Bargaining in career concerns model

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ФЕДЕРАЛЬНОЕ ГОСУДАРСТВЕННОЕ АВТОНОМНОЕ ОБРАЗОВАТЕЛЬНОЕ УЧРЕЖДЕНИЕ

ВЫСШЕГО ПРОФЕССИОНАЛЬНОГО ОБРАЗОВАНИЯ

«НАЦИОНАЛЬНЫЙ ИССЛЕДОВАТЕЛЬСКИЙ УНИВЕРСИТЕТ

«ВЫСШАЯ ШКОЛА ЭКОНОМИКИ»

Международный институт экономики и финансов

Выпускная квалификационная работа - бакалаврская работа

Переговорный процесс в рамках карьерного роста

Bargaining in career concerns model

по направлению подготовки 38.03.01 «Экономика»

образовательная программа «Программа двух дипломов по экономике НИУ ВШЭ и Лондонского университета»

Шацова Алина Кирилловна

Научный руководитель Г. А. Лукьянов

Москва 2018



Contents

Abstract

Introduction

1. Literature review

2. Model

3. Multi-period model extension

Conclusion

Appendix

References



Abstract

worker firm incentive contract

The problem of effective incentivizing workers has always been one of the most challenging questions in creating firms' labor policies. There are various types of incentivizing schemes like bonus-capped compensation contracts or equity based ones. In this paper I am going to show that equity based contracts are an optimal incentivizing decision for a firm as well as for workers and should be implemented at all levels of labor force. Another popular issue is the choice between internal and external CEOs, which rises from the difference in their abilities and in amount of compensation demanded. I will show that even external CEOs are becoming more popular among global companies, internal candidates have better perspectives for promotion that depend positively on their own skills but negatively on skills of the current CEO. In my research I use a two-period version of the career concerns model, where the low-position worker can receive a promotion and become a CEO, while a CEO has risk to be fired. In my model the worker has private information about his abilities that is not the case in standard career concerns' framework.



Introduction

Recently, a growing attention has been payed to the issue of promotion perspectives of internal workers in comparison to agents externally hired at top management positions. This question is now studied more carefully due to unprecedented rise in share of externally hired chief executive officers (CEOs) in global companies that contradicts to the usual concept stating that CEO from the outside is mostly hired when the company is in bad operation condition and great strategy shifts are needed. According to the latest PwC Strategy& research at 2015 that studied 2500 largest world companies the share of candidates hired on CEO positions from outside had increased at nearly 50% (from 14% to 22%). The internally promoted CEOs are still more preferable in big companies and in firms where the tenure of the former CEO is long or in case when the chairman hires their first CEO at the company. However, external requirement of CEOs became likely to be used not only by firms with poor performance but also by companies which chairman had no CEO experience there and where previous CEO was an outsider as well. Such data suggests that the tendency in recruitment decisions has been changing and hiring CEOs from outside is no longer a decision of last resort.

Figure 1. Source: Outsider CEOs 2015 CEO Success study (PwC's Strategy&, 2016)



Another issue raised in my paper is the problem of effective incentivizing workers that has always been one of the most challenging questions in creating firms' labor policies. The various types of compensation contacts including bonus-capped and equity based ones are widely used among different companies subject to their types and preferable rewarding tactics. One of the arguable effects of incentivizing schemes based on share cropping is a dramatic increase in CEOs' earnings in comparison to usual workers' wages that are usually fixed ones. According to Economic Policy Institute report the earnings gap between average worker and CEO has increased significantly presenting 271-to-1 ratio in 2016. However, a really attention-grabbing fact is the rate of increase in CEOs' compensation level that has reached a 937% mark since 1987 while the average worker's wage has risen only at 11.2% during the same period on the basis of information from the same resource. Such data questions the suitability of compensation policies undertaken by firms' principals that is challenged by difficulties in observing agent's impact in final output and, consequently, in calculation of optimal compensation. "There is no one that can definitively say that's too much or too little," says the Stanford professor N. Bloom about bringing out the CEO's impact in the company's total output. In my model I am going to determine the optimal compensation schemes that are based on learning about the agents' abilities that provide the basis for determining personal share of output.

The main aim of my research is derivation of optimal compensation contracts that incentivize workers and maximize firm's benefits. Also I am going to construct the promotion policy based on the agents' performance applying theoretical model. Consider a two-period model (t = 1, 2) where a firm makes recruitment decisions for both positions over two periods of time. It has two workers throughout its whole functioning period: a low position worker who doesn't have enough information about her promotion perspectives, so acts myopically; and a CEO. The promotion policy I want to propose as an optimal one is based on the principle that the firm compares abilities of the agents and makes a decision about putting a low position employee forward to CEO's position (1), firing the former CEO and hiring a new worker at a low position (2); keeping both agents at their positions (3) or hiring new CEO if the previous one has shown her incompetence and, consequently, keeping the low position employee without promotion (4); so, at any period of time the number of employees in the firm is equal to two. Neither of these decisions contains firing a low position worker due to the principle of human capital value that assumes that firm finds it ineffective to fire a worker due to the economic value of her skills acquired. But this principle doesn't relate to the CEO as any her unsuccessful decision tends to be critical for the firm. All recruitment decisions are based on comparison of both agents' abilities that imply competence in the area of working, skills in making output maximizing decisions and other qualities that lead to successful performance. I have chosen ability as determinant of a worker's promotion perspectives as it is one of the most accurate indicators; however, workers' abilities in my model are assumed to be unknown by firm initially and are learned by a principal during the working process in contrast to a worker herself who has a perfect knowledge about them. I assume that the low position employee's abilities and level of effort (amount of force and time) executed are the determinants of her output. Supposing, that amount of effort exerted is positively and deterministically (in the sense that once effort and ability are known, output is known as well, i.e. output of the low position worker does not have any random component) related to the level of abilities I believe that the principal can extract information about worker's abilities from her output and basing on the value received make decision about her promotion perspectives. Talking about CEO's performance I suppose that her abilities level is the single significant determinant of her final output due to another nature of tasks, so the high level of output straightly tells about the level of CEO's abilities and her perspectives in the company. Also, within the framework of my goal I will demonstrate that the compensation strategy that presents the share of worker's final output is applicable for low position employees and CEOs either as it makes it possible to incentivize both of them to show maximally possible output even considering myopic behavior of first ones and unstable state of last ones.

1. Literature review

My research is based on ideas developed in various articles studying firms' preferences in candidates for the CEO position selection, ways the compensation schemes are implemented and the role of workers' abilities in them.

The first one to construct a career concerns model was Fama (1980), whose aim was to find a policy against moral hazard caused by information asymmetry in the dynamic principal-employee context. He considered that the promotion and reputation perspectives mitigate earnings based incentivizing policies as they make an agent to execute more effort. Such proposition is partially used in my model, however I tend to show, that even if workers in low positions behave myopically, there may a be a contract that maximally incentivizes them. One of the basic researches that I used to construct my career concerns model is `A Theory of Wage Dynamics' (M. Harris and B. Holmstrom, 1982) which goal was to develop a wage dynamics model that works in conditions of unknown worker's abilities and where learning is one of the key ingredients. It gave me an initial notion about the structure of compensation contracts that include the learning process. The primary purpose of this paper was to show the relationship among worker's ability, earning and experience that would be supported by stylized facts. As a result, one of its findings was that firms tend to provide workers with wage guarantees that are expected to prevent adverse changes in workers' perceived abilities due to idiosyncratic nature of uncertainty in agents' ability and their risk aversion that. This inference is supposed to accommodate empirical findings about the earning level of labor with high abilities. However, this model was based on the assumption of incomplete but symmetrical information which contradicts to my model setup that supposes asymmetry of information which leads to adverse selection and moral hazard. Also it studied changes in wage contracts for the worker at the stable position without considering promotion perspectives. Holmstrom (1999) assumes an infinite time-periods model where neither numerous principals nor a worker know about candidate's abilities. Within this framework he surveyed the deterministically related outputs and wages and investigated optimal strategies of principals choosing wage levels and workers choosing level of effort exerted. These derivations were made ignoring promotion perspectives, but gave me a basis for assuming deterministic connection between elements constituting output. In contract to this model F. Palomino and E. Peyrache (2012) supposed that the candidates know their level of abilities making principal in their model face moral hazard and adverse selection as well as in my model. The authors of the paper propose co-existence of several types of compensation contracts as the decision of problems caused by asymmetry of information implying capped-bonus and equity based contracts in their pure form as well as in a mixed one. By offering a menu of contracts to an agent they try to determine a more precise form of optimal form of compensation scheme that would be an incentive for workers to exert higher level of effort. My conclusion that the compensational scheme should be based on the workers' performance coincides with this article's findings. However, I will base on comparison of bonus-capped and equity based contracts made by Lazear (2000). He came to decision that the equity based contracts can be an optimal decision of compensating workers, but my conditions for deriving them differ from ones he determined. In addition to studying the type of compensation scheme F. Palomino and E. Peyrache (2012) had a goal to determine the difference between CEOs from outside and ones promoted internally by dividing them on candidates with different levels of general and firm-specific skills. My model differs from this one as I apply division by overall agents' abilities and by diverse possibilities of promotion by learning the worker's behavior from the lower position as it is done by W. Chan (1996). In his paper author analyzed external recruitment and internal promotion in an economic contest and determined that the level of effort executed can be induced by earnings spread manipulations, but he failed to explain the stylized facts that the externally hired managers are preferred to internal ones only if their performance is significantly greater then insiders' level of output in the environment of fair contest; that is the difference from my model. Difference in preferences for external and internal CEO was also researched by Hermalin (2005) who determined that the external CEOs have compensation contracts that differ not only by level of earnings but also by tenure. I am not investigating the difference between outside CEOs' and inside ones' that do not relate to the level of earnings, but, in contrast to Hermalin (2005) I consider moral hazard as well as adverse selection in completing contracts for different types of CEOs.

2. Model

Consider a risk-neutral firm that proposes two types of positions to its potential workers: the low position (L) and the chief executor officer (CEO) position (H). The external competition for lower position is created by applicants from outside who may be new entrants into the market or an employee changing her career for any exogenous reasons not related to this model propositions. Outside candidates for CEO positions tend to be selected from CEOs in other companies in the market who have shown effective performance. Assume that the worker's output on the low position (L) depends on her ability and her effort, in the multiplicative way as follows:

As the firm doesn't know about the candidates' ability initially and learns about it in the course of working process, but workers are perfectly informed about their abilities at any stage of the process; ability of the newly hired worker is assumed to be distributed uniformly between 0 and 1, so ~ U [0; 1]. is the effort executed, that corresponds to the ability of the worker and her incentives According to my assumption of multiplicative nature of the employer would wish the more able worker (whose is higher) to exert more effort. This relationship can be shown mathematically:The worker who executes high level of effort bears costs related to it (, it is an increasing value and can be presented as. CEO's output is binomially distributed with the probability of success ( equal to worker's ability (и) and the probability of failure ( equal to. Assume that the output of worker at top management position doesn't depend on her effort as due to the changes in nature of tasks caused by promotion any level of effort exerted will not affect significantly in comparison to CEO's abilities that have a crucial impact on possibility of sufficient level of her final output.

There may be several scenarios for workers over the t = 2 horizon: The externally hired in the first period low position worker may be:

1. left at the same position without promotion in the second period considering the value of human capital

2. promoted to the CEO position at t = 2

Externally hired CEO may be:

1. left at her position

2. fired in favor of an insider promotion

3. replaced by another external candidate in case of poor performance

The low position worker promotion is left to the discretion of shareholders and depends on agent's performance as well as on performance of a present CEO. However, I assume that the worker at a low position doesn't have enough information about the promotion policy, so she behaves myopically, making decisions about presenting her abilities and exerting effort basing only on the compensation level at a given period of time.

Affected by assumptions mentioned above structure of compensation contracts and promotion perspectives in my model differ by the position of the worker. So, conditions for workers should include the following:

Low position worker's condition: (1)

High position worker's condition: (2)

where is the wage of the low position worker at the first period that depends on her output showed at the end of the period; is the worker's promotion probability that depends on both her and CEO's output; is the worker's wage in the second period in case of promotion that depends on worker's abilities only due to the nature of output distribution at the top management position and is the worker's wage in case of staying at the lower position and depends on her abilities and level of effort executed. Conditions for top manager of the firm imply externally hired CEO's wage at the first period; CEO's career perspectives that depend on both CEO's and low position worker's outputs and CEO's wage at second period provided success in first period . Assume that, as if the low position worker is promoted / left at her position, then the CEO is fired / left at her position ; in other cases like leaving both agents at their positions or replacing a former CEO with another one from the outside .

I use backward induction in my model as well as it is used in any standard career concerns model. At the first stage I will find out the optimal compensation contracts for lower position worker at the second period of time when the worker's ability is already known. Firm's aim here is to provide the worker with the incentives to exert maximally effective level of effort, so its maximization program may be presented as follows:

(3)

subject to:

Participation constraint: (4)

Limited-liability constraint: (5)

Proposition 1. is presented as a growing function of if the worker exerts the sufficient level of effort that corresponds to the firm's output maximization goal; otherwise a principal punishes the worker by leaving her without compensation:

. (6)

Optimal level of effort calculated is positively related to the worker's ability, so it follows that the greater is the agent's ability, the higher is the impact from effort executed on her output and compensation contract as a consequence. As a consequence the agent has no incentive to hide her abilities or exert less level than it is possible in accordance to her abilities even if she doesn't have any promotion perspectives.

Low position worker's wage at the second period in case of promotion ( is equal to:

(7)

Proposition 2. The forecasted compensation contracts for low position workers in case of promotion is positively related to worker's ability that gives worker an incentive to show her maximum during the working process at the new position and, consequently, tend to show successful amount of output.

In order to determine the worker's promotion perspectives her optimal compensation contract at the higher position should be compared to former CEO's ones. In order to find out the average level of former CEO's output I need to bring out the posterior distribution of top manager's output given success in the first period:



It is used to make a decision whether to leave her at top position or fire her and recruit a new CEO externally.

Considering top management position, the worker's career perspectives may be as follows:

and (9)

. (10)

Proposition 3. The former CEO may stay at her position only if she performs successfully and the executive worker fails to show more that the optimal level of output; in other cases, such as CEO's poor performance or sufficient level of output shown by lower position agent, she will be fired. The promoted internal worker with high enough level of abilities is preferred by firm due to the principle of human capital value.

Posterior distribution of the CEO's output given failure in the first period is not needed to be determined. In case of observed earlier firm will maximize its benefits and successfully performed former CEO's working incentives providing the following compensation contract in the second period:

Proposition 4. The most efficient firm's decision is to provide the CEO who is left at her position with the fixed compensation level equal to of her output.

Assume that in the first period the firm relies on the abilities indicated by candidates while hiring the CEO from outside and can't determine them till the first period ends. In this case optimal compensation level determined by firm should be equal to the expectations about the output that will be shown at the end of the first period:

Proposition 5. In case of hiring an external CEO a principal fixes her compensation level as a half of the output the recruited CEO will show at the end of the first period.

This share payed to a just hired from outside CEO is lower than the share expected to be received by a CEO at the second period in case of her success, so it incentivizes her to show her abilities clearly during the working process. Given such values of CEO's compensation contracts the promotion perspectives of low position workers can be determined as

Proposition 6. The lower position worker can be promoted at CEO position in case when she shows the sufficient abilities (greater than the former CEO's potential output in second period) even if the former top manager had a successful performance and in case when the former CEO showed poor performance and lower position worker's abilities turned out to be greater than the potential output of a new CEO from outside.



Figure 2: Distribution of if Figure 3: Distribution of if occurred to be greater than occurred to be greater than within two periods (expectations from new CEO performance) within two periods

Now, given information about potential outputs, abilities and compensation level for workers in the second period, I am going to determine the optimal level of compensation for executive worker at the first period. Accepting a position in the company a candidate tends to maximize her utility from working there and the utility function of the agent at a lower position is

as it includes the promotion perspectives calculated above. The probability in case (I) is equal to 1 as if the low position worker sows abilities greater than successfully performed CEO's ones she will definitely be promoted. Case (II) contains probability , as the probability that the former CEO shows poor performance is equal to from the perspective of the low position worker who cannot assess CEO's ability. Considering the myopic behavior of workers and, consequently no relation of effort to the promotion perspectives, such utility function incentivizes worker with greater level of ability to apply for this position in contrast to workers with low ability which positively affects the potential firm's output. Assume that the compensation contract is equity based and is equal to

(15)

where is share of worker's output that is used as a compensation for an agent.

The worker's utility maximization program in case (III) is as follows:

(16)

where that shows that with such utility function worker's level of effort has a greater impact on the final output if the worker's ability is high and the worker's output positively relates to the worker's ability. So the firm's maximization problem is

subject to:

Participation constraint: (18)

Limited-liability constraint: (19)

Proposition 7. The most optimal compensation level for an externally hired low position worker with unknown ability is from her output from the firm's perspective.

This share of output is payed to a low position worker from the outside without taking into account her initial ability; however, it depends on the worker's output, so incentivizes candidates with high level of ability to show it clearly and exert as high level of effort as possible during the working process even not accounting promotion perspectives of the worker.

3. Multi-period model extension

In the previous model I developed the promotion perspectives for low position workers and CEOs considering their performance at the two-period horizon. Now I am going to extend the framework to an arbitrary number of periods (T) and determine agents' promotion perspectives taking into account their performance during the infinite number of periods. There will be no changes in compensation schemes for the worker at low position as she is not fired from the firm even after showing insufficient outcome by virtue of principle of human capital value. The main difference here is possibility of keeping CEO at her position even after a failure but only if the number of her failures is less or equal to the number of successful performances. In order to find out the new promotion perspectives I, firstly, will determine the posterior distribution of CEO's output in case when she shows nothing but successful performance in every period which will determine the lowest level of low position worker's abilities that is needed to be promoted definitely not taking into attention CEO's performance:

This result shows that the probability of is increasing with each next period as the output is distributed as a function of that is growing more dramatically than the previous ones. The compensation contract will look like one in the two-period model, but now it will be seen that the CEO's compensation doesn't depend only on the one period output but on the previous ones too:

Proposition 8. Compensational level increases with CEO's output that positively depends on the number of successful periods of time, as is the share of CEO's output that will be payed to her in case of continuous sequence of successful performances.

In order to find out the lowest border in needed level of low position worker's abilities that has to be overcame to have a chance to be promoted I should find out posterior distribution of CEO's output considering the equality of the number of successful performances to the number of failed ones. For simplicity it can be shown on the example when CEO succeeds in first period and fails in second one:

Such simplification is made for reasons that at any period of time which may contain equal number of successes and failures CEO's output can be shown as a parabola concaved downwards with maximum at and ends in which means that the average posterior distribution of CEO's output in such case is equal to. So, considering these values I can determine promotion perspectives of low position worker that are equal to:

Proposition 9. The greater is the number of periods implied in the firm's functioning time, the higher level of abilities from the internal candidate is needed in case of the highly skilled CEO. But in comparison to unskilled CEO or an externally hired one the requirements for the internal candidate abilities stay the same as in two-period model.

CEO's career perspectives are as following:

Proposition 10. The greater is the number of periods the more stable the highly skilled CEO's position, as she meets weaker competition from external and internal candidates and she is not fired after a failure if she has shown enough number of successful results earlier. However, a CEO with relatively low experience high pressure from inside and outside competitors and has low chances to stay in the firm for numerous time periods.



Conclusion

In my paper I have considered a situation when a firm possesses two workers at two different positions, low and top management ones, and a firm's principal makes decisions about these agents' promotion perspectives and compensation contracts. From such model I determined that in case when workers' abilities are learned by firm during the working process and their output depends on agent's abilities and effort at the low position and on her abilities only at CEO position, equity based compensation scheme if it is applied for workers at both positions is an effective way to incentivize them. This conclusion coincides with stylized facts that the equity based contracts are becoming more popular among large companies, however, such form of incentivizing is usually applied for top management agents that causes growing earnings gap between lower and higher position workers. The result of my paper tells that the equity based compensation for lower position agent may be an optimal decision for firm implying the elements of intra-firm competition. But I assumed that the workers behave myopically, so the next step in my research may be derivation of optimal compensation contract based not only on competitive behavior of CEOs but also on competitive behavior of workers.

This competition is based on promotion rules that are determined in my research as well. According to my derivations the probability of internal candidate promotion depends negatively on the abilities of the top manager and positively on the abilities of the low position worker. The more precise results show that the external candidate for CEO position has same chances as an internal one in case of unskilled former CEO but has no chances for promotion if the former CEO has high level of abilities in contrast to internal candidates that may show level of abilities that is sufficient to replace the former CEO. So the dramatic increase in share of CEOs hired from outside isn't connected with sharp changes in firms' policies but with other facts like a possible increase of companies controlled by blockholders who prefer hiring external CEOs as empirical studies have shown or other reasons that should be determined.

All in all, in question of incentivizing workers the equity based contracts may be an effective decision if are undertaken for all positions in the company and are tightly tied to the personal share of output. This policy is effective even in frames of competition among CEOs from outside and insiders, however the last ones a still more preferable by firms due to possibility to learn their abilities before recruiting them for a higher position.



Appendix

1. Taking derivative from (3) with respect to :

FOC:

Solving this equation I get .

2. Calculating (11):

3. Calculating (17):

Taking derivative from (17) with respect to :

FOC:

4. Calculating (21):



References

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Frйdйric Palomino, Eloпc Peyrache - `Internal versus external CEO choice and the structure of compensation contracts'- Journal of Financial and Quantitative Analysis, Volume 48, Issue 4, August 2013 , pp. 1301-1331

Edward P. Lazear - `Performance Pay and Productivity' - AMERICAN ECONOMIC REVIEW, VOL. 90, NO. 5, DECEMBER 2000 (pp. 1346-1361)

William Chan - `External Recruitment versus Internal Promotion' - Journal of Labor Economics, 1996, vol. 14, issue 4, 555-70

Benjamin E. Hermalin - `Trends in Corporate Governance' - The Journal of Finance 60(5):2351-2384 · February 2005

Holmstrцm, Bengt - `Managerial Incentive Problems: A Dynamic Perspective' - The Review of Economic Studies, 1999, 66 (1), 169-182

Fama, Eugene F, - `Agency Problems and the Theory of the Firm'- The journal of Political Economy, 1980, pp. 288-307

DeGroot, Morris H - `Optimal Statistical Decisions'- Vol. 82, John Wiley & Sons, 1970

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Kahn, Lisa B and Fabian Lange - `Employer Learning, Productivity, and the Earnings Distribution: Evidence from Performance Measures'- The Review of Economic Studies, 2014, 81 (4), 1575-1613

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Gillan, S. L.; Hartzell, J. C.; and Parrino, R.. - `Explicit versus Implicit Contracts: Evidence from CEO Employment Agreements'- Journal of Finance, 64 (2009), 1629-1655

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