We develop a model that clarifies how to measure CEO incentive strength and how to reconcile the enormous differences in pay sensitivities between executives in large and small firms. The crucial parameter is shown to be the elasticity of CEO productivity with respect to firm size. We find that CEO marginal products rise significantly with firm size (confirming Rosen's conjecture that CEOs of large firms have a "chain letter" effect on firm performance), and overall CEO incentives are roughly constant, or decline slightly, with firm size. We employ a multitask model to discuss implications for the design of control systems.

ABSTRACT We empirically analyze the dynamics of executives' pay‐to‐performance sensitivities. Option pay‐to‐performance sensitivities become weaker as options fall underwater, often leading to pressures to reprice options or restore pay‐to‐performance sensitivity in other ways. Building a detailed data set on executives' portfolios of stock and options, we find that the responsiveness of pay‐to‐performance sensitivities (created by all executive holdings of stock and options) to changes in stock price is large. The elasticity of pay‐to‐performance sensitivities with respect to stock price decreases is about 0.7 and is larger for high‐option executives and for executives with high percentages of options already underwater. The dominant mechanism through which companies offset declines in option pay‐to‐performance sensitivities is larger option grants following stock price declines; on average, these larger grants restore approximately 40% of the stock‐price‐induced pay‐to‐performance sensitivity declines. Option repricings are inconsequential in this regard, despite the attention they have attracted. In looking at positive returns, we find the reverse: higher returns both directly increase pay‐to‐performance sensitivities and lead to larger option grants, which raise pay‐to‐performance sensitivities further. Thus, option grants to executives tend to be largest following large stock price increases or large stock price decreases.