The Rodney L. White Center for Financial Research Dynamic Incentive Accounts

Contracts in a dynamic model must address a number of issues absent from static frameworks. Shocks to rm value may weaken the incentive e¤ects of securities given to the CEO (e.g. cause options to fall out of the money), and the impact of some CEO actions may not be felt until far in the future. To address these concerns, we derive the optimal contract in a setting where the CEO can a¤ect rm value through both productive e¤ort or costly manipulation, and may undo the contract by privately saving. The e¢ cient contract takes a surprisingly simple form, and can be implemented by a Dynamic Incentive Account. The CEOs expected pay is escrowed into an account, a fraction of which is invested in the rms stock and the remainder in cash. The account features state-dependent rebalancing and time-dependent vesting. It is constantly rebalanced so that the equity fraction remains above a certain threshold; this threshold sensitivity is typically increasing over time even in the absence of career concerns. The account vests gradually both during the CEOs employment and after he quits, to deter short-termist actions before retirement. Keywords: Contract theory, executive compensation, incentives, principal-agent problem, manipulation, private saving, vesting. JEL Classification: D2, D3, G34, J3 aedmans@wharton.upenn. edu, xgabaix@stern.nyu.edu, tsadzik@nyu.edu, sannikov@gmail.com. For helpful comments, we thank Zhiguo He and Eric Talley, and seminar participants at the Harvard Law School / Sloan Foundation Conference on Corporate Governance, the NBER, NYU and the University of Chicago. Qi Liu and Andrei Savotchkine provided excellent research assistance. 1 1 Introduction Many classical models of CEO compensation consider only a single period, or multiple unlinked periods. However, the optimal contract in a static analysis may be suboptimal in a dynamic world where the CEOs current actions, such as his e¤ort or savings/consumption choice, impact future periods. For example, short-term contracts can encourage the CEO to manipulate earnings or scrap investment projects to boost the current stock price at the expense of fundamental value; these long-run costs may not appear until after the CEO has retired. By privately saving, the CEO can separate his consumption stream from the path of income provided by his contract, and thus undo the intended incentives. Securities given to incentivize the CEO may lose their power over time: if rm value declines, options fall outof-the-money and bear little sensitivity to the stock price. In addition to the three above challenges, a dynamic setting also provides opportunities absent from a static framework  in particular, the rm has the option to reward current e¤ort with future rather than contemporaneous compensation. This paper analyzes optimal executive compensation in a dynamic model that allows for all of the above complexities, which are likely important features in real life. Despite the complications that result from a dynamic setting, the optimal contract is surprisingly simple and features intuitive economic principles. We rst consider an in nite horizon model where the CEO has no option to manipulate earnings or privately save, to provide a benchmark against which to analyze the e¤ect of introducing these complexities. In this baseline model, the optimal contract is time-independent: the sensitivity of pay to the rms return is the same in each period. The relevant measure of incentives is the percentage change in CEO pay for a percentage change in rm value; translated into real variables, this is the fraction of CEO pay that comprises of stock. If the CEOs outside option doubles, his total pay doubles but the relative weighting on cash and stock remains the same. Thus, the contract is also scale-independent. This result extends to a dynamic setting Edmans, Gabaix and Landier (2009), who advocated this incentive measure in a one-period model with a riskneutral CEO. The optimal contract also involves consumption smoothing. Since the agent is risk-averse, it is e¢ cient to spread the reward for e¤ort across all future periods rather than concentrating it in the current period (the deferred reward principle). This result 2 is consistent with Boschen and Smith (1995), who nd that rm performance has a much greater e¤ect on the present value of future pay rather than on contemporaneous pay. With a nite horizon, the sensitivity of income to rm returns is now increasing over time the increasing incentives principle. As the CEO approaches retirement, there are fewer periods in which to spread the reward for e¤ort, and so the reward in the current period must increase. We thus generate a similar prediction to Gibbons and Murphy (1992), but without invoking career concerns. Allowing the CEO to manipulate the stock price has two e¤ects on the optimal contract, which must change to prevent such behavior. The CEOs income is now sensitive to rm returns even after retirement, to deter him from inating the stock price just before he leaves. In addition, the contract sensitivity now must rise over time, even in an in nitehorizon model. This is because the CEO bene ts immediately from short-termism as it boosts his current consumption, but the cost is only su¤ered in the future and thus has a discounted e¤ect on the CEOs utility. Therefore, an increasing slope is needed to ensure that the CEO loses more dollars in the future than he gains today. By contrast, the possibility of private savings does not change the contracts sensitivity to rm value, since it does not a¤ect the CEOs e¤ort. Instead, the ability to save privately a¤ects the level of pay, causing it to increase more rapidly over time. Rising pay e¤ectively saves for the CEO, thus removing the incentive for him to do so privately. In practice, the optimal contract can be implemented in a straightforward manner. When initially appointed, the CEO is given a Dynamic Incentive Account: a portfolio of which a given fraction is invested in the rms stock and the remainder in cash. As time evolves, and rm value changes, this portfolio is constantly rebalanced, so that the fraction in the rms stock remains su¢ cient to induce e¤ort at minimum risk to the CEO. For example, a fall in the share price decreases the equity in the incentive account below the threshold fraction; this is addressed by using cash in the account to purchase stock. By contrast, if the stock appreciates, some of the equity can be sold without falling below the threshold, to reduce the risk borne by the CEO. The required fraction represents the contracts sensitivity, and so is constant in an in nite horizon model where manipulation is impossible, and increasing over time otherwise.