# Regression Analysis in Antitrust Litigation and the Potential Biases Caused by Omitted Factors

One of the most relied upon statistical tools implemented by economists is regression analysis, a method with which to study the relationship between a variable of interest and “additional explanatory variables that are thought to produce or be associated with changes in the variable of interest.”[1] Using this tool, theoretical relationships can, with a properly specified regression model, be measured and quantified.[2] Regression analysis can be particularly useful in the context of antitrust litigation. Economic experts are often called upon to assist in these proceedings to assess what effect, if any, the alleged conduct had. For example, in cases involving anticompetitive conduct such as attempted monopolization or price fixing, an economist may test whether the alleged conduct elevated prices to plaintiffs.[3]

In the context of assessing antitrust impact in a price-fixing case, a regression can be used to model the relationship between the prices actually paid by plaintiffs (using historical transaction data) and the supply and demand conditions that affected those prices over time. However, real-world markets are complex, and those supply and demand conditions may be constantly changing. As a result, the economist must take care to properly identify the relevant factors that affect prices.[4]

A “dummy overcharge” regression is one type of model frequently used in antitrust litigation.[5] This type of regression is used to estimate changes in prices after “controlling” for how supply and demand conditions—factors present absent the alleged conduct—affect prices paid by plaintiffs. The remaining “unexplained” portions of price changes are referred to as the “overcharge,” attributed to the effect of the alleged conduct. This approach assumes that all relevant supply and demand factors (i.e., factors affecting prices) have been identified and controlled for in the regression to ensure that the “unexplained” price change is solely attributable to the alleged conduct. An economist should isolate the effect of the alleged conduct from other economic factors or else risk attributing changes in prices due to changes in supply and demand conditions to the alleged conduct.[6]

When constructing a regression, an economist constructs a hypothesis as to which explanatory variables are associated with the variable of interest. This process requires careful consideration, as excluding a relevant variable can introduce what is known as “omitted variable bias.”[7] A regression that suffers from omitted variable bias may produce unreliable results that do not accurately measure the relationships being studied.[8] For example, say there is a market of widgets made of plastic. A regression studying the price of these widgets that fails to account for the cost of plastics would suffer from omitted variable bias. If the price of plastic increased and widget prices increased to reflect higher costs, then a regression that fails to control for the cost of plastic may incorrectly attribute an increase in the price of widgets to the alleged conduct rather than to the higher cost of plastic.[9] Constructing a reliable regression requires careful study and identification of the factors relevant to the relationships being assessed and the economic theory underlying those relationships.[10]

Regression analysis can be a particularly useful tool to model complex, real-world market dynamics, but a regression can suffer from bias if underlying assumptions are not met.[11] In the context of omitted variable bias discussed above, although a regression can still produce an estimate of the “unexplained” effect on price attributable to the alleged conduct, this estimate may potentially over- or under-estimate the effect, if any, of that alleged conduct and therefore fail to be a reliable estimate of impact to plaintiffs.

[1] Rubinfeld, Daniel L. “Reference Guide on Multiple Regression,” *Reference Manual on Scientific Evidence: Third Edition, Ch. 8*, 2011 (“Reference Guide on Multiple Regression”), p. 305; Greene, William H. *Econometric Analysis*, Seventh Edition, Pearson, 2011 (“Econometric Analysis”), p. 51.

[2] Studenmund, A. H. *Using Econometrics: A Practical Guide*, Seventh Edition, Pearson, 2017, p. 5.

[3] ABA Section of Antitrust Law, *Econometrics: Legal, Practical, and Technical Issues*, Second Edition, 2014 (ABA Econometrics), Ch. 2.C.

[4] Reference Guide on Multiple Regression, p. 305; ABA Section of Antitrust Law, *Proving Antitrust Damages: Legal and Economic Issues*, Third Edition, 2017 (“ABA Proving Antitrust Damages”), pp. 163-164.

[5] ABA Econometrics, pp. 312-314; ABA Proving Antitrust Damages, Ch. 6.F.

[6] ABA Proving Antitrust Damages, Ch. 4.C; ABA Econometrics, pp. 103-104; Quantitative Methods in Antitrust, p. 738.

[7] Econometric Analysis, pp. 259-260; Angrist, Joshua D., and Jörn-Steffen Pischke. *Mostly Harmless Econometrics: An empiricist's companion*. Princeton University Press, 2009, pp. 44-45; Stock, James H., and Mark W. Watson. *Introduction to Econometrics*, Third Edition, Pearson, 2011, pp.180-182.

[8] Rubinfeld, Daniel L. “Quantitative Methods in Antitrust.” *Issues in Competition Law and Policy*, 2008 (“Quantitative Methods in Antitrust”), pp. 216-217, 738; ABA Proving Antitrust Damages, Ch. 4.B.

[9] ABA Proving Antitrust Damages, Ch. 8.

[10] Davis, Peter, and Eliana Garcés. *Quantitative Techniques for Competition and Antitrust Analysis*. Princeton University Press, 2010, p. 79.

[11] ABA Econometrics, p. 68.

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