Economists--and econometrics--have been involved in empirical legal studies for generations. This is particularly true for anti-trust doctrine, both its development and current application. Legal challenges to proposed mergers, and questions relating to anti-competitive spill-over effects, including market concentration, remain a staple for empirical analyses.
In the anti-trust context, one intuitive move involves assessing whether "prices are positively related to measures of concentration, such as the Herfindahl-Hirschman Index (HHI), comparing across different geographic markets or time periods." Pursuing such a question can involve (and frequently does involve) something as simple (and potentially powerful) as regressing price on the HHI.
Despite whatever intuitive appeal such a move holds, in a recent brief essay--co-signed by many leading law and economics scholars (including, and I add in interest of full disclosure, my Cornell colleague George Hay), On the Misuse of Regressions of Price on the HHI in Merger Review, the authors caution against such a move as it invites one basic fundamental problem: Mistaking correlation for causation. And it is for the essay's description of just how such a basic mistake can arise (rather than it's specific application in the anti-trust context) that I recommend this essay, especially to younger, developing empirical legal scholars.
As it relates to the specific anti-trust point developed in the essay, the authors' argue that: "The underlying problem with regressions of price on the HHI is that the relationship between price and the HHI is not causal. Instead, both are equilibrium outcomes that are determined by demand, supply, and the factors that drive them. Thus, a regression of price on the HHI does not show the sort of causal effect that would be helpful in predicting the competitive effects of a merger." More specifically, as the "HHI can take values ranging from 0 to 10,000, with the former corresponding to a fragmented market with infinitesimal firms, and the latter to monopoly. All else equal, a decrease in the number of firms leads to a higher HHI. However, the HHI can increase if, for a given number of firms, the market shares of the larger firms increase."
The root problem, of course, flows from challenges posed by “endogeneity” or “simultaneity.” Such problems lurk "when a clear causal path between two variables is posited by the relevant economic theory but the causal factor (on the right side of the regression equation) is either correlated with unobserved factors or, more subtly, is simultaneously determined by the variables (in this case, price) on the left side of the regression. A famous example of simultaneity involves price and quantity, which are simultaneously determined in the classic economic model of supply and demand." The problems posed by "endogeneity” or “simultaneity," of course, are not limited to the anti-trust realm. An excerpted abstract follows.
"It might seem natural to determine whether prices are positively related to measures of concentration, such as the Herfindahl-Hirschman Index (HHI), comparing across different geographic markets or time periods. This might be implemented by using a simple regression of price on the HHI. However, for reasons that we describe, regressions of price on the HHI should not be interpreted as establishing causation. That is, they do not inform how a change in concentration from a merger would affect prices. Courts and other policy-makers should not rely on regressions of price on the HHI for the purposes of antitrust merger review."
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