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This section focuses on economics expert testimony in antitrust litigation. Most such testimony is based upon regression studies executed by the testifying expert, so the discussion begins there. This material is widely misconstrued by courts. But again, this is not the fault of the courts so much as it is the result of the failure of counsel to educate the courts on how the current admissibility criteria apply to this subject area. In one of the important cases discussed here, counsel, who described himself as specializing in handling experts, lacked the specialized skills necessary to exclude clearly inadmissible expert testimony. As a result, he lost an important part of his case that he perhaps should have won.
There is a long and well-established history of regression based expert testimony in the antitrust cases. Regression and hypothesis testing are applied to determining whether an antitrust violation has taken place and also to the calculation of antitrust damages when a violation has been established. This analysis is often based on comparing actual prices to the "but for" price that would have existed in the absence of a violation. See section 2.a. Regression is used to calculate damages when antitrust violations are alleged to have caused a plaintiff to over pay for a product, such as In re Chicken Antitrust. See Proving Antitrust Damages: Legal and Economic Issues, Section of Antitrust Law of the American Bar Association, 1996, at 174, (discussing the particulars of the regression model used in Chicken Antitrust), and In re Corrugated Container Antitrust Litigation Id. At 175. It is used to calculate damages from exclusionary practices, such as in Key Enterprises v. Venice Hospitals 919 F.2d 1550 (11th Cir. 1990) and Aspen Skiing Co. v. Aspen Highlands Skiing Corp. 472 U.S. 585 (1985). Id., at 209-26. It has been used to calculate damages from Robinson Patman violations Alan's of Atlanta v. Minolta Corp., 903 F.2d 1414 (11th Cir. 1990) Id., at 243.
Antitrust presents an interesting scenario for analyzing admissibility of expert testimony. Because so many of the most interesting cases are pre-Daubert, the opinions on the governing law are of limited interest. The testimony is, however, of great interest, because there is a wealth of pre-Daubert expert testimony that was done in accordance with the standards that economists apply to their non-litigation work. This testimony typically meets the Daubert criteria because the Daubert criteria are based upon scientific principals that had governed economics research for decades when they first informed the law through their incorporation into Daubert. More importantly, there is information available about some of the pre-Daubert cases that illuminates Daubert in important ways. The insight provided in some of the older cases is important in understanding the current cases, which we take up in the next section.
Paralleling the antitrust caselaw is a substantial pedagogic literature that addresses the "scientific method" discussed in Daubert, the ways in which the scientific method and the econometric and statistical methods that it governs form the core of economics research methodology, and how these methods are applied in producing admissible expert testimony. Proving Antitrust Damages cited supra, is part of that literature. Part of the strategy of this chapter to fit a representative introduction to scientific antitrust expert testimony into a small space is to cite to accessible but sophisticated materials in the scientific/legal branch of the antitrust literature. Interestingly, since most of this literature is pre-Daubert, the fact that it relies on the scientific principles articulated in Daubert is all the more telling. In the language of Daubert’s progeny, not only do the techniques exposited in this literature have non-litigation uses, they were developed by scientists for scientific research with no concern for litigation or the law. The fact that the law is irrelevant to them should make them more reliable in the eyes of the law.
While a comprehensive assessment of expert testimony in antitrust is far outside the scope of this chapter, by drawing on the statistical tools developed in sections V.A and V.B, much of the expert testimony materials in a range of cases can be illustrated in a case study of the expert testimony used in In re: Ampicillin Antitrust Litig. The expert testimony in Ampicillin made extensive use of regression-based hypothesis testing and is highly instructive. See Rubinfeld and Steiner, Quantitative Methods in Antitrust Litigation. Law and Contemp. Probs., Autumn 1983, at 69 (providing, in the words of two of the experts in the Ampicillin case, a description of the regression analysis that was the basis for the ampicillin expert testimony.) Section V.C.2 takes up this analysis and generalizes it to some other cases, while section V.C.3 discusses current 11th Circuit cases, some of which apply sophisticated Daubert and econometric analysis.
Two of the testifying experts in the Ampicillin Antitrust litigation have published an article that provides a much deeper look into regression based expert testimony than is provided in the opinioins. See Rubinfeld and Steiner, Quantitative Methods in Antitrust Litigation. Law and Contemp. Probs., Autumn 1983, at 69. Although it predates Daubert by ten years, even on a casual reading Rubinfeld and Steiner sounds like it is echoing Daubert on testing and error rates. This is because Daubert was informed by the scientific literature and Rubinfeld and Steiner is a scientific-literature import into the legal literature. There are several of these scientific imports into the legal literature, many of which are cited throughout this chapter. Several of these are jointly authored by economists and lawyers or by legally sophisticated economists, and they tend to be among the most informative works available. In many cases, how the language of the scientific literature has been imported into the cases is important, so the balance of this section quotes liberally from Rubinfeld and Steiner.
In the Ampicillin litigation plaintiffs alleged that Ampicillin prices had been propped up by illegal antitrust activity. Ampicillin prices had declined during the alleged antitrust activity, but plaintiffs alleged that a quicker and sharper market price decline would have occurred absent the antitrust violation. This allegation implies a testable hypothesis. Rubinfeld and Steiner at 105 [observing that “[s]uch an issue is typical of many antitrust issues in that it poses a set of competing hypotheses to be evaluated. The plaintiffs’ hypothesis was that the presence of generic houses in the market resulted in a lower price; the defendant’s hypothesis was that the presence of generic houses had no effect on price. The two hypotheses are clearly mutually exclusive. . . . The choice between these hypotheses is one that can be handled in the context of classical statistics and econometrics. The null or initial hypothesis is set to be the well-defined hypothesis of no effect. This hypothesis is then tested against the alternative hypothesis that there is some effect. A null hypothesis of this type can be tested directly using a t-test within a multiple regression framework. If the null hypothesis is rejected at the appropriate level of significance, such as 1%, 5%, or 10%, the conclusion is that the data support the plaintiffs’ hypothesis. However, a failure to reject the null hypothesis supports the defense.”).
This hypothesis test begins the Daubert analysis. The testing is operationalized by specifying a model, including dependent and explanatory (or independent) variables and using data to estimate the parameters (the regression coefficients and standard deviations) of the resulting model. These resulting parameters are used to test the desired hypothesis(es). See Rubinfeld and Steiner at 105, [noting that "[t]he initial step in analyzing whether there is an effect in any particular case is to define the list of variables to be studied. . . . Once the variables have been listed . . . verbal hypotheses can be translated into specific, statistically testable null hypotheses. . . . Once the null hypothesis has been specified, one chooses the appropriate form for the multiple regression and estimates the model using an appropriate data set. The estimated model is then used to perform the test of hypotheses described previ­ously. The result should indicate whether or not there has been an effect."
Specifying a model requires setting out what variables are believed to impact the price of ampicillin. In this case, the first step is to use an underlying understanding of economics and of the institutions of the ampicillin market to model the factors expected to determine the price of ampicillin in the market. Surely the cost of ampicillin production will matter, as might competition and the time period in which the ampicillin is produced. See Rubinfeld and Steiner at 106-7 for an explanation of the slightly more complex model actually used in the case.
Specifically, assume that the price of a bottle of ampicillin is determined by four variables.
(1) Cost, C = an index of the cost of production of ampicillin.
(4) Generic Competition Variable, N = number of generic houses that bid.
Rubinfeld and Steiner at , discussing a similar model and noting that “e is a random disturbance term. See also Section V.A for discussion of the disturbance term.
It is important to include all the variables that are likely to affect P, but the object of the exercise is to determine if N impacts P, for this supports plaintiff’s contention. The impact of N on P is determined by a hypothesis test of b=0. See Rubinfeld and Steiner at 106-7 (noting that “[t]he null hypothesis of no effect with respect to generic house competition is the hypothesis that b=0, while the alternative hypothesis is that b . . . is . . negative”).
This is the prototype of the testing requirement articulated in Daubert. As in section V.A, associated with this test will be the rate of error of the test. Also, as supra, this rate of error is known as the level of statistical significance.
Testing the hypothesis requires gathering relevant data, estimating the regression equation and analyzing the resulting parameter estimates. The regression analysis will generate, for each variable, two parameter estimates. The first of these will be the coefficient estimate, which is the regression's estimate of a, b, c & d. The second will be a standard deviation for each coefficient estimate. Taken together, the coefficient estimate and the standard deviation of the coefficient estimate generate the hypothesis test discussed in Daubert. It is typical for economists to report such results in a table similar to TABLE 1, which is an abbreviated version of a similar table that appears in Rubinfeld and Steiner at 107.
This table summarizes the results of hypothesis tests on all of the explanatory variables. An economist would say that Table 1A shows that the coefficient on N is not statistically significant, or that the coefficient is not differentiable from zero. In a Daubert hearing the same information would be asserted as ‘the hypothesis test on N fails to show that it impacted the price of Ampicillin when tested with a 5% rate of error.’ On the other hand, the hypothesis that C does not affect the price of Ampicillin is rejected at an error rate of 5%. Recall that a t-statistic of 2.0 is the rule of thumb cutoff for the hypothesis test to support the hypothesis that N affects P.
The other interesting thing to note about Table 1 is that it is divided into two parts. Table 1B exists because there is concern that costs may influence the price of ampicillin in a more complicated way than is captured by the regression specification employed to generate the results found in Table 1A. In particular, the concern is that it may be that production cost increases affect price more when cost is already fairly high. As a result, the proper specification may include the square of cost as an explanatory variable. Table 1B shows results for a regression equation that includes this variable. This is an example of the model specification problem discussed in section V.A. Notice that while the coefficients in the table change, the coefficient on N is very small and continues to be statistically insignificant (and fails the Daubert factor 1 test at any rate of error that is ever used for such tests). In this case, both specifications present evidence that the number of generic houses have no statistically significant impact upon the price of Ampicillin.
The Daubert summary of the investigation into the impact of the presence of generic houses on the price of Ampicillin is that the testimony has been Daubert tested, and the test prescribed by factor 1 shows that, in the relevant range, the number of generic houses bidding on Ampicillin contracts does not affect the price at which Ampicillin is sold, at the levels of error that economists apply to their non-litigation work. So far, the testimony seems admissible.
There are two important things to note about the preceding description. The first is that this is a typical application of regression in expert testimony and the discussion is typical of how economists review their results. Therefore, this is not just an antitrust example, it is an example of how regression analysis is applied in the scientific community and of how regression is required to be applied forensicly.
The second is that the basis of the economists work is the hypothesis testing that some commentators believe cannot be widely done in the economic analysis that underlies expert testimony in antitrust litigation. Indeed, the most important point to be made about this table of coefficient estimates and t-statistics is that its purpose is to report on the testing of hypotheses of the sort that the Daubert court discusses and that scientifically unsophisticated commentators have dubbed as being impossible in most economics expert testimony work. See section V.C.3. Such a table of hypothesis tests is present in almost all credibly published empirical economics research, and usually the point of such a table is to show the results of the hypothesis tests that are the core of the economists work. Here the point is simpler. Here the point is merely that hypothesis tests are the core of the economist's work and that hypothesis testing, far from being impossible in most economics is, indeed, required in most economics. Suggestions to the contrary are almost universally ill informed.
Professors Rubinfeld and Steiner have served as experts in a number of other antitrust litigations and, in addition to its discussion of the ampicillin litigation, their Quantitative Methods in Antitrust Litigation discusses their statistical analyses in In re: Plywood Antitrust Litig., In re: Uranium Antitrust Litig., and Pacific Mailing Equipment v. Pitney Bowes.
Note the analogue to what could be called "but for" returns in the event study technique of section V.B, where regression techniques are used to estimate what the return on a security would have been, "but-for" the release of fraudulent information. While there are surely very large differences in actual practice detail, the conceptual problem is the same, and that is to estimate the market price of the security or the product in the absence of the fraud or the antitrust activity.
If the point of this section can be summarized into a single notion, it is that hypothesis testing at particular error rates was a staple of the methods of expert testimony in antitrust for decades before Daubert first articulated "testing" and "error rates" as criteria for admissibility of expert testimony. They have been the staples of almost all credible non-forensic economics for much longer than that.
Section V.B began with the proposition that since virtually all credible economics, as practiced outside of the courtroom, so routinely meets the test that the Daubert Court articulated, there is little room to argue against requiring that economics based expert testimony be tested by the Daubert factors, but noted also that there is a contrasting view. This contrasting view manifests itself in one of the cases discussed in this section.
Many of the post-Daubert opinions are applying increasingly sophisticated scrutiny to the econometric analysis that underlies proffered expert testimony. Two such opinions were written by the same 11th Circuit trial judge in the same month and are somewhat complimentary. These opinions look carefully at econometric issues like model selection, heteroskedasticity and regression model assumptions that importantly inform the trial court's reliability investigation required by Daubert.
The court in In Re: Polypropylene Carpet Antitrust Litigation, 966 F. Supp. 18 (N.D. Ga. 1997), held a hearing to determine whether an expert’s proposed methodology would “comport with the basic principles of econometric theory,” id., at 26, and agreed that the economist’s “multiple regression analysis is a scientific endeavor whose admissibility in court proceedings must be determined using the test set forth in Daubert v. Merrell Dow Pharmaceuticals, Inc.” Id. The court then analyzed econometric model selection, including some of the possible different independent variables that could be included and then analyzed the hidden the perils of trying a large number of variables in a regression and excluding the ones that don’t seem to fit. Id. at 27.
In Estate of Bud Hill v. ConAgra, 1997 U.S. Dist. LEXIS 13083, an unreported opinion by the same judge, the court articulates some of the particular shortcomings that can cause regression to fail a Daubert test. Bud Hill at *16. Defendant challenged the reliability of plaintiff’s expert’s testimony on the ground that it failed to satisfy the regression assumptions (the court calls them principals). In particular, defendant alleged that the plaintiff had failed to test whether the error term of the regression formula was independent of the included explanatory variables. Id. This is the specification error problem of section V.A.
The court investigates and determines that defendant fails to show that the regression violates the independence assumption “in a way that the analysis fails to follow standard, acceptable econometric practices.” The court reasoned that the evidence cited by defendants “does not show that Dr. Jackson failed to test for the independence assumption. Rather, Defendants' evidence shows only that Dr. Jackson failed to test whether his formulas satisfy . . . the "constant variance assumption." Id at 17. The court faults the defendant’s failure to define the constant variance assumption (what we call the heteroskedasticity problem), id, or establish that the constant variance assumption must be fulfilled in order to perform a valid regression analysis. Id.
The court noted that it had ”reviewed many materials concerning multiple regression analysis, and understands the basic principles underlying this econometric technique. In fact, the Court understands from its own research that the assumptions of independence and constant variance are indeed related to a large degree.
Nonetheless, the burden of explaining how Dr. Jackson's failure to satisfy the constant variance assumption impacts the regression analysis belongs to Defendants, as they are the parties raising the issue. Defendants' failure to discharge this burden is reason alone to deny summary judgment with respect to this issue.” Bud Hill at *18.
Second, the Court believes sufficient evidence exists to support a reasonable inference that Dr. Jackson properly tested the assumptions specified in Defendants' argument. Dr. Jackson defines the "constant variance assumption" as a need to correct for possible heteroscedasticity in the regression formula. Heteroscedasticity occurs "when the disturbance or error associated with a multiple regression model has a nonconstant variance; that is, the error values associated with some observations are typically high, whereas the values associated with other observations are typically low." Rubinfeld, supra, at 464. Stated differently, heteroscedasticity "occurs when errors in the analysis do not occur randomly, but rather vary in direct relation to the values of the coefficients" associated with explanatory variables.
Dr. Jackson agrees that his model indeed contains heteroscedastic disturbances, and that he did not correct these disturbances before reaching the conclusions in his report. (Jackson Aff. P 18-19.) Dr. Jackson cites two reasons for this course of action. First, Dr. Jackson states that, to compute t-statistics for formulas that are based on very large sample sizes (as is the case here), a regression analysis may use an estimate of the standard errors for its coefficients in lieu of the classic least squares estimates for these coefficients. n9 (Id. at P 15.) This procedure, according to Dr. Jackson, eliminates the need to correct forheteroscedasticity. (Id.) Second, Dr. Jackson states that, because the disturbance creating the heteroscedasticity varies systematically, the presence of the heteroscedasticity alone can be interpreted as further support for a conclusion that Defendants manipulated the tare weights. (Id. P 19.) In other words, the systematic nature of the variation suggests deliberate manipulation of the tare weights, according to Dr. Jackson.
For these reasons, the Court concludes Defendants' evidence is insufficient to show that Dr. Jackson failed to test properly the assumptions underlying his regression analysis. Bud Hill at *19-*22.
While the omission of variables from a regression analysis may render the analysis less probative than it otherwise might be, it can hardly be said, absent some other infirmity, that an analysis which accounts for the major factors must be considered unacceptable as evidence. . . . Normally, failure to include variables will affect the analysis' probativeness, not its admissibility. Bazemore at 400.
As the econometric discussion of section V.A demonstrates, when variables are improperly omitted from a regression study, the outcome is that the resulting estimators lose the desirable properties that make them scientifically reliable, and lost with this scientific reliability is the estimates evidentiary reliability. While econometrics is a powerful tool, when it is used other than in accord with the assumptive structure upon which it is built, the answers that it produces are really answers to questions other than the ones that were thought to be being asked of it. A misspecificed model must fail a Daubert examination because its tests are invalid, the error rates of those tests are unknowable, misspecified models are not generally accepted and are poor candidates for peer-reviewed publication because of the well-known invalidity both of its tests and the error rates of those tests. Bazemore may accommodate model misspecification. Daubert does not, and it will be interesting to see if the Court takes the opportunity to conform Bazemore to its more sophisticated analysis in Daubert.
Judge Posner provides an accessible but sophisticated 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 section V.D. on expert testimony in employment litigation.
One commentator has recently observed that "[i]t is doubtful that much economic testimony would survive a strict and literal application of the Daubert factors. . . .few economic techniques of the ilk utilized in antitrust litigation could be "tested" in the sense contemplated by Daubert, i.e., falsified." Gavil, After Daubert: Discerning the Increasingly Fine Line Between the Admissibility and Sufficiency of Expert Testimony in Antitrust Litigation, 65 Antitrust L. J. 663, 673-4. The cases of section V.C.3.a, would seem to refute this assertion and it is interesting to contrast it with the views of the scientifically sophisticated commentators cited elsewhere in this chapter. See Rubinfeld and Steiner at 70 [noting that "hypothesis testing is particularly useful for dealing with questions of whether an antitrust violation has occurred], Rubinfeld Econometrics in the Courtroom, 85 Colum. L. Rev. 1048 at 1049 [noting that "the most prominent application of econometric methods" is "the use of significance levels for hypothesis testing," (or to use the less descriptive term employed in Daubert, falsification)]. Proving Antitrust Damages, at 145 [beginning a full chapter discussion of the use of econometrics and statistical analysis in antitrust by stating that "[r]egression analysis is a statistical technique that . . .can assist an antitrust plaintiff in proving both the fact and the amount of its injury," before going on to develop the notions of hypothesis testing and falsifiability for application to antitrust damage calculations] This list of contra citations could continue almost without end.
The author himself notes that his "exposition of 'falsifiability' and 'rate of error' is somewhat simplistic," Gavil at 675, note 48. The resulting observations may have just given way to the preponderant evidence on the role of testing in economics and econometrics, except that these "simplistic" arguments were made in the commentator's discussion of the trial courts analysis of expert testimony in City of Tuscaloosa v. Harcross Chems., 877 F. Supp. 1504 (N. D. Ala. 1995). When Tuscaloosa v. Harcross went up to the 11th Circuit on appeal, an amicus brief that echos these misconceptions was filed in support of Tuscaloosa and the Court cited to the brief with approval in a footnote that has been cited by another 11th Circuit trial court. The connection may just be coincidence because the amici did not cite to Gavil, but regardless, this commentary is apparently adopted in the 11th Circuit, subject to how the Circuit interprets Tuscaloosa in subsequent opinions.
In Tuscaloosa v. Harcros, the 11th Circuit generally reversed the district court's exclusion of proffered antitrust expert testimony and stated that many of the problems in the district court's opinion "might have been avoided had the district court simply held a Daubert hearing to allow the parties to clarify their positions, as well as the law, regarding the admissibility of these experts' testimony." Tuscaloosa at 565, n.21.
With respect to admissibility of the experts' testimony, the court affirmed that "[e]xpert testimony may be admitted into evidence if: (1) the expert is qualified to testify competently regarding the matters he intends to address; (2) the methodology by which the expert reaches his conclusions is sufficiently reliable as determined by the sort of inquiry mandated in Daubert; and (3) the testimony assists the trier of fact, through the application of scientific, technical, or specialized expertise, to understand the evidence or to determine a fact in issue. See Fed. R. Evid. 702; Daubert, 509 U.S. at 589, 113 S. Ct. at 2794. Id. at 562.
The Court quoted Daubert for the propositions that "the inquiry envisioned by Rule 702 is . . . a flexible one", and that "many factors may bear on the inquiry" into the reliability of the testimony. To the four Daubert factors, the Court added a fifth, "the existence and maintenance of standards controlling [its] operation" (referring to the operation of the experts methods. Id. at 563, n.16.
The Court reversed the district court's exclusion of the expert's testimony, writing that his "testimony is entirely within his competence as a statistician" and that "his testimony regarding estimated damages, are the products of simple arithmetic and algebra and of multiple regression analysis, a methodology that is well-established as reliable." Id. at 566.
Perhaps the court's observation about testing will be limited to "arithmetic and algebra," which surely are admissible without a testing requirement, although, at least in the former case, there is question as to how the expert testimony will assist any but the most innumerate trier of fact. However, to apply such statements to an economist's regression analysis would fly in the face of the overwhelming preponderance of the informed literature, which generally accepts hypothesis testing as the sine qua non of regression analysis.
Finally, the court added to the Daubert factors a fifth factor, the existence and maintenance of standards controlling the use of the expert's methods. Id. at 563. Section V.A. discusses the basic standards for the use of regression, and these standards virtually all relate to assuring that the hypothesis tests based upon the regression are competent. Thus, this criteria alone, if applied to the expert's regression analysis, seems to mandates hypothesis testing, because it mandates that hypothesis tests be done competently. It is somewhat unclear why the court would articulate such a criterion and then pronounce its intention to disregard it.
Testing is of such critical concern because it is very easy for an expert to weave lingo together into a compelling and convincing story that has no basis in fact. Hypothesis testing can reveal such errors. Section V.D considers an example of a superficially compelling expert's story that can be debunked by proper controls on the testing of hypotheses.
d. Allapattah Services Inc. v. Exxon, 61 F. Supp. 2d 1335 (S.D.Fla. 1999).
Allapattah Services held several days of Daubert hearings, citing to Daubert for the eleventh circuits five factors for admissibility of expert testimony (Daubert's four plus "the existence of standards" factor discussed supra.) See Allapattah Services at 1338. The Court then cited to Tuscaloosa for the 11th Circuits opinion on the proper way to apply those factors to an economist's testimony. The Court wrote that "the Eleventh Circuit, in a pre-Kumho case, discussed, in a footnote, the proper inquiry regarding the reliability of the methodologies implemented by economic and statistical experts in the Daubert context. The entire footnote is set forth because of its importance to this court's analysis." Id. at 1339. The referenced footnote is footnote 25, discussed at length supra, which explains why testing is not applicable to economist's expert testimony.
The proffered expert testimony in Allapattah Services did include regression testimony and made multiple references to hypothesis testing in admitting the testimony of both experts. Allapatha at 1350 (noting that the expert used "controls for extraneous causal factors, together with the application of regression analysis to test the validity of the relevant statistical hypotheses . . .") Id. at 1353 and (then noting that "each expert tested his hypotheses . . ."). This seems like a standard Daubert hearing, admitting testimony that seems reasonable, with some attention paid to the expert's hypothesis tests. As indicated supra, it must remain to be seen how 11th Circuit courts apply footnote 25 of Tuscaloosa that directs attention away from Daubert's testing factor.

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