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Murphy (1986) characterizes the incentive contract for CEOs in a multi-period principal- agent setting. In his model, the agent works for a fixed number of periods. His model

implies that pay increases are spread evenly throughout the remaining years, i.e., good performance is rewarded as a shift in the earning-tenure profile. This in turn implies that pay-for-performance sensitivity increases with tenure because for later years, the reward is spread among fewer years. Thus the same increase in output causes greater increase in annual compensation.9 The econometric model is ∆ln(Salary+Bonus)it =

α+β(Y ears as CEO) +δ(Rate of return on common equity)it+it. Murphy uses CEO

compensation data between 1974 and 1984. He divides the data into three sub-samples; the first sub-sample is for CEOs with tenure of 4.6 and less, the second sub-sample is for CEOs with tenure between 4.6 and 9.9 and the third sub-sample is for CEOs with tenures greater than 9.9. Murphy finds that δ is smaller for those with longer tenure. Thus the estimated results show that pay-for-performance actually decreases with tenure, which is inconsistent with the standard results of principal-agent theories. 10

Gibbons and Murphy (1992) develop a model that characterizes the incentive con- tract when the agent has reputational career concern. In their model, good current per- formance positively affects the CEO’s assessed ability, as assessed by the shareholders. The assessed ability is interpreted as the “reputation” of the CEO. A good reputation causes an increase in his or her future compensation, thus creating incentives for CEOs to exert effort even without an explicit incentive contract. However, the reputational concerns disappear as the CEO reaches his or her retirement. To supplement such a loss

9_{Therefore, the implication that pay-for-performance increases with tenure depends on the finiteness}

of a CEO’s lifetime.

in incentive, firms may intensify pay-for-performance sensitivity as the CEO approaches his or her retirement. Gibbons and Murphy’s model has two implications: (i) Hold- ing CEO tenure constant, pay-for-performance sensitivity increases as CEOs reach their retirement. (ii) Holding years to retirement constant, pay-for-performance sensitivity increases as CEO tenure increases. The second implication is relevant for our study.

The reason for the second implication is as follows. First, because of the agent’s risk aversion, the standard trade-off between incentive and uncertainty holds, i.e., pay-for- performance sensitivity decreases with the uncertainty of business performance. Suppose that the firm’s output is given byyt=η+at+t whereη is the unobservable ability of

a CEO (unobservable both by CEOs and the shareholders), at is the effort and t is the

usual independent random shocks. Notice that there are two sources of uncertainty to both shareholders and the CEO,ηandt. Althoughηis not directly observable (both by

the shareholders and by the CEO), it can be inferred by repeatedly observing the firm’s output over time. Because the uncertainty about the ability of the CEO decreases over time, so does the overall uncertainty of the business outcome. By the inverse relationship between incentive and uncertainty, Gibbons and Murphy show that pay-for-performance sensitivity should decrease with tenure.

Their econometric model to test the pay-for-performance incentive relationship is the following. ∆(Salary+Bonuses)it =β1(low tenure dummy)×∆ln(F irm V alue)it+

P1988

n=1972βn(nth year dummyit)×∆ln(F irm value)it+β0(other variables)it. The the-

performance sensitivity and CEO tenure. They used CEO compensation data between 1971 and 1989 to estimate this model. They find a positive but statistically insignificant coefficient. The implication of their theory that incentive and uncertainty have a positive relationship is thus not strongly supported by the data. Nonetheless, they finds evidence that pay-for-performance sensitivity increases as the agent reaches his or her retirement, although the magnitude of the increase in pay-for-performance sensitivity is surprisingly small. For the CEOs with cash earning of $562,000, 10% change in shareholders wealth corresponds to $7,300 of CEO ’s wealth change for CEOs more than three years from retirement, but $9,500 for CEOs fewer than thee years to retirement.

Note again that the basic reason why pay-for-performance increases with tenure in Gibbons and Murphy (1999) is because of the standard inverse relationship between incentive and risk. Contrary to such standard results, Prendergast (2002) shows that un- der some conditions pay-for-performance sensitivity is non-decreasing with uncertainty. In his model, uncertainty dictates if the principal chooses “input-based compensation” or “output-based compensation”. For input-based compensation, the agent is rewarded by his or her input, i.e., if he or she is keeping busy. On the other hand, output-based compensation ties the compensation to the output, i.e., the firm’s value. It is assumed that making output-based compensation incurs a fixed cost to the firm so firms want to avoid output-based compensation if necessary. Assuming that the agent observes the business environment better than the principal, if the uncertainty of the business environment is significant, the principal delegates the decision making power to the

agent. However, to keep the agent from abusing the delegated power, the principal uses output-based compensation. In other words, under greater uncertainty, the benefit of delegating decision making power to the agent exceeds the cost of making output-based compensation. If the business environment is less uncertain, the principal keeps the decision making power to himself or herself and uses input-based compensation. Since output-based compensation ties compensation to output, we are likely to observe greater pay-for-performance sensitivity when uncertainty is large.

Tadelis (2002) shows that incentive from a reputational concern is ageless: The optimal incentive contract is the same for both younger and older workers. In Tadelis’ model, reputation is a tradeable good. Suppose that the agent works for two periods, then retire. At the beginning of the period, the agent buys a “name” by working for a company. Upon retirement, he or she sells the name. In the first period, the reputation affects the second period income which creates an incentive. In the second period, the reputation determines the price at which the agent can sell the name, creating continued concerned for reputation. The author shows that the incentive in the first period and the second period are quantitatively equivalent. Tadelis is mainly concerned with the relationship between incentive and the years to retirement, thus his task is not to show the relationship between incentive and tenure. However, if all agents are assumed to begin their tenure as CEOs at the same ages, his model suggests that pay- for-performance sensitivity is constant with regard to tenure.