Cross Validation Methods in Antitrust Class Action Litigation

ABSTRACT In antitrust class action lawsuits, judges or juries are often asked to make decisions based on the results of economic regression analysis. In this paper we show how out-of-sample prediction used as a method of cross validation can help evaluate model reliability. We apply this technique to two models, a pooled model and an unpooled, or “sub-regression” model, that are often presented at the class-certification stage of litigation. The sub-regression method, while unbiased, displays larger estimator variance. This variance is problematic because it increases the likelihood of a false negative whereby a subgroup improperly displays no overcharge due to the additional flexibility introduced by the sub-regression method. These groups, without an overcharge, can be the basis for rejection of class certification, but the cross-validation technique we employ shows the regressions producing these statistically insignificant results often produce poor out-of-sample predictions as well. We show that cross-validation techniques have the potential to introduce rigor to such empirical work in ways that are more reliable and relatively easier to understand for judges and juries, and we recommend them as useful model-selection tools when comparing pooled versus sub-regression models rather than goodness-of-fit statistics or a strict (reject/do not reject) Chow test for poolability.