Current tests for mergers are in practice deeply flawed.
As many recent critics have observed, American antitrust authorities have for decades used only one yardstick to assess mergers: the highly questionable consumer welfare standard. As a result, they have drawn most of their econometric tools from the neoclassical theory of the consumer, not of the firm.
If one accepts the assumption of consumer “rationality” in those models and actually has data on all of a household’s sources of income and expenditures, then those econometric methods are well-suited to the task of estimating the location and shape of demand curves. This is because, under the rationality assumption, the behavior of each household (seen as one entity) satisfies certain mathematical conditions which help to “identify” the demand curves. These helpful conditions go by the names of “adding up,” “homogeneity,” “symmetry,” and “negativity.”
The problem is that household-level data is frequently missing in antitrust cases. In the absence of such data, many antitrust econometricians close their models by assuming that the aggregate data could have been generated by an imaginary “representative consumer” (or representative household). This works because if the aggregate data could have been generated by such a representative consumer, then the helpful conditions of “adding up,” “homogeneity,” “symmetry,” and “negativity” can be imposed and the analysis can proceed in the absence of household-level data.
But there are only three situations in which the representative consumer assumption is justifiable. Two of them require that the graphs of consumption versus income (called “Engel Curves”) are straight lines for every good. It is widely recognized that there is no empirical support for such Engel curves.
The third situation is called “exact nonlinear aggregation.” Deaton and Muellbauer show that this does not require linear Engel curves, and so the assumption of exact nonlinear aggregation has been widely adopted, as, for example, in studies using the Almost Ideal Demand System, “AIDS”. But my new INET working paper shows that making that assumption leads to the following unrealistic conclusions:
- If there is a commodity whose consumption by one household completely flattens out for large incomes, then in order for a representative consumer to exist, all the Engel curves of that household do have to be linear from that income level on up.
- If there is a commodity whose consumption flattens out for large incomes for all households, then in order for a representative consumer to exist, all the Engel curves of every household do have to be linear from that income level on up.
- If there is a commodity that a household never consumes, then in order for a representative consumer to exist, all the Engel curves of that household do have to be linear for all values of income.
- If there is a commodity that is an inferior good for a household – that is, a good that the household buys less of as its income rises — then in order for a representative consumer to exist without all the household’s other Engel curves being linear, the consumption of this good must fall with income but must never become constant—a completely non-intuitive requirement that is not obviously true at all.
The upshot is that exact nonlinear aggregation has considerably less appeal than the previous literature suggests.
But the situation is even worse. Even if one is willing to make the heroic assumption of exact nonlinear aggregation, it is still not safe to adopt the four representative consumer restrictions. That is only possible if one has data on every commodity the households in the aggregate purchase—and even if one does have that data, one’s estimate will suffer from an aggregation bias that my paper explains. If one does not have such comprehensive data but does have income data for every household, then I show that symmetry and negativity but neither adding up nor homogeneity can be imposed. If one does not have income data for every household, none of the four representative consumer conditions hold, and imposing them is an error.
It thus turns out that the data requirements for imposing the four representative consumer conditions are much stronger than usually believed. If one lacks individual household-level data and only has, for example, scanner data from retail stores, none of the four representative consumer conditions should be imposed, and econometric estimation becomes considerably more difficult and less informative. The conclusion has to be that current tests for mergers are in practice deeply flawed.
