Career concerns and Bayesian overconfidence of managers

Accepted Manuscript

Career Concerns and Bayesian Overconfidence of Managers Sadettin Haluk Citci, Eren Inci PII: DOI: Reference:

S0167-7187(16)30023-6 10.1016/j.ijindorg.2016.04.005 INDOR 2294

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International Journal of Industrial Organization

Received date: Revised date: Accepted date:

18 March 2015 11 March 2016 13 April 2016

Please cite this article as: Sadettin Haluk Citci, Eren Inci, Career Concerns and Bayesian Overconfidence of Managers, International Journal of Industrial Organization (2016), doi: 10.1016/j.ijindorg.2016.04.005

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Highlights • Managerial overconfidence can be a rational response rather than a personal trait. • A manager, whose contract may not be renewed upon poor performance, chooses risky

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projects. • More than half of the managers estimate their abilities to be better than average.

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• There can be underconfident managers in equilibrium but they never form majority.

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Career Concerns and Bayesian

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Overconfidence of Managers∗ Sadettin Haluk Citci†and Eren Inci‡

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10 March 2016

Abstract

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We show that managerial overconfidence can be a rational response to the economic and institutional environment, rather than a personal trait. A manager, whose con-

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tract may not be renewed upon poor performance relative to his peers, chooses risky projects in the firm. This may result in more than half of the managers rationally esti-

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mating their abilities to be better than average. Although there can be underconfident managers in equilibrium, it is never the case that more than half of them estimate their

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abilities to be below average in any equilibrium. Keywords: Bayesian rationality; better than average; career concerns; overconfi-

dence; underconfidence

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JEL Codes: D82; D83; G02; G30; M51

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We would like to thank Martin Peitz, two anonymous referees, and session participants at the 40th Annual Conference of the European Finance Association and the 3rd All-Istanbul Economics Workshop for their valuable comments. Inci would like to acknowledge financial support from the Turkish Academy of Sciences (Outstanding Young Scientist Award - TUBA-GEBIP) and the recognition by the Science Academy (Turkey) via their Young Scientist Award (BAGEP). Any remaining errors are our responsibility. † Tel.: 90-262-605-1431; fax : 90-262-654-3224. Address: Gebze Technical University, Department of Economics, P.K.:141, 41400 Gebze - Kocaeli, TURKEY. E-mail address: [email protected]. ‡ Tel.: 90-216-483-9340; fax : 90-216-483-9250. Address: Sabanci University - Faculty of Arts and Social Sciences, Orhanli / Tuzla 34956 Istanbul TURKEY. E-mail address: [email protected].

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Introduction

Although overconfidence can be a personal trait, often it is a rational reaction to the economic and institutional environment. Experiments show that whether individuals behave over- or

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underconfidently depends on the difficulty of the tasks they are assigned (Moore and Healy, 2008). Managers are particularly known to be overconfident individuals, but why? Imperfect judgments may well be the reason for the prevalence of overconfidence in managerial labor markets, but is it possible for “rational” managers to choose to be overconfident? Building

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on the insights provided in Benoit and Dubra (2011), this paper explains how overconfidence may arise as an implication of managers’ strategic choices.

As Moore and Healy (2008) mention, there are at least three definitions of overconfidence: a person can overestimate his absolute performance, overestimate his relative performance,

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or be overly precise in his estimations. In this paper, we deal with the second type of overconfidence, in which one’s relative ranking in the ability distribution matters. In particular, we

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provide a career-concerns-based strategic explanation for why overconfidence is so prevalent in managerial labor markets. A manager faces the risk of dismissal if he performs worse than

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his peers. This naturally creates a career-concern motive and encourages him to exaggerate his relative ability. To avoid dismissal, he may choose risky projects in the hope that he can

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attribute a worse outcome to bad luck. This is because the outcome of a project depends not only on his managerial abilities but also on the characteristics of the project itself.

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Identifying the source of overconfidence is important for corporate governance. If it is a

personal trait, it requires monitoring schemes to detect overconfident individuals. However, if it originates in managers’ incentives and strategic choices, then it is not inevitable and can be fixed by changing the incentive schemes and institutional structures. Indeed, in our setting, the presence of Bayesian overconfidence depends crucially on the presence of layoff-risk-based career concerns. We show that there would be no overconfidence if the firm

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eliminated the risk of dismissal and instead offered a future compensation scheme increasing in current performance. Moreover, we show by examples that various incentive schemes, such as bonus contracts or fixed-wage contracts with a severance payment option, may also affect the presence of overconfidence in the market.

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Identifying whether a certain population exhibits overconfidence, or misconfidence in general, is another important issue. The general approach to this is to see if more than half of the population view themselves as better than the median. The most famous example of the better-than-average effect is reported by Svenson (1981): 93 percent of American drivers believe that they are better drivers than the median. When this effect is present in

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a sample, then some of those individuals must exhibit overconfidence. Thus, questionnaires or tests can identify the existence of overconfidence in that sample. As a result, we say that there is identifiable overconfidence in such situations. However, there is also overconfidence that tests cannot identify. Some individuals may believe that they are above average even

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though they are not (overconfidence) and others may believe that they are below average even though they are not (underconfidence).1 In the end, the fraction of individuals who

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believe they are above average (median) may be no more than half, and a test may not be able to identify overconfidence even though there are overconfident (and underconfident)

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individuals in the population. As a result, we say that there is unidentifiable overconfidence in such situations. Our theory shows that both identifiable and unidentifiable misconfidence

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occurs in some cases and that such behaviors can be purely Bayesian rational.2

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We show our results in a general setting with a continuum of abilities and a fairly general technological specification. To set the stage, we illustrate some of our results with a simple example here. Consider an environment in which potential projects that a manager can 1 We make our definitions based on averages rather than medians just to be able to refer to the famous “better-than-average effect.” Otherwise, there is no distinction between average and median in our setting because each type is equally likely throughout the paper. 2 As a matter of fact, overconfidence found in past experiments is subject to this kind of Benoit and Dubra (2011) critique. A recent paper by Benoit, Dubra, and Moore (2015) underlines such pitfalls in the previous work and devises tests that are resilient to such criticisms.

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choose are characterized by their probabilities of failure. Suppose, in particular, that the √ √ outcome of the project is θ − r with probability r, and θ + r with probability 1 − r, where θ is managerial ability and r is the project’s probability of failure. The managerial ability can be either high (θ = 5/2) or low (θ = 1), and each ability type is equally likely in the

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¯ is 7/4. If the population. Hence, the average (and the median) ability in the population, θ, firm could observe the ability of a manager, it would want to hire a high-ability one who would in turn choose the project with r = 1/6, which maximizes the expected return of the project. The problem is that the ability of the manager is yet to be (perhaps) discovered upon seeing a project’s outcome.

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In such a setting, the manager’s best project is the project whose success outcome, when it is managed by a low-ability manager, overlaps exactly with the failure outcome when it is √ √ managed by a high-ability one: 5/2 − r = 1 + r, which gives r = 9/16 in equilibrium. If this overlapped outcome is observed, the firm is unable to figure out whether the manager

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is a high-ability type who failed or a low-ability one who succeeded. Nevertheless, the firm’s expectation about the type of the manager is (1 − 9/16) × (1) + (9/16) × (5/2) = 59/32,

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which is higher than the average ability of 7/4. Consequently, the firm keeps him upon observing this overlapped outcome. He is also retained by the firm when he turns out to be

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a high-ability manager who produced the success outcome. His contract is only not renewed when he turns out to be a low-ability manager who failed, which happens with probability

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(1/2) × (9/16) = 9/32. Hence, although each type is found equally in the population, the probability of the contract of a manager of an unknown type not being renewed is only 9/32.3

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In fact, the strategy of overlapping project outcomes minimizes the probability of not being retained by the firm in this example. Thus, this strategy protects the manager against bad

3 Remember that, in this example and throughout the paper, we assume that each type is equally likely in the population. However, our argument holds even with skewed distributions of ability. Assume, for example, that 60 percent of the managers have high ability and 40 percent of them have low ability. A manager would still choose r = 9/16. Then, he is not retained by the firm with probability (40/100) × (9/16) = 9/40. Hence, in this example, 77.5 percent of the managers would think that they are above average while in fact only 60 of them are so.

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faith to some extent. Two implications of the above example are important. First, not only the firm but also the majority of the managers (i.e., 1 − (9/32) = 23/32 of them) rationally estimate their ability to be above average (and median) in a Bayesian sense. This is a completely Bayesian-rational

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explanation for overconfidence. Benoit and Dubra (2011) call this “apparent overconfidence,” as there is in fact no irrationality in the observed outcome even though it is impossible for more than 50 percent of the population to be above the median ability. The second important implication is about the inefficiency of overconfidence. The expected contribution p √ of the project’s characteristics in our example is (1 − 2r) r = −(2/16) 9/16, thus the

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equilibrium project choice has negative net present value.4 This may explain why there is a

correlation between overconfidence and inefficient investment activities. As a matter of fact, Malmendier and Tate (2005ab, 2008), Gervais, Heaton, and Odean (2011), and Ben-David, Graham, and Harvey (2013) show that overconfident managers may destroy firm value by, for

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example, engaging in too many or inefficient merger activities. We, however, have a different mechanism. Overconfidence does not result in inefficient actions as a personal trait in our

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setting; rather, managers’ career concerns result in inefficient actions as well as Bayesian

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overconfidence.

Three key assumptions are essential in our setting, and all these assumptions point to

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the fact that overconfidence is dependent on the economic and institutional environment. First, the firm should have no commitment power to keep hiring a manager who possesses

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below-average ability. Otherwise, it can simply promise to hire all agents no matter what happens and eliminate career concerns. We impose this assumption by requiring firms to contract for only one period at a time. Second, we assume that the project outcome is observable but not verifiable by the firm. Otherwise, as we show in Section 4.1, the firm could offer performance-based contracts, such as bonuses or a fixed wage with a severance payment option, to eliminate the distortion in project choice. Third, firms that did not hire 4

Note that the average ability is high enough that the firm still wants to hire a manager.

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an agent are unable to observe his project outcome. Otherwise, as we show in Section 4.2, it would become feasible to offer below-average managers compensation based on estimated abilities in the second period, rather than not renewing their contracts. There are many papers in the literature concentrating on overconfidence, many of which

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take it as a primitive assumption and look at its implications for the economy. However, a handful of papers rationalize overconfidence. Zabojnik (2004) mentions that many individuals can be overconfident because they stop testing their abilities once they obtain favorable self-assessments. Van den Steen (2004, 2011) shows that Bayesian-rational individuals with differing priors are likely to be relatively overconfident about their predictions and overop-

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timistic about their chances of success. Our paper is most closely related to the paper by Benoit and Dubra (2011). They mention that there exist likelihood functions, such as the ones satisfying the monotone signal property, which make it possible for the majority of individuals in a Bayesian-rational population to rank themselves as better or worse than

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average. That is, they underline “apparent overconfidence” when agents learn from events drawn from a distribution. However, they do not explain why overconfidence is more preva-

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lent than underconfidence, although both are possible depending on the characteristics of the likelihood functions. We allow managers to realize the learning process and let them

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choose the event-generating process by endogenizing project choice. Hence, in our setting, the strategic actions of managers generate Bayesian overconfidence endogenously in equi-

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librium. However, although there can be underconfident managers in equilibrium in our setting, a majority of managers never choose to be underconfident in equilibrium because it

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can only increase the probability of their contract not being renewed. Only a few theoretical works look at the interaction between overconfidence and corpo-

rate governance. Roll (1986) suggests that overconfidence can explain corporate takeovers. Hackbarth (2008) studies the impact of overconfidence on corporate financial policy and firm value. Goel and Thakor (2008) show that overconfident managers are more likely to be promoted than their rational counterparts. Kyle and Wang (1997) show that hiring an 7

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overconfident trader in a duopoly environment serves as a commitment device. Englmaier (2011) argues that a similar commitment motivation may lead firms to hire overoptimistic managers in an R&D rat race. Gervais, Heaton, and Odean (2011) argue that moderate levels of overconfidence make managers more attractive to firms, which is also beneficial for

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those managers. In our setting, a manager who precisely estimates or overestimates his type to be above average is always rehired in the next period, whereas a manager who precisely estimates or underestimates his type to be below average is always fired. Hence, we explain the prevalence of overconfidence in the managerial labor market even though there is no benefit of managerial overconfidence to the firm. More importantly, managerial overconfidence

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is not exogenous in our setting; it is endogenously generated in the employment relationship. The paper is organized as follows. Section 2 introduces the model. Section 3 presents the analysis and derives the results. Section 4 shows that changing the economic and institutional environment may alter the presence of overconfidence in the market. Section 5 models

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bargaining between the firm and the manager in a simple way to justify an assumption of

The Model

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2

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the base model. Section 6 concludes.

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We present a variation of the model presented in Citci and Inci (2012). There is a riskneutral firm looking to hire a manager and a unit mass of risk-neutral managers differing in

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their managerial abilities. Each manager is indexed by i, and his ability is represented by ¯ 5 The θi , which is uniformly distributed on the interval [θL , θH ] with mean (and median) θ. distribution of abilities is common knowledge, but the ability of a manager is unknown to all parties, including the manager himself. Thus, ex ante, all parties rationally estimate the ¯ Consequently, a priori, a manager is randomly matched with ability of any manager to be θ. 5

Overconfidence may be defined over the means or medians of ability distributions. In our setting, the uniform distribution assumption prevents any potential ambiguity about the definition of overconfidence because here the mean and the median are the same.

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the firm, and the game we describe below is a game between these two parties.6 There are two time periods in which a firm operates, but, for simplicity, we do not discount future payoffs and do not allow for borrowing or lending. In each period, a manager chooses the project to be undertaken by the firm. The outcome of a project is either success or

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failure, but each project has a different probability of failure, denoted by r ∈ [0, 1], which is assumed to be not contractible. We make two essential assumptions about the project outcome. First, the project outcome is observable but not verifiable for the firm so that performance-based contracts are infeasible.7 Second, a firm that does not hire a manager is unable to observe his project outcome so that the second-period wages of below-average

The project outcome, y, is given by

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managers cannot depend on their estimated abilities.8

(1)

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y = θi + s(r),

where s(r) is the project-specific payoff. Thus, not only does the project choice matter to

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the project outcome, but the manager’s ability also contributes to it. This project-outcome function is consistent with the empirical literature showing that both managerial abilities

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and managerial actions matter in the firm.

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The distribution of s(r) is common knowledge and is given by

s(r) =

  

f (r) probability 1 − r

  −f (r) probability r,

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where f (r) is an increasing and twice-continuously differentiable function with f (0) ≥ 0. The

6 Alternatively, one can think of a game between the firm and a manager who withdraws his ability from the ability distribution without observing it. In both interpretations, the ability distribution is the ability distribution of the population of managers. 7 Section 4.2 shows why this is essential. 8 Section 4.1 shows why this is essential.

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fact that f (r) is increasing captures the idea that assets with higher default risks also have higher risk premiums, just like in collateralized debt obligations (CDO) or bank loans. Thus, there is a collection of investment projects with different realized returns and probabilities of failure pairs, resulting in different expected values for each project. Although obtaining

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closed-form solutions becomes difficult, if not impossible, this technological specification could be generalized even more and generate the same results, as long as the state realizations are not asymmetric in favor of the success outcome and f (r) is not convex.9

The core model concentrates on showing that career concerns may generate overconfidence. So, to simplify the analysis, we assume that the manager is paid a fixed wage, w,

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in both periods. We assume that two-period contracts are infeasible. Thus, the firm has no commitment power to keep hiring low-ability managers in our setting; otherwise, it could solve the moral hazard problem in project selection simply by promising to hire all agents. The manager cares about not only his compensation in the first period but also his expected

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compensation in the next period, which depends on his layoff risk, which is influenced by the realized outcome at the end of the first period. To be more precise, although the manager’s

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ability is unknown at the beginning of the first period, the firm and the manager himself update their beliefs about his ability once the project outcome is observed at the end of the

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first period. Consequently, the manager’s project choice in the first period affects his con-

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9 In line with our specification here, many project-choice problems in real life involve making a choice between projects with different average returns. In our case, r sorts projects according to their probability of failure (or likelihood of default). The specification that f (r) is strictly increasing in r implies that projects with lower probability of failure (i.e., safer projects) yield lower returns in the non-default state compared to the riskier projects. For instance, in a credit relationship, f (r) being strictly increasing means that the creditor requires higher interest rates from loan applicants who are more likely to default (i.e., loan takers with higher r). Likewise, this means that the risk premium is higher for riskier CDOs. We should also note here that although we have a preference for simplicity in the model, we think that the mechanism we focus on is quite general. All we need is some overlap of project outcomes from different types of managers, which prevents the firm from identifying the manager’s type, which may in turn cause Bayesian overconfidence in the first place. For example, concavity of f (r) is not strictly required for obtaining overconfidence. Likewise, symmetricity of s(r) is not required, either, and the contribution of ability to return does not have to be linear (i.e., y = g(θi ) + s(r) would also work). Adding some noise into the project outcome to represent macroeconomic shock unrelated to project choice and ability does not change the results because the firm can filter the noise. However, we do require that the choice of r has an impact on both the project return and the probability of failure.

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tract renewal potential in the next period, which motivates his career concerns and distorts his project choice in the first period. ¯ his reservation payoff is As long as a manager’s type is not certainly known to be below θ, u > 0, which is assumed to be low enough to guarantee the firm’s participation (a sufficient

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condition for non-negative profits for the firm is θL > u, which we assume). Because the firm captures all the bargaining power with a take-it-or-leave-it kind of contract, the optimal fixed wage is in fact equal to the manager’s reservation payoff. To allow for non-renewal of the employment contract in equilibrium in the simplest way possible, following Bushman, Dai, and Wang (2010), we assume that, if the manager’s contract is not renewed or if he

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rejects the firm’s compensation offer, he exits the labor market and receives zero in the next period.10 Moreover, the reservation payoff of a rehired manager is assumed to be the same as that of a newly hired manager. Bushman, Dai, and Wang (2010) provide detailed

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justifications for such downward rigidities in reservation payoffs.

The time proceeds as follows. The firm makes a take-it-or-leave-it wage offer to the

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manager, promising to pay a fixed wage w at the end of the period if he accepts the offer. If he rejects the offer, he receives his reservation payoff u and exits the labor market. Otherwise,

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he makes a project choice once he is employed by the firm. Then, outcome y is realized at the end of the period, the firm makes the promised wage payment, and both the firm and

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the manager himself update their beliefs about his ability. Then, the next period starts. Depending on the expected ability level of the manager formed at the end of the first period,

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the firm makes a take-it-or-leave-it offer to the old or a newly hired manager by offering a fixed wage w in this period. If the old manager’s contract is not renewed, he exits the labor market and receives zero. At the end of the period, the outcome is realized, the manager is paid his wage, and the firm is dissolved. We define our notions of misconfidence as follows. 10

Section 5 justifies this assumption in a bargaining framework between the firm and the manager.

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Definition 1 (i) We say that there is no misconfidence in the population if there are no above-average-ability managers estimating their abilities to be below average and no belowaverage-ability managers estimating their abilities to be above average. (ii) We say that there is identifiable overconfidence (underconfidence) in the

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population if more than half of the managers estimate their abilities to be above (below) average. In general, we say that there is identifiable misconfidence in such situations. (iii) We say that there is unidentifiable overconfidence (underconfidence) if some managers estimate their abilities to be above (below) average although they are in fact not,

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and the total fraction of managers estimating their abilities to be above (below) average is no more than half. In general, we say that there is unidentifiable misconfidence in such situations.

To finalize the description of the model, consider the benchmark situation where the firm

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observes both the manager’s project choice and his ability. In such a case, it would clearly employ the highest-ability manager. This manager would have no career concerns, as he does

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not face any risk of dismissal. Thus, he would simply choose the project with probability of failure r∗ that maximizes expected joint surplus, θH + (1 − 2r)f (r). It is easy to see that r∗

Analysis

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is less than 1/2 in any interior solution.

We proceed by backward induction. The analysis of the second period is trivial because the manager has no career concerns in this period, after which the firm is dissolved, and moreover he is paid a fixed wage. As a result, he is indifferent between any project choices in this period. We employ the reasonable tie-breaking convention that when the manager is indifferent between projects, he chooses the firm-optimal one characterized by r∗ . The expected outcome is larger if the firm hires a manager with a higher expected ability. This 12

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yields the optimal contract renewal rule for the firm: The firm renews the contract of the current manager if and only if his expected ability, given the outcome realization in the previous period, E[θi | y(θ, r)], is higher than the expected ability of a new manager hired ¯ Otherwise, it hires a new manager in the second period. from the managerial labor market, θ.

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We now turn to the first period to show that career concerns induced by layoff risk can lead to Bayesian misconfidence in the managerial labor market. We show that there are three possibilities in equilibrium, depending on which project choice the manager finds to be optimal. In some cases, there is no misconfidence in equilibrium, in the sense that there is no manager with above (below) average ability estimating his type to be below (above) average.

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In some other cases, some managers estimate their abilities to be above average although they are in fact not, while an equal fraction of others estimate their abilities to be below average although they are in fact not. There is unidentifiable misconfidence in these cases. Yet, in the remaining cases, more than half of the managers estimate their abilities to be

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above average, and a smaller fraction of managers whose abilities are actually above average estimate their abilities to be below average. Thus, we have identifiable overconfidence and

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unidentifiable underconfidence in such cases.

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Here is how we distinguish among the three cases. A manager is in a position to choose the project to be undertaken by the firm, but he does not know his own type. So, in making

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his decision, he has to acknowledge that he might be anywhere in the type distribution. In the worst case, he is the lowest type. If he chooses a strategy so that his success outcome

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does not coincide with the failure outcome of a manager who is above average, his type is inferred upon realization of any first-period outcome, and his contract is not renewed. Thus, one limiting strategy is to overlap his success outcome with the failure outcome of the ¯ θL + f (r) = θ¯ − f (r), which gives f (r) = (θH − θL )/4. Another limiting average type, θ: strategy is to overlap his success outcome with the failure outcome of the highest type, θH : θL + f (r) = θH − f (r), which gives f (r) = (θH − θL )/2. These two conditions give us three different classes of strategies to consider: 13

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1. Non-overlapping strategies (all the strategies satisfying f (r) ≥ (θH − θL )/2): With these strategies, even the success outcome of the lowest type does not overlap with the failure outcome of any existing type. So there is no overlapping. 2. Dovish-overlapping strategies (all the strategies satisfying f (r) ≤ (θH − θL )/4): With

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these strategies, the success outcome of the lowest type is only sufficient to overlap with the failure outcome of the average type. So the overlapping process is somewhat conservative here.

3. Hawkish-overlapping strategies (all the strategies satisfying (θH − θL )/4 < f (r) <

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(θH − θL )/2): With these strategies, the success outcome of the lowest type is able to overlap with the failure outcome of the best type. So the overlapping process is somewhat aggressive here.

To see if there is misconfidence in the managerial labor market upon employing one of

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these strategies, we now consider each of them in turn. At the same time, we also discuss

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which strategy is the equilibrium strategy under which conditions. With non-overlapping strategies, the proposed equilibrium strategy of the manager is

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to choose projects with higher probabilities of failure, specifically those satisfying f (r) ≥ (θH − θL )/2. Consider first the subclass in which this condition holds with strict inequality.

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Then, the success outcome of below-average types cannot coincide with any existent above¯ Therefore, average type. Formally, we have θ + f (r) > θH − f (r) for all θ ∈ [θL , θ).

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the exact ability of a manager is perfectly inferred upon observing his project’s outcome. Thus, we get no misconfidence whatsoever in this subclass. This means that, by employing non-overlapping strategies, no manager can successfully raise his probability of being rehired above 1/2, which is the probability of being rehired when he truthfully reveals his type by his project choice. Consider next the subclass in which the condition holds with equality. Now, only the worst type’s success outcome and the best type’s failure outcome can coincide (i.e., θL +f (r) = θH −f (r)) and there are no other overlapping outcomes since θ+f (r) > θH −f (r) 14

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¯ In this case, the firm perfectly infers the ability of the manager when for all θ ∈ (θL , θ). it observes any outcome level different from the overlapped outcome. Hence, we also get no misconfidence with this strategy subclass. Consequently, whether the condition holds with equality or inequality, there is no misconfidence when non-overlapping strategies are

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employed by the manager. We record this result in the following lemma. Lemma 1 (non-overlapping strategies) If a manager chooses a project whose probability of failure satisfies f (r) ≥ (θH −θL )/2, then his ability is perfectly inferred upon outcome realization. There is no misconfidence in the managerial labor market.

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An important corollary follows immediately when the condition for non-overlapping strategies holds for the corner case in which r = 0. Then, we have θH − θL ≤ 2f (0), which is a primitive condition composed of parameters of the model. If this condition holds (i.e., when there is a low range of abilities in the managerial labor market), the only viable

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strategies are non-overlapping ones. But we have already shown that there is no misconfidence with them. Therefore, when there is a low range of abilities (i.e., when θH − θL is

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lower than 2f (0)), all parties, including the manager himself, precisely estimate the ability

θH- θL

-2rf(r)

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θL

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of the manager in equilibrium.

2

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A

θ1

θ1+ f (r )= θ2-f (r )

2r f( r )

θ

2( 1-r ) f (r ) C

B

θ2 θH- θL θH - 2 (1 -r ) f( r ) 2

D

Figure 1 The Partition of Managers with Dovish-overlapping Strategies

With dovish-overlapping strategies, the proposed equilibrium strategy of the manager is to choose projects with lower probabilities of failure, specifically those satisfying f (r) ≤ (θH − θL )/4. Figure 1 portrays a representative partition of managers with such strategies. By construction, there has to be a θ1 -type below average and a θ2 -type above average such 15

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that the success outcome of the θ1 -type coincides with the failure outcome of the θ2 -type, ¯ That is, and additionally, the expected ability in this outcome is exactly θ.

(3)

¯ (1 − r)θ1 + rθ2 = θ.

(4)

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θ1 + f (r) = θ2 − f (r)

Solving these equations for θ1 and θ2 simultaneously yields θ1 = θ¯ − 2rf (r) and θ2 = θ¯ + 2(1 − r)f (r). There are four partitions of interest, from A to D, whose lengths are reported in Figure 1. The solutions to (3) and (4) have already shown that the length of partition

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B, denoted by |B|, is 2rf (r), and that of partition C, denoted by |C|, is 2(1 − r)f (r). Because the distance between θL and θ¯ (thus between θ¯ and θH ) is (θH − θL )/2, the length of partition A, denoted by |A|, is (θH − θL )/2 − 2rf (r), and that of partition D, denoted by |D|, is (θH − θL )/2 − 2(1 − r)f (r).

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Given that the expected ability of a θ1 -type overlapping his success outcome with θ2 ¯ it is easy to see that the expected ability of managers type’s failure outcome is exactly θ,

ED

¯ while that of those in partition D is higher than or equal in partition A is less than θ, ¯ whether they obtain the success or failure outcome. However, the expected ability of to θ,

PT

managers in partition B is higher than or equal to θ¯ if they obtain the success outcome, which happens with probability 1 − r. As a result, [2rf (r)(1 − r)]/(θH − θL ) fraction of managers in

CE

this partition estimate their abilities to be above average even though their ability is actually below average (overconfidence).11 Conversely, the expected ability of managers in partition

AC

C is less than θ¯ if they obtain the failure outcome, which happens with probability r. As a result, [2rf (r)(1 − r)]/(θH − θL ) fraction of managers in this partition estimate their abilities to be below average even though their ability is actually above average (underconfidence). Therefore, although some partitions of the population exhibit overconfidence while others 11

This is because if a manager in partition B obtains the success outcome that coincides with the failure outcome of a manager in partition D, he has to statistically conclude that he is more likely to be a manager in partition D, who has above-average ability, although he is in fact a manager in partition B.

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exhibit underconfidence, they veil each other in the aggregate. Consequently, the total fraction of managers in the overall population whose ability is expected to be above average is exactly 1/2.12 Thus, there is unidentifiable misconfidence with dovish-overlapping strategies. One caveat is in order. The total fraction of managers who have some kind of misconfi-

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dence is [4rf (r)(1 − r)]/(θH − θL ). Because 4r(1 − r) can at most be 1, 4rf (r)(1 − r) can at most be f (r). Moreover, with dovish-overlapping strategies, f (r) is less than (θH − θL )/4, which means that the total fraction of managers who have some kind of misconfidence can be at most 1/4 with these strategies. Thus, questionnaires measuring misconfidence based on the fraction of individuals reporting themselves to be above/below average would identify

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no misconfidence in this market, although the underlying distribution does have both overand underconfident managers.

Lemma 2 (dovish-overlapping strategies) If a manager chooses a project whose prob-

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ability of failure satisfies f (r) ≤ (θH − θL )/4, then an equal fraction of over- and underconfident managers cohabit the managerial labor market. The total fraction of these two groups is

ED

less than a quarter of the population. There is unidentifiable misconfidence in the managerial labor market.

PT

There is an important corollary to this lemma. Because exactly half of the managers

CE

are estimated to be above average, employing a dovish-overlapping strategy does not in fact lower layoff risk. Hence, a manager is indifferent between employing a dovish-overlapping

AC

strategy and employing a strategy that perfectly reveals his true ability (for example, a non-overlapping strategy). Moreover, whenever it is viable, a strategy that lowers layoff risk below 1/2 strictly dominates any other non-overlapping and dovish-overlapping strategies. In fact, we show later that there are such hawkish-overlapping strategies. 12

The total fraction of managers who estimate their abilities to be above average is equal to (|D| + (1 − ¯ By choosing r) |B + C|)/(4f (r)) = 1/2 in the overall population. θ1 is just one generic type who is below θ. a different r, any type in this range could be put into the position of θ1 . Hence, we can generate the same result for all other types.

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Finally, with hawkish-overlapping strategies, the proposed equilibrium strategy of the manager is to choose projects with intermediate probabilities of failure, specifically those satisfying (θH − θL )/4 < f (r) < (θH − θL )/2. This strategy ensures that, for most of the possible realized outcomes, the firm cannot infer the exact ability of the manager because

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an “overlapped outcome” can be either the success outcome of a below-average manager or the failure outcome of an above-average manager. In this sense, this strategy reduces the signaling power of outcome observations. More importantly, when the probability of failure for a chosen project is sufficiently high, the firm has to believe statistically that this observed outcome is more likely to be the failure outcome of an above-average manager than

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the success outcome of a below-average manager.

θ1+ f (r )= θ4-f (r )

2( 1-r ) f (r )

2r f( r )

θ1 A

θ2 B

C

θ3

D

θH

θ4

E

F

θ2+ f (r ) = θH-f (r )

ED

θL+ f (r ) = θ3-f (r )

θ

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θL

PT

Figure 2 The Partition of Managers with Hawkish-overlapping Strategies

CE

Figure 2 portrays a representative partition of managers using hawkish-overlapping strategies. Now, there is a θ1 -type below average who can overlap his success outcome with the failure outcome of a type above average, denoted by θ4 , and the expected ability when this

AC

¯ In addition, the lowest type, θL , can overlap his overlapped outcome level is observed is θ. success outcome with the failure outcome of a type above average, denoted by θ3 . Similarly, there has to be a θ2 -type who can overlap his success outcome with the failure outcome of

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the highest type, θH . Mathematically, we have

θ1 + f (r) = θ4 − f (r)

(5)

(1 − r)θ1 + rθ4 = θ¯

θ2 + f (r) = θH − f (r).

(7)

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θL + f (r) = θ3 − f (r)

(6)

(8)

Solving for (5) and (6) simultaneously and reorganizing the other two equations, we get the distance between types: θ1 = θ¯ − 2rf (r), θ2 = θH − 2f (r), θ3 = θL + 2f (r), and

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θ4 = θ¯ + 2(1 − r)f (r). This time, we have six partitions of interest, from A to F , shown in Figure 2. By construction, the mass in partitions A and E, B and F , and C and D are equal to one another and their lengths are given by

θH − θL − 2rf (r) 2 θH − θL |B| = |F | = − 2 (1 − r) f (r) 2 θH − θL |C| = |D| = 2f (r) − . 2

(9) (10) (11)

PT

ED

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|A| = |E| =

Because the expectation between θ1 and θ4 is equal to the average, when the overlapped

CE

outcome is produced, the expected ability of managers in partitions A and C has to be less ¯ whether they obtain failure or success. For the same reason, the expected ability than θ,

AC

of managers in partitions D and F has to be higher than or equal to θ¯ regardless of the outcome they produce. However, the expected ability of managers in partitions B and E is less than θ¯ for the failure outcome, which happens with probability r, but higher than or equal to θ¯ for the success outcome, which happens with probability 1− r. Hence, as with dovish-overlapping strategies, some partitions of the overall population exhibit misconfidence in equilibrium. In particular, 1−r fraction of managers in partition B exhibit overconfidence

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and r fraction of managers in partition E exhibit underconfidence.13 The total fraction of those whose ability is expected to be higher than or equal to θ¯ is given by |D + F | + (1 − r) |B + E| . θH − θL

(12)

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Therefore, unlike with dovish-overlapping strategies, now more than half of the managers in the market estimate their abilities to be above average if (12) is higher than 1/2; more than half of them estimate their abilities to be below average if (12) is less than 1/2; and exactly half of them estimate their abilities to be above/below average if (12) is exactly

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equal to 1/2. Making the necessary substitutions from (9)–(11) and simplifying shows that (12) is higher than 1/2, if and only if r > 1/2. This means that more than half of the managers estimate their abilities to be above average, thus some of them have to exhibit overconfidence with hawkish-overlapping strategies, if and only if r > 1/2; more than half of

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the managers estimate their abilities to be below average, thus some of them have to exhibit underconfidence, if and only if r < 1/2; and exactly half of the managers estimate their

ED

abilities to be above/below average if and only if r = 1/2. Note that even though exactly half of the population estimates their abilities to be above/below average when r = 1/2,

PT

there is still unidentifiable misconfidence in the population (i.e., 1 − r fraction of those in partition B are overconfident and r fraction of those in partition E are underconfident in

CE

Figure 2).

AC

Lemma 3 (hawkish-overlapping strategies) If a manager chooses a project whose 13

Another curious finding here is the non-monotonicity in the contract renewal process when the manager employs hawkish-overlapping strategies. In a complete information world, the contract of such managers should not be renewed. However, given incomplete information, the firm is able to correctly identify only the extremes, “too good” managers in partition C and “too bad” managers in partition A. Intuitively, lower ability ones are too bad so that they are correctly identified. However, a too good (but still below average) manager has to behave too much talented to overlap his outcome with a nonexistent ability level in the ability distribution. However, medium-ability ones still have some chance of being misidentified and incorrectly retained. A similar problem occurs for above-average managers, too. If a manager is somewhat good (partition D) or extremely good (partition F ), he is sure to be retained because his output is a perfect indicator of his type. If he is in the middle, he has some risk of not being rehired, although in a complete information world, he would certainly have been retained.

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probability of failure satisfies (θH − θL )/4 < f (r) < (θH − θL )/2, then, (i) more than half of the managers estimate their abilities to be above average if and only if r > 1/2, thus there is identifiable overconfidence (and unidentifiable underconfidence in partition E);

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(ii) more than half of the managers estimate their abilities to be below average if and only if r < 1/2, thus there is identifiable underconfidence (and unidentifiable overconfidence in partition B);

(iii) exactly half of the managers estimate their abilities to be above/below average if and

and underconfidence in partition E).

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only if r = 1/2, but there is still unidentifiable misconfidence (overconfidence in partition B

By construction, hawkish-overlapping strategies are viable only if 2f (0) < θH − θL <

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4f (1). This also implies that, if the ability distribution satisfies 4f (1/2) ≤ θH − θL < 4f (1), then identifiable overconfidence is a possibility with hawkish-overlapping strategies, but iden-

ED

tifiable underconfidence is not because r is higher than 1/2 in this range. Conversely, if the ability distribution satisfies 2f (0) < θH − θL ≤ 2f (1/2), then identifiable underconfidence is

PT

a possibility with hawkish-overlapping strategies, but identifiable overconfidence is not. If the ability distribution satisfies 2f (0) < θH − θL ≤ 2f (1/2), then choosing an r such

CE

that r < 1/2 is the only possibility with hawkish-overlapping strategies. In such a case, identifiable underconfidence occurs if a hawkish-overlapping strategy is employed, but identifiable

AC

overconfidence cannot. However, the manager is not bound to choose a hawkish-overlapping strategy. He can also consider choosing non-overlapping or dovish-overlapping strategies. Thus, while identifiable overconfidence is not an issue here, identifiable underconfidence is. Nevertheless, because the firm’s and managers’ expectations are the same, identifiable underconfidence also means that the firm’s expectation about the manager is below average. Managers never choose a strategy that generates identifiable underconfidence because it

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only increases the probability of not being rehired, and, given the parameter range, they can always choose a non-overlapping or dovish-overlapping strategy. Thus, identifiable underconfidence (in the sense that more than half of the managers believe that they are below average) never happens in equilibrium.

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Proposition 1 In equilibrium, it is never the case that more than half of the managers estimate their abilities to be below average. That is, identifiable underconfidence never occurs in equilibrium.

If the ability distribution satisfies 2f (1/2) < θH − θL < 4f (1), then choosing an r such

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that r > 1/2 is the only possibility with hawkish-overlapping strategies. In such a case, identifiable overconfidence occurs. Alternatively, if it is in his best interest, the manager can also consider a non-overlapping or dovish-overlapping strategy. However, a career-concerned manager would want to employ the strategy leading to identifiable overconfidence because

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the firm and the manager share the same information, and a strategy leading to identifiable overconfidence improves expectations about managerial ability. The following equation

PT

ED

determines implicitly the equilibrium project choice in this case.

4rf (r) = θH − θL .

(13)

CE

This project choice ensures that there are no underconfident managers in the market in the sense that no manager with above-average ability estimates his ability to be below average.

AC

Moreover, more than half of the managers estimate their abilities to be above average, thus there is identifiable overconfidence in equilibrium. Proposition 2 If the ability distribution satisfies 2f (1/2) < θH − θL < 4f (1), then more than half of the managers estimate their abilities to be above average in equilibrium. Thus, there is identifiable overconfidence in equilibrium. Moreover, there are no underconfident managers in the market. 22

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The above discussion can be summarized as follows. Career concerns of managers lead them to try to improve the firm’s expectations about their abilities. In order to “hide” their abilities, they choose projects with hawkish-overlapping strategies that lead them to believe their own “lies.” This constitutes the source of Bayesian-rational overconfidence. We

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get identifiable overconfidence in equilibrium if the ability distribution satisfies 2f (1/2) ≤ θH − θL < 4f (1). Otherwise, we get either no misconfidence, in the sense that every manager precisely estimates his abilities, or unidentifiable misconfidence (over- or underconfidence), which is sure to be less than a quarter of the population. In no case do more than half of the managers in the market estimate their abilities to be below average. Thus, identifiable

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underconfidence never occurs in equilibrium. This may explain why overconfidence is so widely alluded to in managerial labor markets, while underconfidence is not. So far, we have explained why there is overconfidence but not underconfidence in managerial labor markets. The next point of interest is whether Bayesian overconfidence affects

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which types of managers are selected in the second period. In equilibrium, in addition to managers who are actually above average, the ones who are below average but perceived to

ED

be above average are rehired in the second period. To be more precise, among the belowaverage managers, the ones who overestimate their abilities to be above average are rehired,

PT

while the contracts of those who precisely estimate their abilities to be below average are

CE

not renewed. This leads to another important result of our paper. Proposition 3 A manager who precisely estimates or overestimates his type to be above

AC

average is rehired. The contract of a manager who precisely estimates or underestimates his type to be below average is not renewed. The reason is obvious: Both the firm and the manager have the same information and

expectations. The implication of this result for the case in which the ability distribution satisfies 2f (1/2) < θH − θL < 4f (1) is particularly interesting. In such a case, the contracts of above-average managers are always renewed in equilibrium, but among the below-average 23

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managers, only the overconfident ones are rehired, and the contracts of those who precisely estimate their abilities to be below average are not renewed. Propositions 1 and 3 together explain why managers are particularly known to be overconfident. The former states that identifiable underconfidence is never an issue in equilibrium, and the latter explains how

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overconfident managers survive at the firm over time. An important puzzle in behavioral economics and corporate governance is why firms promote overconfident managers. Existing studies generally attempt to explain this puzzle by presenting several benefits of managerial overconfidence for firms (see, e.g., Gervais, Heaton, and Odean, 2011). Unlike these studies, in our setting the firm derives no benefit from

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Bayesian overconfidence. Instead, career concerns lead managers to choose projects in the hope of hiding their actual abilities from the firm. If they succeed in this strategy, they themselves also believe in their overestimated abilities in a Bayesian-rational way. Hence, our mechanism indicates that rather than managerial overconfidence as a personal trait en-

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suring selection, career concerns induced by the manager-selection process produce Bayesian

ED

overconfidence in the managerial labor market. Our theory points to a reversal of causality between risk-taking behavior and managerial

PT

overconfidence. In behavioral finance, managerial overconfidence is frequently associated with the risk-taking behavior of managers. There is almost a consensus in the literature

CE

that overconfidence leads managers to take risky and inefficient actions (Malmendier and Tate, 2008; Galasso and Simcoe, 2011; Gervais, Heaton, and Odean, 2011; Hirshleifer, Low,

AC

and Teoh, 2012). We have a related result, but the causality flows in the opposite direction: Managers take risky, value-destroying actions in the firm due to career concerns, and these actions actually lead them (and all other parties) to overestimate their abilities. We have already shown that when hawkish-overlapping strategies are viable, only projects whose probability of failure is higher than 1/2 can produce overconfidence and improve the career of a manager. However, excluding the contribution of the manager’s ability to the project, the expected return from the project E[s(r)] = (1 − 2r)f (r) has a negative value beyond 24

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r = 1/2. Hence, in our setting, overconfidence does not cause risky actions as a personal trait; rather, managers’ career concerns lead them to choose those actions and result in Bayesian overconfidence in the market.

Limitations of Endogenous Overconfidence

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4

As we mention in the Introduction, identifying the source of overconfidence is important for corporate governance. If overconfidence is a strategic reaction to the economic and

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institutional environment, it responds to changes in institutions or incentives. To facilitate this idea, we now provide two examples. The following subsection concentrates on showing how the emergence of identifiable overconfidence is dependent on the fine details of the economic and institutional environment. The subsection following next shows how providing incentives eliminates overconfidence from the market.14 We are comprehensive in neither of

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the examples, as incentives and institutions are designed to address not just misconfidence

Institutions

CE

4.1

PT

to deal with them.

ED

but many other informational problems, and there are strands of literature that explore how

In the core model, the manager loses his job if his ability is perceived to be less than that

AC

of his potential replacements, and this creates his career concerns. In essence, we assumed that firms that do not hire a manager are not able to observe his project outcome so that the second-period wages of managers cannot be made contingent on their estimated abilities. Inspired by Holmstrom’s (1999) career-concerns setting, we now relax this assumption and consider a less extreme version of career concerns in which the manager’s future wage 14

These results suggest that incentive structures other than firing threats can better deal with the overconfidence problem, which implies that firms should not use firing threats so frequently. In line with this insight, Jenter and Lewellen (2014) find that only 40 percent of all CEO turnovers are performance induced.

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is a linear-increasing function of his expected ability. That is, w(E[θi | y(θ, r)]), where ∂w(E[θi | y(θ, r)])/∂E[θi | y(θ, r)] = c > 0. Thus, maximizing future compensation is equivalent to maximizing expected ability. Now, the manager tries to maximize the overall expectation of his ability as much as possible rather than trying to maximize his likelihood

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of being above average. We have already established that only hawkish-overlapping strategies can alter expectations about a manager’s ability, and this results in identifiable overconfidence only if r ∈ (1/2, 1). Now, refer back to Figure 2. For any risk choice with hawkish-overlapping

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strategies, the (maximized) expected ability with such strategies is given by

E[θi | y1 (θ, r)] = Pr {θ ∈ A} (rE[θi | A] + (1 − r)E[θi | A ∧ E]) + Pr {θ ∈ B} (rE[θi | B] + (1 − r)E[θi | B ∧ F ]) + Pr {θ ∈ C} E[θi | C]

M

+ Pr {θ ∈ D} E[θi | D]

ED

+ Pr {θ ∈ E} (rE[θi | A ∧ E] + (1 − r)E[θi | E]) (14)

PT

+ Pr {θ ∈ F } (rE[θi | B ∧ F ] + (1 − r)E[θi | F ]).

That is, a manager is in partition A with probability Pr {θ ∈ A}, and he is expected to be

CE

in partition A if his project produces the failure outcome, which happens with probability r, and he is expected to be either in partition A or E if his project produces the success

AC

outcome, which happens with probability 1 − r. This explains the term in the first line of the expression. Other lines are derived similarly. Substituting for the probability and expected value expressions yields ¯ E[θi | y1 (θ, r)] = θ,

(15)

which means that the posterior belief upon outcome realization exactly equals the prior belief about the manager. Therefore, when the manager’s future wage is an increasing function

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of his expected ability, no project choice with a hawkish-overlapping strategy can improve his career concerns. Hence, he is indifferent between project choices in this case, including not just those with hawkish-overlapping strategies but also those with non-overlapping and dovish-overlapping strategies. Our tie-breaking convention requires the manager to choose

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the firm-optimal project characterized by r∗ in this case, and because r∗ < 1/2 there will be no identifiable overconfidence.15

Proposition 4 When the manager’s future wage is an increasing function of his expected ability, just half of the managers estimate their abilities to be above or below average. There

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is no identifiable overconfidence, although there may be unidentifiable misconfidence in the managerial labor market. None of the strategies can improve expectations about managerial ability, thus the manager is indifferent between project choices.

Therefore, if a manager faces an upward-sloping compensation schedule (rather than the

M

risk of dismissal induced by relative performance evaluation), the majority of managers do not necessarily estimate their abilities to be better than average in the managerial labor

ED

market. This is in fact a validation of our idea that overconfidence is a rational reaction to the economic and institutional environment rather than a personal trait that cannot be

PT

changed immediately. With dismissal, the manager is concerned only about whether he is above average; however, in the increasing-wage schedule setting, he is concerned about the

CE

whole distribution, which eliminates the strong motivation for identifiable misconfidence in

AC

equilibrium.

This result indicates that if the firm could eliminate layoff-risk-based career concerns, or

in other words, if it could commit to retain the manager even when it has the opportunity to replace him with a better one, then the incentives for overconfidence would be greatly diminished. 15

Even without this tie-breaking convention, the manager is indifferent among non-overlapping, dovishoverlapping, and hawkish-overlapping strategies. Therefore, identifiable overconfidence can occur only if the manager happened to choose a hawkish-overlapping strategy.

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4.2

Incentives

We now show how providing incentives may eliminate overconfidence. At this point, we should note again that firms provide incentives for various other reasons, not just to eliminate

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misconfidence. Here, we allow the firm to offer a performance-based contract. We provide two different (and very simple) payment mechanisms, a fixed-wage contract with a severance payment option and a bonus contract. For simplicity and brevity, we concentrate on an environment where there are only two ability types, high (θH ) and low (θL ), and each type is

example we have in the Introduction.

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equally likely in the population. This is, in fact, the generalization of the two-type numerical

Consider a fixed-wage contract with a severance-payment option. The firm pays a fixed wage of w and a severance payment of S if it does not renew the contract of the manager. From an ex ante point of view, the probability of not being rehired is 1/2 in the case where

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the manager chooses r∗ . Thus, the expected compensation of the manager is w + S/2. If the

w+

S ≥ u, 2

(16)

PT

ED

firm wants the manager to choose the project with r∗ , the individual rationality constraint,

must hold. Moreover, the firm does not need to pay a penny more than the manager’s

CE

reservation payoff, which means that this constraint binds. Thus, the optimal severance payment must satisfy S = 2(u − w).

AC

There is an additional constraint to be satisfied. When the manager chooses the project

with r∗ , we know that his first-period compensation is given by the left-hand side of (16), and he earns exactly his reservation payoff u in the second period if he is rehired, which happens with probability 1/2. Thus, his two-period earnings will be w + S/2 + u/2. He

may alternatively choose the project with r¯ that optimally “hides” his type, which will lower his probability of not being rehired. In that case, his first-period compensation is w and 28

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again he earns his reservation payoff in the second period. But this time his probability of not being rehired is lower and equal to r¯/2. Thus, his two-period expected earnings will be r/2)S. For the severance-payment scheme to work, this has to be lower than w+[(2−¯ r)/2]u+(¯ his two-period expected earnings when he chooses the project with r∗ . Substituting the value

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of S from the individual rationality constraint shows that a compensation of u ≥ 2w with S = 2(u − w) would ensure that the manager chooses the project with r∗ . Such a choice is fully revealing, thus we get no misconfidence.

Proposition 5 An optimal fixed-wage contract with severance payment may result in no

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misconfidence in the managerial labor market.

Intuitively, the severance payment makes the career concern sufficiently less important, and the stock payment makes the manager a claimant in the project outcome, both of which will lead him to choose the project with r∗ , which in turn results in no misconfidence.

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One can also get the same result with a bonus contract. The firm’s goal is to ensure that

ED

the manager chooses the project with r∗ in the first period. Consider the bonus contract in which the firm pays a fixed bonus equal to u if the manager obtains any of the four outcome levels associated with this project and zero otherwise. He will not be retained by the firm if

PT

his ability is inferred to be below average at the end of the period. Clearly the manager will

CE

choose the project with r∗ . It is also the least costly way of providing incentives because it pays no more than his per-period reservation payoff. Thus, it is an optimal contract. This

AC

means that, unless any two outcome realizations coincide by chance with those of the project with r∗ , the type of the manager will be inferred, thus there will be no misconfidence in the market.

Proposition 6 An optimal bonus contract may result in no misconfidence in the managerial labor market. These two examples clearly show how emergence of overconfidence and its degree depend 29

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on the fine details of the institutional environment and the incentives provided by the firm.

5

A Simple Bargaining Framework

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The analysis so far has concentrated on a case where the firm makes a take-it-or-leave-it contract offer to the manager. In such a framework, the firm has all the bargaining power, thus extracting all the surplus in the employment relationship. While this framework is simpler to analyze and captures the main effect we have concentrated on, in reality the

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manager also earns some surplus. In this section, we provide a simple framework in which the manager has some bargaining power. The firm still has no commitment power to keep hiring a manager, and project outcome is still observable but not verifiable. In the base model, we assume that the reservation payoff of a below-average manager

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decreases, thus becoming lower than that of an above-average manager so that a manager has incentives to appear above average in the first place. The bargaining framework presented

ED

here justifies this assumption. In particular, it derives in a natural fashion that ex ante a manager has incentives to appear to be above average because he obtains some surplus

average.

PT

due to his bargaining power, and he loses this surplus when his type turns out to be below

CE

Our bargaining framework is a strategic bilateral bargaining game16 and follows Acharya and Volpin’s (2010) setting. The firm can bargain with one manager in each period. At

AC

the beginning of a period, the firm makes a wage offer to the manager. If the manager rejects this offer, he gets an opportunity to make a counter-offer to the firm with probability µ ≥ 0; otherwise, he gets a final offer from the firm with the complementarity probability 1 − µ. If these final offers are rejected, both parties receive their reservation payoffs, which 16

Mortensen and Pissadires (1999, pp. 2592–2593) point out that the Nash bargaining outcome is interpreted as a solution to a strategic bargaining game.

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are normalized to zero.17 Here, µ is the manager’s bargaining power in the employment relationship. In the end, the manager gets µ portion of the whole surplus in each period while the firm gets 1 − µ portion of it. As in the base model, the manager, whether old or new, chooses the value-maximizing

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project with probability of failure r∗ in the second period. Hence, the firm renews a manager’s ¯ Otherwise, hiring a new manager, whose contract only if his type is inferred to be above θ. ¯ yields higher surplus, thus higher profits to the firm, compared to ability is expected to be θ, the surplus in the case when it renews the contract of the incumbent manager, whose ability is inferred to be below average. Thus, the incumbent manager has incentive to appear above

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average.

Unlike the base model, there is no fixed wages, thus we have to be careful in determining the manager’s equilibrium project choice. Obviously, choosing the value-maximizing project

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in the first period strictly dominates any strategy other than hawkish-overlapping strategies. It is because such strategies do not increase a manager’s probability of keeping his

ED

position in the second period while they decrease his first-period compensation relative to the value-maximizing project. So, the manager’s choice is basically between choosing the

PT

value-maximizing project with r∗ and the hawkish-overlapping strategy that increases his probability of keeping his position in the second period.

AC

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Let r¯ be the r value solving

max{µ θ¯ + (1 − 2r) f (r) + p(r)µ θ¯ + (1 − 2r∗ ) f (r∗ ) }, r

(17)

where r is chosen among the set of hawkish-overlapping strategies and p(r) is the manager’s probability of keeping his position in the second period. Therefore, r¯ is basically the local maximizer of hawkish-overlapping strategies. If it yields a sufficiently high career benefit 17

Under mild conditions, the results are qualitatively the same if both parties have positive reservation payoffs.

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that dominates the payoff loss in the first period due to not choosing the value maximizing project with r∗ , then it is, in fact, the global maximizer, and thus the manager’s equilibrium choice. Hence, there will be Bayesian overconfidence if the career benefit of choosing the project with r¯ is higher than the benefit of choosing the value-maximizing project with r∗ .

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This describes an inequality to be satisfied for Bayesian overconfidence to emerge:

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1 r) f (¯ r) µ θ¯ + (1 − 2r∗ ) f (r∗ ) + µ θ¯ + (1 − 2r∗ ) f (r∗ ) <µ θ¯ + (1 − 2¯ 2 
r¯  ¯ µ θ + (1 − 2r∗ ) f (r∗ ) . + 1− 2 (18)

We construct this inequality as follows. If the manager chooses the value-maximizing project in the first period, he obtains µ(θ+(1−2r∗ )f (r∗ )) in that period and keeps his position with probability 1/2 in the second period, and chooses the value-maximizing project again,

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thus obtaining once again µ(θ+(1−2r∗ )f (r∗ )). This forms the left-hand side of the inequality. If, however, he chooses the project with r¯ in the first period, he obtains µ(θ + (1 − 2¯ r)f (¯ r))

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in that period and keeps his position with probability 1 − (¯ r/2) in the second period, and chooses the value-maximizing project, thus obtaining µ(θ + (1 − 2r∗ )f (r∗ )). This forms the

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right-hand side of the inequality. Simplifying it and acknowledging the fact that ex ante the

(1 + r¯) (1 − 2r∗ ) f (r∗ ) − 2 (1 − 2¯ r) f (¯ r) θ¯ > , 1 − r¯

(19)

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¯ we find that there can be Bayesian overconfidence if manager expects his type to be θ,

which puts a restriction on the average type.18 In sum, the base model can easily be extended to a bargaining framework. The optimal

contract renewal rule remains the same in this framework, all the rest of our analysis in 18

Remember that hawkish-overlapping strategies require 2f (1/2) < θH − θL < 4f (1), which restrict the range of abilities. Hence, given that there is enough freedom to choose θL , (19) can be satisfied within this constraint. For example, one can easily check that the numerical example we have in the Introduction satisfies this inequality.

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Section 3 would then apply, and we get endogenous overconfidence in some cases. More importantly, this setting justifies our assumption that the reservation payoff of below-average managers gets lower than that of above-average ones.

Conclusion

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6

In this paper, building on the framework established in Benoit and Dubra (2011), we provide a Bayesian-rational explanation for managerial overconfidence and explain why over-

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confidence is so prevalent in managerial labor markets. Our analysis is novel in that it endogenizes overconfidence by managers’ choice of projects. If a manager faces the risk of dismissal upon poor performance relative to his peers, he is likely to choose a project that allows him to hide his managerial type as much as possible. This leads a manager to choose risky projects and to overestimate his ability relative to others. We show that this

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is a feasible strategy in managerial labor markets with some specific range of abilities. It is

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never the case that more than half of the managers underestimate their abilities in equilibrium because strategies generating underconfidence in equilibrium diminish managers’ career prospects. We also show that project choices resulting in identifiable overconfidence have

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negative net present values.

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Our model yields at least two empirical predictions. First, none of the managers who are not retained after relative performance evaluation are overconfident. Thus, in reality we

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expect overconfidence to be less prevalent among managers whose contracts are not renewed. Second, overconfidence decreases as managers learn their types over time, and it is negatively related to career concerns. Thus, we expect it to decrease with managers’ age, because older managers have more experience and lower career concerns. Our theory points out that the probabilities of different states are in fact partly shaped by the choices of individuals via which overconfidence may emerge. We do not deny that

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imperfect personal judgments may play an important role in the presence of managerial overconfidence, but we believe that, in many cases, overconfidence is a strategic choice in response to the economic and institutional environment rather than an innate quality of individual managers. Managers may find it optimal to behave overconfidently in certain

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economic and institutional environments and not in others.

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