In deciding on whether a proposed merger is anticompetitive, economists, lawyers and judges used to begin their analysis by asking a single question: what market are we worried about? New tools in the field of industrial organization have made it unnecessary to define "the market."

In the past, economists sought to measure market power with the Herfindahl-Hirschman Index, which is determined by adding the squares of the market shares of all firms involved. If the Herfindahl is low, there are many competitors and exercising market power should be hard; a high Herfindahl, on the other hand, was thought to warn of a concentrated market in which price rises are easier to sustain.

The Herfindahl's great virtue is its simplicity. But that virtue masks two shortcomings. First, there is often no clear way to define what market is at stake. In the current investigation of the proposed alliance between British Airways and American Airlines, for example, the carriers assert that the relevant market is travel between the United States and Europe (of which their combined share is modest). European Union officials, on the other hand, have focused on travel between the United States and Britain (of which their combined share is huge). Second, even when the scope of the market is clear, the relation between the Herfindahl and market power is not. America's soft-drink industry, to take one example, is noted for price competition although only two firms, Coca-Cola and PepsiCo, control three-quarters of sales.

Frustration with the Herfindahl's failings has led economists in a different direction. Instead of calculating market shares, they seek to gauge if an arrangement such as a merger will drive prices higher than they would be otherwise. This has become possible with the spread of two technologies during the past decade: desktop computers with extraordinary number-crunching power and the scanners used at retailers' check-outs.

These techniques were first applied in 1995, when Interstate Bakeries, America's third-largest wholesale baker, proposed to buy rival Continental Baking. Instead of arguing about whether the market for white bread is separate from the market for rye, the government obtained scanner data from a commercial-information company, providing weekly details about average prices and sales volumes for dozens of different breads in various cities.

Thousands of equations later, economists from the Department of Justice concluded that the price of Interstate's sliced white breads strongly affected sales of Continental's Wonder bread, and vice versa, but made little difference to sales of other white breads or other varieties, such as rye. Having shown that each company's brands were the main restraint on the other's prices, the authorities moved to block the merger. In the end Interstate met their objections by selling some of its brands and bakeries.

The empirical analysis went still further with last year's proposed merger of Staples and Office Depot, two chains of office-supply "superstores" in America. By traditional lights, the merger posed no problems, as thousands of retailers sell office supplies. But when economists hired by the Federal Trade Commission (FTC) scrutinized sales prices and quantities for every item sold by each chain, the computers spotted a pattern: Staples's prices were lower in cities where Office Depot also had a store than in cities where it had none. This was strong and unexpected evidence that the merger would allow Staples to raise prices. A court then blocked the merger.

Since this econometric approach can directly predict whether a merger will raise prices for consumers, there is no need to infer the price effect from looking at the degree of market concentration.