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E-MailThis post comes from Alex Edmans at the Wharton School, University of Pennsylvania.
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.
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Coles, Lemmon and Wang (2002) also have a calibration model that addresses similar issues. That paper presents a parsimonious, structural model that captures primary economic determinants of the relation between firm value and managerial ownership. Supposing that observed firm size and managerial pay-performance sensitivity (PPS) maximize value, we invert our model to panel data on size and PPS to obtain estimates of the productivity of physical assets and managerial input. Variation of these productivity parameters, optimizing firm size and compensation contract, and the way the parameters and choices interact in the model, all combine to deliver the well-known hump-shaped relation between Tobin’s Q and managerial ownership (e.g., McConnell and Servaes (1990)).
Our structural approach illustrates how a quantitative model of the firm can isolate important aspects of organization structure, quantify the economic significance of incentive mechanisms, and minimize the endogeneity and causation problems that so commonly plague empirical corporate finance. Doing so appears to be essential because, by simulating panel data from the model and applying standard statistical tools, we confirm that the customary econometric remedies for endogeneity and causation can be ineffective in application.
In a second paper we address the joint decision of CEO incentives and board structure — Coles, Lemmon, and Wang (2006). We specify a simple structural model of the firm to isolate the economic determinants of key aspects of organization form in a value-maximizing contracting environment. Optimal firm size, managerial ownership, and board independence are jointly determined by exogenous parameters defining the productivity of physical assets, managerial input, inside director expertise, and outside director advising and monitoring The model provides an equilibrium explanation for the cross-sectional relationships among managerial ownership, board structure, and firm performance observed in data. Using the model for policy analysis, our approach also explains the observed changes in compensation structure following new requirements for board independence.