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.* [...]