The DOJ/FTC have announced upcoming workshops to review the Merger Guidelines, which are now (depending on whether you count the 1997 revision) either about to start or about to end their teenage years -- i.e., in an awkward stage.
Recently the paper by Shapiro and Farrell on upward price pressure came to my attention:
We propose a simple, new test for making an initial determination of whether a proposed merger between rivals is likely to reduce competition and thus lead to higher prices. Under current antitrust policy, the government can establish a presumption that a proposed horizontal merger will harm competition by defining the relevant market and showing that the merger will lead to a substantial increase in concentration in that market. However, this approach can perform poorly in markets for differentiated products, where market boundaries are unclear and the proximity of the products sold by the merging firms is a key determinant of the merger's effect on competition. Our test looks for upward pricing pressure (UPP) resulting from the merger. We develop a simple diagnostic for UPP based on the price/cost margins of the products sold by the merging firms and the magnitude of direct substitution between the two firm's products. We argue that our approach is well grounded in economics, workable in practice, and superior to existing methods in a substantial class of mergers.
In general, I am enthusiastic about this paper and what it signifies about how this administration will approach these complex problems. In short, UPP avoids the rather artificial analysis of market share using HHI by substituting a direct measure of relative cross-elasticity (or, more precisely, the diversion rato) adjusted by profit margins. In other words, within the UPP framework, the higher the profit margins and the lower the cross-elasticity, the more likely the merger will be bad for consumers. Both economists and lawyers should appreciate how this is a vast improvement over the entirely static calculation of HHI for the market pre- and post-merger.
But for me the problems with HHI suggest a different angle of attack. More specifically, if we agree that one of the core problems with HHI is that it provides too static a picture of competition, then one can justly ask whether UPP really solves the core problem rather than substituting a different (albeit better) measure of the prospective effect of the merger.
What is HHI? For the uninitiated, HHI is an index calculated by adding in quadrature the market share (usually in percentage units) of various companies pre- and post-merger. One of the consequences of adding in quadrature, of course, is that the square of the post-merger market share will always be less than the sum of the two pre-merger companies' market shares squared. Why is that?
I do not know what H and H or others have to say. At first, I was putting off this post until I could find out. Today I realized that that could be a long while. So I will offer my own thoughts.
In probability theory, we add the error of normal variables in quadrature. In other words, if a calculation depends on two measurements, each of which has a certain tolerance for error (e.g., 10 meters plus or minus 2 meters and 4 meters plus or minus 1 meter), then the result of the calculation will be the sum of the measurements, but the error will be the sum of the squares of the errors (i.e., here, 2^2 + 1^2 = 5), not merely the sum of the errors (i.e., 2 + 1 = 3).
The reason errors are added in quadrature is because an error in one direction can cancel an error in the other. That is, if the two measurements are made along the same dimension of units, a statistical fluctuation in the positive direction for one can cancel a statistical fluctuation in the negative direction for the other.
This all carries over very naturally to our analysis of HHI. At bottom, what HHI invites us to imagine is that our market share percentages are actually the variance (or, if the distribution is gaussian, the "standard deviation") of some distribution of possible market share. Hence, to determine market share after combining two distributions associated with two companies, we add in quadrature.
Notice that if we think about market share in these terms, then there is an implicit role for time in the picture. Namely, the distributions are produced by "measurements" in the form of dealflow that result in a distribution with particular variance over some period of time. If the distributions are not stationary (and why would they be?), then that variance should fluctuate. But only when two distributions are combined in the sense that they stop competing for the same dealflow will their variance change discontinuously. That fits nicely with the HHI picture.
But what does it leave out? How about how the variance is changing over time? Wouldn't you like to know whether the distributions are getting fatter are narrower over time?
On my view, the key parameter for defining competition is change in distribution width per unit time. In practice, this would produce a dimensionless number, the internal rate of return, or IRR. If, even adjusting for mergers, a company has posted an IRR over a certain percentage, then there is a reasonable chance that their growth has been built through the use of unsustainable modes of operating, such as fraud.
UPP is an improvement, but doesn't really get to the core problem, which is dynamic.
UPDATE: Investigation of Herfindahl's early papers shows an infatuation with the chi-squared distribution. There are serious fundamental problems with relying upon a chi-squared distribution to fit market concentration, perhaps the most important of which is that market shares cannot and should not be assumed to be independent. Another is that any actual distribution of market shares will probably not be stationary, either over same-width intervals or at different length intervals. We should have cast this kind of theory to the flames a long time ago.
The entropy concentration index is an interesting slice at the problem of characterizing concentration, and brings out the fact that it is the correlation of market shares rather than their statistical independence per se that makes HHI unrealistic. But the entropy index fails for the same reason -- i.e., that market share measurements are not uncorrelated, as they must be for entropy to be an extensive quantity (i.e., for S of 1 and 2 combined to equal S1 + S2). In this regard, a generalization to nonextensive entropy metrics might be considered useful. But there are conceptually and practically simpler ways to get at the degree of correlation in market share, such as cross-correlations in the time-series of cash-flows of different firms.
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