In Re Polypropylene Carpet Antitrust Litigation

93 F. Supp. 2d 1348 | N.D. Ga. | 2000

93 F. Supp. 2d 1348 (2000)

In re: POLYPROPYLENE CARPET ANTITRUST LITIGATION.
This Order relates to: All Cases.

No. MDL 1075.

United States District Court, N.D. Georgia. Rome Division.

March 28, 2000.

Randall Lee Allen, Teresa Thebaut Bonder, Alston & Bird, Atlanta, GA, Emmet J. Bondurant, II, James Scott McClain, Timothy S. Rigsbee, Bondurant Mixson & Elmore, Atlanta, GA, David R. Aufdenspring, Dean S. Daskal, Robert Moore Travis, John M. Gross, Gelnn Johnson, Powell Goldstein Frazer & Murphy, Atlanta, GA, Tony Glen Powers, Rogers & Hardin, Atlanta, GA, W. Pitts Carr, Jan Renee' Kastanakis, Carr Tabb Pope & Freeman, Atlanta, GA, Robert Maddox Brinson, Brinson Askew Berry Siegler, et al., Rome, GA, Randy Scott Chartash, Office of Atty. Gen., Atlanta, GA, Charles Conrow Murphy, Jr., Vaughan & Murphy, Atlanta, GA, John Robert Fitzptrick, Barbara Webb Cash, U.S. Dept. of Justice, Antitrust Div., Atlanta, GA, Michael D. Hausfeld, Cohen Milstein Hausfeld & Toll, Washington, DC, Edward Hine, Jr., Hine & Niedrich, Rome, GA, Michael Dockterman, pro hac vice, Wildman Harrold Allen & Dixon, Chicago, IL, Richard A. Lockridge, pro hac vice, Joseph Bruckner, pro hac vice, Lockridge Grindal Nauen, Minneapolis, MN, Laurie Webb Daniel, Gregory J. Digel, Keith H., Reisman, Holland & knight, Atlanta, GA, Joseph Goldberg, pro hac vice, Freedman Boyd Daniels Hollander, Albuquerque, NM, Leonard Barrack, pro hac vice, Steven A. Asher, pro hac vice, Barrack Rodos & Bacine, Philadelphia, PA, Goirdon Ball, pro hac vice, Office of W. Gordon Ball, Knoxville, TN, Martin D. Chitwood, Craig Gordon Harley, Atlanta, GA, David LeBron McGuffey Coppedge Leman & Ward, Dalton, GA, J. Robert Williamson, Scroggins & Williamson, Atlanta, GA, Arthur N. Bailey, pro hac vice, Office of Arthur NM. Bailey, Jamestown, NY, Eugene A. Spector, pro hac vice, spector Roseman & Kodroff, Philadelphia, for Counsel to Serve, movant.

Jerome J. Froelich, McKenney & Froelich, Atlanta, GA, for John Doe, movant.

ORDER

HAROLD L. MURPHY, District Judge.

This case is before the Court on Defendant Beaulieu of America's Motion to Exclude Testimony of David R. Kamerschen and James T. McClave [340], Motion by Defendants Mohawk Industries, Inc., and Aladdin Mills, Inc., to Exclude Expert Testimony of Dr. James T. McClave and Dr. David R. Kamerschen [341], Motion of Shaw Industries, Inc., to Exclude Certain Opinions of Dr. James T. McClave [343], and Motion of Shaw Industries, Inc., to Exclude Portions of the Testimony of Professor David R. Kamerschen [345].

I. Background

This case involves allegations that Defendants engaged in a scheme to fix and maintain the price of polypropylene carpet. In support of these allegations, Plaintiffs seek to introduce the testimony of two experts, Dr. James T. McClave and Dr. David Kamerschen.

Dr. Kamerschen is an industrial economist retained by Plaintiffs to analyze whether the conditions in the polypropylene carpet market during a particular period were consistent with competitive or collusive activity. Dr. Kamerschen's analysis focuses upon the structure of the industry, the behavior of firms in the market, and the performance of those firms. (Hr'g Tr. of Feb. 2, 2000 ("2/2 Tr."), at 12-13.)

With respect to the structure of the carpet industry, Dr. Kamerschen examined the following factors to determine whether a climate conducive to price fixing existed during the time period at issue: seller concentration; barriers to entry into the market; degree of vertical integration; product differentiation; technological development; and elasticity of demand. (Kamerschen Expert Report 7-14.) Additionally, Dr. Kamerschen identified the geographic concentration of carpet manufacturers and the existence of trade associations as factors that promote the potential for the establishment of an effective pricefixing scheme. (Id. at 15-16.) Finally, Dr. Kamerschen analyzed the performance of firms in the market in terms of cost-adjusted price as a factor related to the existence of collusive activity. (2/2 Tr. at 15.)

Dr. McClave is an econometrician retained by Plaintiffs to ascertain damages in this case. To calculate damages, Dr. McClave developed a model of polypropylene carpet prices using multiple regression analysis. Dr. McClave employed the model to forecast competitive prices during the time period at issue, and identify any difference between the actual prices of polypropylene carpet and the forecasted competitive prices during that period.

Defendants object to the admissibility of testimony by Dr. McClave and Dr. Kamerschen, arguing that Plaintiffs have failed to satisfy the evidentiary standard set forth in Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579, 113 S. Ct. 2786, 125 L. Ed. 2d 469 (1993). On January 31, 2000, the Court began a four-day hearing in this matter.

At the hearing, Plaintiffs presented testimony from Dr. McClave, Dr. Kamerschen, and Dr. J. Douglas Zona, an economist who submitted a rebuttal report in support of the admissibility of Dr. McClave's expert testimony. Defendants offered testimony from Dr. Daniel L. Rubinfeld, an economist by training who teaches both law and economics, and Jim Prater, a manager of carpet manufacturing facilities for Defendant Shaw Industries, Inc. ("Defendant Shaw"). Based on the testimony adduced at the hearing, the reports and deposition testimony by both parties' experts, and the extensive briefing offered by the parties, the Court concludes that much of Dr. Kamerschen's testimony and all of the testimony by Dr. McClave is admissible.

II. Standard for Admission of Expert Testimony

For approximately seventy years, federal courts faced with challenges to the admissibility of expert witness testimony spent a good deal of effort to determine whether the basis for the testimony was "sufficiently established to have gained general acceptance in the particular field in which it belongs." Frye v. United States, 293 F. 1013, 1014 (D.C.Cir.1923); United States v. Piccinonna, 885 F.2d 1529, 1531-32 (11th Cir.1989). In 1993, the Supreme Court belatedly recognized that the Federal Rules of Evidence had supplanted this standard of admissibility. Daubert, 509 U.S. at 587, 113 S. Ct. 2786. Accordingly, the Federal Rules of Evidence serve as the cynosure for the task at hand.

Federal Rule of Evidence 702 speaks most directly to the admissibility of expert testimony. Rule 702 provides:

If scientific, technical, or other specialized knowledge will assist the trier of fact to understand the evidence or to determine a fact in issue, a witness qualified as an expert by knowledge, skill, experience, training, or education, may testify thereto in the form of an opinion or otherwise.

Fed.R.Evid. 702. In accordance with Rule 702, the Court may admit expert testimony if: (1) the witness is "qualified as an expert," such that the witness can testify competently with regard to a matter at issue; (2) the testimony is reliable enough to be considered knowledge in the context of the relevant discipline; and (3) the testimony is relevant, in that it assists the trier of fact to understand or come to a conclusion regarding a material issue. City of Tuscaloosa v. Harcros Chems., Inc., 158 F.3d 548, 562 (11th Cir.1998).

To qualify to testify as an expert, a witness must be able to testify competently regarding the matters she intends to address by virtue of her education, training, experience, knowledge, or skill. See Fed.R.Evid. 702; Wheat v. Sofamor, S.N.C., 46 F. Supp. 2d 1351, 1356-57 (N.D.Ga.1999); Everett v. Georgia-Pacific Corp., 949 F. Supp. 856, 857 (S.D.Ga.1996).

Before admitting the testimony of a witness qualified as an expert, however, the Court must engage in a "preliminary assessment of whether the reasoning or methodology underlying the testimony is scientifically valid and of whether that reasoning or methodology properly can be applied to the facts in issue." Daubert, 509 U.S. at 592-93, 113 S. Ct. 2786. The objective of this assessment "is to ensure the reliability and relevancy of expert testimony." Kumho Tire Co. v. Carmichael, 526 U.S. 137, 152, 119 S. Ct. 1167, 143 L. Ed. 2d 238 (1999); accord Allison v. McGhan Med. Corp., 184 F.3d 1300, 1311-12 (11th Cir.1999) ("The judge's role is to keep unreliable and irrelevant information from the jury because of its inability to assist in the factual determinations, its potential to create confusion, and its lack of probative value."). The focus of the Court's preliminary assessment, the reliability and relevance of expert testimony, requires careful attention.

A. Reliability

Federal Rule of Evidence 702, in conjunction with Rule 403 and Rule 703, imposes a standard of evidentiary reliability that contrasts with the generous approach to admissibility reflected in Rules 401 and 402. Allison, 184 F.3d at 1310; see also Kumho, 526 U.S. at 149, 119 S. Ct. 1167; Daubert, 509 U.S. at 589-91, 113 S. Ct. 2786; cf. Weisgram v. Marley Co., ___ U.S. ___, ___, 120 S. Ct. 1011, 1021-22, 145 L. Ed. 2d 958 (2000) (noting that standards of reliability applied to expert testimony are "exacting"). Specifically, when expert "testimony's factual basis, data, principles, methods, or their application are called sufficiently into question, ... the trial judge must determine whether the testimony has a `reliable basis in the knowledge and experience of [the relevant] discipline.'" Kumho, 526 U.S. at 149, 119 S. Ct. 1167 (quoting Daubert, 509 U.S. at 592, 113 S. Ct. 2786). In other words, the Court's inquiry focuses not on whether the expert is correct, but whether the proponent of expert testimony has established by a preponderance of the evidence that the testimony is reliable in the context of the methodologies or techniques applied within the appropriate field. See Allison, 184 F.3d at 1312.

Several considerations may have a bearing on this issue. Whether a theory or technique has been tested, for example, or subjected to peer review and publication, may help to gauge the reliability of the methodology at issue. Daubert, 509 U.S. at 593, 113 S. Ct. 2786. Similarly, the degree of acceptance within the relevant community, the existence of standards designed to ensure the credibility or accuracy of a particular technique, the likelihood that a particular technique may result in error, and whether the methodology stands up to the standards applied within the relevant field all may help determine whether the methodology is sufficiently reliable to be considered admissible. City of Tuscaloosa, 158 F.3d at 566 n. 25.

In sum, the Court's objective is to make sure that the expert "employs in the courtroom the same level of intellectual rigor that characterizes the practice of an expert in the relevant field." Kumho, 526 U.S. at 152, 119 S. Ct. 1167. In keeping with the varied nature of expert testimony, the Court enjoys "considerable leeway in deciding in a particular case how to go about determining whether particular testimony is reliable." Id. The Court's evaluation of the reliability of expert testimony thus does not depend upon a rigid checklist of factors designed to test the foundation of that testimony. Rather, the gatekeeping inquiry must be tailored to the facts of the case and the type of expert testimony at issue. See id. at 150, 119 S. Ct. 1167; City of Tuscaloosa, 158 F.3d at 566 n. 25 (discussing reliability of testimony by economic and statistical experts).

B. Relevance

The Federal Rules of Evidence also require that expert testimony, like all admissible testimony, relate to a pertinent issue in the case. Indeed, Rule 702 provides that expert testimony must "assist the trier of fact to understand the evidence or to determine a fact in issue." Fed. R.Evid. 702. Even reliable expert testimony, therefore, may be excluded if no logical relationship exists between the testimony and a fact or issue in the case. Daubert, 509 U.S. at 591, 113 S. Ct. 2786; Allison, 184 F.3d at 1312.

III. Discussion

A. Dr. Kamerschen

Dr. Kamerschen is the Jasper N. Dorsey Distinguished Professor of Economics at the University of Georgia. (Pls.' Daubert Ex. 52.) Dr. Kamerschen obtained a Masters degree in economics at Miami University of Ohio in 1960, and a Ph.D. in economics from Michigan State University in 1964. (Id.)

Dr. Kamerschen has authored ten textbooks and approximately 185 journal articles primarily in the area of industrial economics, a field that encompasses both antitrust and regulatory economics. (2/2 Tr. at 7.) Roughly seven of the books and eighty-five of the articles relate at least in part to antitrust economics. (Id.) Furthermore, Dr. Kamerschen's work has been extensively cited by other economists. (Id. at 6-7.) Finally, Dr. Kamerschen on numerous occasions has served as a consultant engaged to conduct "empirical analyses of the structure, conduct, and performance of specific firms, markets, and industries in a variety of different lines of commerce and different sections of the country." (Kamerschen Expert Rep. at 3.) Defendants do not challenge Dr. Kamerschen's qualification to testify as an expert economist in this case, and the Court finds that he is qualified to do so.

1. Dr. Kamerschen's Proffered Testimony

Part of the debate over the admissibility of Dr. Kamerschen's testimony can be resolved by focusing on what Dr. Kamerschen seeks to share with the trier of fact. Dr. Kamerschen purports to have conducted a straight-forward and orthodox analysis of the market for polypropylene carpet products. Under this approach, an economist examines market structure, the conduct or behavior of sellers in the market, and the performance of the market to evaluate whether the characteristics of that market are consistent with competitive or collusive behavior. (2/2 Tr. at 10-15.) Defendants do not challenge the reliability of this approach in general.

With respect to the organization of a market, Dr. Kamerschen considers the degree of seller concentration and the existence of barriers to entry into the market as the most important factors. (Id. at 13.) In this case, Dr. Kamerschen also considered product differentiation, whether Defendants had a similar degree of vertical integration in the manufacturing process, technological development, and the elasticity of demand. (Kamerschen Expert Report 9-14.)

As for the conduct of Defendants, Dr. Kamerschen examined whether there were opportunities for communication between the parties and means to enforce a price-fixing agreement. (Id. at 16-20; Kamerschen Rbtl. Report at 25-32.) Finally, Dr. Kamerschen compared real prices of polypropylene carpet products during the "class period" — the time during which the price-fixing conspiracy allegedly existed — with real prices in the "benchmark period" —the time after the alleged conspiracy ended. (2/2 Tr. at 32.) In conducting this analysis of the performance of the market, Dr. Kamerschen attempted to estimate changes in Defendants' market shares. (Id. at 32-33.) Additionally, Dr. Kamerschen considered Dr. McClave's analysis of the ratio of prices over the polypropylene fiber producer price index, which is discussed in some detail below. Based on Dr. Kamerschen's analysis of the polypropylene carpet industry, Dr. Kamerschen concludes that

the structural characteristics of the olefin carpet market are conducive to the formation and maintenance of a price-fixing conspiracy; the conduct exhibited by the defendants during the class period is consistent with the behavior generally expected of a group of firms actively engaged in a price-fixing conspiracy; and the economic performance by the polypropylene market is consistent with a successful price fixing conspiracy.

(Kamerschen Rbtl. Report at 37) (emphasis added).

At the hearing, Dr. Kamerschen emphasized that he does not purport to testify concerning the precise mechanics of the alleged conspiracy based upon the communications among carpet manufacturers. (2/2 Tr. at 47-48, 51, 97.) Moreover, Dr. Kamerschen stated that he does not intend to offer an opinion concerning the pricing structure in the polypropylene carpet industry or the correlation between the prices of various types of carpet. (Id. at 109-10.) Finally, Dr. Kamerschen testified that he does not seek to opine that the conspiracy necessarily began or ended on particular dates. (Id. at 9, 84.) The Court also finds that Plaintiffs have not adduced sufficient evidence to demonstrate the reliability of such testimony.^[1]See City of Tuscaloosa, 158 F.3d at 565 (affirming exclusion of expert's characterizations of documentary evidence more appropriately left for independent evaluation by fact finder). The Court also excludes expert testimony based on the existence of litigation involving allegations of price-fixing of nylon carpet products. Such testimony from an expert is prejudicial and inadmissible. Fed.R.Evid. 403. Defendants make a number of additional objections that require a more detailed discussion.

2. Conclusions of Conspiracy

Defendants criticize Dr. Kamerschen both for stating or implying that Defendants engaged in a conspiracy to fix prices and for refusing to state that Defendants engaged in a conspiracy. (Def. Shaw's Mot. Exclude at 22; Def. Mohawk's Mot. Exclude at 28; Def. Beaulieu's Mot. Exclude at 14.) At the hearing, Dr. Kamerschen again made clear that he seeks to testify only that the climate of the polypropylene market during the relevant time period was consistent with a finding that Defendants engaged in a conspiracy to fix prices. (2/2 Tr. at 35, 84, 142.)^[2] As a general matter, this type of opinion testimony may be helpful to the trier of fact. City of Tuscaloosa, 158 F.3d at 565 (finding that expert data and testimony "need not prove the plaintiffs' case by themselves; they must merely constitute one piece of the puzzle that the plaintiffs endeavor to assemble before the jury"). The Court therefore overrules Defendants' objections to this type of testimony on the ground that it would not be helpful to a jury.

3. Use of Census Data

Defendants object to Dr. Kamerschen's opinions derived from data compiled by the United States Bureau of the Census. Defendants criticize this data both because it includes polypropylene products that are not at issue in this case and because it underestimates the production of polypropylene carpet. In support, Defendants proffer a compilation of polypropylene carpet production figures by a number of manufacturers to illustrate the degree by which the Census Bureau underestimated polypropylene carpet production. (Defs.' Daubert Ex. 34; Aff. of David L. Kaserman Ex. 3.) In fact, Dr. Kamerschen agrees that the census data does not accurately reflect Defendants' sales of polypropylene carpet. (2/2 Tr. at 128.)

Proposed testimony must be supported by "`good grounds,' based on what is known." Daubert, 509 U.S. at 590, 113 S. Ct. 2786. Opinions based upon erroneous data, of course, must be excluded. United States v. City of Miami, 115 F.3d 870, 873 (11th Cir.1997) (finding expert relied upon wrong census data to determine relevant labor market); see also Fed. R.Evid. 703. For limited purposes, however, the Court finds that Dr. Kamerschen's analysis based on the Census Bureau data is sufficiently reliable to be submitted to the fact finder.

No one seriously questions whether Defendants were responsible for a significant portion of polypropylene carpet sales during the relevant time period, or whether there is a high degree of seller concentration in this market. Dr. Kamerschen purports to use the census data for the limited purpose of quantifying this degree of seller concentration by examining the percentage of market share attributable to Defendants. (2/2 Tr. at 125, 127-28.) Insofar as the Census Bureau data is confined to this type of question, the Court finds that the data provides sufficiently "good grounds" for Dr. Kamerschen's testimony.

In fact, the figures compiled by Dr. Kamerschen from the census data are consistent with Defendant Shaw's internal calculation of its market share in 1994 and 1995. (Kamerschen Report at 7-8, Ex. F.); cf. Allison, 184 F.3d at 1315-16 (noting courts not precluded from looking at conclusions). Furthermore, Defendants' total market share of polypropylene carpet sales as represented in Exhibit 34 does not contradict the conclusion that this market contains a high degree of seller concentration or that Defendants were responsible for a significant portion of total polypropylene carpet sales. (Defs.' Daubert Ex. 34.) Finally, the Court notes that as a general matter, census data is of the type of data reasonably relied upon by economists. See Clinchfield R. Co. v. Lynch, 784 F.2d 545, 553-54 (4th Cir.1986) (affirming admission of economist's expert testimony based on census data); Beatrice Foods v. Federal Trade Comm'n, 540 F.2d 303, 311-12 (7th Cir.1976) (affirming calculation of market share by FTC based on census data); see also United States v. 0.161 Acres of Land, more or less, situated in City of Birmingham, 837 F.2d 1036, 1041 (11th Cir.1988) (citing Clinchfield to support admissibility of expert testimony based on government statistics).^[3] The Court thus declines to exclude Dr. Kamerschen's opinion testimony concerning seller concentration based in part on census data.

Similarly, Dr. Kamerschen's analysis of census data to provide a general picture of whether price increases accompanied increases in revenue in the polypropylene carpet market is admissible. "Vigorous cross-examination, presentation of contrary evidence, and careful instruction on the burden of proof are the traditional and appropriate means of attacking shaky but admissible evidence." Daubert, 509 U.S. at 596, 113 S. Ct. 2786; see also Allison, 184 F.3d at 1311. Here, the Court finds that the census data is a sufficiently reliable basis for Dr. Kamerschen's opinion whether, in general, price increases accompanied increases in revenue.^[4]

Plaintiffs have not demonstrated, however, that census data may serve as an appropriate basis for any variety of opinion testimony. Indeed, Plaintiffs have adduced no evidence that the census data is a reliable basis for anything more than obtaining a general picture of the polypropylene carpet market.^[5] Because the census data does not accurately represent Defendants' carpet sales, detailed analysis of the data to determine changes in market shares over time or whether Defendants restricted output would likely be misleading and inaccurate. The Court therefore excludes Dr. Kamerschen's testimony on these issues as unreliable under Rule 702.

4. Use of Dr. McClave's Analysis

Dr. Kamerschen considered Dr. McClave's analysis of prices in his evaluation of the performance of the polypropylene carpet market. (2/2 Tr. at 10, 15-16.) Based on Dr. McClave's statistical analysis, Dr. Kamerschen seeks to present testimony concerning the scope and effect of the alleged conspiracy on prices of polypropylene carpet.

Defendants all object to Dr. Kamerschen's use of Dr. McClave's regression model to support his analysis of the polypropylene market. The reason for Defendants' objection is that Dr. McClave and other experts have repeatedly stated that Dr. McClave's model assumes the existence of a conspiracy, and is designed to estimate damages rather than determine whether a collusive price fixing agreement existed during the class period.

Discussed in greater detail below, Dr. McClave's model attempts to describe the most significant variables affecting the ratio of price over fiber costs in the polypropylene carpet industry. Even though Dr. McClave did not attempt to test the hypothesis that Defendants engaged in competitive (or collusive) behavior during the class period, Dr. McClave does attempt to accurately describe changes in the ratio between price and marginal cost over time in the benchmark period, and apply his model to data from the class period.

Federal Rule of Evidence 703 permits an expert to base an opinion on facts or data not admissible in evidence if it is of a type reasonably relied upon by experts in that particular field. Fed. R.Evid. 703. An expert, however, may not simply repeat or adopt the findings of another expert without attempting to assess the validity of the opinions relied upon. In re TMI Litig., 193 F.3d 613, 715-16 (3d Cir.1999) (finding blind reliance by expert on other expert opinions demonstrates flawed methodology under Daubert); TK-7 Corp. v. Estate of Barbouti, 993 F.2d 722, 732-33 (10th Cir.1993) (excluding expert opinion relying on another expert's report because witness failed to demonstrate a basis for concluding report was reliable and showed no familiarity with methods and reasons underlying the hearsay report). Particularly when parties do not have the opportunity to examine the information relied upon, courts must ensure that an expert witness is sufficiently familiar with the reasoning or methodology behind the information to permit cross-examination. TK-7 Corp., 993 F.2d at 732.

Economists frequently look to regression models to explain changes in prices. (2/2 Tr. at 32); Robert E. Hall and Victoria A. Lazear, Reference Manual on Estimation of Economic Losses in Damages Awards, Reference Manual on Scientific Evidence 512-13 (Federal Judicial Center 1994). Moreover, as Defendant Beaulieu aptly recognizes, "[i]ndustrial organization economists frequently use margins to inquire into variations in the relationships among industries, between industry concentration and industry profitability." (Beaulieu Reply Br. at 7.)

In this case, Dr. Kamerschen examined Dr. McClave's model and analyzed Dr. McClave's results in the context of his economic analysis of the performance of the polypropylene market. (2/2 Tr. at 32; Kamerschen Expert Report at 22-25; Kamerschen Rbtl. Report at 35-37.)^[6] Furthermore, Defendants have had ample opportunity to scrutinize Dr. McClave's analysis.

Accordingly, to the extent that Dr. McClave's model is otherwise reliable, Dr. Kamerschen may testify concerning the implications of Dr. McClave's analysis of prices in the context of Dr. Kamerschen's assessment of the performance of the polypropylene carpet market. In other words, Dr. Kamerschen may use Dr. McClave's analysis of polypropylene carpet prices because a regression analysis of changes in the ratio between price and a marginal cost proxy is the type of data reasonably relied upon by industrial economists, and because Dr. Kamerschen reviewed Dr. McClave's analysis and found it acceptable. What Dr. Kamerschen cannot do is represent that Dr. McClave's analysis tested and rejected the hypothesis that Defendants engaged in competitive conduct during the class period. (7/1/99 McClave Dep. at 57) ("I would describe the null hypothesis [of the model to be] that there is no difference, no real or true difference between the margins, average margins, mean margins, between the two periods.").

5. Barriers to Entry, Market Definition, and Other Objections

Defendant Mohawk disagrees with Dr. Kamerschen's analysis of market concentration and vertical integration. (Def. Mohawk's Br. at 30-32.) None of Defendant Mohawk's objections, however, suggest that Dr. Kamerschen's opinions and analysis are not typical of the analysis that characterizes the practice of industrial economists, or that Dr. Kamerschen misapplied a standard methodology. Indeed, Defendant Mohawk's arguments are more suitable to evaluations of credibility than admissibility.

Defendant Mohawk also objects to Dr. Kamerschen's analysis of demand elasticity because he failed to consider shifts in demand, a fact that Dr. Kamerschen readily admits. (Kamerschen Rbtl. Report at 15.) Additionally, Defendant Mohawk challenges Dr. Kamerschen's opinion of barriers to entry, stating that Dr. Kamerschen assumes the existence of barriers because no significant entry into the market occurred during the class period.

The Court believes that Dr. Kamerschen's reasoning on these issues is sufficiently reliable to allow the fact finder to consider his opinion, notwithstanding Defendant Mohawk's observations. Dr. Kamerschen concedes that his analysis of demand elasticity is only "suggestive" because of shifting demand. (Kamerschen Rbtl. Report at 15.) Similarly, Dr. Kamerschen's analysis of entry into the market supports but does not establish that significant barriers to entry exist in this market. Defendant Mohawk's objections merely emphasize the nature of components of Dr. Kamerschen's analysis, but do not support exclusion. Stated another way, Dr. Kamerschen's consideration of several inconclusive factors in the course of his analysis of the polypropylene carpet market does not mean that his analysis is unreliable.

In its post-hearing brief, Defendant Mohawk also challenges Dr. Kamerschen's conclusion that polypropylene carpet products constitute a relevant product market. (Def. Mohawk's Post-Hr'g Br. at 7-10.) Dr. Kamerschen discusses his understanding of a relevant market definition at length in his rebuttal report. (Kamerschen Rbtl. Report at 4-7.)

The Court rejects this objection because it is raised for the first time, by any Defendant, in Defendant Mohawk's post-hearing brief. Cf. Wright v. United States, 139 F.3d 551, 553 (7th Cir.1998) (arguments raised for the first time in a reply brief are waived); International Telecomm. Exch. Corp. v. MCI Telecomms. Corp., 892 F. Supp. 1520, 1531 (N.D.Ga.1995) (same). In fact, while Defendant Shaw and Defendant Beaulieu indirectly challenged Dr. Kamerschen's market definition by contesting Dr. Kamerschen's use of census data to analyze real prices and revenue, described in Dr. Kamerschen's report as a "quasi-5% test," Defendant Mohawk's initial Motion does not quarrel with Dr. Kamerschen's use of census data. Alternatively, the Court finds that Dr. Kamerschen's discussion of the "relevant market" for purposes of his economic analysis is sufficiently reliable to permit the fact finder to consider his opinion. (Kamerschen Rbtl. Report at 4-7) (describing reasoning behind conclusion that polypropylene carpet constitutes a market).

B. Dr. McClave

1. Qualification as an Expert

a. Credentials and Experience

Dr. McClave is the president and C.E.O. of Infotech, a software development and technical consulting firm. (1/31 Tr. at 115.) Although up to eighty percent of Infotech's business relates to software development, Dr. McClave's primary role in the company involves technical consulting in the area of econometrics, the application of statistical methods to business and economic issues. (Id. at 117.)

Dr. McClave represents that he has spent his entire career applying statistics to business and economic issues. (Id. at 124.) Dr. McClave received a doctorate in statistics from the University of Florida in 1971. (McClave Expert Report App. B.) From 1971 to 1989, he held teaching positions at the University of Florida in the statistics department, the college of business administration, and the department of decision and information sciences. (Id.) Dr. McClave remains an adjunct professor in business and economic statistics at the University of Florida's Graduate School of Business. (Id.) Additionally, Dr. McClave has authored five textbooks in the area of statistics, two of which deal specifically with business and economic issues. (1/31 Tr. at 119.) All of Dr. McClave's textbooks emphasize multiple regression, the statistical technique that is at issue in this case.

Prior to this case, Dr. McClave on numerous occasions has been offered as an expert in the area of econometrics or statistics in antitrust cases. (Id. at 125); see also City of Tuscaloosa, 158 F.3d at 564-66; State of Ohio v. Louis Trauth Dairy, Inc., 925 F. Supp. 1247, 1249 (S.D.Ohio 1996). Over the past twenty-five years, Dr. McClave has offered opinions on multiple regression models in between fifty and seventy-five federal and state cases. (1/31 Tr. at 123.) Up to half of those cases involved allegations of bid-rigging or price fixing. (Id.)

b. Opinions based on Economics

Although Dr. McClave has extensive experience applying statistical techniques to economic issues, Dr. McClave disclaims expertise in the area of economics or market behavior. (2/1 Tr. at 93.) Accordingly, Defendants object to testimony from Dr. McClave that may be grounded in economic theory.

As Dr. McClave stated at the hearing, econometrics involves the "statistical analysis of an economic problem." Meghnad Desai, Applied Econometrics 2 (1976). The simplicity of this description may obscure the fact that economic theory often determines the focus of the empirical analysis. Peter Kennedy, A Guide to Econometrics 69 (2d ed.1985).

Dr. McClave's testimony relates to an econometric model designed to estimate competitive prices during the class period. Insofar as economic theory is important to this model, the Court is untroubled by testimony from Dr. McClave in this context. Dr. McClave's education and experience indicate that he is well-qualified to express opinions concerning the application of statistical techniques to economic issues — which includes the use of economic relationships or principles in the design of a multiple regression model.

Of course, Dr. McClave may not be qualified to offer opinions on the types of evidence that economists identify as indicia of collusive activity. See City of Tuscaloosa, 158 F.3d at 565. But that type of testimony is not at issue here. Plaintiffs present Dr. McClave as an expert in the area of econometrics to provide testimony concerning an estimation of damages in this case. The Court finds that Dr. McClave is qualified as an expert to supply such testimony.

2. Dr. McClave's Model

Dr. McClave developed a multiple regression model to forecast competitive prices during the class period.^[7] Regression analysis is a well-worn statistical technique used in a variety of contexts to examine the nature of the relation, if any, between two or more variables. See City of Tuscaloosa, 158 F.3d at 566; Engineering Contractors Ass'n of South Florida, Inc. v. Metropolitan Dade County, 122 F.3d 895, 917 (11th Cir.1997); Petruzzi's IGA Supermarkets, Inc. v. Darling-Delaware Co., 998 F.2d 1224, 1237-38 (3d Cir. 1993); In re Polypropylene Carpet Antitrust Litig., 996 F. Supp. 18, 26 (N.D.Ga. 1997). A regression model is an equation that seeks to account for the major independent influences on the dependant variable —the variable that is estimated or forecast by the model—in order to arrive at a reliable prediction of the dependant variable. Hoffman, supra, at 350; Rubinfeld, supra, at 425.

Inclusion of irrelevant variables or omission of relevant variables is to be avoided. Kennedy, supra, at 69. Econometricians use economic theory along with statistical techniques to identify the correct set of explanatory variables for a particular model. Kennedy, supra, at 69. With respect to changes in prices, changes in costs are one obvious explanatory variable.

The dependant variable in this model consists of a ratio of market price over a measure of fiber costs. The factors used by Dr. McClave to predict the value of the dependant variable are: the manufacturing style of the carpet, the selling style of the carpet, the shipping point of the carpet, and the quantity of carpet ordered. (McClave Expert Report at 5.) Because the price of cut portions of carpet are typically higher than prices for rolls of carpet, Dr. McClave estimated two separate models for each Defendant, one for rolls and one for "cuts." (Id. at 7-8.)^[8]

Using these models to estimate competitive prices during the class period, Dr. McClave estimates an average overcharge of 8.3 percent by Defendants during the class period. (McClave Rbtl. Report at 20.) Applying this figure to all class purchases during the relevant time period, Dr. McClave estimates that Defendants overcharged Plaintiffs in the amount of $222,963,542.00. (Id.)

Defendants suggest three factors by which to evaluate the reliability of Dr. McClave's multiple regression analysis: (1) the assumptions upon which the model is predicated; (2) whether the model accounts for the major factors that affect the dependant variable; and (3) the data used by Dr. McClave. Defendants contest both the data used by Dr. McClave to conduct his analysis and the design and assumptions of Dr. McClave's regression model.

a. Assumptions of the Model

1. Specification of Dependant Variable as Price over Fiber Cost

Defendants argue that Dr. McClave's model is flawed and unreliable because it specifies as the dependant variable a ratio of price over a measure of fiber cost.^[9] Defendants maintain that specification of the dependant variable in this manner generates damages because changes in the ratio can result from increases in fiber costs, a change which has nothing to do with collusive activity.

The dispute in this case over the dependant variable primarily concerns how Dr. McClave incorporates the influence of costs on prices in his model. The parties agree that polypropylene fiber costs account for a significant portion of the cost of manufacturing polypropylene carpet — up to seventy percent of total costs depending upon the style. (2/2 Tr. at 209.) Changes in the cost of fiber thus have a large influence on changes in the price of polypropylene carpet.

Dr. McClave's model, however, does not identify polypropylene costs as an independent variable. Rather, Dr. McClave specified the ratio of polypropylene carpet price over a measure of polypropylene fiber costs as his dependant variable.

Three reasons support Dr. McClave's decision not to use costs as an independent variable. First, there is limited data by which to estimate the relation between price and cost in the benchmark period. (1/31 Tr. at 173.) Second, the difference in values for certain measures of fiber costs between the benchmark and the class period raised the prospect of an extrapolation error.^[10] (Id. at 176.) Third, there exists a concern that changes in the ostensible dependent variable, price of polypropylene carpet, may affect the value of the cost of polypropylene fiber. (Id. at 181.) There are a number of names for this concern, including endogeneity or simultaneity. See Rubinfeld, supra, at 432 & n. 40. All of these factors would affect the reliability of the results of a model that specified as an independent variable the measure of polypropylene fiber costs used by Dr. McClave.

Defendant Beaulieu challenges Dr. McClave's conclusion that the data is insufficient in the benchmark period to estimate the relation between cost and price. Dr. McClave performed an analysis called a "Chow test" of one of Defendant's expert's models, probably to examine whether the value of a coefficient used in the model remained constant between the benchmark period and the class period. See Kennedy, supra, at 74-76 (discussing risks of assumption that coefficient of independent variable remains constant over time). Based on Dr. McClave's analysis, Defendant Beaulieu argues that enough data must exist in the benchmark period to use cost as an independent variable. (Beaulieu's Reply at 8.) Use of data from the benchmark period in a Chow test, however, does not establish that enough data exists to reliably estimate the relation between cost and price in the benchmark period. See Kennedy, supra, at 87-88 (discussing Chow test). In other words, the reliable estimation of a coefficient is a completely different task from testing whether the coefficient is unchanged from one data set to the next. Moreover, Defendants do not challenge Dr. McClave's conclusion that endogeneity between fiber costs and polypropylene carpet price as well as the potential extrapolation problem weigh against use of fiber cost as an independent variable.^[11]

Whatever the reasons for designating price over fiber costs as the dependant variable, Defendants contend that this relationship assumes that the price of polypropylene carpet moves in lockstep with changes in the price of polypropylene fiber, an assumption that Defendants argue has no likeness in economic reality. Stated another way, Defendants contend that changes in fiber costs do not necessarily correspond with changes in the remaining variable costs of producing polypropylene carpet. Defendants illustrate their argument with a variety of simple mathematic examples, but the upshot is that in order for the ratio of prices over fiber costs to remain the same over time, increases in fiber costs must accompany even greater increases in price.^[12] Because prices do not increase (or decrease) in this manner, Defendants argue that Dr. McClave's model is unreliable.

Defendants' argument assumes that when fiber costs increase, the remaining costs of producing polypropylene carpet remain fixed or do not increase in a similar fashion. In fact, there is evidence that other variable costs of producing carpet increased along with fiber costs during the relevant time period. See (Pl.'s Daubert Ex. 110) (graph showing steady increase in labor costs from class to benchmark periods).^[13] As long as changes in fiber costs reflect the changes in the variable costs of producing polypropylene carpet, Defendants' argument has little force.

Indeed, changes in fiber costs during the relevant time period reflect changes in the total variable cost of producing polypropylene carpet. Dr. McClave chose fiber costs as a proxy for marginal cost, the cost of producing one more unit of production. See (McClave Rbtl. Report at 5); Jeffrey M. Perloff, Microeconomics 200 (1999) ("A firm's marginal cost (MC) is the amount by which a firm's cost changes if the firm produces one more unit of output."). Dr. McClave was not concerned with the value of fiber costs, but whether changes in fiber costs accurately reflected changes in marginal costs over time. (2/1 Tr. at 140.)

To test whether changes in fiber cost reflect changes in the variable cost of producing carpet — and therefore changes in marginal cost — Dr. McClave constructed an index of polypropylene carpet costs. Dr. McClave called this index the Marginal Cost Index ("MCI"), and used data supplied by the Bureau of Labor Statistics ("BLS"). (Pl.'s Daubert Ex. 70.) Because fiber costs account for seventy-three percent of costs in the MCI, changes in fiber costs unsurprisingly correlate highly with changes in the MCI. (Pl.'s Daubert Ex. 74.)

Setting aside for the moment Defendant Shaw's challenge to Dr. McClave's use of BLS data, the comparison of the BLS index for fiber costs and the MCI suggests that changes in fiber costs reflect changes in the variable cost of producing polypropylene carpet. Indeed, Defendant Shaw's internal cost data appears to show the same thing. The shape of the graph illustrating changes in Defendant Shaw's fiber cost for one carpet style, Volunteer 20, closely mimics the shape of the graph showing changes in Defendant Shaw's average costs for producing polypropylene carpet. (Def. Shaw's Daubert Ex. 27.) These results are to be expected because fiber costs account for such a great percentage of total polypropylene carpet costs. The similar shape of the graphs also suggests that changes in Defendant Shaw's remaining variable costs, perhaps due to technological improvements, did not significantly affect the high correlation between changes in fiber costs and changes in total variable costs.

Finally, Plaintiffs have explained why economic theory predicts that the ratio between price and marginal cost may be greater in a collusive environment compared to the ratio in a competitive environment. In a perfectly competitive environment, the profit-maximizing price equals marginal cost. (2/3 Tr. at 42); 3 Phillip Areeda and Herbert Hovenkamp, Antitrust Law ¶ 753b2 (Rev. ed.1996). In such an environment, firms continue to expand production until their return in revenue no longer exceeds the cost of producing the next unit of production.

In the real world, market forces put pressure on the relation between price and marginal cost to tend toward some optimal level. (2/1 Tr. at 92-93; 2/3 Tr. at 230-32.) Moreover, prices reflect changes in marginal cost. (1/31 Tr. at 146-47; 2/3 Tr. at 180.) In an environment with little competition, however, firms naturally can charge relatively higher prices in relation to costs. (Zona Rbtl. Report at 5 & n.6); see also 2A Areeda and Hovenkamp, supra, ¶ 507b (discussing relationship between demand elasticity and the Lerner Index — the excess of price over marginal cost as proportion of price, a measure of a firm's ability to price profitably above marginal cost). "Accordingly, non-competitive performance could be indicated by prices greater than marginal cost ...." 6 Areeda and Hovenkamp, supra, ¶ 1431c.^[14] Dr. McClave's model purports to identify and account for the non-collusive factors that affect this relationship in the class and benchmark periods.

In sum, Plaintiffs have adduced sufficient evidence to support the idea that changes in fiber cost reflect changes in the variable costs of producing polypropylene carpet. The Court also finds that Plaintiffs have adequately explained the rationale behind use of the ratio of price to fiber cost as the dependant variable in Dr. McClave's model. Lastly, the Court believes that use of this ratio as the dependant variable, in itself, does not render Dr. McClave's model unreliable.

2. Relationship in Movement of Prices Between Carpet Styles

Defendant Beaulieu argues that Dr. McClave's model assumes that the prices of different carpet styles move in the same direction. At the hearing, Defendant Beaulieu presented a graph which suggests that the prices of 20 ounce level loop carpet, grass styles, and Berber styles often do not correlate with each other. (Def. Beaulieu's Daubert Ex. B18.)

Dr. McClave's model does not assume that the prices of carpet styles move together; it includes independent variables for manufacturing and selling styles. (McClave Rbtl. Report at 19-20.) The Court finds no evidence that Dr. McClave's model assumes a structural relationship between the modeled carpet styles, or that the differing prices between carpet styles would affect the reliability of the model. The Court therefore overrules this objection.

3. Dates of Benchmark Period

The class period in this case extends from July 1991 through June 1995. (McClave Report at 3.) The benchmark period begins on July 1, 1995, and extends to June 30, 1998. (Id. at 4.) The beginning of the benchmark period corresponds with the guilty plea of Johnny West, an alleged participant in the price-fixing scheme. Defendants argue that Dr. McClave should have divided the class and benchmark periods in June 1994, to correspond with a grand jury investigation into alleged price-fixing.

The Court overrules this objection. Dr. McClave's failure to incorporate data from June 1994 to July 1995 in the so-called benchmark period does not suggest that the data used to design Dr. McClave's model is unreliable. As long as the model incorporates the most significant explanatory variables that affect the price of polypropylene carpet, the model should be able to identify whether the alleged conspiracy, if it existed, had any affect on prices between June 1994 and July 1995. If the alleged conspiracy collapsed in the wake of the grand jury investigation, the model should show that too. The Court therefore concludes that Dr. McClave's decision to frame his analysis by the date that Mr. West entered a guilty plea does not implicate the methodological reliability of his model.

Additionally, Dr. McClave use of the July 1, 1995, date is consistent with the class allegations in this case. Dr. McClave's analysis therefore is designed to be relevant to the issues before the fact-finder. The Court thus rejects Defendants' arguments concerning the date of the benchmark period.

4. Use of Logarithm and "Overcharges" in Benchmark Period

Defendant Shaw argues that Dr. McClave's use of logarithms in his model poses some risk of unreliability. Other than the possibility that use of logarithmic functions may have produced "overcharges" in the benchmark period, however, Defendant Shaw does not specify why logarithmic functions are inappropriate in this case.

Logarithms are commonly used in regression analysis when, for example, a logarithmic function better expresses the relationship between an independent variable and the dependant variable. Hoffman, supra, at 346; Rubinfeld, supra, at 449 n. 58. The use of a logarithm, in itself, raises no inherent danger that the results of the regression analysis will be unreliable.

As for "overcharges" in the benchmark period, Dr. McClave's model estimates "overcharges" of 0.5 percent for Defendant Shaw, 0.8 percent for Defendant Mohawk, and 0.1 percent for Defendant Beaulieu. (McClave Report at 10.) Dr. McClave explains that these overcharges result from the fact that "high volume transactions were, on average, subjected to higher margins on a per unit basis than low volume transactions. Thus, the weighted average of the residuals (which, unweighted, sum to zero) remains positive during the benchmark period." (McClave Rbtl. Report at 11; 7/1/99 McClave Dep. at 59-60.) Defendant Shaw's expert, Dr. Rubinfeld, suggests that these overcharges provide a basis for adjusting Dr. McClave's damages estimate. Even if the finding of an overcharge in the benchmark supports an adjustment of the alleged overcharge in the class period — an issue that Defendants can argue about later — the Court finds that the model's estimate of minimal overcharges in the benchmark period does not establish that Dr. McClave's methodology is unreliable. The Court therefore overrules these objections to the admissibility of Dr. McClave's testimony.

5. Examination of History of Dr. McClave's Analysis

Defendant Shaw argues that Dr. McClave's model is unreliable because Dr. McClave destroyed notes, internal memoranda, communications with counsel, and other documents generated during the course of his analysis. The Court overrules this objection.

This argument is recycled from a discovery dispute that the Court resolved last summer. In the Order disposing of this issue, the Court found that Defendant Shaw had failed to adduce evidence to "indicate that Dr. McClave or his employees engaged in a scheme to deprive Defendants of necessary information." (Order of June 10, 1999, at 5.) The Court sees no reason to revisit this issue at this time.

Furthermore, Defendant Shaw's objection does not impugn the reliability of Dr. McClave's model; instead, Defendant Shaw's argument suggests that it might be able to establish the unreliability of the model if only it had additional information. Defendants, however, have had ample opportunity to examine the methodology and reasoning underlying Dr. McClave's analysis. The Court therefore overrules this objection.

b. Accounting for Major Independent Variables

1. Exclusion of Demand Variable

Defendants also make a more familiar challenge to the reliability of Dr. McClave's model — that it omits important explanatory variables. Defendants argue that omission of a variable for demand in Dr. McClave's model demonstrates that the model is unreliable. Defendant Shaw maintains that because Dr. McClave's model does not consider demand, the model does not consider downward pressures on price such as the growing popularity of non-carpet substitutes during the relevant period, Defendant's Shaw's entry into the retail market, and shifts in the popularity of carpet products.

In Bazemore v. Friday, the Supreme Court addressed whether a multiple regression analysis is admissible when it does not consider potential variables that may have an effect on the object of the analysis. 478 U.S. 385, 400, 106 S. Ct. 3000, 92 L. Ed. 2d 315 (1986). Although some regression models may be so "incomplete as to be inadmissible as irrelevant," the Supreme Court found that "[n]ormally, failure to include variables will affect the analysis' probativeness, not its admissibility." Id. at 400 & n. 10, 106 S. Ct. 3000. Unless the party challenging a regression model proffers evidence that an omitted variable "is correlated with the dependant variable and is likely to affect the result of the regression analysis," the Court will not find that omission of the variable implicates the reliability of the model. Estate of Bud Hill v. ConAgra Poultry Co., No. 94-CV-0198, 1997 WL 538887, at *8 (N.D.Ga. Aug. 25, 1997). Merely pointing to economic conditions that may affect the dependant variable is not enough to call into question the reliability of an econometric model. See id. at *7; In re Industrial Silicon Antitrust Litig., Nos. 95-2104, 95-1131, 96-2003, 96-2111, 96-2338, 1998 WL 1031507, at *3 (W.D.Pa. Oct.13, 1998).

Dr. McClave states that he omitted a variable for demand for reasons similar to his decision not to use a variable for cost as an independent variable: lack of data and the risk of extrapolation error. (2/1 Tr. at 54.) Furthermore, when Dr. McClave attempted to test the relation between demand and price, the results were inconsistent with the basic economic principle that increases in demand result in increases in price. (Id. at 55.)

Between the class and benchmark periods, demand for polypropylene carpet was increasing. (Pl.'s Daubert Ex. 69.) Defendant's expert, Dr. Rubinfeld, agrees. (2/3 Tr. at 169.) Accordingly, Dr. McClave's model does not ignore a factor that would tend to put a downward pressure on prices in the benchmark period compared to the class period. Cf. In re Aluminum Phosphide Antitrust Litig., 893 F. Supp. 1497, 1504 (D.Kan.1995) (finding unreliable a regression model that omitted factors, such as declining demand, that tended to reduce prices in benchmark period). In fact, when Dr. McClave attempted to include a variable to account for aggregate demand, his estimate of damages increased. (Pls.' Daubert Ex. 79.)

More importantly, Defendants do not offer a statistical analysis of demand and price of polypropylene carpet to explain why exclusion of a variable for demand establishes the unreliability of Dr. McClave's model. Similarly, Defendant Shaw does not relate its evidence concerning the increase in popularity of non-carpet flooring products or the increase in buying groups to the overall demand for polypropylene carpet, the prices of carpet products included in Dr. McClave's model, or alleged changes in the price elasticity of demand. (Def. Shaw's Daubert Ex. 5, 6.)^[15]

Defendant Shaw does provide a graph that compares its total sales with sales of the carpet styles modeled by Dr. McClave. (Def. Shaw's Daubert Ex. 27.) The graph of total sales, however, contains carpet styles that are not at issue in this case. Furthermore, the removal of filters from Dr. McClave's model does not significantly alter the damages estimate. (McClave Rbtl. at 10; Pl.'s Daubert Ex. 79) (removal of all filters increases estimation of damages by .1 percent). Finally, Defendant Shaw does not proffer evidence that the alleged reduction in demand for the modeled styles during the benchmark period correlates with the dependant variable and is likely to affect the result of Dr. McClave's analysis. See Estate of Bud Hill, 1997 WL 538887, at *7-8. For these reasons, the Court overrules Defendants' objections based on Dr. McClave's failure to incorporate a variable for demand in his model.

2. Failure to Include Variables Identified at Class Certification Stage

Defendant Beaulieu argues that Dr. McClave's model is unreliable because it differs from the description of the regression model offered by Plaintiffs at the class certification stage. The Court rejects this argument.

Sound econometric practice requires the identification of potential independent variables "before any empirical testing of the appropriateness of potential independent variables." Kennedy, supra, at 69. Statistical techniques then help determine which variables to include in the model. The fact that Plaintiffs' regression model has evolved since the class certification stage raises no serious issue, so long as the model satisfies Plaintiffs' burden under Rule 23 as they represented at the class certification hearing, and is otherwise reliable.

3. Macroeconomic Factors, Bargaining Power, and Capacity Utilization

Defendant Shaw argues that factors "such as levels and changes in income, interest rates or business cycle characteristics; capacity utilization; Shaw's entry into the retail business; and the growing power of buyers throughout the 1990's" all could account for changes in margins between the class and benchmark periods. (Def. Shaw's Mot. Exclude McClave Testimony at 38.) These observations, based on Dr. Rubinfeld's expert rebuttal report, are free of any attempt to estimate whether these factors actually had an impact on margins during the benchmark or class periods, or whether the impact was statistically or practically significant. (7/7/99 Rubinfeld Dep. at 215-16, 221.)

As a result, Defendant Shaw's catalogue of potentially important considerations do not support a finding that Dr. McClave's analysis is unreliable. See Estate of Bud Hill, 1997 WL 538887, at *8. In other words, Defendant Shaw's arguments fail to call Dr. McClave's methodology "sufficiently into question" for the Court to determine that exclusion of these considerations renders the model unreliable. See Kumho, 526 U.S. at 149, 119 S. Ct. 1167. The Court therefore overrules these objections to the admissibility of Dr. McClave's testimony.

c. Data Used in Dr. McClave's Model

1. Aggregation of Quarterly Transaction Data and Exclusion of Data

Defendants argue that Dr. McClave's model is unreliable because it excludes a large amount of data. Additionally, Defendant Shaw contends that the model "aggregates data excessively."

Dr. McClave excluded a large portion of data from his analysis by imposing filters that, for example, required manufacturing and selling styles to have at least thirty quarterly transactions for at least three quarters during the benchmark period. (McClave Report at 7.) Furthermore, Dr. McClave limited the data to styles that showed sales in both the benchmark and class periods. (Id.) Dr. McClave also excluded custom carpet styles, grass styles, and transactions identified as sales to Defendants' mills or employees. (Id.)

Exclusion of outliers is a common practice in statistical analysis. Moreover, removing the filters from Dr. McClave's model does not significantly alter Dr. McClave's damage estimate. (McClave Rbtl. at 10; Pl.'s Daubert Ex. 79) (removal of all filters increases estimation of damages by .1 percent). The Court thus finds that Dr. McClave's exclusion of data is not a source of unreliability.

With respect to the aggregation of data, Defendant Shaw asserts that averaging a customer's transactions for a given style in a particular quarter "distorts the highly individualized nature of this market." (Def. Shaw's Mot. at 37.) Defendant Shaw relies upon Dr. Rubinfeld's expert report for this conclusion. Dr. Rubinfeld warns that aggregating quarterly transactions overlooks "the possibility that a customer can negotiate price based on its purchases of a style at every location the customer operates, at every point the supplier ships from, or even more plausibly, based on the customer's total purchases of all styles from the supplier." (Rubinfeld Report at 31.) Dr. Rubinfeld is "troubled" by this point, but has conducted no empirical analysis to determine if in fact the aggregation of quarterly transactions results in any significant bias. (7/7/99 Rubinfeld Dep. at 97.) For this reason, the Court declines to find that Dr. McClave's model is unreliable because of the aggregation of quarterly transactions, notwithstanding Dr. Rubinfeld's concerns. See Estate of Bud Hill, 1997 WL 538887, at *8.

2. Use of Polypropylene Fiber Producer Price Index (PPI) as measure of Fiber Cost

The PPI is an industry-wide index of the cost of polypropylene fiber published by the U.S. Bureau of Labor Statistics ("BLS"). The BLS publishes producer price indices measuring changes in price for virtually the entire spectrum of output by U.S. producers. Bureau of Labor Statistics, Frequently Asked Questions (last modified Oct. 7, 1999) http://stats.bls.gov/ppifaq.htm# 1>. As a general matter, these producer price indices are a common source of data used by economists and econometricians. (1/31 Tr. at 144; 2/3 Tr. at 59, 158.)

Defendant Shaw challenges Dr. McClave's selection of the PPI to measure changes in fiber costs during the class and benchmark periods, arguing that Dr. McClave should use Defendant Shaw's internal cost data in his analysis. The decision to use the PPI rather than Defendant Shaw's internal cost data is a significant one, because use of Defendant Shaw's data in Dr. McClave's model reduces Defendant Shaw's alleged overcharges by 87 percent. (Rubinfeld Report at 28, Ex. 6; 2/3 Tr. at 90.) The PPI clearly does not correlate highly with Defendant Shaw's internal measure of fiber costs or total variable costs. (Def. Shaw's Daubert Ex. 27.)

Defendant Shaw contends that econometricians must use firm-specific cost data when available. (Def. Shaw's Post-Hr'g Br. at 10) (citing Matsushita Elec. Indus. Co. v. Zenith Radio Corp., 475 U.S. 574, 106 S. Ct. 1348, 89 L. Ed. 2d 538 (1986)). The use of industry-wide indices, Defendant Shaw argues, may ignore firm-specific efficiencies and technological advances that reduce costs. (Decl. of Daniel L. Rubinfeld at 1.) Specifically, Defendant Shaw argues that the PPI misrepresents Defendant Shaw's costs by failing to account for technological change at Defendant Shaw's manufacturing plants and the purchase of a yarn extrusion facility in 1992.^[16]

The Court finds, however, that Plaintiffs have established by a preponderance of evidence that Dr. McClave's use of the PPI for polypropylene fiber has a reliable basis in the knowledge and experience of econometrics. Federal Rule of Evidence 703 authorizes experts to base an opinion upon data that itself is not admissible if the data is "of a type reasonably relied upon by experts in the particular field in forming opinions or inferences upon the subject." Fed.R.Evid. 703. If the reliability of this data is sufficiently at issue, however, the Court must determine whether the expert's testimony has "a reliable basis in the knowledge and experience of [the relevant] discipline." Kumho, 526 U.S. at 149, 119 S. Ct. 1167 (quoting Daubert, 509 U.S. at 592, 113 S. Ct. 2786).

As an initial matter, Matsushita does not support the proposition that econometricians who wish to testify as experts in federal court must choose firm-specific data over industry-wide indices when such data is available. First, the portion of Matsushita cited by Defendant Shaw addresses whether an expert economic report proffered by the plaintiffs in that case was sufficient to withstand summary judgment; the admissibility of the report was not before the Court. 475 U.S. at 594 n. 19, 106 S. Ct. 1348; see also In re Visa Check/MasterMoney Antitrust Litig., No. 96-CV-5238, 2000 WL 220507, at *7 n. 6 (E.D.N.Y. Feb.22, 2000) (distinguishing Matsushita on this ground). Second, the Supreme Court simply concurred with the conclusion that the expert report rested upon assumptions about the defendants' actual costs that were "implausible and inconsistent with record evidence." 475 U.S. at 594 n. 19, 106 S. Ct. 1348. The Supreme Court made no observation about the use of industry-wide data or firm-specific data for purposes of economic analysis.

In fact, firm-specific accounting data may not provide information that is relevant to economic analysis. 2A Areeda and Hovenkamp, supra, ¶ 520a (discussing deficiencies in accounting data, particularly accounting profits); cf. (Pl.'s Daubert Ex. 34) (internal memo describing new formula for calculating margins). For example, accounting costs do not include opportunity costs that are important to economists. Id. ¶ 520a; (2/3 Tr. at 195.) The Court therefore rejects the argument that firm-specific data necessarily is more appropriate than industry-wide data for purposes of economic analysis.

With respect to Defendant Shaw's internal cost data, Plaintiffs argue that the data is unreliable because of evidence that Defendant Shaw made adjustments to the costs recorded in its internal cost records. (Pl.'s Daubert Exs. 30, 32, 33.)^[17] Plaintiffs also note that Defendant Shaw's data occasionally lists different costs for transactions involving the same carpet style on the same day. (McClave Decl. ¶ 4.)

This evidence is unpersuasive. Plaintiffs have not shown that adjustments to the cost data or different prices listed for the same carpet products would affect the reliability of a damages estimate using this data. Furthermore, Defendant Shaw has demonstrated that this evidence relates to a very small portion of the data set, and would not affect a statistical analysis based on this data. (Rubinfeld Decl. ¶ 19.) Defendant Shaw also has adduced evidence that carpet prices are set according to the date of an order, which explains why prices of the same product listed on the same day in a cost sheet may differ. (2/3 Tr. at 70.)

Plaintiffs also argue that use of Defendant Shaw's data is inappropriate because no firm-specific costs are available from the other defendants, and Defendant Shaw's costs could not be used in an analysis of Defendant Mohawk or Defendant Beaulieu. The lack of data availability for the other Defendants in this case, however, provides no basis for using cost figures that may be disadvantageous and inaccurate with respect to Defendant Shaw.

Nonetheless, the Court believes that Dr. McClave's decision to use the PPI instead of Defendant Shaw's cost figures is based upon sound econometric practice and experience. First, Defendant Shaw's internal costs show a steep decline between the last quarter of 1992 and the first quarter of 1993 that may reflect an internal accounting change. Second, Defendant Shaw's costs may not be a good proxy for marginal costs. Third, Defendant Shaw has not shown that technological improvements in polypropylene carpet production undermine the reliability of the PPI for polypropylene fiber as applied to Defendant Shaw.

Defendant Shaw does not dispute the fact that an accounting change would make Defendant Shaw's costs inappropriate for use in Dr. McClave's analysis. (2/3 Tr. at 197-98.) Instead, Defendant Shaw argues that the steep decline in costs accurately reflects the reduction in costs obtained after purchase of a yarn extrusion facility and through technological improvements. (Cook Aff. ¶ 5.)

Defendant Shaw purchased a yarn extrusion facility in the fall of 1992. (2/2 Tr. at 171, 209.) According to Defendant Shaw, the purchase of this facility significantly reduced Defendant Shaw's fiber costs.

Defendant Shaw's non-fiber related costs at its Winchester, Tennessee, facility also experienced a steep decline during this period. (Prater Aff. Ex. 1.) Defendant Shaw argues that concurrent technological improvements at the facility caused this reduction in non-fiber costs. No similar reduction in costs, however, accompanied subsequent technological improvements at the Winchester facility. (2/2 Tr. at 221-23.) The absence of similarly dramatic changes in Defendant's non-fiber costs from the steady installation of newer and faster machines during the 1990's belies Defendant Shaw's argument that the steep decline in non-fiber costs in the first quarter of 1993 is due to technological change.

Plaintiffs have also adduced evidence that in the last quarter of 1992, Defendant Shaw decided to "standardize [its] costing policy" with respect to yarn obtained from its newly-purchased extrusion facility and yarn from an existing plant. (Pls.' Daubert Ex. 92.) Defendant Shaw denies that any accounting change resulted in the reduction in costs. (Aff. of Don Cook ¶¶ 1-2, 5.)

Even apart from this issue, however, Defendant Shaw's internal cost data is not necessarily the best measure of marginal cost. Marginal cost is an accounting concept not found in business accounts. 2A Areeda and Hovenkamp, supra, ¶¶ 504b, 1431c; (2/3 Tr. at 181.) Moreover, marginal cost does not include fixed costs that do not vary with small changes in production. 2A Areeda and Hovenkamp, supra, ¶ 504b.

Marginal cost normally cannot be measured at all, but rather only proxied for by average variable cost. This typically is a legitimate practice if marginal cost is roughly constant, which commonly is the case. Nevertheless, a measure of actual production costs, even the incremental cost of producing the last unit, may not be a valid indication of economic marginal cost. The relevant cost concept is opportunity cost. The opportunity cost of a variable input may exceed its accounting cost if, due to scarcity, it is valued in alternative uses at more than its accounting cost.

Gregory J. Werden, Demand Elasticities in Antitrust Analysis, 66 Antitrust Law Journal 363, 394 (1998); accord (2/3 Tr. at 194-95.) A firm's measure of its own costs thus may not provide a workable proxy for marginal costs, and may even be affected by the existence of a price-fixing conspiracy. Id. ¶ 521;; (McClave Decl. at 3 n.4.)^[18] "Consequently, persistent and substantial differences between price and marginal cost strongly suggest either that excess returns have in fact been earned or that they could have been earned even though the books show otherwise." 2A Areeda and Hovenkamp, supra, ¶ 521.

Defendant Shaw argues, however, that use of the PPI for polypropylene fiber fails to account for significant reductions in its costs resulting from technological improvements in the carpet industry. (2/3 Tr. at 104-05.) In fact, econometricians have long recognized the importance of understanding the effect of technology because it implicates a change in the relationship between inputs and production. See Desai, supra, at 137-67 (discussing ways to account for technological change); M. Hashem Pesaran and Peter Schmidt, Introduction, Handbook of Applied Econometrics Volume II, 1-2 (1997).

The PPI for fiber, however, is likely to reflect some of the technological advancements in the production of fiber. (2/3 Tr. at 161-62, 193.) Furthermore, Defendant Shaw has failed to proffer statistical or other evidence that technological improvements made such dramatic changes in variable costs other than fiber that changes in fiber costs do not reflect changes in variable costs. See supra Part III.B.2.a.1. While Dr. Rubinfeld suggests that technological improvements in the carpet industry resulted in reductions in labor costs, (2/3 Tr. at 29), in fact Defendant Shaw did not reduce its labor force as a result of technological improvements, and labor costs steadily increased from 1993 through 1998. (2/2 Tr. at 224; Pls.' Daubert Ex. 110.)

In sum, even if Defendant Shaw did not alter its accounting methods, Plaintiffs have adduced sufficient evidence that Dr. McClave's decision not to use Defendant Shaw's internal costs was reasonable and grounded in the knowledge and experience of econometrics. The Court also finds that Plaintiffs have adduced sufficient evidence to support Dr. McClave's use of the PPI for polypropylene fiber in his model. The Court therefore overrules Defendant Shaw's objection based upon use of the PPI for polypropylene fiber.

IV. Conclusion

ACCORDINGLY, the Court GRANTS IN PART AND DENIES IN PART Defendant Beaulieu of America's Motion to Exclude Testimony of David R. Kamerschen and James T. McClave [340], GRANTS IN PART AND DENIES IN PART Motion by Defendants Mohawk Industries, Inc., and Aladdin Mills, Inc., to Exclude Expert Testimony of Dr. James T. McClave and Dr. David R. Kamerschen [341], DENIES Motion of Shaw Industries, Inc., to Exclude Certain Opinions of Dr. James T. McClave [343], and GRANTS IN PART AND DENIES IN PART Motion of Shaw Industries, Inc., to Exclude Portions of the Testimony of Professor David R. Kamerschen [345]. The Court grants in part and denies in part Defendants' Motions with respect to certain testimony by Dr. Kamerschen, and denies Defendants' Motions with respect to the testimony of Dr. McClave.

NOTES

[1] This does not mean, of course, that Dr. Kamerschen cannot testify concerning the scope of his assignment, the temporal focus of his analysis, or the identity of producers in the market.

[2] Plaintiffs do not offer Dr. McClave for the purpose of expressing opinions on the existence of a conspiracy to fix prices, testimony that in any case the Court would find inadmissible.

[3] Although Clinchfield was decided prior to Daubert, the Court of Appeals for the Fourth Circuit properly focused on Federal Rule of Evidence 703 to determine whether to admit opinion testimony based on census data. 784 F.2d at 553-54.

[4] Dr. Kamerschen examined the data to support his opinion that demand is relatively inelastic and his conclusion that polypropylene carpet constitutes a separate market from other carpet products. (Kamerschen Report at 13; Kamerschen Rbtl. Report at 7, 15.)

[5] Dr. Kamerschen adjusted the census data based upon conversations with unnamed Bureau of Census employees. (2/2 Tr. at 124-26.) The Court does not believe that Dr. Kamerschen's modifications based on these conversations repair the data such that it may be used for any specific calculation of Defendants' market shares.

[6] The Court rejects Defendants' argument that Dr. Kamerschen must conduct an independent review of Dr. McClave's statistical analysis, as opposed to the economic reasoning behind Dr. McClave's model, before he can rely upon Dr. McClave's analysis. (2/2 Tr. at 99-100.) Such a requirement imposes an undue restriction on expert testimony, and is not consistent with Rule 703.

[7] The Court rejects Defendant Beaulieu's argument that Dr. McClave conducted not a multiple regression analysis, but "an analysis of variance [ANOVA] or Cell Means model." (Def. Beaulieu's Mot. Exclude at 30.) There is wide agreement that Dr. McClave used multiple regression analysis to construct his model, and Defendant Beaulieu has not mentioned this argument since its opening brief.

[8] Dr. McClave represents that his models have high R2 values. (McClave Report at 8-9 & App. D.) A high R2 indicates that the independent variables in a model are very good at accounting for the dispersion of the observed values of the dependant variable around its mean, one measure of the degree of association between independent variables and the dependant variable. Paul J. Hoffman et al., Guide to Regression Analysis, Expert Evidence 337-39 (1997); Daniel L. Rubinfeld, Reference Guide on Multiple Regression, Reference Manual on Scientific Evidence 456-57 (Federal Judicial Center 1994). Defendants do not challenge this or other statistical properties of Dr. McClave's model.

[9] The Court addresses Dr. McClave's selection of the measure of fiber costs infra Part III. B.2.c.2.

[10] Such an error may occur, for example, in a model that attempts to predict the growth rate in the height of a seventy-year-old person by looking at data from when the person was thirteen years old.

[11] Dr. Rubinfeld testified at the hearing that an alternate technique, called instrumental variable estimation, may be used to estimate the relationship between a dependant variable and an endogenous explanatory variable. (2/3 Tr. at 136-37.) Defendants opted not to raise this point in their briefs. In any case, instrumental variable estimation raises its own complications. See Kennedy, supra, at 115, 133-34.

[12] Specifically, for the ratio to remain constant when fiber costs increase, price must increase by the amount of increase in fiber costs multiplied by the ratio of price over fiber costs.

[13] Defendant Shaw has submitted graphs that illustrate the change in total manufacturing costs other than raw materials at a manufacturing plant located in Winchester, Tennessee. (Aff. of Roger Welch Ex. 2; Aff. of Jim Prater Ex. 1.) The graphs indicate a steep decline in costs between the third or fourth quarter of 1992 and the first quarter of 1993, followed by relatively stable costs through 1998. (Welch Aff. Ex. 2; Prater Aff. Ex. 1.) Not limited to variable costs, the graphs include fixed costs and reflect changes in the product mix at the Winchester plant to focus on cheaper, more "manufacturing-friendly" products. (2/3 Tr. at 214, 216-17.)

[14] The Court is mindful of the distinction between examining changes in the ratio of price over a marginal cost proxy, at issue in this case, and concluding that anti-competitive behavior exists simply because prices may exceed a surrogate for marginal cost. See 6 Areeda and Hovenkamp, supra, ¶ 1432d2.

[15] Defendant Shaw also cites to Exhibit 7, which was not admitted into evidence at the hearing. (Def. Shaw's Post-Hr'g Br. at 18.)

[16] Dr. Rubinfeld also criticized use of the PPI for polypropylene fiber based on a conversation he had with a BLS employee. (2/3 Tr. at 61-62.) Defendant Shaw does not raise this argument in its post-hearing brief.

[17] The Court does not consider cost sheets labeled "Estimate," because these cost sheets may not refer to actual cost data of the carpet products at issue. (2/3 Tr. at 80.)

[18] Defendant Shaw criticizes the "lazy monopolist" theory, which predicts that a firm may operate inefficiently due to the absence of a competitive environment. Nevertheless, the Court believes that the theory remains a consideration that is grounded in the knowledge of the relevant field. 2A Areeda and Hovenkamp, supra, ¶ 521 (citing lack of competition as reason that accounting profits might reflect lack of incentive to engage in cost-cutting).