CEO pay: Gabaix and Landier (QJE, 2008)

WHY HAS CEO PAY INCREASED SO MUCH?

XAVIER GABAIX AND AUGUSTIN LANDIER

ABSTRACT
This paper develops a simple equilibrium model of CEO pay. CEOs have different talents and are matched to firms in a competitive assignment model. In market equilibrium, a CEO’s pay depends on both the size of his firm and the aggregate firm size. The model determines the level of CEO pay across firms and over time, offering a benchmark for calibratable corporate finance. We find a very small dispersion in CEO talent, which nonetheless justifies large pay differences.  In recent decades at least, the size of large firms explains many of the patterns in CEO pay, across firms, over time, and between countries. In particular, in the baseline specification of the model’s parameters, the sixfold increase of U.S. CEO pay between 1980 and 2003 can be fully attributed to the sixfold increase in market capitalization of large companies during that period.

I finally got around to reading this paper carefully because I'm tentatively planning to go over it in class.  It's a great example of why a paper doesn't need to be true to be useful.  I forget the precise quote (or even the source), but one viewpoint is that economists are unlike other social scientists because "we'd rather have a theory be precise than vague."

Gabaix and Landier develop a simple supply-and-demand model of the CEO labor market where the returns to CEO "talent" (or "ability") increase with firm size.  Mathematically, this means CEO ability and firm size are complements in production, which implies that in a competitive equilibrium there will be "positive assortative matching."  This kind of "matching" is common in many economic models, and ability-size complementarity is an important explanation for why large firms higher more skilled workers and why large cities attract more skilled workers.

From this single assumption (complementarity between ability and firm size) and a bunch of technical mathematical conditions based on "extreme value theory" (which aren't that restrictive), you get two main results:

1. The elasticity of CEO pay with respect to firm size is g - b in the cross section (where g and b are parameters of their model)
2. The elasticity of CEO pay with respect to firm size is g in the time series (where g is same constant as above)

The paper then documents in the data that at any point in time (from 1970 forward), the cross-sectional elasticity between CEO pay and firm size is roughly 1/3 (so g - b = 1/3), while within the U.S. over time the elasticity of CEO pay with respect to firm size is 1 (so g = 1). 

In my opinion, what's so interesting about this paper is that it's actually somewhat difficult to write down a simple model which generates such different cross-sectional and time-series predictions.  For example, a "skimming" view of CEO pay which posits that CEOs capture a percentage of firm profits (or revenues) would give the same cross-sectional and time-series predictions.  You could enrich the "skimming" model so that the amount you can skim depends somehow on overall the size distribution of firms, but that certainly would not be the simplest "skimming" model you could write down, while (technical conditions aside), this is one of the simplest supply-demand models you could come up with.

So overall, while I think this model is quite clearly not a literal description of reality, it's a really simple way to capture the main features of the data.  I also give the authors credit for being extremely upfront about the fact that their model does a really poor job describing the data before 1970 (and they generously cite the recent work of Frydman and Saks, who take a longer-run, historical view of CEO compensation).

I should also be clear that I don't think it makes sense to think about CEO pay as being set purely in supply-demand equilibrium, even as an approximation.  I think that issues of corporate (mis)governance and social norms matter a lot in determining CEO pay.  But this paper is still very useful because it shows that any theory of CEO pay needs to be able to account for both facts above and have an additional prediction which would make it empirically distinguishable from this simple supply-demand theory.

UPDATE: The quote above isn't exactly what I meant; I meant to write something along the lines of "we'd rather have a theory be precisely false than vaguely true."

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