Optimal CEO Incentives

In my paper A Multiplicative Model of Optimal CEO Incentives in Market Equilibrium (co-authored with Xavier Gabaix and Augustin Landier, both of NYU Stern), which was recently accepted for publication in the Review of Financial Studies, we contribute to the growing debate on whether executive compensation results from rent extraction or optimal contracting. We construct a model of what the level of incentives should be, and how they should vary with firm size, if pay is set optimally. In our model, CEO effort has a multiplicative effect on firm value. This is realistic for the vast majority of CEO actions, which can be “rolled out” across the entire firm and thus have a greater effect in a larger company. We also assume that the cost of effort to the CEO is proportional to the CEO’s wage. Richer CEOs are willing to spend more to consume leisure time, which is consistent with their greater expenditure on most goods and services.

There are two pieces of evidence (both from Jensen and Murphy (1990)) that are often used to support claims of inefficiency: (1) CEOs only lose $3.25 for every $1,000 loss in firm value, an effective equity share of only 0.325%, and (2) This effective equity share is strongly declining in firm size, i.e. incentives are particularly low in large firms. To evaluate whether these facts indeed reflect inefficiency, we calibrate the model and find that the above two facts are in fact quantitatively consistent with our optimal contracting benchmark, contrary to some earlier interpretations.

On point (1), since effort has a percentage effect on both firm value and CEO utility, the optimal contract prescribes the required percentage change in pay for a one percentage point increase in firm returns (“percent-percent” incentives) – not the dollar loss in CEO pay for a dollar loss in firm value (“dollar-dollar” incentives) which is often measured. In turn, dollar-dollar incentives equal percent-percent incentives multiplied by the CEO wage and divided by firm value. Since firm value is substantially greater than the CEO’s salary, high percent-percent incentives equal low dollar-dollar incentives, exactly as found by Jensen and Murphy.

On point (2), with a multiplicative effect on firm value, the dollar benefit from effort is proportional to firm size, i.e. has a size-elasticity of 1. With a multiplicative effect on CEO utility, the dollar cost of effort is proportional to the CEO’s wage. However, wages have an elasticity of only 1/3 with size. Therefore, dollar-dollar incentives should optimally decline with firm size with an elasticity of 1/3 – 1 = -2/3. This prediction matches the data very closely – we find an elasticity of -0.61. Simply put, since effort has such a large dollar effect in large firms, the CEO will work even if he has a small effective equity share.

The multiplicative production function does not apply to all CEO decisions. Perk consumption reduces firm value by a fixed dollar amount independent of size. We show that stock compensation is ineffective at deterring additive actions such as perks. This is because perks have a tiny effect on the stock returns of a large company – a $10m corporate jet only reduces the return of a $10b firm by 0.1%. The ineffectiveness of contracts gives rise to a role for active corporate governance, e.g. direct monitoring by boards to scrutinize such perks. Similarly, while our model is able to reconcile (1) and (2) with optimal contracting, there are many other features of observed contracts (e.g. golden parachutes, hidden compensation) about which our model is silent and which may indeed result from rent extraction.

The model also proposes a new measure of CEO incentives. We advocate “percent-percent” incentives as the optimal measure as they are independent of firm size (unlike “dollar-dollar” incentives) and thus comparable across different firms. Translated into real variables, this measure equals the dollar change in wealth for a one percentage point change in firm value, divided by annual pay. This data is available at http://finance.wharton.upenn.edu/~aedmans/data.html. The full paper is available for download here.