تجزیه و تحلیل پرت آماری در حمایت از شکایت های قانونی: مورد پل ، ایگلر و کاکتوس فیدر، در برابر اپرا وینفری و همکاران.

In the 1990s three decisions of the United States Supreme Court raised standards for admissibility of scientific and special knowledge testimony in Federal trials. Many states have adopted comparable standards. Expert economic testimony that seeks to prove facts from statistical generalizations has received considerable scrutiny in litigation. This article focuses on the nitty-gritty of performing regression studies that can meet the new standards for admissibility. The article redefines chance outliers in terms of tail probabilities of distributions. Tests for presence of outliers produced by anomalous factors are specified in terms of number of diagnosed outliers and waiting-times of their occurrence.

“It has just stopped me cold from eating another burger”, so said Oprah Winfrey in her broadcast of April 16, 1996. She was responding to a guest's disturbing account of cattle feeding practices in the United States. The topic of Ms Winfrey's April 16, 1996 show was “Dangerous Foods”. The show included a discussion of bovine spongiform encephalopathy, or “Mad Cow Disease”. There had been increasing media coverage of “mad cow disease” for a considerable number of months. In Paul F. Engler and Cactus Feeders, Inc., v. Oprah Winfrey et al. plaintiffs sought a substantial award of damages from defendants, alleging the total damages to be $4,893,843. Plaintiffs claimed to have suffered economic harm because of a sudden and unusual decrease of the cattle prices in April 1996, which—they asserted—was caused by Oprah Winfrey's actions. Plaintiffs contended that, but for actions of Oprah Winfrey et al., such a decline would not have occurred under the market conditions which prevailed up to that time. Plaintiffs were cattle producers who sold fed cattle to meat packers. Plaintiffs alleged that by broadcasting this segment of Ms Winfrey's show defendants published or allowed to be published disparagements of the beef industry and of the safety of American beef. Plaintiffs alleged that defendants’ actions caused the price of fed cattle to decline, and that the price decrease in turn directly or proximately caused them to suffer economic damage: (1) Plaintiffs alleged that defendants’ actions forced them to sell cattle for less than they would have sold them had the market prices not declined significantly. Plaintiffs alleged that the damage from that cause was $198,562. (2) Since—plaintiffs alleged—they experienced greater uncertainty as a result of Ms Winfrey's broadcast, they increased their hedging activities, which—they argued—caused Cactus Feeders, Inc. to suffer economic harm, the total damage allegedly being $4,695,281. The complaint and rebuttal are briefly summarized in Section 1.1. Daniel Slottje of KPMG Peat Marwick (Dallas, TX) was a testifying expert for defendants. I served as a non-testifying statistical and econometrics consultant on the defense research team. My assigned task was to evaluate the plaintiffs’ statistical evidence and argumentation. Quite properly, neither defendants’ testifying experts nor their non-testifying consultants were apprised of the nature of defense counsel's strategies of persuasion. The chief econometric task was to determine whether plaintiffs’ economics expert had established a prima facie statistical case for the occurrence of anomalous outliers in fed cattle prices during the weeks including and immediately following the Oprah Winfrey show on April 16, 1996. With reference to any batch of data in which it appears, an outlier is an entry that differs markedly from most of the other entries in the batch. Barnett and Lewis (1994, pp. 7–8) “… describe an outlier in a set of data to be an observation (or subset of observations) which appears to be inconsistent with the remainder of that set of data.” Sprent (1998, p. 57) describes an outlier as “… an observation so remote from other observations as to cause surprise.” The immediate cause of surprise is the very low relative frequency with which such observations have occurred in the past. [ 3.1 and 3.2 will introduce a more precise definition of ‘outlier’ in terms of statistical probability.] Outliers can occur by pure chance; they can also be produced by the sole action of anomalous factors. Generally, however, outliers are mixtures of chance effects and anomalous effects. Performance of statistical diagnosis of outliers is logically prior to non-statistical substantive testing of any proffer of anomalous causes of their occurrence. In Paul F. Engler and Cactus Feeders, Inc., v. Oprah Winfrey et al. the overall relevant period for outlier diagnosis—from first week of January 1994 through last week of August 1996—was set by plaintiffs’ experts and accepted by defendants’ counsel. Plaintiffs’ experts also specified a shorter period, the second quarter of 1996, as relevant for some outlier diagnoses; see Figs Fig. 1, Fig. 2 and Fig. 3. In the case of Fig. 3, which described the daily futures prices on the Chicago Mercantile Exchange, plaintiffs’ experts asserted, in effect, that the relevance of previous price history could be safely limited to the preceding eleven market days of April 1996 for determining unusual daily price declines. 3 Full-size image (9 K) Fig. 1. Cactus feeders, Inc. prices received for all fed steers for the weeks ended March 29, 1996–June 28, 1996. Figure options Full-size image (10 K) Fig. 2. Texas and Oklahoma Panhandle fed cattle market prices fed steers for the weeks ended March 29, 1996–June 28, 1996. Figure options Full-size image (11 K) Fig. 3. 1996 Chicago mercantile exchange June futures price April 1, 1996–June 28, 1996. Figure options The statistical argumentation in Paul F. Engler and Cactus Feeders, Inc., v. Oprah Winfrey et al. is a matter of interest and growing concern to statisticians, econometricians, economists, attorneys and should be a matter of concern to anyone who teaches statistical inference to students in academic economics programs. This is due to implications of the 1993 and 1995 Supreme Court rulings in William Daubert et al. v. Merrell Dow Pharmaceuticals, Inc. [United States Supreme Court (509 U.S. 579, 1993)] and ibid [U. S. Court of Appeals for the Ninth Circuit (43 F.3d 1311, 1995)], subsequent rulings in General Electric Co. v. Joiner (522 U. S. 136 1997) and Kumho Tire Co. v. Carmichael (119 S. Ct. 1167, 1999) on the admissibility of scientific and other kinds of professional testimony in Federal litigation. 4 In Daubert, Joiner and Kumho Tire the Supreme Court established new standards for admitting expert testimony in federal trials. 5 In Kumho Tire the Court ruled that there was no need to distinguish between scientific knowledge and other specialized knowledge, hence bringing the expert testimony of economists under the Daubert rules. The new federal rulings demand for admissibility at trial—among other things—that economists’ statistical analyses meet considerably higher standards than traditionally have been required by peer reviewers and editors for publication in economics journals. Economists who testify as experts or expect to testify as experts have a special interest and concern because of trial judges’ growing resistance to admitting economic testimony they do not consider to meet the Daubert challenges. In some recent antitrust cases trial judges have ruled as inadmissible economic testimony proffered by prominent academic economists, including the testimony of at least one Nobel Prize winner, cf. Hechler (2002). In that case the trial judge asserted the expert to be ignorant of relevant facts and to be offering opinions without scientific basis. In Paul F. Engler and Cactus Feeders, Inc., v. Oprah Winfrey et al. plaintiffs’ expert economist did not test the statistical hypotheses which underlay the estimated regression equation, (2.2), from which he argued that Ms Winfrey's broadcast produced negative outliers, or exceptional declines, in fed cattle prices thereby causing harm to plaintiffs. In that respect, the statistical analysis proffered by plaintiffs’ expert economist was typical of much statistical analysis that is currently published in respected journals of economics. While Engler et al. v. Winfrey et al. took place after the Daubert rulings, discovery and trial took place before Kumho Tire Co. v. Carmichael established that special knowledge testimony should meet Daubert challenges for admissibility. During that period it was uncertain whether the Daubert criteria applied to proffered testimony on matters outside of the hard sciences—to social science generally and to economics in particular. So it might have appeared to plaintiffs’ experts that omission of tests of statistical hypotheses needed to validate their use of regression techniques would be no bar to its admissibility at trial. Indeed, it might have appeared to plaintiffs’ economic expert that admissibility of the methods to be discussed in this article, widely practiced by statisticians, of testing the assumptions of regression, risked denial on the grounds that they had been able only to attract minimal support among published economists, cf. William Daubert et al. v. Merrell Dow Pharmaceuticals, Inc. (509 U. S. 579, 1993), also Foster and Huber (1999, p. 285). By the same token, admissibility of Schumpeter's concept of ‘external factor’—see Section 1.2—and the statistical method of abstraction from external factors, Schumpeter (1939), might have appeared dubious to plaintiffs’ experts, since economists have rarely employed them in regression studies. Journal articles that are intended to be only expositive of statistical methods associated with regression ordinarily do not include tests of the statistical assumptions that validate the use of regression. An econometric classic, Haavelmo (1947), is a case in point: Haavelmo employed real national income data to illustrate novel methods of estimating the marginal propensity to consume. The fact that the hypotheses of statistical independence, normal distribution of disturbances and constant variance actually were in good agreement with those data was not mentioned by Haavelmo because that special information would not have helped readers understand his exposition of the methods. Basmann (1974, pp. 213–231) employed Haavelmo's data to illustrate the derivation and use of distribution functions of econometric estimators associated with Haavelmo's model. Since the article was only expositive, scarce space was not devoted to the unhelpful fact that the regression statistics comfortably “passed” the runs test, several normality tests, and tests for constant variance. The rationale for that omission in expositive articles is the same as for omitting those tests in econometric textbook chapters that focus on regression techniques. On the other hand, the omission of tests of regression assumptions from books and journal articles that purport to be asseverative of economic reality renders their conclusions incapable of meeting the Daubert requirement that the proffered conclusion actually be tested, cf. Foster and Huber (1999, p. 284). After Daubert, admission of regression studies as expert testimony which omit those tests risks the charge of judicial error and overturn by appellate judges. The purpose of this article is to describe and explain most of the nitty-gritty involved in the statistical inference phase of plaintiffs’ experts’ task in cases like that of Paul F. Engler and Cactus Feeders, Inc., v. Oprah Winfrey et al. Section 2 describes the statistical part of plaintiffs’ argument, including the expert's regression estimates. In Section 3 I introduce a precisation of the concept of objective outlier widely used in current exploratory data analysis as well as a straightforward generalization of the concept. Simulation studies are reported, which assessed the error-rates—the sensitivity, specificity, predictive values of positive and negative diagnoses by outlier screening methods. Of special relevance are the error-rates encountered in using the observed regression residuals to diagnose outliers in the nonobservable random disturbances of the underlying model. Section 4 describes the use of the binomial distribution and the negative binomial distribution in distinguishing diagnosed outliers that are produced by anomalous factors from diagnosed outliers that occur by chance. This section also includes a brief description of the confirmation of the presence of anomalous outliers. Section 5 describes the complete testing of plaintiffs’ regression model and several of its closely related versions. Two of the regression equations involve the first lagged values of the dependent variable (average weekly price of fed cattle). Results of a simulation study of statistical estimation of those equations are reported, as well as simulated error rates for the diagnosis of outliers by screening of residuals. Section 6 briefly examines the result of inflating the conventional probability of a chance outlier (0.00698) to 0.05. The appendix contains a few remarks concerning the use of outlier diagnoses with generalized least squares regression and with simultaneous equations estimation methods.