The forbidden regression of price on HHI

I recently came across a neat paper by around 25 economists (former chief economists at the US’ FTC and DoJ Antitrust Division) which provided a rebuke of attempts by econometricians to study the relationship between price and the Herfindhal-Hirschman Index (a measure of concentration).

As a general rule, when two firms merge horizontally (i.e. at the same level within the same market), there are two mechanisms which would tend to push prices up and a counteracting force which would put downward pressure on prices. The first two mechanisms (which tend to increase price) are called unilateral and co-ordinated effects. Unilateral effects come from the fact that the merged entity has more market power than before, and it can use this market power (to some degree) to push up prices.* Coordinated effects comes from the fact that a merger results in (at least) one fewer firms being in the market, which makes it easier for the remaining firms in the market to collude with each other, to set higher prices. In short, these upwards pricing pressures will be stronger, the larger the market shares of the merging firms and the fewer competitors that exist in the market.

On the other hand, the merger may result in increased efficiencies – one such efficiency can come from reducing duplicated overhead costs or another can come from increased bargaining power with suppliers. These increased efficiencies may be passed on to consumers, in the form of lower prices, thereby dampening the price-increasing effect of mergers from above.

Whether prices increase or decrease following a merger depends on many factors which affect the strength of these mechanisms. Generally speaking, efficiencies resulting from a merger aren’t that strong (and may not be passed on to consumers), whilst unilateral effects tend to dominate, leading to higher prices post-merger.

An econometrician may well want to put this to the test, and see whether more concentrated markets (that is, markets with fewer firms, or markets which are dominated by a few very big firms) indeed have higher prices. One idea to test this, would be to regress price on HHI (a measure of how concentrated markets are**) and see whether the correlation is positive, negative or zero. The theory above would predict a positive correlation.

The problem – as outlined by the FTC/DoJ authors – is that this is a bad idea: both price and HHI are equilibrium variables which are determined by demand and supply. Thus, the resulting regression is not causal because there is no causal relationship to estimate!

This is the essential point to remember – these are two equilibrium concepts and there is no causal relationship between them. The issue is not endogeneity bias (i.e. we need to control for other factors to establish the causal relationship) but a fundamental issue that no causal relationship exists to be estimated.

The authors also point out that there are many reasons why HHI may vary across markets and time periods – what matters is the reason for variation (and the effect on prices), not the correlation with price. They show an example where a cost reduction for a small firm would cause lower prices and a lower HHI (positive correlation), whilst the same cost reduction for a larger firm in the market would cause lower prices but an increase in HHI (a negative correlation). In both cases, there has been no merger which affects HHI (instead, it comes from changing costs, potentially as a result of investment) and yet, depending on which firm sees this positive cost shock, we see a different story for the correlation.

The authors point out that the only time it might be interesting to study the correlation between price and HHI is that if the variation in HHI is driven solely by changes in competition, e.g. past mergers which have similar competitive effects to a proposed merger which is being investigated. In this case, the relationship is still not causal but the correlation might be informative on the likely impact of a proposed merger on price, so long as the evidence used is comparable.

You can read more about this topic by checking out the paper here, they include some nice numerical examples to help make their point and generally provide more nuance on merger policy and the use of concentration indices.

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*I have oversimplified a bit here, maybe a future post will explore this in more detail but an interested student can take a look more into unilateral effects to understand the conditions under which prices would rise.

**The Herfindahl-Hirschman Index (HHI) is calculated as the sum of squared market shares and is a number between 0 and 10,000. Because market shares are squared, this gives greater weight to larger firms. A HHI of 10,000, indicates a single monopolist, whilst a value of 0 indicates many small firms with no market power.

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