Performance-induced CEO turnover

Dirk Jenter Stanford University and NBER

djenter@gsb.stanford.edu

Katharina Lewellen Tuck School at Dartmouth

katharina.lewellen@dartmouth.edu

December 2014

This paper revisits the relationship between firm performance and CEO turnover. We drop

the distinction between forced and voluntary turnovers and introduce the concept of

performance-induced turnover, defined as turnover that would not have occurred had

performance been “good”. We document a close link between firm performance and CEO

turnover and estimate that almost 50% of turnovers in the first eight tenure years are

performance induced. This is significantly higher than the number of forced turnovers

identified in prior studies. We contrast the empirical properties of performance-induced

turnovers with the predictions of Bayesian learning models of CEO turnover. Learning by

boards about CEO ability appears to be slow, and boards act as if CEO ability were subject to

frequent and sizeable shocks.

1

Replacing badly performing CEOs is one of the key responsibilities of corporate boards,

and the relationship between CEO turnover and firm performance has been studied

extensively. The prior literature has found only modest effects of firm performance on CEO

turnover. Depending on the sample and the performance measure used, the estimated

probability of a forced CEO turnover is between 2 and 6 percentage points higher per year for

a bottom decile performer than for a top decile performer.1 Consequently, Jensen and Murphy

(1990) and others conclude that dismissals are not an important source of CEO incentives.

Several papers have proposed that the relative paucity of forced CEO turnovers after bad

performance is due to CEO entrenchment and weak corporate governance (Weisbach (1988),

Hermalin and Weisbach (1998), Taylor (2010)).

This paper does away with the distinction between forced and voluntary turnovers and

instead introduces the concept of performance-induced turnover, defined as turnover that

would not have occurred had performance been “good”. The probability of performance-

induced turnover at performance level tx is identified from the difference between the

turnover probability at tx and the turnover probability at a high performance threshold ,

such as the 95th percentile of the performance distribution. The assumption is that turnovers

at and above this performance level are unrelated to performance and, thus, occur at any level

of performance. Any higher turnover probability at performance levels below the threshold is

assumed to be caused by performance being worse. These additional turnovers are labelled as

performance-induced.

We find that a large fraction of CEO turnovers are performance induced, and that the

frequency of performance-induced turnovers is about twice as high as the number of forced

turnovers identified in prior studies. Based on our estimates, almost 40% of all CEO

turnovers are performance induced. In the first eight years of tenure, this percentage is close

to 50%.

The probability of performance-induced turnover increases with tenure at first and peaks

in tenure years 7 to 8. In contrast, forced turnovers, classified using the literature’s most

popular classification algorithm, peak in tenure year 2 already. The likely reason for this

discrepancy is that most departures of long-tenured CEOs are pre-announced retirements,

1 See, for example, Coughlin and Schmidt (1985), Warner, Watts, and Wruck (1988), Weisbach (1988), Jensen and Murphy (1990), Denis, Denis, and Sarin (1997), Murphy (1999), and Huson, Parrino, and Starks (2001).

2

which are classified as voluntary turnovers. However, our analysis reveals that a substantial

fraction of these departures are in fact performance induced, which means that many more of

them occur at low than at high levels of performance.

We contrast the empirical properties of performance-induced turnovers with the

predictions of Bayesian learning models of CEO turnover, which are the most frequently

used theoretical framework of the prior literature.2 The evidence is inconsistent with the

literature’s workhorse model in which boards learn from firm performance about constant

CEO ability. This model predicts that boards assign the same weight to all lags of the

performance signal. Empirically, performance-induced turnover is driven by performance in

the most recent three to four years but is insensitive to performance further in the past.

Moreover, the weights assigned to past performance show little to no decline with tenure for

the first ten tenure years. The degree to which these weights decline indicates the degree to

which boards’ beliefs about CEO ability are becoming more precise. The fact that these

weights are not declining with tenure suggests that boards’ beliefs are not converging.

The evidence suggests a version of the Bayesian learning model in which CEO ability or,

more likely, match quality is changing over time. With changing CEO ability, boards

optimally assign larger weight to more recent performance signals than to older ones.

Intuitively, shocks to CEO ability increase the relative importance of newer performance

signals, which are most informative about current CEO ability. With changing CEO ability,

the variances of boards’ beliefs about CEOs also decline more slowly, if at all, and the beliefs

remain sensitive to new performance signals even late in tenure.

The shocks to CEO ability that reconcile the Bayesian learning model with the data are

fairly large. The evidence shows that, even though CEO turnovers are highly sensitive to

current performance and performance in the previous year, they are essentially unrelated to

performance four and more years ago. This suggests that CEO ability (or match quality)

changes sufficiently fast that performance from four years ago is uninformative about CEO

ability today. In the same vein, to keep the variance of boards’ beliefs (and the sensitivity of

these beliefs to new performance signals) constant, the shocks to CEO ability have to undo

any learning effects from the performance signals. The sensitivity of turnover to current

performance shows that current performance is informative about CEO ability, which in turn

2 See, for example, Harris and Holmström (1982), Holmström (1982), Murphy (1986), Gibbons and Murphy (1992), Hermalin and Weisbach (1998), and Taylor (2010, 2013).

3

implies that the shocks to ability have to be large enough to reverse the associated gains in

belief precision.

Finally, the observation that performance-induced turnover probabilities increase slowly

with tenure and peak in tenure years 7 to 8 is further evidence that learning about CEO ability

is slow. It is, however, also consistent with high costs of turnover, or with incumbent CEOs

having higher expected ability than potential replacements. Both imply that small negative

signals early in tenure do not trigger turnovers, which instead increase with tenure as

negative signals accumulate. In this context, it is interesting to note that the turnover rate for

rank-and-file employees tends to peak after only 3-6 months of tenure, and thus much earlier

than for CEOs (Farber (1994)). This suggests that the ability of rank-and-file employees is

revealed more quickly, or that turnover costs are smaller, or that the ability difference

between incumbents and replacements is smaller.

Most prior studies on the relationship between firm performance and CEO turnover have

focused on so-called “forced” CEO turnover. The literature has devised a number of

algorithms to distinguish between forced and voluntary departures based on CEO age, press

reports, and other information.3 Inevitably, any algorithm misclassifies some turnovers, and

any misclassifications affect the estimated frequency of forced turnover and its estimated

relation to firm performance. Moreover, CEO departures can be forced without being due to

bad performance, and departures can be due to bad performance without being forced. For

example, bad performance might cause CEOs to voluntarily retire early, while outstanding

performance might cause boards to convince CEOs to stay beyond scheduled retirement

dates.

In contrast, our approach makes no a-priori determination whether a particular departure

is forced or voluntary, and instead considers all departures as potentially performance-

induced. Intuitively, we treat the turnover frequency of very high-performing CEOs as the

benchmark and identify performance-induced turnovers from the additional turnovers

observed for worse-performing CEOs. Thus, the focus is on the extent to which bad

performance causes turnover, independently of who initiates the departure, the board or the

CEO. This perspective is useful, not only because it avoids biases due to misclassifications,

3 See, for example, Warner, Watts, and Wruck (1988), Dennis and Dennis (1995), Kim (1996), and Parrino (1997).

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but also because future firm performance is determined by whether bad CEO-firm matches

are dissolved, independently of whether the CEO is forced out by the board or not.

Section 1 of this paper reviews Bayesian learning models of CEO turnover and derives

testable implications. Section 2 describes the estimation of performance-induced turnover in

detail. Section 3 describes the data and presents summary statistics. Section 4 presents and

interprets the empirical results. Section 5 provides further discussion of the results, and

Section 6 concludes.

1 Theoretical framework

1.1 A simple Bayesian learning model of CEO turnover

This section describes a simple Bayesian learning model of CEO turnover. Its ingredients

are similar to the more complex models in Jovanovic (1979), Harris and Holmström (1982),

Murphy (1986), Gibbons and Murphy (1992), Hermalin and Weisbach (1998), and Taylor

(2010). A corporate board hires a new CEO of unobservable and uncertain ability. The board

updates its beliefs about the CEO after observing signals of ability, such as firm performance.

These updates can cause the board to fire the CEO.

We denote the board’s initial prior about the CEO’s ability as 0 and assume that it is

normally distributed with a mean of and a variance of . For simplicity, set 0. Every

period, the board learns from firm performance about CEO ability. Firm performance xt is

given by the CEO’s true ability plus a normally distributed i.i.d. noise term with mean zero

and variance :

 1

where ~ 0,t t tx Nr

  (1) 

The board updates its believes about ability every period according to Bayes’ rule. The mean

of the board’s posterior estimate of CEO ability is a weighted average of the board’s initial

prior (normalized to zero) and all signals received since the CEO’s hiring. Specifically, after

observing performance in period t, the posterior mean is:

2 11 11 0( )

ˆt t

t i ii it

r rx x

r tr

(2)

5

where is the variance of the board’s posterior estimate in t-1. The board fires the CEO

when the posterior mean in year t falls below an endogenous threshold .4 This simple

framework has two testable implications:

1. The board puts equal weight on each of the past performance signals when forming its

estimate of CEO ability.

This prediction follows directly from the assumptions that the CEO’s ability, and the

relationship between ability and the signal, are constant over time.

2. The sensitivity of the board’s estimate of CEO ability to any of the performance

signals declines with tenure.

In tenure year t, the weight on prior signal xi equals , which diminishes with t.

Intuitively, the marginal value of each signal decreases as the number of signals goes up and

the board’s beliefs about CEO ability become more precise. Empirically, the speed with

which the weights on the performance signals decline with tenure indicates the speed with

which the board is learning about CEO ability.

1.2 Extension: changing CEO quality

The prior literature assumes that CEO ability is constant.5 However, CEO ability or, more

likely, the quality of the CEO-firm match might change over time due to changes in the firm,

its environment, or the CEO himself. In this section, we modify the simple learning model by

assuming that the CEO’s true ability follows a random walk:

(3)

The i.i.d. shocks are normally distributed with a mean of zero and a variance of . The

random shock occurs in the beginning of each period t, before the board observes the

signal xt. The board then forms its posterior belief and fires the CEO when the posterior

mean falls below the threshold . The model with changing CEO ability has two testable

implications:6

4 The threshold results from the board trading off the costs of firing the CEO against the expected benefit of replacing him. See Hermalin and Weisbach (1998) and Taylor (2010) for examples. 5 See, for example, Harris and Holmström (1982), Murphy (1986), Gibbons and Murphy (1992), Hermalin and Weisbach (1998), and Taylor (2010, 2013). Kim (1996) is a notable exception. 6 The derivation of all results is in Appendix A.

6

1. When forming beliefs about CEO ability, boards assign larger weight to more recent

performance signals than to older ones.

Intuitively, random shocks to CEO ability increase the importance of current performance

signals, which are informative about the most recent shocks, relative to older signals. The

rate at which the weights on past performance decline depends on the size of the shocks to

CEO ability. The ratio of the optimal weight on a signal from last period relative to the

weight on a signal from the current period is <1, where σ is the variance of the

board’s posterior beliefs last period and is the variance of the shock to ability. Thus, if the

shock to ability doubles the variance of the board’s beliefs, the signal from the current period

receives twice the weight of the signal from the last period.

2. The larger the shocks to ability, the more sensitive the board’s beliefs remain to current

performance as tenure increases.

Without shocks to ability, as tenure increases, the board’s beliefs about the CEO become

more precise, and the sensitivity of these beliefs to new performance signals declines. With

shocks to ability, the variance of the board’s beliefs declines more slowly, if at all, and the

beliefs remain more sensitive to new performance signals. Empirically, the degree to which

the sensitivity of beliefs to performance declines with tenure indicates the degree to which

these beliefs are becoming more precise. If the sensitivity does not decline with tenure, then

boards’ beliefs are not converging.

1.3 Estimating Bayesian learning models of CEO turnover

To estimate Bayesian learning models of CEO turnover, one needs to add a mean-zero

noise term to the (so far) deterministic relationship between prior performance and the

board’s estimate of CEO ability. Consider, for example, a sample of CEOs in tenure year t=2

with information on performance in years t=1 and t=2 and a variable fire equal to one for

CEOs dismissed in year 2:

(4)

1 (5)

If the noise term is normally distributed, this model can be estimated with a probit

regression of CEO turnover in year 2 on firm performance in years t=1 and t=2. The latent

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variable in the probit model is the board’s posterior estimate of CEO ability, , and the

probit coefficients correctly estimate the weights the board assigns to prior performance

when assessing CEO ability:

1 (6)

Φ

Estimating (5) with maximum likelihood yields consistent estimates of the weights on

prior performance for the case with constant CEO ability in equation (2), or for the case with

time-varying ability in equation (A3) in Appendix A.

2 Performance-induced turnover

Estimating models of CEO dismissals, such as the models in the previous section,

requires distinguishing dismissals from other CEO departures. In reality, CEO turnovers

occur for many reasons: Some CEOs are dismissed for poor performance, while other CEOs

are fired for other reasons, such as personal scandals or violations of rules or laws. Many

CEOs depart voluntarily, and these departures can be either related or unrelated to

performance (e.g., accepting a more attractive position elsewhere vs. retiring for health

reasons). Unfortunately, firms are not required to reveal the true reason for a CEO departure,

and might be less likely to do so if a CEO is fired.

To address this problem, the prior literature tries to distinguish forced from voluntary

departures using information on CEO age, turnover announcements, whether the departing

CEO remains on the board, and press reports.7 Inevitably, any algorithm that relies on

incomplete and often misleading information misclassifies some turnovers. Moreover, CEO

departures can be forced without being due to bad performance, and departures can be due to

bad performance without being forced. For example, a well-performing CEO might be forced

out because of a personal scandal, and a badly-performing CEOs might decide to voluntarily

retire early.

7 For representative examples of classification procedures, see Warner, Watts, and Wruck (1988), Dennis and Dennis (1995), Kim (1996), and Parrino (1997).

8

The approach taken in this paper is to do away with any a-priori distinction between

forced and voluntary turnover. Instead, we simply ask whether bad firm performance leads to

CEO-firm separations. What matters for future firm performance is whether bad CEO-firm

matches are dissolved; whether this dissolution involves a CEO firing, a voluntary retirement,

or anything between these two extremes is of secondary importance.8 To operationalize this

idea, we introduce the concept of performance-induced turnover, defined as turnover that

would not have occurred had performance been “good”.

Conceptually, we model the CEO turnover probability as the sum of two independent

turnover processes, one of which is unrelated to performance and one of which is negatively

related to firm performance.

  . . . .turn t other perf ind t other perf ind tP x P P x P P x    (7) 

We are interested in estimating the intensity of the process for performance-induced

turnover. Reordering equation (7) yields

  . . 1

turn t otherperf ind t

other

P x PP x

P

   (8) 

In order to estimate (8), we assume that the probability of performance-induced turnover

is zero at and above some high performance threshold , such as the 95th percentile of the

performance distribution. All turnovers observed at and above are assumed to be unrelated

to performance and, thus, to occur at any level of performance.9 Hence, the turnover

frequency at and above forms the empirical estimate of otherP . Any higher turnover

probability observed at performance levels below the threshold is assumed to be caused by

performance being worse. These additional turnovers yield the empirical estimate of perf indP .

Concretely, the probability of performance-induced turnover at performance level

is calculated from the difference between the turnover probability at and the

turnover probability at the performance threshold :

8 This idea is explicit in competitive assignment models of workers or executives to firms (Jovanovic (1979), Eisfeldt and Kuhnen (2013)): a CEO-firm match dissolves when the match surplus falls below the firm’s and the CEO’s outside options, and for many separations the distinction between quits and firings is not meaningful. 9 A violation of this assumption would lead us to underestimate the frequency of performance-induced turnover. See Section 2.4 for further discussion.

9

ˆ , 0

ˆˆ

,1

turn t turn

perf ind t

turn

Max P x P XP x X

P X

(9)

The numerator is set to zero when this difference is negative (this occurs mostly at

performance levels above the threshold). The denominator is an adjustment for CEOs that

experience both performance-induced turnover and other, not performance-related turnover

in the same year. 10

The only ingredient in the computation of , is an estimate of the turnover-

performance relation . Itis therefore important to choose the right functional form

for the estimation of . A standard probit model with linear performance terms, such

as that in eq. (5), is not appropriate if the set of turnovers includes events unrelated to

performance, such as planned retirements or departures due to ill health. With a probit model

(and a negative effect of performance on turnover), the turnover probability must go to zero

at very high levels of performance. If there are turnovers that occur independently of

performance, a probit model cannot fit the data.

We use two approaches to model the empirical relationship between CEO turnover and

firm performance. The first approach is a simple modification of the standard probit model.

The second approach explicitly allows for both performance-induced and other turnovers.

2.1 A probit model with performance deciles

To allow the turnover probability to converge to a non-zero level at high levels of

performance, we model as a probit with performance-decile indicators:

∙ ⋯ ∙ ′ ∙ (10)

to are indicators for performance deciles and is a vector of controls. This

specification allows the estimation to match the empirical turnover probability in each

performance decile. The probability of turnover unrelated to performance, , is

calculated as the implied turnover probability with performance in the top decile. Given this

estimate, the probability of performance-induced turnover is calculated from equation (9).

10 For example, a CEO aged 65 might have retired independently of performance but, if performance was also bad, would have been fired had he not retired.

10

This approach is straightforward and close to the models used in the prior literature, but it

has two disadvantages: First, the need to create decile indicators restricts the model to a

single performance measure. If boards assign unequal weights to performance at different

lags, then this model is unable to accommodate it. Second, the coefficients estimated from eq.

(10) do not correspond to the coefficients in the learning models in Section 1 and, hence,

cannot be used to test predictions from these models.

2.2 A two-probit model

The second approach to modeling the turnover probability explicitly allows for two

independent turnover processes, one that is affected by performance and one that is not. We

use probit specifications for both processes:

∙ 1 ∙ ∙ ′ ∙ (11)

is a vector of performance measures and and are vectors of controls. Because

there are two turnover processes, one of which is not a function of performance, the total

turnover frequency can decline with without converging to zero at high performance

levels. The two-probit model has the added advantage that it can accommodate multiple

performance measures, including multiple lags of performance. Moreover, the coefficients on

correspond to the coefficients in the Bayesian learnings models in Section 1, and hence,

can be used to test predictions from these models.

2.3 A numerical example

We illustrate the estimation using a simple numerical example with two types of

departures: performance-driven departures (dismissals) and departures unrelated to

performance (retirements). In any year, the CEO can choose to retire, the board can decide to

dismiss the CEO, or both events can occur simultaneously. The econometrician cannot

distinguish dismissals from retirements but can observe whether a turnover has occurred:

1 ∙ (12)

We assume that the noise terms in both turnover processes follow a standard normal

distribution. Dismissals occur with probability ∙ and retirements

occur with constant probability . The parameters , , and are set

to -1.4, -1.6, and -0.4 to approximate the empirical turnover probabilities from Section 4. The

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performance measure is assumed to be normally distributed with a mean of 0.1 and a

standard deviation of 0.3 (to match the empirical section, performance is scaled by its

standard deviation).

Figure 1 shows the probabilities of turnovers, dismissals, and retirements by performance

decile in a large simulated sample (n = 1,000,000). The figure also shows estimates of

performance-induced turnover obtained using the two methods described in the previous

sections. Both procedures first estimate the probability of total turnover using

either eq. (10) for the probit model with decile dummies or eq. (11) for the two-probit model.

The performance-induced turnover probability , is then computed using eq.

(9) with the threshold set to the 95th percentile of the performance distribution. The

estimated probabilities are averaged within each performance decile and the averages plotted

in Fig. 1.

Fig.1: Estimating performance-induced turnover: numerical example. The simulated sample has 1,000,000 CEO-years. Dismissals occur with probability P Φ β β ∙ x and retirements occur with probability P Φ α . Parameters α , β , andβ are set to -1.4, -1.6, and -0.4, respectively; is normally distributed with a mean of 0.1 and a standard deviation of 0.3. Total turnover is governed by eq. (12). The turnover-performance relation P x is estimated using either a standard probit model with decile dummies (eq. (10)) or the two-probit model (eq. (11)). The performance term is scaled by its standard deviation. Performance-induced turnover, defined in eq. (9), is calculated for each observation with X equal to the 95th percentile of the performance distribution. All probabilities depicted in the figure are averages across observations within each performance decile.

0.00

0.05

0.10

0.15

0.20

0.25

0 1 2 3 4 5 6 7 8 9

Probab

ility

Performance decile

Total turnover

Dismissals

Retirements

Perf.‐ind. turnover: two‐probit model

Perf.‐ind. turnover:probit with deciles

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Both methods – the simple probit with dummies and the two-probit model – produce

nearly identical estimates of performance-induced turnover. The figure also shows that the

performance-induced turnover probabilities are slightly below the true dismissal

probabilities. This is because the performance-induced turnover calculation assumes that all

turnovers at and above are not caused by bad performance. In this sample, however, the

dismissal probability at the 95th percentile threshold is still 0.9%.

To assess the behavior of the estimation methods in samples sized like the empirical data,

we repeat the estimations in 500 simulated samples of 23,000 observations each. Table 1

shows summary statistics for the simulated dismissal probabilities and the estimated

performance-induced turnover probabilities. As before, the performance-induced turnover

probabilities tend to be slightly below the dismissal probabilities. The bottom panel of Table

1 shows summary statistics for the estimated coefficients on firm performance in the two-

probit models. Both the mean and median estimates are close to the true coefficient of

-0.40. Hence, the two-probit estimation can be used to recover structural parameters of

the underlying model from the data.

2.4 Discussion

The concept of performance-induced turnover and its empirical measure ,

offer a new way to analyze the relation between firm performance and CEO departures.

Importantly, performance-induced turnover differs from forced turnover in that it includes

any type of departure caused by bad performance, independently of whether the decision is

made by the board or the CEO himself. This includes firings by the board, but also cases in

which bad performance causes CEOs to give up voluntarily or to retire early. In the same

spirit, forced turnovers that are unrelated to performance, for example those caused by

personal scandals or violations of rules, do not qualify as performance induced.

A practical advantage of the approach is that estimating , does not require

that the researcher distinguish forced from voluntary turnovers or determine a priori which

turnovers are due to bad performance. More fundamentally, performance-induced turnover is,

arguably, more relevant for the allocation of managerial talent to firms than forced turnover.

What matters for firm performance is whether bad CEO-firm matches are dissolved; whether

this dissolution involves a CEO firing, a voluntary retirement, or anything between these two

extremes is of secondary importance.

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There are two caveats. First, the estimation of performance-induced turnover requires

choosing a performance threshold above which all turnovers are assumed to be independent

of performance. To the extent that this assumption is violated, ,

underestimates how many turnovers are caused by bad performance. This occurs if there are

turnovers caused by bad performance even above the performance threshold (i.e., turnovers

that would not have happened had performance been even better). This also occurs if there

are turnovers above the threshold that are caused by good performance (i.e., that would not

have happened had performance been lower). An example are successful CEOs who are hired

away by other firms. Both violations cause our approach to overestimate the number of

turnovers that are unrelated to performance, and hence to underestimate the number of

turnovers that are due to bad performance. In robustness tests, we find that the results are

robust to using a range of thresholds. The turnover-performance relation flattens out at high

levels of performance, which supports the assumption that most turnovers in this region are

unrelated to performance, and which also makes the exact choice of less important.

Second, for reasons already discussed, performance-induced turnover does not equal the

CEO dismissals in the Bayesian learning models discussed in Section 1. For example, CEOs

who give up because of bad performance play no role in these models but are included in

performance-induced turnover. It is important to keep this distinction in mind when

interpreting any differences between the predictions of the models and the empirical

properties of performance-induced turnover.

3 Sample and data

The construction of the CEO turnover sample starts with all firms in the Standard &

Poors ExecuComp database from 1993 through 2011. The database lists top executives in all

S&P 500, S&P MidCap, and S&P SmallCap firms. We record a CEO turnover whenever the

CEO identified in ExecuComp changes. Using news searches in the Factiva database, each

turnover is verified and mistakes corrected. The resulting sample has 6,493 CEO spells with

31,652 CEO-years and 3,529 turnovers in 3,154 firms. Merging with control variables

reduces the sample in the analyses to 5,356 CEO spells with 25,632 CEO-years and 2,919

turnovers in 2,955 firms. Table 2 shows descriptive statistics for the sample.

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All CEO turnovers in the panel from 1993 to 2010 are classified as either voluntary or

forced using the Parrino (1997) algorithm. Section 4.3 and Appendix B describe details of the

classification procedure. The required turnover announcements, press reports, and CEO ages

are obtained by searching the Factiva database. For the years 2002 to 2010, we combine our

own data collection with data from Peters and Wagner (2009). This procedure yields 879

forced and 2,395 voluntary turnovers in 27,708 CEO-years. Merging with control variables

reduces the sample to 735 forced and 2,010 voluntary turnovers in 22,465 CEO-years.

Financial statement data is from the Compustat database and stock return data from the

Center for Research in Security Prices (CRSP). The measure of firm performance used in the

CEO turnover regressions are average monthly stock returns scaled by their standard

deviation. The standard deviation is measured over 48 months, ending with and including the

period over which stock returns are averaged. The reason for normalizing stock returns by

their standard deviation is to make the returns of more and less volatile firms comparable.

4 Empirical analysis

This section presents the empirical estimates of performance-induced turnover. The

analysis uses the two estimation approaches described earlier: the standard probit with

performance decile indicators and the two-probit model. Section 4.1 uses the full CEO panel

from 1993 to 2011. Section 4.2 divides the sample based on CEO tenure. Section 4.3

compares performance-induced turnover to forced turnover. Section 4.4 examines how

performance-induced turnover has changed over the sample period.

4.1 Performance-induced turnover in the full sample

This section estimates performance-induced turnover using the full CEO panel from 1993

to 2011. The results from the standard probit with decile indicators are in Table 3. The

dependent variable is set to one for tenure years with CEO turnover and to zero otherwise.

The key independent variables are decile indicators for the firm’s past stock price

performance. Performance is measured as average monthly stock returns scaled by their

standard deviation. Because it is not a priori known how many years of performance boards

take into account when assessing CEOs, the regressions use four different performance

windows. In the first three regressions, returns are measured from tenure year -1, -2, or -3

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through year zero (the turnover year), respectively. The fourth regression measures

performance over the CEO’s entire tenure up to (and including) year zero.

The implied turnover probabilities are reported in Panel B. The probability of

performance-induced turnover is computed, as in eq. (9), from the difference between the

model-implied turnover probability for a given observation and what this probability would

have been had performance been in the top decile. Hence, the performance-induced turnover

probability is the additional turnover probability attributed to performance being worse than

in the top decile.

The results show that CEO turnover is strongly linked to performance and that a

substantial fraction of turnovers are performance-induced. Depending on the performance

window, the average implied turnover probability if performance is in the top decile is

between 7.7 and 8.1% per tenure year. This probability rises to between 17.6 and 18.9% in

the bottom decile. The average performance-induced turnover probability varies between 4.1

and 4.5% per tenure year. With a total turnover probability of 11.77% per tenure year, these

estimates imply that between 35 and 38% of all turnovers are performance induced. Looking

across columns, lengthening the performance window first slightly increases and then

decreases the estimated probability of performance-induced turnover. We examine the effects

of performance at different lags more carefully using the two-probit model next.

Table 4 shows results from the two-probit model. Panel A presents coefficient estimates

for both turnover equations – one including firm performance and one without. Panel B

presents the implied turnover probabilities. The probabilities of performance-induced

turnover are computed as in eq. (9). The calculation uses the 95th percentile of the

performance distribution as the threshold above which all turnovers are assumed to be

unrelated to performance.11 The first two regressions use scaled stock returns from years -2

and -3 through year zero (the turnover year) as performance measure. The estimates of

performance-induced turnover of almost 4.5% per tenure year are similar to the

corresponding estimates using the standard probit (with decile indicators) in Table 3. As in

the simulations in Section 2.3, both estimation approaches yield almost identical estimates of

performance-induced turnover.

11 For regressions with more than one performance term, the percentiles are from the distribution of the coefficient-weighted sum of the performance terms.

16

An advantage of the two-probit model is that it accommodates multiple performance

terms and can thus assign different coefficients to performance at different lags. The third

regression in Table 4 includes three separate performance terms for scaled stock returns in

tenure years -2, -1, and zero. The fourth regression adds scaled stock returns in tenure

year -3.

The Bayesian learning model with constant CEO ability (described in Section 1.1)

predicts that boards assign the same weight to all lags of the performance signal. This

prediction is strongly rejected by the estimates in Table 4. More recent performance in tenure

years 0 and -1 receives significantly higher weight than performance in previous years. For

example, in column 4, the coefficient on performance in tenure year -1 is -0.22, compared to

-0.15 and -0.08 for years -2 and -3. Wald tests indicate that these differences are statistically

significant, with chi-squared statistics of 6.48 (p=0.01), 17.41 (p=0.00), and 4.95 (p=0.03) for

years -1 and -2, -1 and -3, and -2 and -3, respectively.12 In an untabulated regression, we have

included an additional performance term for tenure year -4, which received an insignificant

coefficient of -0.03.

One potential explanation for boards assigning higher weight to more recent performance

is that CEO ability, or the quality of the CEO-firm match, changes over time (see Section

1.2). The rapid decline of the coefficients on lagged performance in Table 4 suggests that the

necessary shocks to CEO ability are large. For example, performance three years ago

receives only about one-third of the weight of current performance, and performance from

four or more years ago is mostly ignored. In the context of the Bayesian learning model in

Section 1.2, this only makes sense if CEO ability (or match quality) changes so rapidly that

performance from four years ago is almost completely uninformative about CEO ability

today.

The results in Table 4 also imply that turnover regressions that use only one performance

term are misspecified. These regressions implicitly impose the same weight on all

performance signals within the performance window, while the evidence shows that boards

put more weight on more recent performance. Hence, the two-probit model, which

12 The coefficients on performance in tenure years 0 and -1 are more difficult to compare but suggest the same pattern. If there is a turnover, some of the year 0 performance is before and some after the turnover. Performance that occurs after a turnover cannot predict the turnover and should lower the coefficient on year 0 performance. Hence, the similarity of the coefficients on year 0 and year -1 performance suggests that boards assign higher weight to year 0 performance before a turnover than to performance in year -1.

17

accommodates multiple performance terms with different weights, has an advantage over the

probit model with decile indicators.13 Based on the two-probit models in columns 3 and 4,

between 38 and 39% of all CEO turnovers are performance induced.

The estimates in Tables 3 and 4 show that performance has a stronger effect on CEO

turnover than suggested by the prior literature. Most prior studies focus on forced CEO

turnovers, which are identified using press releases, news reports, announcement dates, and

CEO age. Typical studies classify between 13 and 20% of turnovers as forced.14 Our

estimates suggest that there are twice as many performance-induced turnovers as turnovers

the literature classifies as forced. This is the more surprising given that forced turnovers

include CEO dismissals that are unrelated to firm performance, such as firings for personal

scandals or violations of rules. Hence, our estimates suggest a much tighter link between firm

performance and CEO turnover than previously discovered.

4.2 CEO turnover across tenure

This section explores how the turnover-performance relationship changes with tenure.

The Bayesian learning models, and especially the model with constant CEO ability, predict

that the weights boards assign to lagged performance decline with CEO tenure. As boards’

beliefs about their CEOs become more precise, each performance signal should affect these

beliefs less. To test this prediction, we split the sample into three tenure periods: tenure years

3-6, 7-10, and 11-18. Choosing these relatively long periods allows us to estimate the

coefficients on performance with higher precision. Table 5 shows results from estimating the

two-probit model separately in each subsample. Each regression includes all performance

lags that are statistically significant at the 10 percent level.

There are three important results. First, for CEOs of all tenure levels, turnover is a

function of recent performance but not of performance in the more distant past. For example,

even in tenure years 11-18, only returns in the current and the previous three years are

statistically significant. When the fourth lag is included, the coefficient on performance in

13 The implied turnover probabilities in Panel B are consistent with this observation. The difference in turnover probabilities between good and bad performers, and thus the probability of performance-induced turnover, is slightly higher in columns 3 and 4 (with multiple performance terms) than in columns 1 and 2 (with a single performance term). 14 Using different algorithms, the percentage of CEO turnovers classified as forced is 20% in Warner, Watts, and Wruck (1988), 18% in Dennis and Dennis (1995), 13% in Parrino (1997), 13% in Huson, Parrino, and Starks (2001), 16% in Huson, Malatesta, and Parrino (2004), 13% in Engel, Hayes, and Wang (2003), 19% in Brookman and Thistle (2009), and 17% in Taylor (2010).

18

year -4 is -0.01, with a t-statistic of -0.2 (untabulated). These results again contradict the

learning model with constant CEO ability, according to which all performance lags should

affect CEO turnover equally. Instead, boards act as if performance from four and more years

ago contains almost no information about CEO ability (or match quality) today.

Second, the coefficients on firm performance show little to no decline with CEO tenure.

The learning models predict that the coefficients on past performance should decline with

tenure as boards’ beliefs about CEO ability become more precise. The results in Table 5

provide little support for this prediction. The coefficient on year-zero performance is almost

exactly the same in years 11-18 as in years 3-6 (with estimates of -0.210 and -0.207,

respectively). The coefficient on performance in year -1 shows a small decline from -0.275 in

years 3-6 to -0.238 in years 7-10 and declines substantially only in years 11-18. None of the

declines are statistically significant. The coefficients on performance in years -2 and -3

actually increase with tenure. Thus, there is little evidence that boards respond less strongly

to new performance signals in late tenure than in early tenure, or that their views of CEO

ability are converging over time. This evidence is consistent with a model in which boards’

learning is hampered by shocks to CEO ability.

Fig. 2: Performance-induced turnover in tenure time. The figure shows the implied turnover probabilities from a two-probit model relating CEO turnover to current and lagged performance and the

0%

2%

4%

6%

8%

10%

12%

2 3‐4 5‐6 7‐8 9‐11 12‐16 >=17

Probab

ility of turnover

CEO tenure

Perf.‐ind. turnover Other turnover

19

same control variables as in Table 5. The model allows for different intercepts and different coefficients on performance in each of seven tenure groups: tenure year(s) 2, 3-4, 5-6, 7-8, 9-11, 12-16, and 17 and higher. The number of included current and lagged annual performance terms is two for tenure year 2, three for tenure years 3-4 and 5-6, and four for all other tenure years.

Third, the frequency of performance-induced turnover first slightly increases with tenure

and starts to decline relatively late. In Table 5, the performance-induced turnover probability

is 5.22% per year in tenure years 3-6, 5.25% in 7-10, and 4.25% in 11-18. To examine the

tenure-turnover relation in finer detail, Fig. 2 shows the implied turnover probabilities from a

two-probit model with the tenure years partitioned into seven groups (years 2, 3-4, 5-6, 7-8,

9-11, 12-16, and 17 and higher). The model allows the intercepts and the coefficients on

performance to vary across the seven periods. The results confirm that the probability of

performance-induced turnover first rises with tenure, starting from 4.7% in tenure year 2,

peaks at 5.5% in tenure years 7-8, and then declines slowly to 3.8% in tenure years 17 and

higher. Notably, according to these estimates, almost exactly 50% of turnovers in the first

eight tenure years are performance induced.

Bayesian learning models of CEO turnover can produce turnover probabilities that first

rise and then decline with tenure. The slow increase in turnover frequencies in early tenure

and the late peak in tenure years 7-8 suggest that boards do not determine CEO quality

quickly, or that boards require large negative updates about CEO ability before dismissing

CEOs. Slow learning about CEO ability might be caused by ability changing over time.

Requiring large negative updates about CEO ability before a dismissal is consistent with

significant CEO turnover costs, and with incumbent CEOs who have higher expected ability

than replacement CEOs.

4.3 Forced CEO turnover

This section compares performance-induced turnover to forced CEO turnovers, which are

the focus of the prior literature. Because firms are not required to reveal the true reasons for a

turnover, prior studies use different algorithms to sort turnovers into those that are forced and

those that are voluntary. The most widely used algorithm was introduced by Parrino (1997)

and uses press reports, the time between the turnover announcement and the actual turnover,

and the CEO’s age at departure to classify turnovers as either forced or voluntary.15 Appendix

15 The Parrino algorithm has been used in, among others, Parrino (1997), Farrell and Whidbee (2000, 2003), Huson, Parrino, and Starks (2001), Huson, Malatesta, and Parrino (2004), Yermack (2006), Lel and

20

B gives a detailed description of the steps involved in the classification. Applying the Parrino

algorithm to our CEO panel for the 1992 – 2010 period yields 879 forced and 2,395

voluntary turnovers in 27,708 tenure years.

Table 6 shows standard probit regressions of an indicator for forced CEO turnover on

contemporaneous and lagged scaled stock returns and other controls.16 Years with voluntary

CEO turnovers are included as non-events in the regressions. This analysis replicates

standard CEO turnover regressions in the literature. Panel A shows the regression

coefficients and Panel B the implied turnover probabilities.

The first regression in Table 6 uses the entire CEO panel. The results show that forced

turnovers are strongly linked to prior performance. The probability of a forced turnover rises

from 0.4% at the 95th percentile of the performance distribution to 7.2% at the 5th percentile.

The overall probability of a forced turnover of 2.7% per year is, however, considerably lower

than our estimate of the probability of performance-induced turnover (4.7% per year in Table

4). Similar to performance-induced turnovers, forced turnovers are a function of relatively

recent performance only. In the full panel, four lags of performance are statistically

significant at the 10% level, and the coefficients on more recent performance are significantly

larger than on performance further in the past.

The next three regressions explore how the forced turnover-performance relationship

changes with tenure. We again split the sample into three tenure periods – tenure years 3-6,

7-10, and 11-18 – and estimate turnover regressions separately in each sample. Each

regression includes all performance lags that are statistically significant at the 10 percent

level.

The results confirm that, for CEOs of all tenure lengths, forced turnover is a function of

recent performance but not of performance in the more distant past. For example, in tenure

years 11-18, only returns in the current and the previous three years are statistically

significant. When the fourth lag is included, the coefficient on performance in year -4

is -0.03, with a t-statistic of -0.6 (untabulated). Hence, the learning model with constant CEO

Miller (2008), Brookman and Thistle (2009), Peters and Wagner (2009), Bushman, Dai, and Wang (2010), Taylor (2010), Kaplan and Minton (2012), and Jenter and Kanaan (2014). 16 Because there are very few forced turnovers at very high levels of firm performance, following the literature and using a standard probit regression for forced (as opposed to all) turnover is appropriate.

21

ability, according to which all performance lags should affect CEO turnover equally, seems

to be an equally bad match for forced turnovers as for performance-induced turnover.

A notable difference between forced CEO turnovers and performance-induced turnovers

is that forced turnovers peak early in CEO tenure and decline rapidly as tenure increases. In

Table 6, the probability of a forced turnover is 4.2% per year in tenure years 3-6, 3.4% in

years 7-10, and 2.1% in years 11-18. To examine this decline in more detail, Fig. 3 shows

forced turnover probabilities for eight tenure year periods (years 1, 2, 3-4, 5-6, 7-8, 9-11, 12-

16, and 17 and higher). The forced turnover probability is 2.2% in the first tenure year, peaks

at 4.9% in tenure year 2, and declines monotonically thereafter to 1.1% in tenure years 17

and higher.

Fig. 3: Forced turnover in tenure time. The figure shows the probability of a forced CEO turnover in eight tenure periods: tenure year(s) 1, 2, 3-4, 5-6, 7-8, 9-11, 12-16, and 17 and higher. Turnovers are classified as forced using the Parrino (1997) algorithm.

A comparison of Figures 2 and 3 shows that the estimated probabilities of forced and

performance-induced turnover are of the same magnitude in tenure year 2 but diverge rapidly

as tenure increases. In tenure years 17 and higher, the performance-induced turnover

probability is 3.8% per year while the forced turnover probability is only 1.1%. This large

difference is likely explained by the fact that most departures of long-tenured CEOs are pre-

0%

1%

2%

3%

4%

5%

6%

1 2 3‐4 5‐6 7‐8 9‐11 12‐16 >=17

Probab

ility of turnover

CEO tenure

Forced CEO  turnover

22

announced retirements, which the Parrino algorithm classifies as voluntary turnovers.

However, our analysis reveals that a substantial fraction of these departures are in fact

performance induced, which means that many more occur at low than at high levels of

performance.

Finally, one can apply the distinction between performance-induced and other turnover to

forced turnovers as well. As before, one uses the turnover rate at a high benchmark level of

performance as estimate of the rate of turnover that is not caused by bad performance. Any

additional turnovers at lower levels of performance are assumed to be due to bad

performance and labelled as performance induced. Using the 95th percentile of the

performance distribution as the level at which forced turnovers are assumed to be unrelated to

performance, Panel B of Table 6 shows that between 80 and 90% of forced turnovers are in

fact performance induced. This high percentage is a direct consequence of the fact that there

are few forced turnovers at high levels of performance, which suggests that most forced

turnovers would not have occurred had performance been (much) better. However, the results

in Tables 4 to 6 also show that, even though most forced turnovers are performance induced,

there are many more performance-induced turnovers that the Parrino algorithm classifies as

voluntary.

4.4 Changes in performance-induced turnover over time

This section examines how performance-induced turnover changes during our sample

period from 1993 to 2011. We split the sample into three subperiods from 1993-1999, 2000-

2005, and 2006-2011. Table 7 shows results from estimating the two-probit model separately

in each period. Each regression includes all performance lags that are statistically significant

at the 10 percent level. The regression results are in Panel and the implied turnover

probabilities in Panel B.

The results suggest that level of performance-induced turnover increases from 1993-99 to

2000-05 and then declines again in 2006-11. The estimated rates of performance-induced

turnover are 4.06%, 5.20%, and 4.02% in the three periods, respectively. In parallel, the total

turnover rate increases from 11.7% in 1993-99 to 13.3% in 2000-05, which is consistent with

Kaplan and Minton’s (2011) conclusion that CEO turnover has been rising since the 1970s.

However, the turnover rate falls back to 12.00% in 2006-11, which suggests that the upward

trend in CEO turnover has come to a halt toward the end of our sample. Notably, the

23

coefficients on firm performance in the turnover regressions are considerably smaller in

2006-11 compared to the previous two periods, which might suggest that boards reacted less

strongly to stock price movements during the period of the recent financial crisis.

5 Discussion

5.1 Other determinants of CEO turnover

We have contrasted the empirical properties of performance-induced turnover with

predictions from the Bayesian learning models of CEO turnover described in Section 1.

However, these highly stylized models at best capture some of the factors determining CEO

turnover in reality. This section offers a brief discussion of other likely determinants of CEO

turnover.

5.1.1 Learning-by-doing

Theories of learning-by-doing posit that CEOs build up firm-specific human capital

through their on-the-job experience. As tenure increases, incumbent CEOs’ expected ability

improves, on average, relative to that of potential replacements. The main empirical

implication is that performance-induced turnovers should decline with tenure (Garen (1988)).

The empirical result that performance-induced turnover rises, if slightly, until tenure

years 7-8 does not disprove the importance of learning-by-doing. However, it suggests that

other factors, such as slow learning about CEO ability or high turnover costs, dominate in the

first tenure years.

5.1.2 Increasing entrenchment

Theories of increasing entrenchment predict that the cost of dismissing CEOs increases

with tenure. This might, for example, be because the CEO is gradually appointing his

supporters to the board of directors (Hermalin and Weisbach (1998)). The main empirical

prediction is again that performance-induced turnovers should decline with tenure.

As before, the empirical result that performance-induced turnover rises slightly until

tenure years 7-8 does not disprove the importance of increasing entrenchment. However, it

suggests that other factors dominate in the first tenure years.

24

5.1.3 Heterogeneity and selection

The Bayesian learning models in Section 1 assume that CEOs are heterogeneous in their

ability and predict that, as tenure increases, the surviving CEOs are selected for higher

ability. However, there are other dimensions of heterogeneity that these models ignore. For

example, CEOs might differ in their level of entrenchment, or firms might differ in their

ability to evaluate their CEO. As tenure increases and CEOs are being replaced, the

remaining pool of surviving CEOs would then be increasingly selected for being entrenched,

for working for firms which are unable to evaluate CEOs, and for other factors associated

with less turnover.

The main empirical prediction is again that performance-induced and other turnover

should decline with tenure. As before, the result that performance-induced turnover rises

slightly until tenure years 7-8 doe not disprove the importance of heterogeneity and selection,

but does suggest that other factors dominate at first.

5.2 Underestimating performance-induced turnover

There are several reasons to believe that our estimates of performance-induced turnover

underestimate the true number. First, the actual performance measures used by boards to

evaluate CEOs are unknown, and boards have access to (likely many) performance signals

that are unobservable to the econometrician.17 Using the wrong performance measure implies

that we underestimate the effect of (correctly measured) performance on CEO turnover.

Specifically, it causes us to overestimate the number of turnovers at high levels of

performance, and hence the number of turnovers unrelated to performance, and to

underestimate the number of turnovers at low levels of performance, and hence the number

of performance-induced turnovers.

Second, stock returns are not an ideal measure of firm performance in CEO turnover

regressions because stock prices are forward looking. Specifically, stock prices incorporate

investors’ assessment of the probability of a CEO turnover. If investors deem a turnover

highly likely, then stock prices and returns reflect the expected value of the firm not under

17 See Cornelli, Kominek, and Ljungqvist (2013) for evidence on the importance of “soft” information in the evaluation and firing of CEOs.

25

the incumbent but under a successor CEO. This reduces the predictive power of stock prices

for CEO turnover and biases the estimates of performance-induced turnover downward.18

Third, estimating performance-induced turnover requires choosing a performance

threshold above which all turnovers are assumed to be independent of performance. To the

extent that this assumption is violated, we overestimate the number of turnovers unrelated to

performance and, as a result, underestimate how many turnovers are caused by bad

performance. This occurs if there are turnovers caused by bad performance above the

performance threshold, i.e., turnovers that would not have occurred had performance been

even better. An example are CEOs who retire at, say, the 95% percentile of the performance

distribution but would have stayed had performance been at the 99% percentile. This also

occurs if there are turnovers above the threshold that are caused by good performance, i.e.,

that would not have happened had performance been lower. An example are successful CEOs

who are hired away by other firms. Both violations cause us to overestimate the number of

“other” turnovers, and hence to underestimate the number of turnovers that are due to bad

performance.

It is difficult to assess by how much we underestimate the frequency of performance-

induced turnovers. However, our estimates already indicate that close to 40% of all turnovers

are performance-induced, and that almost 50% of turnovers in the first eight tenure years are

in this category. This suggests that many, or possible even most, CEOs leave their position

because of a performance-induced turnover.

6 Conclusion

This paper introduces the concept of performance-induced turnover, which is defined as

turnover that would not have occurred had performance been “good”. The probability of

performance-induced turnover at a given performance level is estimated from the difference

between the turnover probability at that level and the turnover probability at some high

performance threshold, such as the 95th percentile of the performance distribution. The

assumption is that turnovers at and above this performance threshold are unrelated to

performance and, thus, occur at any level of performance. Any additional turnover

18 See Dow and Gorton (1997), Bond, Goldstein, and Prescott (2010), and Edmans, Goldstein, and Jiang (2012, 2014) for analyses of feedback effects between corporate actions and stock prices.

26

probability at performance levels below the threshold is assumed to be caused by

performance being worse. These additional turnovers are labelled as performance induced.

We find that CEO turnover is closely linked to firm performance and that

performance-induced turnovers are significantly more frequent than the forced turnovers that

are the focus of prior studies. We estimate almost 40% of all CEO turnovers to be

performance induced. In the first eight years of tenure, this percentage is close to 50%.

We contrast the empirical properties of performance-induced turnovers with the

predictions of Bayesian learning models of CEO turnover. The evidence suggests a version of

the Bayesian learning model in which CEO ability or, more likely, match quality is changing

over time. Specifically, performance-induced turnover is driven by performance in the most

recent three to four years, and is insensitive to performance further in the past. Moreover, the

sensitivity of turnover to past performance shows little to no decline with tenure for at least

the first ten years of tenure. Both observations, as well as the slow increase of performance-

induced turnover with tenure and its late peak in tenure years 7-8, are consistent with a model

in which boards’ learning about CEOs is hampered by shocks to CEO ability or to the quality

of the CEO-firm match.

27

Appendix A: A Bayesian learning model with shocks to CEO quality

As in Section 1.1., we assume that the board’s initial prior about the CEO’s ability 0 is

normally distributed with a mean of and a variance of . We set 0 for simplicity.

CEO ability follows a random walk:

where ~N 0, (A1)

Every period, the board updates its prior about ability based on firm performance xt:

x α ϵ whereϵ ~N 0, (A2)

The random shock occurs in the beginning of each period t, before the board observes the

signal xt. The board then forms its posterior belief and fires the CEO when the posterior

mean falls below the endogenous threshold .

Note that the posterior belief in period t no longer corresponds to the prior belief in the

subsequent period t+1 because the board expects quality to change randomly in the

beginning of t+1. This random shock adds to the board’s uncertainty about ability in t+1, so

that the variance of the prior belief in t+1 equals (compared to simply in the model

without shocks to quality). Concretely, the board’s initial beliefs at the end of period t=1, 2,

and 3 are: 19

(A3.1)

, + (A3.2)

, , , + (A3.3)

, (A3.4)

As is apparent from equation (A3), the board no longer assigns equal weights to signals

received at different times in the past when forming its beliefs. Signals from the more distant

19 A general expression for the posterior mean in year t is: α ∑ φ , x , with φ , 1 for

i=0, and φ , ∏ k , with k for i>0.

28

past receive a lower weight because they are less informative about current ability. By how

much a lagged signal is downgraded depends on how much uncertainty the shocks add to the

board’s beliefs, as measured by the terms kt,i < 0. To see the intuition, consider equation

(A3.2) for t=2. To form its posterior believe in t=2, the board discounts the once-lagged

signal x1 by a factor of , . Thus, if the second-period shock to ability doubles the

variance of the board’s prior compared to the pre-shock belief, then , and x1 gets half

the weight of x2. It is straightforward to see that , 1 in the special case with constant

ability described in Section 1.1 0 , and that , 0 if the shocks to ability are so large

that x1 becomes completely uninformative about ability in t=2 ∞ .

The board’s uncertainty about ability could either increase or decrease with tenure. This

follows from the expression for the variance of the posterior belief in year t:

(A4)

Whether is higher or lower than depends on the strength of the signals relative to the

magnitude of the shocks. Whether the board’s uncertainty declines or increases with tenure

can be inferred from how the weight on the most recent performance changes with tenure:

based on equations (A3), a board whose prior tightens assigns lower weight to the most

recent performance signal as tenure increases.

29

Appendix B: The Parrino classification algorithm

The Parrino (1997) algorithm classifies CEO departures as forced or voluntary based on

information in departure announcements and press reports. The algorithm consists of three

steps. First, all cases in which the press reports that a CEO is forced out, fired, ousted, or

leaves due to policy differences or pressure are classified as forced. Second, all cases not

classified as forced and with a CEO under the age of 60 are reviewed and reclassified as

forced if (1) the stated departure reason is not death, poor health, or acceptance of another

position, or (2) the CEO is retiring but does not announce the retirement at least six months

before the departure. Third, all cases classified as forced in the previous step are investigated

again and reclassified as voluntary if the press convincingly explains that the CEO is leaving

for personal or business reasons unrelated to the firm’s activities, or if the CEO remains or

becomes chairman of the board after the resignation.

30

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Taylor, Lucian A., 2013, CEO wage dynamics: Estimates from a learning model, Journal of Financial Economics 108, 70-98.

Warner, Jerold B., Ross L. Watts, and Karen H. Wruck, 1988, Stock prices and top management changes. Journal of Financial Economics 20, 461-492.

Weisbach, Michael S., 1988, Outside directors and CEO turnover. Journal of Financial Economics 20, 431-460.

Yermack, David, 2006, Golden handshakes: Separation pay for retired and dismissed CEOs, Journal of Accounting and Economics 41, 237-256.

33

Table 1: Estimating performance-induced turnover: numerical example. The simulation is based on 500 randomly generated samples of 23,000 CEO-years, and the table shows descriptive statistics for the estimates across the 500 samples. In the simulations, the CEO is dismissed each year with probability

∙ , the CEO retires each year with probability , or both events occur simultaneously. Total turnover is governed by eq. (12) in the paper. Parameters α , β , andβ are set to -1.4, -1.6, and -0.4, respectively; is normally distributed with a mean of 0.1 and a standard deviation of 0.3. The performance term is scaled by its standard deviation. The performance-induced turnover probabilities are estimated using either the two-probit model (eq. (11)) or the standard probit model with decile dummies (eq. (10)). Performance-induced turnover, defined in eq. (9), is calculated for each observation with X equal to the 95th percentile of the performance distribution. In each simulation, probabilities are averaged across observations within each performance decile. The bottom panel of the table shows descriptive statistics for the estimated coefficients of the two-probit models across the 500 simulations.

      Performance‐induced turnover probabilities (estimated) 

  Dismissals probabilities (observed)    Two‐probit    Standard probit with decile dummies 

Perf. decile  Mean  Median  Std  Mean  Median  Std  Mean  Median  Std 

1  0.155  0.154  0.008  0.147  0.147  0.009  0.148  0.147  0.009 

2  0.094  0.094  0.006  0.087  0.087  0.007  0.087  0.087  0.007 

3  0.072  0.072  0.006  0.064  0.064  0.006  0.065  0.065  0.006 

4  0.057  0.057  0.005  0.049  0.049  0.006  0.049  0.049  0.006 

5  0.046  0.046  0.004  0.038  0.038  0.006  0.039  0.038  0.006 

6  0.037  0.037  0.004  0.029  0.029  0.005  0.029  0.029  0.005 

7  0.030  0.030  0.003  0.021  0.021  0.004  0.022  0.022  0.004 

8  0.023  0.022  0.003  0.014  0.014  0.003  0.015  0.015  0.003 

9  0.016  0.016  0.003  0.008  0.008  0.002  0.009  0.009  0.002 

10  0.008  0.008  0.002  0.001  0.001  0.000  0.000  0.000  0.000 

      Two‐probit parameter estimates        Coefficient Mean  Median  Std 

      1 ‐1.598  ‐1.598  0.090 

      2 ‐0.401  ‐0.400  0.050 

  1 ‐1.408  ‐1.398  0.058 

34

Table 2: Descriptive statistics. The sample consists of 2,955 ExecuComp firms from 1992 to 2011 with 5,356 CEOs and 25,632 CEO-years. Book assets are in $ millions. Book-to-market is the ratio of the book value to the market value of common equity, where the book value of common equity is defined as shareholders’ equity plus deferred taxes plus balance sheet tax credits minus the book value of preferred stock. Dividend payer is an indicator for firms that pay dividends during the fiscal year. ROA is operating cash flow divided by book assets. Both the book-to-market ratio and ROA are winsorized at the 1% level.

   Mean Median P10  P90  SD

Book assets  10,483 1,230 153  16,254 59,487

Book‐to‐market  0.55 0.46 0.16  1.02 0.40

ROA  0.16 0.15 0.03  0.30 0.13

Dividend payer  0.60 1 0  1 0.49

CEO age  55.67 56 46  64 7.48

CEO tenure  9.32 7 2  20 7.81

35

Table 3: Performance-induced turnover using standard probit models with performance decile indicators. Panel A shows probit regressions of an indicator variable for CEO turnover on indicator variables for deciles of the performance distribution. Performance is measured as average monthly stock returns scaled by the standard deviation of returns. Returns are measured over tenure years [-1,0], [-2,0], [-3,0], and from tenure start to year 0 in regressions 1, 2, 3, and 4, respectively, where year 0 is the year of the CEO turnover. Panel B shows the implied turnover probabilities. The probabilities are calculated by setting the measure of firm performance to the desired level while leaving all control variables at their actual values and averaging the implied probabilities across observations. The probability of “other turnover” is calculated by setting the performance measure to the top decile of the performance distribution for each observation. The probability of “performance-induced turnover” is calculated from the difference between the implied total turnover probability and the implied probability of “other” turnover for each observation (see equation (9)). Panel A: Probit regressions 

  (1)    (2)    (3)    (4)    Coefficient  T‐stat. Coefficient T‐stat. Coefficient T‐stat. Coefficient T‐stat.

Scaled return t=[‐1, 0]  Scaled return t=[‐2, 0]  Scaled return t=[‐3, 0]  Scaled return t=[tenure start, 0] Decile 1  ‐  ‐  ‐  ‐ 2  ‐0.181***  [‐4.02]  ‐0.131**  [‐2.92]  ‐0.131**  [‐2.90]  ‐0.0949*  [‐2.05] 3  ‐0.218***  [‐4.77] ‐0.265*** [‐5.71] ‐0.283*** [‐6.06] ‐0.172*** [‐3.66]4  ‐0.349***  [‐7.46] ‐0.343*** [‐7.23] ‐0.228*** [‐4.93] ‐0.229*** [‐4.79]5  ‐0.294***  [‐6.31]  ‐0.311***  [‐6.72]  ‐0.300***  [‐6.36]  ‐0.258***  [‐5.35] 6  ‐0.349***  [‐7.38]  ‐0.351***  [‐7.36]  ‐0.339***  [‐7.11]  ‐0.376***  [‐7.56] 7  ‐0.344***  [‐7.31]  ‐0.413***  [‐8.52]  ‐0.432***  [‐8.80]  ‐0.375***  [‐7.36] 8  ‐0.425***  [‐8.82]  ‐0.471***  [‐9.65]  ‐0.481***  [‐9.81]  ‐0.439***  [‐8.50] 9  ‐0.556***  [‐11.13] ‐0.527*** [‐10.56] ‐0.562*** [‐11.05] ‐0.371*** [‐7.45]10  ‐0.527***  [‐10.60] ‐0.568*** [‐11.24] ‐0.561*** [‐10.89] ‐0.495*** [‐9.31]

Age  0.0151***  [5.64]  0.0147***  [5.44]  0.0142***  [5.25]  0.0135***  [5.00] Age 61‐63  0.294***  [7.79]  0.297***  [7.85]  0.302***  [7.96]  0.294***  [7.79] Age 64‐66  0.669***  [14.43]  0.674***  [14.47]  0.680***  [14.55]  0.681***  [14.62] Age > 66  0.387***  [6.05]  0.398*** [6.20] 0.411***  [6.37] 0.400*** [6.23]Tenure  ‐0.0100***  [‐6.22] ‐0.0100*** [‐6.22] ‐0.0100*** [‐6.19] ‐0.00560*** [‐3.36]Dividend  ‐0.0905***  [‐3.52]  ‐0.100***  [‐3.88]  ‐0.108***  [‐4.15]  ‐0.118***  [‐4.54] Book/market  ‐0.043  [‐1.39]  ‐0.0666*  [‐2.13]  ‐0.0975**  [‐3.08]  ‐0.121***  [‐3.74] Log assets  0.0268***  [3.86]  0.0243***  [3.50]  0.0239***  [3.42]  0.0284***  [4.09] ROA  ‐0.0306  [‐0.30]  0.00151  [0.01]  0.057  [0.54]  0.0918  [0.86] Pre‐tenure return  ‐1.425*  [‐2.38] ‐1.622** [‐2.68] ‐1.824**  [‐3.00] ‐1.956** [‐3.17]Constant  ‐1.892***  [‐12.84] ‐1.824*** [‐12.26] ‐1.790*** [‐12.00] ‐1.857*** [‐12.42]

N  22758     22758     22758     22758 

36

Panel B: Implied turnover probabilities                            

  (1)  (2) (3) (4)

Scaled return t=[‐1, 0]  Scaled return t=[‐2, 0]  Scaled return t=[‐3, 0]  Scaled return t=[tenure start, 0] Decile 1  18.64%  18.93%  18.75%  17.64% 2  14.35%  15.73%  15.56%  15.39% 3  13.56%  12.84% 12.33% 13.71%4  11.02%  11.34% 13.43% 12.54%5  12.04%  11.94%  12.01%  11.98% 6  11.02%  11.19%  11.27%  9.87% 7  11.11%  10.10%  9.67%  9.90% 8  9.71%  9.15%  8.89%  8.88% 9  7.74%  8.31% 7.71% 9.96%Decile 10  8.14%  7.72% 7.72% 8.05%

Perf.‐ind. turnover  4.09%  4.49%  4.48%  4.13% Other turnover  8.14%  7.72%  7.72%  8.05% All turnover  11.77%        11.77%        11.77%        11.77%    

37

Table 4: Performance-induced turnover using the two-probit model. Panel A shows estimates of two-probit regressions of an indicator variable for CEO turnover on firm performance and controls. Performance is measured as average monthly stock returns scaled by the standard deviation of returns. Returns are measured over tenure years [-2,0] and [-3,0] in regressions 1 and 2 and using separate return terms for different tenure years in regressions 3 and 4, respectively. Year 0 is the year of the CEO turnover. Panel B shows the implied turnover probabilities. The probabilities are calculated by setting the measure of firm performance to the desired level while leaving all control variables at their actual values and averaging the implied probabilities across observations. The probability of “other turnover” is calculated by setting the performance measure to the 95th percentile of the performance distribution for each observation. The probability of “performance-induced turnover” is calculated from the difference between the implied total turnover probability and the implied probability of “other” turnover for each observation (see equation (9)). Panel A: Two‐probit regressions 

  (1)    (2)    (3)    (4)    Coefficient T‐stat. Coefficient T‐stat.    Coefficient T‐stat. Coefficient T‐stat.

Probit 1: Scaled return t=[‐2, 0]   ‐0.312***  [‐10.77] Scaled return t=[‐3, 0]   ‐0.302***  [‐10.83] Scaled return t=0  ‐0.213*** [‐8.74] ‐0.206*** [‐7.43]Scaled return t=‐1  ‐0.235*** [‐9.50] ‐0.222*** [‐8.11]Scaled return t=‐2  ‐0.132***  [‐6.64]  ‐0.145***  [‐6.29] Scaled return t=‐3  ‐0.081***  [‐3.61] 

Age  0.00739  [1.71]  0.00777  [1.81]  0.00662  [1.55]  0.00762  [1.59] Tenure   ‐0.00758* [‐2.20] ‐0.00642* [‐1.96] ‐0.00808* [‐2.26] ‐0.0111** [‐2.61]Dividend  ‐0.419*** [‐6.51] ‐0.426*** [‐6.37] ‐0.436*** [‐6.81] ‐0.420*** [‐5.92]Book/market  0.0206  [0.40]  ‐0.0423  [‐0.81]  0.041  [0.76]  ‐0.0249  [‐0.39] Log assets  ‐0.0297*  [‐1.99]  ‐0.0262  [‐1.80]  ‐0.0327*  [‐2.14]  ‐0.0252  [‐1.50] ROA  ‐0.219  [‐1.48]  ‐0.157  [‐1.05]  ‐0.23  [‐1.54]  ‐0.183  [‐1.00] Pre‐tenure return  ‐1.498  [‐1.92]  ‐2.002*  [‐2.56]  ‐1.256  [‐1.56]  ‐1.243  [‐1.43] Constant  ‐1.440*** [‐5.91] ‐1.437*** [‐5.98] ‐1.407*** [‐5.93] ‐1.426*** [‐5.21]

Probit 2: Age  0.0344***  [4.44]  0.0330***  [4.13]  0.0335***  [4.46]  0.0291***  [3.52] Age 61‐63  0.457***  [5.64]  0.475***  [5.56]  0.452***  [6.02]  0.460***  [5.58] Age 64‐66  0.915***  [8.28]  0.941***  [8.12]  0.899***  [8.91]  0.892***  [7.96] Age > 66  0.435** [3.10] 0.474** [3.25] 0.428** [3.25] 0.456** [3.17]Tenure   ‐0.0108*** [‐3.47] ‐0.0118*** [‐3.69] ‐0.0102*** [‐3.43] ‐0.0106** [‐3.29]

38

Dividend  0.413***  [3.77]  0.434***  [3.91]  0.387***  [3.73]  0.382***  [3.37] Book/market  ‐0.124  [‐1.63]  ‐0.112  [‐1.46]  ‐0.132  [‐1.80]  ‐0.0991  [‐1.24] Log assets  0.0836***  [5.78]  0.0833***  [5.59]  0.0830***  [5.98]  0.0842***  [5.53] ROA  0.717** [3.02] 0.795*** [3.29] 0.697** [3.05] 0.869*** [3.51]Pre‐tenure return  ‐1.282  [‐1.20] ‐1.013 [‐0.92] ‐1.452 [‐1.41] ‐1.168 [‐1.10]Constant  ‐4.699***  [‐10.34]     ‐4.661***  [‐9.98]     ‐4.587***  [‐10.34]     ‐4.354***  [‐9.00] 

N  22758     22758     22758     19536 

     Panel B: Implied turnover probabilities                               

  (1) (2)   (3) (4)

5th percentile  18.45%  18.46%  18.80%  19.49% 15th percentile  15.17%  15.18%  15.23%  15.78% 25th percentile  13.59%  13.63%  13.57%  14.15% 35th percentile  12.50% 12.53% 12.45% 13.03%45th percentile  11.62% 11.66% 11.54% 12.14%55th percentile  10.87%  10.92%  10.79%  11.34% 65th percentile  10.17%  10.23%  10.07%  10.63% 75th percentile  9.45%  9.54%  9.34%  9.88% 85% percentile  8.71%  8.76%  8.56%  9.08% 95% percentile  7.68% 7.69% 7.52% 8.00%

Perf.‐ind. turnover  4.45%  4.45%  4.61%  4.72% Other turnover  7.68%  7.69%  7.52%  8.00% All turnover  11.77%        11.77%        11.77%        12.33%    

39

Table 5: Performance-induced turnover by tenure. Panel A shows estimates of two-probit regressions of an indicator variable for CEO turnover on firm performance and controls. Performance is measured as average monthly stock returns per tenure year scaled by the standard deviation of returns. Year 0 is the year of the CEO turnover. Panel B shows the implied turnover probabilities. The probabilities are calculated by setting the measure of firm performance to the desired level while leaving all control variables at their actual values and averaging the implied probabilities across observations. The probability of “other turnover” is calculated by setting the performance measure to the 95th percentile of the performance distribution for each observation and averaging. The probability of “performance-induced turnover” is calculated from the difference between the implied total turnover probability and the implied probability of “other” turnover for each observation (see equation (9)).

Panel A: Two‐probit regressions 

Tenure years 3‐6  Tenure years 7‐10  Tenure years 11‐18 

   Coefficient  T‐stat.     Coefficient  T‐stat.     Coefficient  T‐stat. 

Probit 1: 

Scaled return t=0  ‐0.210***  [‐6.84]  ‐0.268***  [‐5.35]  ‐0.207***  [‐3.89] 

Scaled return t=‐1  ‐0.275***  [‐7.79]  ‐0.238***  [‐5.25]  ‐0.123**  [‐2.78] 

Scaled return t=‐2  ‐0.116***  [‐4.31]  ‐0.134***  [‐3.44]  ‐0.158***  [‐3.37] 

Scaled return t=‐3  ‐0.0990*  [‐2.38]  ‐0.121*  [‐2.36] 

Age  0.00728  [1.04]  ‐0.00104  [‐0.10]  0.00987  [1.15] 

Tenure   0.0332  [1.16]  ‐0.0364  [‐0.90]  0.00872  [0.40] 

Dividend  ‐0.411***  [‐5.34]  ‐0.533***  [‐3.90]  ‐0.523**  [‐2.84] 

Book/market  0.0486  [0.65]  ‐0.0669  [‐0.57]  ‐0.125  [‐0.93] 

Log assets  ‐0.0533*  [‐2.38]  0.0252  [0.91]  ‐0.0255  [‐0.71] 

ROA  ‐0.206  [‐1.03]  ‐0.117  [‐0.36]  ‐0.374  [‐1.06] 

Pre‐tenure return  ‐0.982  [‐0.89]  ‐1.06  [‐0.69]  ‐0.97  [‐0.49] 

Constant  ‐1.464***  [‐3.89]  ‐1.046  [‐1.66]  ‐1.724**  [‐3.19] 

Probit 2: 

Age  0.0568*  [2.09]  0.0586**  [2.92]  0.0369*  [2.47] 

Age 61‐63  0.208  [1.25]  0.375**  [2.88]  0.308*  [2.41] 

Age 64‐66  0.915***  [3.71]  0.787***  [4.36]  0.692***  [4.07] 

Age > 66  0.392  [1.01]  0.0699  [0.22]  0.128  [0.51] 

Tenure   0.0960*  [2.19]  0.0475  [1.27]  ‐0.0209  [‐1.04] 

Dividend  0.43  [1.80]  0.487*  [2.36]  0.426  [1.93] 

Book/market  ‐0.26  [‐1.82]  ‐0.0657  [‐0.52]  0.0679  [0.50] 

Log assets  0.0681*  [2.47]  0.0710**  [2.79]  0.111***  [3.77] 

ROA  ‐0.0245  [‐0.05]  0.357  [0.76]  1.950***  [4.17] 

Pre‐tenure return  ‐3.00  [‐1.32]  ‐1.41  [‐0.85]  ‐1.52  [‐0.98] 

Constant  ‐6.312***  [‐4.05]     ‐6.354***  [‐5.43]     ‐4.989***  [‐5.02] 

N  9338     5408     4845 

40

Panel B: Implied turnover probabilities                      

Tenure years 3‐6  Tenure years 7‐10  Tenure years 11‐18 

5th percentile  18.33%  22.32%  18.79% 

15th percentile  14.33%  17.70%  15.79% 

25th percentile  12.43%  15.68%  14.35% 

35th percentile  11.04%  14.27%  13.44% 

45th percentile  9.95%  13.23%  12.70% 

55th percentile  9.08%  12.31%  12.06% 

65th percentile  8.23%  11.55%  11.41% 

75th percentile  7.40%  10.74%  10.78% 

85% percentile  6.49%  9.92%  10.07% 

95% percentile  5.31%  8.85%  9.13% 

Perf.‐ind. turnover  5.22%  5.25%  4.05% 

Other turnover  5.31%  8.85%  9.13% 

All turnover  10.21%        13.65%        12.82%    

41

Table 6: Forced turnover using standard probit models. Panel A shows probit regressions of an indicator variable for forced CEO turnover on firm performance. Performance is measured as average monthly stock returns scaled by the standard deviation of returns. Panel B shows the implied turnover probabilities. The probabilities are calculated by setting the measure of firm performance to the desired level while leaving all control variables at their actual values and averaging the implied probabilities across observations. The probability of “other turnover” is calculated by setting the performance measure to the 95th percentile of the performance distribution for each observation. The probability of “performance-induced turnover” is calculated from the difference between the implied total forced turnover probability and the implied probability of “other” forced turnover for each observation (see equation (9)).

Panel A: Probit regressions 

   All tenure years     Tenure years 3‐6     Tenure years 7‐10     Tenure years 11‐18 

   Coefficient  T‐stat.     Coefficient  T‐stat.     Coefficient  T‐stat.     Coefficient  T‐stat. 

Scaled return t=0  ‐0.205***  [‐8.20]  ‐0.233***  [‐8.31]  ‐0.265***  [‐6.19]  ‐0.168***  [‐3.45] 

Scaled return t=‐1  ‐0.293***  [‐11.47]  ‐0.332***  [‐11.02]  ‐0.295***  [‐6.85]  ‐0.233***  [‐4.82] 

Scaled return t=‐2  ‐0.149***  [‐5.71]  ‐0.133***  [‐4.61]  ‐0.220***  [‐4.66]  ‐0.081  [‐1.55] 

Scaled return t=‐3  ‐0.0987***  [‐3.79]  ‐0.0979*  [‐2.25]  ‐0.134*  [‐2.56] 

Scaled return t=‐4  ‐0.0433  [‐1.77]  ‐0.0920*  [‐2.17] 

Age  ‐0.00721  [‐1.45]  0.00139  [0.27]  ‐0.0206*  [‐2.51]  ‐0.00349  [‐0.35] 

Age 61‐63  ‐0.322***  [‐3.55]  ‐0.542***  [‐3.97]  ‐0.134  [‐0.96]  ‐0.469*  [‐2.41] 

Age 64‐66  ‐0.394**  [‐2.88]  ‐0.677**  [‐2.68]  ‐0.109  [‐0.49]  ‐0.41  [‐1.62] 

Age > 66  ‐0.182  [‐1.32]  ‐  [.]  ‐0.0512  [‐0.16]  ‐0.734  [‐1.88] 

Tenure   ‐0.0187***  [‐3.96]  0.0121  [0.51]  ‐0.0946**  [‐2.75]  0.00797  [0.37] 

Dividend  ‐0.305***  [‐5.45]  ‐0.277***  [‐4.58]  ‐0.380***  [‐3.83]  ‐0.288**  [‐2.58] 

Book/market  ‐0.0686  [‐0.98]  ‐0.0208  [‐0.26]  0.0365  [0.33]  ‐0.113  [‐0.84] 

Log assets  0.0523***  [3.35]  ‐0.00858  [‐0.50]  0.0572*  [1.99]  0.0448  [1.36] 

ROA  ‐0.500*  [‐2.39]  ‐0.192  [‐0.85]  ‐0.429  [‐1.22]  ‐0.774*  [‐2.24] 

Pre‐tenure return  ‐3.337**  [‐2.93]  ‐2.529*  [‐2.36]  ‐2.50  [‐1.71]  ‐1.08  [‐0.45] 

Constant  ‐1.400***  [‐5.29]     ‐1.635***  [‐5.62]     ‐0.134  [‐0.27]     ‐1.872**  [‐3.28] 

N  14,541     7,956     4,539     4,247 

42

Panel B: Implied forced turnover probabilities                            

   All tenure years     Tenure years 3‐6     Tenure years 7‐10     Tenure years 11‐18 

5th percentile  7.23%  11.23%  10.07%  5.13% 

15th percentile  4.65%  7.34%  6.10%  3.42% 

25th percentile  3.56%  5.56%  4.51%  2.71% 

35th percentile  2.84%  4.42%  3.49%  2.23% 

45th percentile  2.33%  3.60%  2.75%  1.89% 

55th percentile  1.90%  2.95%  2.13%  1.57% 

65th percentile  1.50%  2.35%  1.64%  1.29% 

75th percentile  1.14%  1.79%  1.19%  1.03% 

85% percentile  0.78%  1.21%  0.75%  0.75% 

95% percentile  0.37%  0.55%  0.30%  0.42% 

Perf.‐ind. turnover  2.39%  3.67%  3.08%  1.72% 

Other turnover  0.37%  0.55%  0.30%  0.42% 

All forced turnover  2.73%        4.19%        3.37%        2.12%    

43

Table 7: Performance-induced turnover in different calendar time periods. Panel A shows estimates of two-probit regressions of an indicator variable for CEO turnover on firm performance and controls. Performance is measured as average monthly stock returns per tenure year scaled by the standard deviation of returns. Year 0 is the year of the CEO turnover. Panel B shows the implied turnover probabilities. The probabilities are calculated by setting the measure of firm performance to the desired level while leaving all control variables at their actual values and averaging the implied probabilities across observations. The probability of “other turnover” is calculated by setting the performance measure to the 95th percentile of the performance distribution for each observation. The probability of “performance-induced turnover” is calculated from the difference between the implied total turnover probability and the implied probability of “other” turnover for each observation (see equation (9)).

Panel A: Two‐probit regressions 

   1993‐1999     2000‐2005     2005‐2011 

   Coefficient  T‐stat.     Coefficient  T‐stat.     Coefficient  T‐stat. 

Probit 1: 

Scaled return t=0  ‐0.254***  [‐4.27]  ‐0.285***  [‐4.93]  ‐0.153*  [‐2.22] 

Scaled return t=‐1  ‐0.238***  [‐4.16]  ‐0.295***  [‐4.12]  ‐0.202***  [‐3.64] 

Scaled return t=‐2  ‐0.194**  [‐3.11]  ‐0.138**  [‐2.69]  ‐0.179***  [‐4.41] 

Scaled return t=‐3  ‐0.139*  [‐2.31]  ‐0.0911*  [‐2.36]  ‐0.0851  [‐1.72] 

Age  0.0150*  [2.25]  0.0213  [1.88]  ‐0.00237  [‐0.15] 

Tenure   ‐0.00688  [‐1.02]  ‐0.0314**  [‐2.99]  0.0037  [0.32] 

Dividend  ‐0.630**  [‐2.88]  ‐0.331*  [‐2.34]  ‐0.359*  [‐2.27] 

Book/market  ‐0.299  [‐1.70]  0.028  [0.23]  0.0967  [0.72] 

Log assets  ‐0.0424  [‐1.17]  ‐0.0297  [‐1.10]  0.00948  [0.23] 

ROA  ‐0.105  [‐0.35]  ‐0.823  [‐1.85]  ‐0.676  [‐0.85] 

Pre‐tenure return  ‐0.139  [‐0.09]  ‐0.514  [‐0.35]  ‐3.522  [‐1.52] 

Constant  ‐1.645***  [‐3.65]  ‐1.999**  [‐3.16]  ‐1.394*  [‐1.97] 

Probit 2: 

Age  0.0258*  [2.15]  ‐0.00608  [‐0.35]  0.0384*  [2.34] 

Age 61‐63  0.452***  [3.60]  0.572**  [3.13]  0.369*  [2.52] 

Age 64‐66  1.095***  [6.31]  0.946***  [4.02]  0.701**  [3.20] 

Age > 66  0.528*  [2.27]  0.809**  [2.64]  0.293  [1.11] 

Tenure   ‐0.0203***  [‐3.94]  0.00353  [0.61]  ‐0.0195*  [‐2.55] 

Dividend  0.542  [1.80]  0.288*  [2.47]  0.171  [1.10] 

Book/market  0.125  [1.12]  ‐0.24  [‐1.61]  ‐0.117  [‐0.74] 

Log assets  0.105***  [3.31]  0.0737**  [2.95]  0.0547  [1.64] 

ROA  1.454***  [3.40]  1.393***  [3.39]  0.599  [1.49] 

Pre‐tenure return  ‐1.20  [‐0.82]  ‐2.39  [‐1.49]  0.94  [0.44] 

Constant  ‐4.554***  [‐5.20]     ‐2.272**  [‐2.81]     ‐4.279***  [‐4.21] 

N  6,283     6,600     6,653 

44

Panel B: Implied turnover probabilities                      

   1993‐1999     2000‐2005     2005‐2011 

5th percentile  19.37%  21.92%  17.81% 

15th percentile  15.52%  16.95%  14.70% 

25th percentile  13.73%  15.11%  13.31% 

35th percentile  12.44%  13.75%  12.42% 

45th percentile  11.47%  12.75%  11.71% 

55th percentile  10.69%  11.86%  11.05% 

65th percentile  9.97%  11.15%  10.48% 

75th percentile  9.30%  10.39%  9.86% 

85% percentile  8.65%  9.54%  9.20% 

95% percentile  7.93%  8.55%  8.30% 

Perf.‐ind. turnover  4.06%  5.20%  4.02% 

Other turnover  7.93%  8.55%  8.30% 

All turnover  11.66%        13.30%        11.99%