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@MISC{9%_,

author = {9% and Sam Allgood and Kathleen A Farrell ; Almazan and Andres and Javier Suarez and ; Bertrand and Marianne and Antoinette Schoar and ; Bond and Itay Philip and Edward S Goldstein and Robert M Prescott ; Bushman and J Raffi and Abbie Indjejikian and ; Smith and Harry Deangelo and Linda Deangelo and ; Demb and Ada and F. Friedrich Neubauer and ; Eisfeldt and Andrea L Adriano and A Rampini ; Fama and Eugene F and Kenneth R French ; Fama and Eugene F and Michael C Jensen and Drew Fudenberg and Jean Tirole and ; Gabaix and Xavier and Augustin Landier and ; Hennessy and Christopher A and Toni M Whited ; Hermalin and Benjamin E and Michael S Weisbach and ; Michaelides and Alexander and Serena Ng},

title = {},

year = {}

}

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### Abstract

Abstract Two percent of CEOs are fired per year on average. To evaluate this magnitude, I solve and estimate a dynamic model of forced CEO turnover. The model features costly turnover and learning about CEO ability. To rationalize the two percent firing rate, boards must behave as if replacing the CEO costs shareholders 5.9% of the firm's assets. This cost mainly reflects CEO entrenchment and poor governance rather than a real cost for shareholders. In terms of both direction and magnitude, the model helps explain the relation between CEO firings and tenure, profitability, and stock returns. Electronic copy available at: http://ssrn.com/abstract=1342547 Previous empirical work has established that CEOs are rarely fired, and that firm performance is a poor predictor of forced CEO turnover. On average, 2% of CEOs at large U.S. corporations are fired each year (e.g., Kaplan and Minton (2006), Huson, Parrino, and Starks (2001)). While many authors find a statistically significant relation between turnover and measures of firm performance, a recent survey concludes that "performance continues to explain very little of the variation in CEO turnover" (Brickley (2003)). For instance, Kaplan and Minton (2006) forecast CEO turnover using lagged profitability and stock returns, and they obtain R-squared values of only 2 to 11%. It is tempting to conclude from these patterns that boards do not act in shareholders' interests. However, the literature provides little guidance for making such a judgment. For example, it is not clear what rate of forced CEO turnover we should expect from boards which do act in shareholders' interests. Therefore, it is difficult to judge whether the observed 2% rate is low or high. This paper's goal is to provide a benchmark for evaluating the frequency of forced CEO turnover and the relation between turnover and firm performance. The benchmark is a dynamic model featuring a rational board that maximizes shareholder value. In the model, the board decides at each point in time whether to fire or keep its current CEO. Some CEOs are more skilled than others, meaning they can produce higher average firm-specific profits. Firing an unskilled CEO is not always in shareholders' interests, because CEO turnover entails a real cost to shareholders. For instance, the firm may have to pay a severance package and executive search fees. Complicating matters, the board cannot directly observe CEO skill, but instead learns about it over time. The board learns in part by observing the CEO's industry-adjusted profits. However, profits are not the only information boards have about CEO skill. For example, stock returns, market share, the CEO's strategic plan, and the CEO's specific actions may also be informative. The model aggregates all this other information into a single additional signal. At each point in time, the board observes profits and the additional signal, assesses the CEO's skill, and then decides optimally whether to replace him with a new CEO of uncertain skill. The model offers an explanation for why profitability poorly predicts forced CEO turnover: Boards rely heavily on information besides profits when evaluating CEO ability. The model predicts that boards rationally rely less on signals of CEO skill which are less precise. Profitability is an imprecise signal, because it is noisy (it fluctuates for reasons unrelated to CEO skill) and persistent (it responds slowly to CEOs' actions). If the profitability signal is much less precise than the board's additional signal, then the board pays little attention to profitability when evaluating the CEO's ability. As a result, profitability poorly predicts forced CEO turnover. The weak predictive relation is in shareholders' best interests, since the board uses the most reliable information to make firing decisions. The model suggests three potential reasons why boards rarely fire CEOs. First, firing a CEO may entail 1 Electronic copy available at: http://ssrn.com/abstract=1342547 large, real costs to shareholders. Second, CEO skill may not matter much. The model predicts that fewer CEOs are fired if there is less variation in skill across CEOs. Intuitively, if CEOs all have roughly the same ability, then there is little incentive to replace one CEO with another, especially if doing so is costly. Third, boards may learn slowly about CEO skill, so that unskilled CEOs survive longer in office and possibly retire before the board decides to fire them. The model predicts that boards learn more slowly when profitability is more volatile or persistent, when the board's additional signal is less precise, or when prior beliefs about CEO skill are stronger. Outside the good-governance benchmark, there is a fourth potential reason why CEOs are rarely fired: Boards dislike firing CEOs for reasons unrelated to shareholder value. For instance, directors may have personal or professional ties to the CEO. Also, firing the CEO may put the directors' own jobs at risk, may require uncompensated effort to find a new CEO, or may hurt directors' chances of being nominated to other boards (Hermalin and Weisbach (1998)). To capture these effects, the model assumes the board incurs a personal utility cost each time CEO turnover occurs. Unlike the real turnover costs discussed in the previous paragraph, the personal costs do not directly affect profits. To the extent that boards honor these personal costs, they deviate from maximizing shareholder value, at least in an ex post sense. It is a challenge to measure the importance of these four potential reasons why CEOs are rarely fired. The board's firing choices are endogenous, which generates endogenous patterns in firm performance. There are no obvious instruments. Several elements of the model are unobservable, including a CEO's actual and perceived skill, the CEO talent pool, the board's additional signals of CEO skill, and the board's personal costs of CEO turnover. Also, some of the reasons interact. For example, variation in CEO skill (reason two) affects the speed of learning (reason three) via the uncertainty about CEOs' ability. Finally, measuring the reasons' magnitudes is difficult. While we can measure directional effects using reduced-form empirical techniques, evaluating magnitudes requires estimating or calibrating an economic model. These challenges lend themselves to a structural estimation approach. The structural approach infers unobservable quantities from endogenous patterns in firing decisions and firm performance. It also takes into account interactions between the four reasons above. Finally, with a structural approach we can assess not only the reasons' directional effects, but also their magnitudes. I estimate the model's parameters by applying the simulated method of moments to data on firm profitability and both forced and voluntary CEO turnover in large U.S. firms from 1971 to 2006. The estimated parameters include the real cost of CEO turnover to shareholders, the variation in skill across potential CEOs, the volatility and persistence of profitability, the precision of boards' additional information about CEO skill, and the personal cost of turnover to the board. Estimates imply that extremely high CEO turnover costs are needed to rationalize the observed rate of forced CEO turnover. Boards behave as if the total cost of firing a CEO is an estimated 5.9% of the 2 firm's assets, or $236 million for the median sample firm. This estimate provides a metric for evaluating the empirical rate of forced CEO turnover: the 2% rate is indeed low, in the sense that an extremely high CEO turnover costs is needed to explain it. The total CEO turnover cost is the sum of real costs to shareholders and personal utility costs to the board. This study disentangles these costs using two assumptions: the personal costs do not affect profits, and the real costs show up in profits in the two years around the succession. I find that the personal cost makes up 4.6% of the total 5.9% turnover cost. In dollar terms for the median firm, the total $236 million turnover cost breaks down into $183 million of personal costs and $53 million of real costs. The board behaves as if firing the CEO costs shareholders $236 million, whereas it really only costs them $53 million. The result is that the board keeps some CEOs whom shareholders would rather see fired. The large personal cost indicates either that CEO turnover is extremely costly to directors (in a utility sense), or that directors do not care much about shareholder value. The model cannot distinguish between these two possibilities. Either way, the results imply CEOs are highly entrenched. One interpretation of this entrenchment is that it reflects poor governance by boards. Consistent with this interpretation, personal turnover costs are significantly smaller in situations with better governance, as proxied by a higher fraction of directors who are not also officers, CEOs who left office in 1990-2006 instead of 1971-1989, or in larger firms where shareholders have greater incentives to monitor the board. A second interpretation is that the level of entrenchment I measure is optimal for shareholders ex ante, for instance, because it allows shareholders to pay the CEO less or hire a better CEO. Consistent with this interpretation, I find no significant relation between personal costs and the fraction of shares owned by the board, another measure of governance quality. On balance, results indicate that the personal turnover costs reflect bad governance. However, not all the evidence above supports this view. As mentioned earlier, profitability poorly predicts forced CEO turnover in the data. To rationalize this pattern, I find that boards' additional signal of CEO skill (the signal unrelated to profits) must have a 5.3 times larger influence on the board's beliefs than profitability has. Essentially, the board's non-earnings signal must be extremely precise, so the board does not put much weight on earnings when evaluating a CEO's ability. As a result, the board's firing decisions are only weakly related to profitability. This result provides a metric for evaluating the profitability-turnover relationship in the data: the relationship is indeed weak, in the sense that to rationalize it, boards must have extremely precise additional information about CEO ability. The estimated model fits the data well. The model predicts that 2.2% of CEOs are fired per year on average, which is close to the 2.3% rate in the data. Because of its dynamic setup, the model can also explain the timing of forced CEO turnover, which depends on how fast the boards learn about CEO skill. The model predicts that the median fired CEO spends a total of four years in office, which exactly matches 3 the empirical median. Also, the model generates a hump-shaped relation between forced turnover rates and tenure, which is similar to the pattern in the data. The model can fit several aspects of the turnoverprofitability relationship. In predictive probit models of forced CEO turnover on lagged profitability, the model generates a pseudo R-squared of only 2%, which is close to the 3% value from the empirical sample. The model can also closely match the empirical probit slopes. The model produces a V-shaped pattern in average profitability around CEO dismissals, which closely matches the empirical pattern. The model also makes predictions about stock returns. The model predicts a -18% abnormal stock return over the five years before forced CEO turnover, on average. On this dimension, the model misses in terms of magnitude: the corresponding empirical return is -35%. However, the model gets the shape right. In both the data and the model, stock prices drop gradually leading up to CEO dismissal and are essentially flat after. While there is a large empirical 1 and theoretical 2 literature on CEO turnover, this is the first study that estimates a structural model of CEO turnover. Therefore, this is one of the first attempts at using an economic model to evaluate the magnitudes in the CEO turnover data. As I discuss later, my model is consistent with several existing empirical findings, and the model also produces new, untested predictions. My goal is not to make a theory contribution, however, but to adapt and estimate existing models, and use the parameter estimates to evaluate empirical magnitudes. Miller (1984) estimates a model similar to mine using labor market data from multiple occupations, such as farm workers. Our models both feature optimal worker separation, a dynamic setup, and learning about skill from the worker's output. However, there are several differences between our models, and we use different data, identification strategies, and estimation methods. 1 E.g., Coughland and Schmidt (1985); 2 E.g., Herschleifer and Thakor (1994, 1998); Hermalin and Weisbach (1998, 2007); Fisman, Khurana, and Rhodes-Kropf (2007); Eisfeldt and Rampini (2007). 4 I present the model in Section 1. Section 2 describes the data and estimation method. Section 3 presents estimation results, and Section 4 discusses robustness. Section 5 concludes. I. Model In this section I develop and solve a model of forced CEO turnover. In the model, a board decides at the beginning of each period whether to fire or keep the current CEO. Some CEOs are more skilled than others, meaning they can generate higher average firm-specific profits. The board faces a tradeoff when deciding whether to fire an unskilled CEO. On one hand, the board cares about future profits and therefore prefers to have a skillful CEO in office. On the other hand, firing the CEO entails a real cost to shareholders as well as a personal utility cost to the board. The board cannot directly observe CEO ability, but instead learns gradually by observing two signals, firm-specific profitability and an additional, unrelated signal. At each point in time, the board makes its best possible assessment of the CEO's ability and then makes an optimal firing decision. A. Assumptions The model features a firm which lives for an infinite number of periods, a large pool of potential CEOs, and a board which makes CEO firing decisions. I set one period equal to a year in the empirical implementation. The board of directors can fire the CEO and hire a new one at the beginning of each period. In addition, a CEO who has already served τ periods voluntarily leaves the firm (he either quits or retires) with exogenous probability f (τ ). 3 The firm's book value of assets equals B t at the beginning of period t. 4 The firm generates profits equal to Y t B t at the end of period t, so Y t is the firm's profitability. 5 Profitability has three components: Component v t is the industry average profitability at time t. Component c is the real cost of CEO turnover, which I define later. Firm-specific profitability y t mean-reverts around α, the current CEO's skill level: The shock t is independently and normally distributed with mean zero and variance σ 2 . To be precise, equation 4 For tractability, and since investment and dividend policy are not a focus of this paper, I assume all profits (including potential negative profits) are immediately paid out as dividends. 5 Profitability is net of CEO pay, which is outside the model. Therefore, the model takes no stand on how the surplus from CEO ability is shared between the CEO and shareholders. 5 notion of CEO skill: A CEO is considered highly skilled (i.e. high α) if he can achieve profitability higher than the industry, on average and in the long run. Parameter φ determines the persistence in firm-specific profitability, y t . y t is a random walk when φ = 0, is iid when φ = 1, and is mean reverting for 0 < φ < 1. I allow persistence in firm-specific profitability for two reasons. First, there is empirical evidence of persistence (e.g. Fama and French (2000)). More importantly, persistence allows a CEO to have long-lasting effects on profitability, which is plausible and affects the firing decision. For instance, after a CEO is fired for poor earnings performance, earnings may continue to be low for a few years even if the new CEO is highly skilled, because it takes time to undo the old CEO's mistakes. During those years, the board would not want to penalize the new CEO for the old CEO's mistakes. In other words, persistence in profitability affects the way the board evaluates CEO ability. , and costs to the board ("personal costs"), denoted c Firm costs include severance or retirement packages, fees to executive search firms, disruption costs, and any other CEO turnover costs which directly affect profits. Personal costs do not affect the firm's profits, but do affect the board members. Examples of personal costs include the loss of the CEO as an ally both within the firm and in the directors' careers outside the firm, any uncompensated effort and stress from the succession process, and in the case of forced turnover, reputation costs from "rocking the boat," which may damage directors' chances of being nominated to other boards (Hermalin and Weisbach (1998) Parameter β is the board's discount factor, with 0 < β < 1. Expectation E t is with respect to the board's information at time t. The board's time-t utility is The board prefers higher profits (the κB t Y t term) and experiences a personal cost from CEO succession (the term). The constant κ > 0 controls the degree to which the board internalizes shareholder value. 6 Yermack (2006) finds that separation pay to CEOs is increasing in firm size. Executive search fees are proportional to CEO compensation (e.g., the Association of Executive Search Consultants, http://www.aesc.org/), which increases in firm size (Gabaix and Landier 6 For instance, we might believe κ is higher when directors have a greater sense of fiduciary responsibility, own more shares or options, or receive greater reputation benefits from their firm's success. CEO firing choices affect the board's utility in two ways. First, they affect profitability Y t , because profitability depends on the acting CEO's ability as well as the firm turnover costs c (f irm) . Second, the board incurs an additional personal cost c (pers) each time it fires the CEO. There is an indeterminacy between κ and c (pers) , since the utility function is defined up to an affine transformation only. I discuss this indeterminacy more later. Substituting If we interpret discount factor β as the firm's cost of capital, then the first term in equation The board can observe all parameters, but cannot observe CEOs' skill levels α. Therefore, when the board observes high firm-specific profitability, it cannot be sure whether this is due to CEO skill (i.e. high α) or luck (i.e. high t ). When the board hires a new CEO, it starts with normally distributed prior beliefs about his ability: The board's prior beliefs match the distribution of skill α in the CEO talent pool. Therefore, parameter σ 0 plays two roles. It is both the initial uncertainty about a newly hired CEO's skill, and also the dispersion in true skill in the population of potential CEO replacements. Each period, the board updates its beliefs about ability α according to Bayes' Rule, using information contained in firm-specific profitability y t , and z t , which is an additional signal of CEO ability. The additional signal represents all information held privately in the firm (e.g. the CEO's specific actions and choices, the performance of individual projects, the CEO's strategic plan, turnover in other senior management), as well as public information (e.g. stock returns, sales growth, market share, discretionary earnings accruals, media coverage). The signal z t contains all information arriving in period t which is not already contained in the firm's profitability. Without loss of generality, I treat this additional information as independent of profitability and centered at the CEO's skill, α. I also assume the signal is normally distributed with constant volatility, and is iid over time: The signal z is more precise when its volatility σ z is lower. Like all models, this model presents a simplified view of the world. The simplifications allow me to 7 The board's firing decisions are optimal ex post, because the board optimizes each period and cannot commit up front to a different long-run policy. Later I discuss whether personal turnover costs may be optimal for shareholders ex ante in a more general model that allows long-run commitments. 7 obtain predictions from the model and identify parameter values from the data. In Section 4 I discuss several elements which are missing from my model, including firm fixed effects, time-varying personal turnover costs, CEO learning on the job, fluctuating CEO skill, board risk aversion, and earnings manipulation. B. Solving the Model First I solve the board's learning problem, which is a Kalman filtering problem. I introduce notation to distinguish between µ inc t , the posterior mean of the incumbent CEO's skill α going into period t, and µ t , the prior mean of the CEO chosen to serve in period t. If the firm decides not to fire the incumbent, then The surprises in persistence-adjusted profitability and the additional signal equal I show in Appendix A 8 that the posterior mean equals the prior mean plus two mean-zero shocks, one from the profitability surprise and one from the z t surprise: The posterior mean follows a random walk with no drift. The board rationally ignores the industry component of profitability, v t , which contains no information about the CEO's skill. Also, the board adjusts for persistence in profitability The following proposition characterizes the board's optimization problem. Proposition 1 (Bellman equation): The board's objective function can be simplified as where the value function V (µ, τ, 0) solves the Bellman equation All technical appendices are available in a separate document available on the author's website: Insert website address here. subject to a boundary condition if the CEO has just retired: Proof in Appendix B. Equation (from the learning rule), and one more year of tenure (hence τ + 1). The boundary condition in equation I obtain an approximate solution for V (µ, τ, 0) by discretizing the state space and iterating on the Bellman equation, as described in Appendix C. I obtain additional predictions by simulating CEO spells from the model. I define a CEO spell as all the periods a CEO serves in office. To simulate a single spell, I draw the CEO's true skill α from the prior distribution, I generate firm-specific profitability y t and additional signals z t using the CEO's true skill α, and I update the board's beliefs according to the learning rule in equation C. Model Predictions In this subsection I discuss the model's predictions about the board's firing policy, the frequency and timing of firings, and turnover's relation to profitability and stock returns. These predictions hold for a wide range of plausible parameter values. However, since I solve the model numerically, I cannot prove the predictions hold for all parameter values, and so I do not present these predictions as formal propositions. The Board's Firing Policy The board fires the CEO as soon as its assessment of the CEO's skill, i.e., the posterior mean of α, drops below an endogenous threshold. The threshold depends on all model parameters, as well as the number of periods the CEO has been in office. Raising the total turnover cost c shifts the firing threshold down, making 9 firings less likely. Intuitively, when firing the CEO is more costly, the CEO must have lower perceived skill to make firing him worth it. This result does not depend on whether cost c is larger due to higher firm turnover costs c (f irm) or higher effective personal turnover costs c (pers) /κ (recall The firing threshold increases with tenure, meaning the board becomes more willing to fire a CEO the longer he has been in office, all else equal. The explanation relates to uncertainty and the CEO's option value. When the firm hires a CEO, it acquires an option to fire him. All else equal, firms prefer higher uncertainty about CEO skill, because higher uncertainty raises the option's value, and the board is risk neutral. Intuitively, firms enjoy the upside of uncertainty by keeping CEOs who end up being highly skilled, but firms avoid the downside of uncertainty by firing CEOs who end up being unskilled. A CEO's uncertainty drops with tenure as the board learns about his skill, so his option value declines and the board becomes more willing to fire him. Hermalin and Weisbach (1998) make a similar prediction. The Frequency and Timing of CEO Turnover I illustrate the model's predictions using the following parameter values: β = 0.9, µ 0 = 1%, σ 0 = 2%, σ = 3%, c = 3%, φ = 0.12, and σ z = 7%. These parameter values are close to the empirical estimates in Section 3. I assume CEOs retire if they complete 15 periods, but not before then. The top panel of INSERT FIGURE 1 NEAR HERE Not surprisingly, firing rates are lower and more CEOs survive to retirement when the total turnover cost c is higher. Consistent with this prediction, Parrino (1997) finds that forced CEO turnover is more likely in homogenous industries. As Parrino notes, the real costs of firing a CEO are probably lower when the firm can find a replacement in a similar firm. Turnover costs also affect the timing of firings. Firings typically happen at later tenures when turnover costs are higher. Hazard rates decline monotonically when c = 0, are hump-shaped when c = 3%, and increase monotonically when c = 5%. Intuitively, the board is cautious and waits for more information when firing the CEO is more costly. The bottom panel of CEOs are roughly alike in terms of their ability (i.e., low σ 0 ), then there is not much incentive to replace one CEO with another, especially when doing so is costly. Prior uncertainty also affects the timing of firings. Firings occur later when prior uncertainty σ 0 is lower. The hazard function is downward sloping when σ 0 = 3%, hump shaped when σ 0 = 2%, and upward sloping when σ 0 = 1%. The board learns more slowly when prior beliefs are stronger (i.e. lower σ 0 ), so it takes longer for the board to decide whether to fire the CEO. Supporting this intuition, the model also predicts that CEOs are fired later when the additional signal's volatility σ z is higher, profit volatility σ is higher, and persistence parameter φ is lower, all of which cause the board to learn more slowly. The board learns more slowly when profitability is more persistent (lower φ), because profitability spends less time closer to its long-run mean, the CEO's skill level α. In other words, when profitability is more persistent, it reacts more slowly to CEOs' actions and is therefore less informative about CEO skill. To my knowledge, no one has tested the reduced-form prediction that firings occur later in office when boards learn more slowly about CEO skill. CEO Dismissals and Profitability Figure 2 illustrates the turnover-profitability relationship by plotting average firm-specific profitability in event time around CEO dismissals. The figure also shows the average across CEOs of µ t = E t [α], the board's posterior mean of the CEO's ability α. INSERT FIGURE 2 NEAR HERE First I discuss the pattern in beliefs about CEO skill, µ t . The posterior mean drops gradually leading up to forced CEO turnover at time zero. In other words, the board's opinion of the CEO deteriorates leading up to his firing. We know this must occur in order for the posterior mean to drop below the firing threshold, so that the CEO is fired at time zero. The posterior mean jumps up to the prior mean following turnover, because the firm hires a new CEO and starts with new prior beliefs about his skill. The average posterior mean creeps up after period zero, because some CEOs are fired after year zero, and survivors are perceived to be more skilled than the average new hire. Next I discuss the pattern in average realized excess profitability. As noted above, the posterior mean skill µ t must drop before the CEO is fired. To cause downward revisions in posterior mean skill µ t , either excess profitability y t or the signal z must repeatedly be lower than expected. On average, excess profitability y t drops leading up to forced CEO turnover at time zero. Consistent with this prediction, Weisbach (1988), Murphy and Zimmerman (1993), Huson, Parrino, and Starks (2001), and others find that CEO turnover is more likely following low profitability; Huson, Malatesta, and Parrino (2004) document a drop in profitability before forced CEO turnover. 11 Average excess profitability rises after the CEO is fired. This prediction is due to a replacement effect and a learning effect 9 . First, the replacement effect: compared to the fired CEO, the new CEO is more skilled on average and hence can generate higher profits. The learning effect is more subtle. Posterior mean skill must drop for the CEO to be fired. In order to "pull down" the posterior mean via Bayesian updating, realized excess profitability typically drops below the posterior mean by the time the CEO is fired. In Even if the firm hires a new CEO with the same low perceived skill, there is still a gap between realized and expected profitability going forward. Therefore, realized profitability is expected to rise, closing the gap. This learning effect is similar to the one in Pástor, Profitability is not a perfect predictor of CEO dismissal in the model, because the board also uses the signal z t to evaluate CEO ability. Even if a CEO achieves very low profitability, he may avoid being fired if the z t signal is high enough. For instance, the board may learn that the low earnings were due to bad luck. The opposite is also possible. Even if profits are not low, the board may nevertheless fire the CEO if the additional signal is low enough. For example, the board may observe the CEO making poor choices and may fire the CEO before his choices affect profits. The top panel of INSERT FIGURE 3 NEAR HERE Firm turnover costs also affect the turnover-profitability relation. The bottom panel of 12 event year -2 to -1 depends on σ z (the volatility of signal z) but not c (f irm) (the firm turnover costs ), so this change in profitability helps measure σ z . Intuitively, from years -2 to -1, the board has not yet decided to fire the CEO, so the firm turnover costs do not yet show up in profitability. The change in profitability from years -1 to 0 depends on both z's volatility and firm costs. Since we have already pinned down z's volatility, we can back out firm costs. I will rely on this result in the empirical section to identify firm costs c (f irm) and signal z's volatility σ z . To my knowledge, no one has tested Several empirical papers estimate logit or probit models that forecast CEO dismissals using lagged profitability (e.g. Kaplan and Minton Stock Returns around CEO Dismissals The board's objective function U t equals the firm's market value in the special case where investors and the board have common beliefs, there are no personal costs of CEO turnover, and the board and investors use the same discount rate β. To build intuition, I obtain predictions about stock returns under these additional assumptions. However, I do not use stock returns to estimate the model, for two main reasons. First, Details on obtaining stock returns are in Appendix D. INSERT FIGURE 4 NEAR HERE II. Estimation First, if the Wall Street Journal reports that the CEO is fired, forced from the position, or departs due to unspecified policy differences, the succession is classified as forced. For the remaining cases, the succession is classified as forced if the departing CEO is under the age of 60 and the Wall Street Journal announcement of the succession (1) does not report the reason for the departure as involving death, poor health, or the acceptance of another position (elsewhere or within the firm), or (2) reports that the CEO is retiring, but does not announce the retirement at least six months before the succession. The circumstances surrounding the departures of the second group are further investigated by searching the business and trade press for relevant articles in order to reduce the likelihood that a turnover is incorrectly classified as forced. These successions are reclassified as voluntary if the incumbent takes a comparable position elsewhere or departs for previously undisclosed personal or business reasons that are unrelated to the firm's activities. 14 I interpret one model period as a year, and I assign successions to the closest fiscal year end. I use data from all years a CEO spent in office, including years before 1971. To avoid estimation bias from this sampling method, I use the same sampling method in my simulation estimator (Section 2.C). The sample does not include CEOs who left office due to a takeover, whose succession was not announced in the Wall Street Journal, or who have missing data in Compustat. I set firm profitability Y t equal to the firm's return on assets (ROA) in year t. 10 Industry average profitability v t is an equal-weighted average of ROA across firms in each of 12 industries defined on Kenneth French's website. When computing v t I use each year's 1,000 largest firms (by lagged assets) in Compustat to avoid bias from changes in Compustat's coverage. CEOs in a given year. Forced CEO turnover appears to be more common in some industries than others. I do not attempt to estimate the board's discount factor β. Instead, I fix the value of β at 0.9, a plausible value given firms' annual cost of capital. For robustness, in Section 4 I estimate the model using other values of β. To explain the intuition for how the remaining parameters are identified, I assume we have data on many CEO spells governed by the same parameters-either a long time series for a single firm, or a large cross section of firms sharing the same parameters. I start with the parameters governing firm-specific profitability and prior beliefs. Time-series autocorrelation in firm-specific profitability helps identify φ, the profitability persistence parameter. After removing the persistent component in profitability, profitability volatility within CEO spells will help identify σ , the volatility of profitability shocks. The average level of profitability helps identify the prior mean skill µ 0 , and dispersion in average profitability across CEOs helps identify dispersion in CEO skill, σ 0 . The endogenous firing decisions complicate identification, but the following trick helps explain the intuition. In the subsample containing only CEOs' first year in office, the board has made no turnover decision yet, so there are no endogeneity concerns in this subsample. For each CEO i in the subsample we can compute persistence-adjusted profitability X i,0 from his first year in office: The mean of X i,0 across CEOs equals the prior mean CEO skill µ 0 , since shocks i,0 have mean zero. The variance of X i,0 across CEOs equals σ 2 0 + σ 2 /φ 2 . The first term in the sum comes from dispersion in skill α across CEOs, and the second term comes from the iid shocks firms receive. Knowing φ and σ , we can back out σ 0 , the dispersion in skill across CEOs. The frequency of forced turnover at different tenures helps identify total turnover costs c = c (f irm) + c (pers) /κ. As we saw in Changes in average firm-specific profitability around CEO dismissals help disentangle the firm turnover cost c (f irm) and effective personal cost c (pers) /κ, and also help identify signal z's volatility, σ z . As we saw in 16 Once we know the firm cost c (f irm) and the total cost c, we can back out the effective personal cost: The ratio c (pers) /κ is identified, but c (pers) and κ are not. In other words, we cannot distinguish between a board with a strong distaste for firing the CEO (large c (pers) ) and a board that does not care much about shareholder value (low κ). I only report estimates of the ratio c (pers) /κ. C. Estimation Method M is a vector of estimated moments from the empirical data, and m s (θ) is a vector of estimated moments from the sth sample simulated using parameters θ. I use 14 moments, defined below. Since my empirical sample contains 981 CEO spells, each simulated sample contains 981 CEO spells as well. Michaelides and Ng (2000) find that using a simulated sample 10 times as large as the empirical sample generates good small-sample performance. I use S = 20 simulated samples to be conservative. I use a simulated annealing optimization algorithm to avoid local minima of (21). Additional details on the procedure are in Appendix E. I estimate the seven parameters using 14 moments. The extra moments will provide a test of the model's over-identifying restrictions. All moments use data on excess profitability y * t , which equals firm profitability Y t minus industry profitability v t . At this point I add i subscripts to index the firms in the sample. The first seven moments are the coefficients from the pooled regression The coefficient ∆ (k) is a fixed effect for whether firm i experienced forced CEO in period t−k. The intercept λ 0 will help pin down the prior mean skill µ 0 , and the slope λ 1 will help pin down the persistence parameter φ. The fixed effects ∆ (k) measure the changes in average profitability around forced turnovers. As discussed in Section 2.B, these changes help measure z's volatility σ z and firm turnover costs c (f irm) . The eighth moment is V ar(δ it ), the variance of the residual from equation The next four moments are forced turnover hazard rates. I define h (k) to be the percent of CEOs fired per year in tenure category (k) years, conditional on the CEO reaching (k). I use hazard rates , and h (8+) . These four rates will help pin down c, the total costs of forced CEO turnover. Using total costs c and firm costs c (f irm) , the model can infer effective personal costs according to c (pers The last two moments help tease apart σ and σ 0 , both of which affect variation in profitability. Both moments use data on persistence-adjusted profitability X it ≡ y * it − λ 1 y * it−1 / 1 − λ 1 , where λ 1 is estimated in regression (22). First, for each CEO j I compute E j [X it ] and V ar j (X it ), respectively, the mean and variance of X it across all the years CEO j spent in office. The 13th moment is E [V ar j (X it )], the mean of CEOs' variances. Since this moment removes the effect of each CEO's ability, it is most informative about σ , the time-series volatility of profitability. The 14th moment is V ar(E j [X it ]), the variance of CEOs' means. 18 This moment is most informative about σ 0 , the dispersion in ability across CEOs, because it measures the cross-CEO dispersion in a proxy for a CEO's ability, i.e., his average realized profitability. Finally, the hazard function for voluntary turnover, f (τ ), is an input to the model. I estimate f (τ ) directly from the CEO turnover database, calculating the frequency of voluntary turnover after τ years conditional on the CEO surviving τ − 1 years, pooling all CEO spells. The hazard rate is low when the CEO first starts in office, and then rises gradually (results available on request). III. Empirical Results A. Parameter Estimates Parameter estimates are in 12 The industry standard CEO search fee is one-third of the CEO's total cash compensation in his first year in office, so the average search fee in my sample is roughly $1 million. 13 Under corporate law, shareholders choose the board of directors. However, DeAngelo and DeAngelo (1989) show that shareholders almost always approve the slate which management proposes. The CEO approves and often proposes the slate (e.g. Mace (1971), Lorsch and MacIver (1989), Demb and Neubauer (1992)). 19 of shareholder value (κ = 100%) then the personal cost is the full $183 million. However, if boards only internalize 1% of shareholder value (κ = 1%) then the personal cost is only $1.83 million. To summarize the main results so far, the model needs huge turnover costs to fit the data, and these costs mainly reflect CEO entrenchment rather than a real cost to shareholders. Entrenchment does not necessarily imply bad governance. Some degree of entrenchment may be optimal for shareholders ex ante. I discuss this issue and present additional evidence in Section 3.C. The estimated prior mean skill µ 0 is 0.88% per year, slightly less than than the 2.0% average industryadjusted profitability in the sample Parameter σ 0 is both the standard deviation of ability across new CEOs, and also the uncertainty about a newly hired CEO's ability. The estimate of σ 0 is 2.42% of assets per year. For comparison, Bertrand and Schoar The estimated persistence parameter φ is 0.125, indicating that firm-specific profitability nearly follows a random walk. In contrast, Fama and French (2000) estimate persistence parameters for ROA roughly equal to 0.6, suggesting that profitability is closer to iid. 14 Our results are different because we estimate fundamentally different economic rates. Fama and French measure mean reversion around firm-specific average profitability, whereas my persistence parameter measures mean reversion around industry average profitability. To illustrate the difference, when I estimate a panel regression of excess profitability on its lag, the estimated slope is 0.89, which is close to my estimate of one minus persistence parameter φ. When I estimate the same regression firm by firm, the firms' average slope drops to 0.59, because I have largely removed the effects of firm-specific average profitability. My model's notion of persistence and CEO skill seems plausible: CEOs are considered skilled not only if they can beat the firm's long-run average profitability, but also if they can increase the firm's long-run average profitability relative to the industry. For robustness, in Section 4.A I introduce firm fixed effects in profitability, which results in a higher estimate of φ. 14 Fama and French 20 To interpret the estimate of σ z , the volatility of the board's additional signal, I compare the influence of the profitability signal and additional z signal on the board's beliefs about CEO skill. Specifically, I compare the change in posterior beliefs resulting from a one standard deviation z shock and a one standard deviation profitability signal shock. The model predicts that the response to the z shock is P ≡ σ /(φσ z ) times larger than the response to the profitability signal shock 15 . The P ratio indicates that the additional z signal is more influential when it is more precise (σ z lower), and when profits are noisier (σ higher) and more persistent (φ lower). Applying the delta method, I obtain an estimate of P equal to 5.3, with a standard error of 0.3. In other words, the additional signal z has a 5.3 times larger influence on the board's beliefs, compared to the profitability signal. This result implies boards rely heavily on non-earnings information when evaluating the CEO. Consistent with this result, Bushman, Indjejikian, and Smith (1996) find that boards give considerable weight to information besides earnings and stock performance when determining a CEO's bonus. It is plausible that boards also use this additional information in firing decisions. B. Model Fit In this subsection I assess how well the estimated model fits empirical patterns in forced CEO turnover, firm profitability, and stock returns. The first test is a formal test of the overall model. Since I estimate 7 parameters using 14 moments, the SMM procedure delivers a χ 2 test of over-identifying restrictions (bottom of INSERT TABLE 3 NEAR HERE Next I examine the 14 moments individually to gauge where the model fails. Each row in 21 detail later. Turning to the forced turnover hazard rates h (k) , the model produces too few firings in the first two years, too many firings in years 3 and 4, and not enough firings after year 7. However, the gap between simulated and empirical hazard rates is less than 1% per year for all four moments, and the model successfully produces the hump-shaped empirical relation between tenure and firings, which Allgood and Farrell ar(δ), E[V ar(X)] and V ar(E[X]). The model therefore appears to closely match time-series volatility in profitability for a given CEO (V ar(δ) and E[V ar(X)]), and also the variation in realized profitability across CEOs, V ar (E[X]). The top panel of INSERT FIGURE 5 NEAR HERE More measures of model fit are in INSERT TABLE 4 NEAR HERE The next diagnostics address the relation between profitability and forced CEO turnover. First, I estimate a probit model which use lagged firm-specific profitability to forecast whether a CEO is fired. I use one year of lagged profitability, although results are similar using three lags. The last columns in 22 The model can fit this feature of the data quite closely, predicting a pseudo-R 2 of 2%. The model generates a weak profitability-firing relation because profitability has a small influence on board's beliefs about CEO skill. As discussed in Section 3.A, parameter estimates imply that the additional signal z has a 5.3 times larger influence on the board than the profitability signal has. Essentially, boards do not rely much on profits when evaluating a CEO's skill, because other, unrelated information is more reliable. The bottom panel of Finally, I assess how well the model matches average stock returns around CEO dismissals. As discussed in Section 1, I derive stock prices from the model by assuming boards and investors have common beliefs about CEO skill. In both the model and the data, the CAR drops gradually leading up to forced turnover, and is essentially flat after. C. Does the Personal Turnover Cost Reflect Bad Governance? A central result of this study is that the model needs a large effective personal turnover cost to fit the data. I offer two extreme interpretations of the large personal cost, and then present evidence on which interpretation is closer to the truth. The bad governance interpretation is that personal cost prevents boards from acting in shareholders' interests, even ex ante. Shareholders would prefer a board with no personal costs, i.e., a board that is more 23 willing to fire the CEO. Shareholders cannot elect such a board in the first place because of problems with the governance system. The good governance interpretation is that the personal cost and resulting CEO entrenchment are optimal for shareholders ex ante. By electing a board with large personal turnover cost, shareholders commit up front to a low probability of firing the CEO. This commitment may benefit shareholders by allowing them to pay the CEO less (Almazan and Suarez If the estimated personal costs truly reflect bad governance, then personal costs should be smaller in firms or years with better governance. To test this hypothesis, I examine whether personal turnover costs are related to measures of governance quality. I split the sample using a measure of governance quality, estimate the model independently in each subsample, and then test whether personal costs are equal across the sub-samples. Fama and Jensen (1983) and 17 I thank Robert Parrino for providing data on board share ownership data (originally from proxy statements) and board composition (originally from the Million Dollar Directory). Both measures are available only up to 1994. I exclude CEO spells with missing governance measures. 24 subsample with more outsiders. Finally, I create a large-firm and small-firm subsample by comparing firms' inflation-adjusted assets to the sample median, $6.6B. If shareholders face a fixed cost of monitoring a board, then they have a larger incentive to monitor boards of larger firms, which tend to make up more of their portfolio. Therefore, the bad-governance story predicts smaller personal costs in larger firms. Parameter estimates for the sub-samples are in Panel A of INSERT This difference in personal costs between subsamples is economically large and statistically significant at the 1% level 18 . Although the personal cost drops, it remains significantly positive in the late subsample. The total turnover cost drops from 8.4% to 4.0% of assets. Lower turnover costs should result in more forced successions, all else equal. Indeed, the percent of successions that are forced rises from 12% to 23% between subsamples in the real data. The model generates a rise from 10% to 23%, a close match. Lower turnover costs are not the only reason firing rates rose over time, according to parameter estimates. Dispersion in ability across CEOs (σ 0 ) is significantly higher in the later subsample (difference has t-statistic=2.4), which raises the benefits of replacing the CEO and increases the speed of learning, both of which contribute to higher firing rates (Section 1). Next I examine subsamples split by board stock ownership. Estimated personal costs are higher in the subsample with higher stock ownership (7.99% vs. 6.41% of assets), but this difference is not statistically significant (t statistic = 0.83). This result is not consistent with the bad governance story. Forced successions are more common in the high ownership subsample (17.6% compared to 12.6%, Panel B). Interestingly, the model attributes the difference not to lower turnover costs, but to more dispersion in ability across CEOs in the high-ownership subsample: σ 0 increases from 3.10% to 3.99% (difference has t-stat = 4.2). The model needs higher ability dispersion in order to fit the higher empirical dispersion in realized profitability across CEOs in the high ownership subsample: σ(E[X]) increases from 12.3% to 24.6% per year in Panel B. Consistent with the bad governance story, personal turnover costs are significantly lower in the subsample with more outsiders on the board (3.00% compared to 8.25%; difference has t-stat 2.7). The lower turnover costs explain why more successions are forced in the subsample with more outsiders (16.0% vs. 11.6%). 18 I conduct inference by assuming estimators from the two sub-samples are uncorrelated with each other. This assumption is plausible under the model's assumption that draws from the CEO talent pool, profitability shocks, and realizations of signal z are all independently distributed across both firms and time. 25 The difference in turnover costs outweighs an effect going in the opposite direction: there is more dispersion in ability across CEOs in the subsample with fewer outsiders (σ 0 of 2.93% vs. 1.98%, difference has t-stat 7.5), which pushes firing rates up in the subsample with few outsiders. Ability dispersion is higher because the model needs to fit the higher dispersion in realized profitability across CEOs in the subsample with few outsiders (σ(E[X]) increases from 10.4% to 17.9% in Panel B). Also consistent with the bad governance story, personal costs are significantly lower in large firms than small firms (0.00% compared to 8.53%, difference has t-stat 7.1). The lower turnover costs explain why more successions are forced in large firms (18.6% vs 15.7%). The difference in turnover costs outweighs an effect going in the opposite direction, namely, there is more dispersion in ability across CEOs in small firms (σ 0 of 3.26% vs. 1.28%, difference has t-stat 35), which tends to push firing rates up in small firms. Ability dispersion is higher because the model needs to fit the higher dispersion in realized profitability across CEOs in small firms (σ(E[X]) increases from 10.3% to 19.1% in Panel B). To summarize, three out of four split-sample tests (year, outsiders, size) are consistent with the badgovernance interpretation of personal costs. The fourth test (stock ownership) does not support the badgovernance view. One could always object that the proxies for governance quality are imperfect. For instance, it may be optimal for shareholders to elect an insider-dominated board if doing so allows shareholders to pay the CEO less or hire a more talented CEO. Such arguments seem like a stretch to this author. I conclude that, on balance, results support the bad-governance interpretation, although not all evidence supports this view. Another message from these tests is that a higher firing rate alone does not constitute evidence of lower CEO entrenchment, because the higher rate may be due instead to higher dispersion in CEO ability or faster learning about CEO ability. My approach teases apart these different drivers of the firing rate. IV. Robustness This section describes robustness exercises regarding firm fixed effects in profitability, a flat firing threshold, a different assumption about voluntary turnover costs, alternate discount rates, and a more aggressive classification of CEO successions into forced and voluntary. I also discuss how earnings manipulation relates to my results. 26 A. Firm Fixed Effects The model attributes all intra-industry variation in average profitability to variation in CEO skill. If there are other reasons why profitability varies, for instance if some industry sectors are more profitable than others, then I over-estimate the variation in CEO skill, σ 0 . Since higher values of σ 0 require higher turnover costs to fit turnover rates, my estimated turnover costs are also biased upwards. To address this concern, I introduce firm fixed effects in profitability, which allows some firms to be more profitable than others for reasons unrelated to CEO ability. If the fixed effects are independent of CEO ability, then we can measure each firm's fixed effect by averaging profitability across multiple CEOs in the firm. After subtracting this average from the firm's yearly profitability, the remaining variation in average profitability across CEOs is due only to variation in CEO ability and not the firm fixed effects. Following this logic, I demean excess profitability y * it at the firm level using Compustat data from 1970-2006, and I estimate the model using the demeaned data. Parameter estimates are in the "fixed effects" rows of The model still needs huge turnover costs to fit the low firing rates, even when we allow firm fixed effects in profitability. INSERT The model assumes the board is risk neutral, and that turnover costs and a CEO's ability are both constant over time. The model predicts that uncertainty about the CEO's skill drops over time due to learning, so the CEO's option value declines with tenure, and hence the firing threshold rises with tenure. In other words, the board is more willing to fire CEOs the longer they have been in office, because the board prefers CEOs with more uncertain skill. Next I discuss four model extensions which could change this prediction. First, the board's effective personal cost of CEO turnover, c (pers) /κ, may increase with tenure as the CEO appoints more of his allies to the board or gains bargaining power. Rising personal costs will lower the 27 slope of the firing threshold, since the board becomes less willing to fire the CEO as tenure increases. The model of Hermalin and Weisbach (1998) makes a similar prediction. Second, if the board is risk averse then it will prefer CEOs with lower uncertainty. Since uncertainty is lower for CEOs who have been in office longer, adding risk aversion to the model will make the board less willing to fire long-tenured CEOs, i.e., will lower the firing threshold's slope. Intuitively, the board may prefer a mediocre CEO who is a known quantity compared to a new CEO whose skill is potentially better but more uncertain. Third, if CEOs gain human capital from learning on the job, and if shareholders receive at least part of the surplus, then boards should be less willing to fire CEOs the longer they have spent in office. In other words, the firing threshold should rise less with tenure. Fourth, CEOs' skill level may fluctuate randomly over time as their human capital gains or loses productivity, e.g., due to changing industry conditions. Random fluctuations in skill cause uncertainty to drop less with tenure, because old signals lose relevance. As a result, the gains in option value from replacing a long-tenured CEO with a new one are smaller, and the threshold's slope is lower. Dangl, Wu, and Zechner (2007) show that when skill fluctuates, the firing threshold can even be perfectly flat. All four extensions suggest the firing threshold increases less with tenure than my main model predicts. Interestingly, the main model can fit the empirical tenure-firing relationship quite well ( Results are in the "flat threshold" rows of Flattening the threshold makes the firing region smaller and forced turnover less frequent. Since the data have not changed, the model compensates by increasing ability dispersion σ 0 , which raises forced turnover rates 28 C. Costless Voluntary Turnover The model assumes forced and voluntary CEO turnover are equally costly. For robustness, I re-solve and re-estimate the model assuming voluntary turnover is costless to the board and to shareholders. The board's optimal firing policy changes, because the board now has an incentive not to fire CEOs who are close to retirement, but instead to wait until they retire at no cost. Overall, there is less of an incentive to fire the CEO when voluntary turnover is costless. The model compensates by raising ability dispersion (σ 0 ) from 2.42% to 3.34% The χ 2 statistic indicates this version of the model fits the data slightly worse than the main model. D. Alternate Discount Rates Next, I estimate the model using different assumed values of β, the board's discount factor. The main results use β = 0.9, and in these robustness tests I use β=0.85 and 0.95. Estimates of model parameters for these two cases are in All else equal, raising β shifts the firing threshold up and hence makes boards more willing to fire the CEO; intuitively, the benefits of firing an unskilled CEO have higher net present value when β is higher. Since the underlying data do not change when we raise β, the model compensates by lowering the board's incentive to fire the CEO by lowering σ 0 , the dispersion in skill. E. Alternate Forced/Voluntary Classification Kaplan and Minton The model tries to match the higher rate of forced turnover by lowering the total costs of turnover from 5.94% to 1.34% F. Earnings Management The model assumes reported earnings equal true earnings. In reality, CEOs have incentives to manipulate earnings in at least three ways. First, if a CEO believes he is close to being fired, then he may try to inflate reported earnings. However, Murphy and Zimmerman (1993) find no empirical evidence of such manipulation. CEOs have incentives to take an earnings bath when they first enter office, in order to unravel any previous manipulation and boost future compensation and chances of staying in office. Finally, CEOs may engage in "signal jamming," injecting noise into earnings to make it harder for the board to learn the CEO's ability (e.g. Fudenberg and Tirole (1986), Hermalin and Weisbach (2007)). While signal jamming may help explain my estimates of profitability volatility and persistence-for instance, why I find volatility σ is 3.4% instead of some lower number-, signal jamming does not imply any obvious bias in these estimates. Signal jamming may also help explain my finding that boards rely heavily on non-earnings signals when evaluating the CEO. V. Conclusion Previous empirical work has established that CEOs are rarely fired, and that profitability poorly predicts CEO dismissals. Attributing these stylized facts to bad governance would be premature, as the literature provides few quantitative benchmarks for how a rational, well governing board would behave. This study provides one such benchmark. I develop and solve a dynamic model which features a rational board, costly turnover, and learning about CEO ability. To gauge magnitudes and overcome endogeneity problems, this study takes a structural estimation approach. I estimate the model's fundamental parameters by applying 30 the simulated method of moments to data on CEO turnover and firm profitability. I find three main results. First, to rationalize the observed rate of forced turnover, boards must behave as if firing the CEO costs shareholders 5.9% of the firm's assets, or $236 million for the median firm. Second, this cost mainly reflects CEO entrenchment and bad governance rather than a real cost for shareholders, although not all evidence supports this view. Third, to rationalize the weak relation between CEO dismissals and profitability, boards must rely very heavily on non-earnings signals of CEO ability. The model can fit several empirical patterns, including the overall rate of forced CEO turnover, the relation between turnover and tenure, the average changes in profitability and stock prices around CEO dismissals, and the forecasting relation between profitability and forced turnover. In almost all cases, the model matches these empirical patterns both in terms of direction and magnitude. One interpretation of these results is that the turnover costs the model needs to fit the data are implausibly large, so the model must be wrong. According to this interpretation, my results present a quantitative CEO turnover puzzle. A second interpretation is that the parameter values are not implausible, and the model is a good description of reality. For instance, high CEO entrenchment is consistent with the CEOs' considerable influence on board selection during the period I study. More work is needed to evaluate these two interpretations. While I have explored a few alternate models, it would be worthwhile to consider models with endogenous board composition, contracting and bargaining between the CEO and board, costly monitoring, and asymmetric information. Like my model, these alternate models should be judged on their ability to explain magnitudes and not just qualitative features of the data.