Lucian A. Taylor
CEO wage dynamics: Estimates from a learning model
Journal of Financial Economics | Volume 108, Issue 1 (Apr 2013): 79–98

This paper examines how learning about a CEO's ability affects the level of her pay. I find that CEO compensation responds asymmetrically to good and bad news: the average CEO captures approximately half of the surplus from good news about her ability, but completely avoids the negative surplus from bad news about her ability. This “downward rigid” pay does not appear to be a result of weak governance. Instead, it may be optimal for risk-averse CEOs who would like insurance against compensation decreasing in response to bad news. In return, risk-averse CEOs are willing to start at a significantly lower pay for this insurance. Since CEOs capture roughly half of the positive surpluses from good news, CEOs and shareholders appear to have roughly equal bargaining power over these surpluses.

There is a considerable debate over the level of executive pay and how it should respond to news about the CEO's ability. A number of scholars (Jovanovic (JPE 1979), Harris-Holmstrom (RES 1982), Gibbons and Murphy (JPE 1992)) argue that CEOs should capture 100% of the surplus from good news, because they could always threaten to take their skills elsewhere at no cost. A few papers (Gabaix-Landier (QJE 2008), Tervio (AER 2008), Alder (2009), Nguyen-Nielsen (2010)) provide estimates of how much CEOs capture from the value they create, and they find numbers varying widely between 2% and 80%. The difference in this paper is that I develop a measure for the surplus created by new information each year, and I allow the estimate of the CEO's share to be different when the surplus is positive and when it is negative. My findings also relate to the discussion on how much say CEOs have in their compensation, since CEOs' share of surplus reflects their bargaining power with shareholders. Finally, Harris-Holmstrom find that CEOs will accept lower wages in return for downward rigidity. In this paper I find that when CEOs are very risk-averse, the savings from these initially lower wages are large. The findings in this paper have implications for CEO compensation contracts, corporate governance and shareholder value.

The model

The approach in this paper is to fit a model to the data. The model consists of CEOs with different abilities. Shareholders and CEOs themselves learn about this ability over time, and use what they learn to update their beliefs about how much the CEO will contribute to future firm profits. The change in this perceived contribution, positive or negative, is a surplus that the CEO and shareholders split according to some predetermined ratio. For example, suppose that after a year of high profits we update our beliefs about a CEO's ability, and as a result the CEO's perceived contribution to next year's profits increases by $10 million. If the CEO obtains a $5 million raise for the following year, then the CEO captures half of the $10 million surplus and shareholders pocket the rest. One main result of this paper is that the CEO's share of positive surpluses is roughly half, but her share of negative surpluses is zero. In other words, when new information suggests the CEO is well suited for the job, the CEO captures about half of the benefit of this positive information, on average. However when new information suggests the CEO is not well suited for her job, her compensation does not decrease in response, on average; she captures none of that negative surplus.

Next, I provide more details about the model and how I arrive at my conclusions. Again, CEOs are born with different ability levels that do not change over their tenure. No one knows what this ability level is, not even the CEOs themselves. Everyone learns about ability over time by observing two types of signals: the firm's realized profit and a shared, additional signal. The additional signal is unrelated to current profitability, and can be thought of as any additional information that an investor might use to judge the quality of a CEO: for instance, the specific actions and choices of the CEO, the performance of individual projects, the CEO's strategic plan, the firm's growth prospects, and media coverage.

The firm's profitability each year depends on CEO ability, aspects of the firm that do not change over time, and random shocks that hit the firm and its industry. At the end of each year, investors and shareholders observe realized profitability, as well as the additional shared information mentioned above, and use these two signals to update their beliefs about the CEO's innate ability.

A CEO's yearly compensation equals a pay level plus a random component that depends on the firm's stock return and the CEO's pay-performance sensitivity. The focus of this paper is the level of pay, not the random component that depends on the CEO's bonus and holdings of stock and options. The CEO's pay level is equal to the previous year's pay level plus the CEO's share of the surplus from learning. For example, suppose that last year's profits were lower than expected, causing the CEO's perceived contribution to next year's profits to drop by $20 million. If the CEO's pay level drops by $2 million compared to the previous year, we would say that the CEO “captures” 10% of the negative $20 million surplus.

I call the CEO's share of positive surpluses θup and her share of negative surpluses is θdown, and I estimate the value of these two (and a few other) parameters. The data sample contains 20,700 firm-year observations and 4,545 CEOs from S&P 1500 firms from 1992–2007. I estimate parameter values using the simulated method of moments (SMM), an estimation technique that finds the parameter values that make the model match the data as closely as possible. Specifically, I ask the model to fit two main features of the data. First, I ask the model to fit the observed stock return volatility during a CEOs' tenures. In both the model and the actual data, stock return volatility decreases with CEO tenure. Second, I ask the model to fit the sensitivity of changes in the level of CEO pay to the previous year's stock return. In both the data and the estimated model, changes in pay are much more sensitive to positive lagged returns than to negative lagged returns. Overall, I find that the model fits the data quite well.


I find that profitability is a very noisy signal of CEO ability, with the profitability shock's standard deviation estimated at about 36%. The additional shared signal however is much more precise, with a standard deviation estimated at about 3.3%. In other words, the additional signal of CEO ability is less noisy than the firm's profits. This result is consistent with research showing that investors use other signals beside profitability to judge CEO ability (Cornelli-Kominck-Ljunqvist (JF 2013), Taylor (JF 2010)). I also find that the standard deviation of prior beliefs about CEO ability is 4.1%, which implies a difference in average profitability between the 5th and 95th percentile CEOs of 13.6% of assets per year, which is quite large.

The estimate of θdown is not statistically significant from zero, while the estimate of θup is 48.9% with high statistical significance. In other words, CEOs avoid negative surpluses while capturing roughly half of positive surpluses.

With this model, I am able to run a counterfactual scenario to estimate the savings (or cost) to firms of having downward rigid pay. I ask how much more we would have to pay CEOs if their pay were not downward rigid. I compare the existing net cost to firms to a case where θdown = θup = 0.49, meaning the CEO's share of a surplus is the same whether the surplus is positive or negative, i.e. about half. When the CEO's relative risk aversion is 0.5, fairly low, the average firm spends 13% ($7.3 million) more on CEO pay under this new scenario without downward rigidity. With a relative risk aversion of 4, the cost to the firm is multiplied by 7.6, representing a $356.4 million increase compared to the case with downward rigid pay. This amount is a non-negligible fraction of the average firm's assets. In sum, I find that we would have to pay CEOs significantly more if CEOs are sufficiently risk averse and if their pay were (counterfactually) not downward rigid. The reason why is that CEOs' pay would become much riskier if it were not downward rigid, so we would have to pay CEOs more to convince them to take the job.

It is also interesting to examine why surpluses are shared the way they are. To begin answering this question, I measure how parameter estimates vary across firms. I find that θup is significantly higher in firms with higher institutional ownership, a proxy for governance strength. This result undermines the notion that CEOs capture more of the surplus from positive news because of weak governance. Similarly, CEOs' share of the surplus from bad news (θdown) does not increase with higher institutional ownership (in fact it seems to decrease, though not significantly so). In other words, CEOs avoid negative surpluses even in firms with strong governance.

Finally, I show that the paper's main conclusions are robust to a number of model extensions. First, I estimate the model using a new vesting measure that accounts for stock- and option-based compensation the year that it vests rather than the year it is granted. I find that pay is still downward rigid, and the share of positive surpluses is still close to half for the CEO, though higher at 68%. Second, I change the model to have the board of directors decide at the end of each year whether to fire or keep its CEO. The main model has CEO tenure pre-determined and independent of the CEO's performance. Again, the main conclusions are unchanged, with pay still downward rigid and θup at 49.4% compared to 48.9% previously. Third, where firm quality was previously a known and constant component, I allow it to be unobserved initially just like CEO talent. Agents learn about firm quality at the same time as they learn about CEO ability. The only parameter that changes significantly as a result is the estimated volatility of profitability shocks, which is expected to decrease since uncertainty about the firm's quality now accounts for some of the volatility in stock returns. I also discuss the effects of allowing persistent shocks to profitability (rather than one-year shocks as before), including effects from the turnover of non-CEO executives, and allowing earnings volatility, sharing rules and CEO ability to vary over time.


I estimate a model in which agents learn gradually about a CEO's ability, and the CEO and shareholders split the surplus resulting from a change in the CEO's perceived ability. CEO pay responds asymmetrically to good and bad news about ability. The level of pay does not drop after bad news, implying the average CEO has downward rigid pay. This result is consistent with the model of Harris-Holmstrom (RES 1982), in which firms optimally insure employees by offering a long-term contract with downward rigid pay. I find that offering downward rigid pay allows firms to pay risk-averse CEOs significantly less, on average. Following good news about CEO ability, the level of pay rises enough for the average CEO to capture roughly half of the positive surplus. This result implies that CEOs and firms have roughly equal bargaining power over these positive surpluses, on average. The asymmetric response is significantly stronger in firms with more institutional ownership, suggesting the result is not driven by weak governance.

This paper's goal is to measure the surpluses from learning and how they are split. An important next step is to understand why surpluses are split the way they are. The cross-sectional analysis begins to answer this question, but there is still important work to be done. Also, this paper focuses on the level of CEO pay while abstracting from incentive compensation. Understanding how strong of incentives and what types of incentives managers should have continues to be an important area for future research.

Unknown artist: Bhutanese thanka of Mount Meru and the Buddhist Universe. Bhutan, 19th century.. Bhutan is the only country to use Gross National Happiness as its official measure of economic progress. GNH was a term coined in 1972 by Bhutan's fourth Dragon King. It symbolized his commitment to modernization, balanced with preservation of its Buddhist spiritual culture. Bhutan's strong Buddhist foundations are expressed in the form of “thanka”—detailed and fine paintings with water color, mineral, or organic pigments on silk or paper, with Buddhist themes, with a typically circular arrangement. This thanka is displayed in the large fort of “Trongsa Dzong,” now used for administrative purposes.