen to be suspect is that of extending the event window to cover the entire class period. See William Beaver & James Malernee, Estimating Damages in Securities Fraud Cases (Cornerstone Research) (detailing a procedure like an event study, but not in event study terminology). See also Janet Alexander, The Value of Bad News in Securities Class Actions, 41 UCLA L. Rev. 1421, 1425 (1994) (providing an example of a rough version of such an approach). This technique attributes all new information released on the security over the entire class period to the fraud. This is an especially attractive technique for plaintiffs' experts in cases where the value of the security has fallen dramatically during the class period for reasons unrelated to the fraud, because such decrements to value increase the resulting damage estimates. This can be made to sound reasonable, even benign. It is not.
b. The Notion of an Abnormal Return
The abnormal return for a day is the actual return for that day minus the return predicted for that day. Once the size of the abnormal return has been estimated for each day in the event window, the daily abnormal returns can be summed to find the cumulative abnormal return, or CAR, which is a measure of the impact of the event on the security's return. Hypothesis testing is used to test the statistical significance of the CAR to determine the probability that a CAR of that particular size had occurred due to random chance rather than in response to the incorporation of new information.
c. Calculating Securities Damages Using an Event Study
(optional, technical, may be omitted without loss of continuity)
The first step in conducting an event study of damages in a securities fraud case is to articulate which information is alleged to be fraudulent and when it is alleged to have adversely affected the price of the subject security. This permits the analyst to specify the event window across which the CAR associated with the fraud is to be calculated. In the most common cases typically analyzed with the event study methodology, determining the appropriate event window is fairly straightforward, although far from trivial. Even in the analysis of a stock’s reaction to the announcement that it is to be the subject of a tender offer, the event is typically defined as the date of the first appearance of the announcement of the tender offer in the Wall Street Journal. In this case, a typical event window might cover the day of the announcement as well as the day before and the day after, because information leaks out to a subset of the informed traders who specialize in gathering and processing information on the security. Event windows vary. If the subject stock is thinly traded, longer windows are appropriate, and if the stock is heavily traded, the event window may not even include the day after the announcement. In many 10b-5 applications, determining the beginning of the event window is particularly difficult because the window should span the time interval within which the "news" is incorporated into the security's price.
The selection of an end date for the event window is fairly simple in the traditional event study context. In an efficient market, the price of the security reacts quickly to new information so there is usually little reason to extend the event window beyond the day after the announcement. In 10b-5 damage calculations the event window surely does end by the time the fraud is formally disclosed. On the other hand, it may end well in advance of the formal announcement, and indeed may close and then reopen, perhaps even several times, as discrete bits of information that tend to expose the fraud are revealed and the market reacts to them. It is, of course, possible simply to use a very long window to calculate the stock's abnormal return, but the longer is the window, the more likely are other security-value-altering pieces of news to enter the market. These are called "confounding events." They are pieces of information that affect market price but are wholly unrelated to the fraud.
d. Calculating Abnormal Returns
(optional, technical, may be omitted without loss of continuity)
Once the event window has been selected and it has been determined whether the event in the event window has been partially anticipated, the actual calculation of the CAR is straightforward. The essence of the analysis is to find a "benchmark" level of performance of a comparable security during the event period and then subtract that level of performance from the security's actual performance during the event window. The benchmark is constructed to mimic the rate of return that the subject security would have had during the event window if the event under analysis had not occurred. Historically this benchmark has been constructed by calculating the average rate of return that is observed for stocks in general that day, and then adjusting that average return for the risk of the subject security. Recent evidence has cast doubt on some of the risk adjustment methods and, independently, models using unadjusted returns seem to perform as well as adjusted-return models. However the benchmark is calculated, subtracting the benchmark level of performance from the stocks actual performance for a particular day in the event window gives the abnormal return (AR) on the stock for that day. If the stock's AR for a day is positive that is taken as evidence that the stock is reacting to the release of some positive news, while a negative AR is evidence that the stock is reacting to some negative news. Often economists believe that it takes more than one day for new information to be fully reflected in a stock's price, so it is typical to add together the stock's ARs for two or three trading days. This summation is called the "cumulative abnormal return" or "CAR" and the CAR is the subject of the hypothesis tests discussed infra.
If the estimated CAR is near zero, this is evidence that the event hypothesized to have affected the value of the security did not actually affect the value of the security. On the other hand, if the CAR differs substantially from zero, that is evidence that the event did affect the value of the security. Indeed, the investigation of whether the CAR is about zero or whether it differs substantially from zero is the financial economics analog of the epidemiology inquiry that the Court required in Daubert. Such an inquiry is conducted by specifying a hypothesis, called the null hypothesis, that CAR is equal to zero, and then testing CAR to see if the scientist can reject (or falsify, to use the word that so concerned the Chief Justice in Daubert) that hypothesis. If the scientist can reject the null hypothesis we can say that CAR differs from zero in a statistically significant manner and the event had an effect on the value of the security. If we fail to reject the null hypothesis we are unable to determine that the event affected the value of the security.
e. Hypothesis Tests and the Statistical Significance of Estimates
A typical hypothesis test involves two hypotheses, a null hypothesis, denoted "Ho," so named because it hypothesizes no effect, and an alternative hypothesis, denoted "H1." This pair of hypotheses is written by economists and other scientists as:
Ho: CAR = 0
H1: CAR ^= 0.
EDITOR: N.B. This reads "not equal to zero." My fonts will not produce the character
This two line expression is read as "the null hypothesis is that the cumulative abnormal return of the subject security during the event window is zero so the event did not affect the return on the security. The alternate hypothesis is that the cumulative abnormal return on the subject security during the event window differs from zero so the event did affect the return on the security."
Economists say that the null hypothesis is rejected "at the 5% level" if the absolute value of the CAR is more than about double its standard deviation. The use of 5% is intended to mean that only one twentieth of the time would a CAR that large be observed if it were being measured over an event window that did not include an event that had truly impacted the security's return.
Conducting the hypothesis test that the Supreme Court describes in Daubert is mathematically equivalent to constructing the confidence intervals that other courts have used. [cite] See Turpin, Berry. The use of a confidence interval often makes the discussion of the statistical significance of an event more intuitive than the hypothesis testing technique can. The "5% confidence interval" is written as:
CAR - (2 x standard deviation), CAR + (2 x standard deviation) ].
If the estimated CAR is 0.02 and the standard deviation is 0.007, then the confidence interval is
[0.02 - (2 x 0.007) , 0.02 + (2 x 0.007)], which is
In words, for the data that generated this CAR and standard deviation, the scientist is 95% certain that the CAR is above 0.006 and below 0.0314. So in this case, the scientist is 95% confident that the CAR of 0.02 is statistically significant, which means that the scientist is 95% sure that the true abnormal return was not zero, and 95% sure that, in this case, the event contained in the event window increased the price of the security. On the other hand, if we consider the same example, but change the assumed standard deviation from 0.007 to 0.011, then the 5% confidence interval would be [-0.002, 0.042]. This says that we are 95% confident that the true CAR is between -0.002 and 0.042. Because this interval contains zero, we can no longer say that the event contained in the event window increased the price of the security and be sure that we are right 95% of the time. Many scientists believe that the 95% confidence level is the "correct" confidence level to use and stop there. Others feel that there is nothing sacred about 95% confidence and would proceed to calculate the 90% confidence interval, which is:
[0.02 - 1.64 x 0.011, 0.02 + 1.64 x 0.011], or [0.00196, 0.03804],
which does not contain zero. So in this case we can reject the null hypothesis at the 90% level, even though we cannot reject the null at the 95% level.
f. In Closing
Daubert articulates four criteria for the admissibility of scientific expert testimony, but points out that "many factors will bear on the inquiry (of what is scientific knowledge), and we do not presume to set out a definitive checklist or test." Science does presume however, and science’s checklist has so informed Daubert that it is difficult to imagine much flexibility in applying Daubert's factors to scientific testimony that would not offend science.
This has not kept courts from misapplying Daubert or the scientific principles that it articulates. While this mostly happens in trial courts, one need look no farther than Kumho for examples. Justice Breyer writes that trial judges should not to be overly concerned with distinctions between “scientific,” “specialized,” and “other,” expert testimony and that it would be difficult for judges to distinguish scientific from non-scientific testimony because there is no clear line dividing the one from the other. This is an interesting observation to be contained in an opinion that extends Daubert, since Daubert drew precisely such a line between scientific and non-scientific testimony when it stated (so correctly) that “[s]cientific methodology today is based on generating hypotheses and testing them to see if they can be falsified; indeed, this methodology is what distinguishes science from the other fields of human inquiry." (Emphasis added.).
The conflict between Daubert's clear articulation of a dividing line between scientific and non-scientific inquiry and Kumho's declaration that no such distinction exists may likely raise a tension between the opinions.