So how does this argument work? Better executive decisions create more economic value. If the number of big companies is greater than the number of good chief executives, competitive bidding will push up pay to reflect the value of the talent.

As Professors Gabaix and Landier predict, chief executives' salaries in different sectors are higher when the capitalization of that sector is higher. A stronger sector means more bidders for a chief executive of a particular kind; an executive who has run one car company can go run another. Chief executives in large industries, therefore, receive more, even after adjusting for the size of their current companies. Business services, computers and banking turn up as exceptions for this comparison; their top executives are overpaid relative to what market capitalization alone would imply. Perhaps chief executives can add more value in more dynamic sectors.

The authors are still working on their international comparisons; it is difficult to compare compensation across countries. But the preliminary results suggest that the total value of the companies in the sector helps predict how chief executives' salaries vary from country to country. Executives of large companies in France have fewer outside opportunities in comparable companies than their American counterparts and they thus receive less compensation, in this case by a factor of 2.4 to 1.

The approach of Professors Gabaix and Landier to executive compensation is influenced by their French background. In the United States, the popular debate turns on merit  whether chief executives are worth the money. In Europe, where inequality is less socially acceptable, the popular debate concerns whether anyone could possibly deserve so much money. This perspective led Professors Gabaix and Landier to focus on explaining the overall level of executive compensation, opening up a new approach to the problem.

The two also find that the best chief executives do not seem to have much more talent than other chief executives in what they define as the top 250. By their calculations, replacing the No. 250 chief executive with the No. 1 will increase the value of the company by only 0.014 percent. The No. 1 chief executive receives much more compensation, but that is mostly because he manages a larger company and thus his talent has a longer reach. That is another way of thinking about why the same chief executive will make more money in a larger marketplace or in a larger country.