Xavier Gabaix and Augustin Landier offer one model in their April 9, 2007 publication in the Quarterly Journal of Economics:
This paper develops a simple competitive model of CEO pay. A large part of the rise in CEO compensation in the US economy is explained without assuming managerial entrenchment, mishandling of options, or theft. CEOs have observable managerial talent and are matched to assets in a competitive assignment model. Under very general assumptions, using results from extreme value theory, the model determines the level of CEO pay across firms over time, and the pay-sensitivity relations. The model predicts a cross-sectional constant-elasticity relation between pay and firm size. It also predicts that the level of CEO compensation should increase one for one with the average market capitalization of large firms in the economy. Therefore, the six-fold increase of CEO pay between 1980 and 2003 can be fully attributed to the six-fold increase in market capitalization of large US companies. The model can also be used to study other large changes at the top of the income distribution, and offers a benchmark for calibratable corporate finance. We find a minuscule dispersion of CEO talent, which nonetheless justifies large pay levels and differences. The empirical evidence is broadly supportive of our model. The size of large firms explains many of the patterns in CEO pay, in the time series, across industries and across countries.
Eduardo Porter tries to summarize this paper:
As companies grow and expand globally, the value of the top executive can grow exponentially. In a study last year, two economists, Xavier Gabaix of the Massachusetts Institute of Technology and Augustin Landier of New York University, argued that the fast rise in pay of corporate C.E.O.’s mostly reflected the growing size of American corporations. Processing reams of data, the economists estimated that hiring the most effective chief executive in the country would, statistically, increase the stock value of a company by only 0.016 percent, compared with hiring the 250th chief executive. But at a company like General Electric, which is worth about $380 billion, that tiny difference would amount to $60 million. This, the economists argued, helps explain why that top chief executive earned five times as much as the 250th. “Substantial firm size leads to the economics of superstars, translating small differences in ability to very large deviations in pay,” the economists wrote.
Relying on this summary, Kevin Drum fires back:
Needless to say, this is ridiculous. For starters, a microscopic number like 0.016% is probably just a statistical artifact. But let’s say it isn’t. Let’s say it’s real. It still doesn’t matter because it’s still plainly too small to be a predictable difference.
When a reader suggested Kevin was being unfair to the authors of the paper, he later noted:
Basically, I’m accepting Gabaix and Landier’s results here. If their research says 0.016%, then for now I’m willing to assume that’s correct. However, if that result is right, I think it’s ridiculous to interpret it as explaining skyrocketing CEO pay. If you could systematically predict who was going to deliver a benefit that small, that would be one thing. In that case, maybe the higher pay would be justified. (Maybe.) But the microscopic size of the difference in measured CEO performance makes that vanishingly unlikely. CEO pay has certainly skyrocketed over the past couple of decades, but minuscule and unpredictable differences in performance don’t seem likely to explain why.
I’ve only skimmed the Gabaix and Landier paper, but it appears to me that the New York Times summary does not give their discussion justice. Maybe the paper is worth a thorough read before we started attacking it.