CEO compensation and the marginal product of the CEO

Responding to an earlier post of mine, the very smart Ian Dew-Becker emailed me the following text:

I saw you had a post up about some work I did with Bob Gordon, and I found your comments very interesting. I have a couple questions that I hope might help clarify your thoughts on the subject.

First, you seem to argue that we would expect a CEO to be paid her marginal product. As you point out, there is ample evidence that a CEO adds far more to the value of a company than she is generally paid. I’m curious, though, what you mean when you say we would expect the CEO to be paid her marginal product. Models in this literature often assume that each firm must hire one CEO. The concept of a marginal product breaks down at this point. The firm can’t hire a second CEO. There is no marginal value. It’s possible that we can look at marginal products in terms of the skill a CEO brings to the firm, but in that case, we would be mixing up marginal and average products if we were to simply look at the total contribution a CEO makes to firm output.

I think you’re correct to point out the institutional factors holding down CEO pay pre-1970. That said though, why didn’t we see CEO pay rising much faster than market cap during the 80’s in order for it to catch up to where it should be? There is a period where the pay-market cap elasticity may have been higher than 1, but it’s only for a few years in the 90’s. Looking at the full 1976-2005 sample, the relationship is nearly unitary (.935, according to Frydman and Saks). So I guess I’m surprised there is no catch up in pay.

I think you’re right to be skeptical of the Bebchuk-Grinstein results. To me, the most interesting result from Gabaix and Landier, no matter what one thinks about their model as a whole, is that the cross-section and time series may show very different patterns. So one wouldn’t necessarily expect the cross-sectional results from Bebchuk and Grinstein to predict the time-series.

One of my biggest concerns with Gabaix and Landier’s model is that it does not display decreasing returns to scale. An analogous example is Berk and Green’s model of mutual funds. They assume that if a manager all of a sudden sees the size of his fund double, he will see lower average returns. I think this is reasonable. When there are not diminishing returns, it is difficult to make models function. Gabaix and Landier are forced to do it by assuming firms never merge. That concerns me in this setting. Dixit-Stiglitz competition is often a reasonable assumption because the models using it do not actually care about firm size or mergers. In the case of CEO pay, however, firm size is clearly critical.

The question about the marginal product of a CEO is a tricky one. I can imagine the following definitions which either express marginal product or some modified version thereof:

1. How much better the highly-paid guy is than a less-well-paid substitute would be.

2. How much better the highly-paid guy is than the next best person (in stochastic terms, that is) the firm would get for that same sum.

3. How much a bit of extra pay causes the CEO to improve effort and thus performance.

4. The complex econometric definition offered by Jensen and Murphy, read pp.33-38 here.

5. Some number between the CEO’s value of leisure and how well the firm would do with no CEO at all.

None of these quite make sense in pure theory, and it is even harder to say which is the most important variable for practice.