2016 International Conference on Mathematical, Computational and Statistical Sciences and Engineering (MCSSE 2016) ISBN: 978-1-60595-396-0
CEO Power, CEO Tenure and Executive Compensation Gap: A Dynamic
Model Based on Non-linear Programming Method
Chang-zheng ZHANG, Qian GUO
*and Xin ZHAO
3Xi’an University of Technology, School of Economics & Management, Xi’an, China
*Corresponding author
Keywords: CEO power, Executive compensation gap (ECG), CEO tenure, Tournament theory.
Abstract. Based on the traditional tournament model, CEO power and CEO tenure are simultaneously introduced to refine the extant tournament model by drawing on insights from behavioral perspective. The new model proposes expected utility maximization function of firm performance and adopts Non-linear Programming method to analyze the relationship among CEO power, CEO tenure and ECG. The results show that CEO tenure can negatively moderate the positive effect of CEO power on ECG, and more importantly, out of firm-friendly motives, new CEO intends to choose a larger ECG than senior CEO given the same arrangement of CEO power.
Introduction
The relationship between CEO power and Executive compensation gap (ECG) has been explored by lots of studies. However, it is still in debates. For example, on one side, Bing-Xuan Lin and Rui Lu (2009)[1] found a positive relation which has been proved by many other studies (Lee K. et al., 2008； Fang Hu et al., 2013) [2] [3]; and on the other side, Zhang Changzheng, & Li Huaizu (2008) [4] have indicated a negative one which has also been proved by some other studies (Ricardo Correa, & Ugur Lel, 2013; Zhang Changzheng et al. 2014) [5] [6]. It can be known that there is still not any widely accepted conclusion on relationship between CEO power and ECG in existing literature.
We argue that the ignorance of the moderating role of CEO tenure in the relationship between CEO power and ECG should be the underlying reason of the debates. In order to fill this theoretical gap, a moderating variable should be introduced into the investigation on the relationship between CEO power and ECG. Since CEO tenure provides a CEO time to circumvent monitoring and incentive alignment mechanisms (Sam Allgood, & Kathleen A., 2000) [7], we propose that CEO tenure can moderate the relationship between the two. Therefore, this research focuses on the following question by building a theoretical model: how and why CEO tenure affects the relationship between CEO power and ECG?
Model
Model Assumptions
Based on assumptions of traditional tournament model (Becker, B., & Huselid, M., 1992; Bognanno, M., 2001; Lazear, E., & Rosen, S., 1981) [8] [9] [10], by considering corporate governance features and adopting the common simplified method in economics (Henderson, & Fredrickson, 2001) [11], the paper constructs a team tournament model with CEO power included.
Assumption 1: In a static model including a firm CEO and two top managers, the participants are all risk neutral, and their reservation utility is zero. Firm CEO can not directly observe the work effort of top managers, and what he can observe is their output.
the tenure grows, however, Torsten Wulf et al. (2010) [12] expect strong performance increases resulting from the selection of a clear paradigm and growing legitimacy, and they do find evidence that a longer CEO tenure leads to higher overall firm performance. The output of top managers (yi) will positively related with T. Following the assumption of traditional tournament model, top managers’ capability and skills are equal, e.g., S1S2 S.
Assumption 3: Firm output is the product of each top manager’s output, and the expression equation is YPy1y2. The equation shows that the whole output depends on the coordination behavior. P is CEO power. The model views top managers as the same, namely, each member has the same influence ability for team output.
Assumption 4: Firm CEO provides different compensation (C1 & C2, C1>C2≥0) to each top manager according to his relative output level. The member with higher output gets the higher reward (C1), and the lower member gets the lower reward (C2). The competition rule is of course the consensus of all the participants.
Assumption 5: Productive effort of member 1 and member 2 is respectively. Total firm resource is R, and thus the resource under team control is PTR. Each member can gain private benefit bi (•) which can be expressed as bi (•) =PTR-ei2/ (2T) (i = 1, 2). The effort cost of top managers is negatively with CEO tenure.
Model Design
According to the fundamental assumptions proposed above, especially the basic principle that top manager’s compensation is only depended on his relative performance under tournament mechanism,
it would be indicated that the likelihood (probability) of gaining C1 for member i (Li) is
1 2
1 2 2 1
1 2
1 2
Pr ( )
Pr ( ).
Pr ( )
( )
i
L ob y y
ob T S Te Te
T ob S e e
TG e e
(1)
In Eq.(1), S1S2, ~ g(), G(·) is the distribution function of , and E()=0, E( 2 )=22
(Because 1, 2 are independent random variables).
The expectation reward of member i is LiC1(1Li)C2, and private benefit is bi(·). Under the
assumption of risk neutral, the expectation utility of member i (Ui) is
) ( )
1
( 2
1
i i i
i LC L C b
U
T e PTR C
CL i
i
2
2
2
(2) Thus member 1 chooses effort degree to maximize his expectation utility, and its first-order condition of utility maximization is
T e e e Lg T e
C 1
2 1 1
1
) (
(3)
To set Eq.(3) equal zero, we get the optimal effort level of 1,
) ( 1 2 2
*
1 T Cg e e
Since G(·) is the distribution function of and E( )=0, E(2 )=22, G(x)＝1-G(-x)，and g(x)=g(-x), then the model gets,
) (
)
(e1 e2 g e2 e1
g (6)
Therefore, under the so-called balance conditions, each top manager shall choose the same effort level, C g T e e
e* 1* *2 2 (0) (7) According to Eq.(7), it can be known that, with the enlargement of ECG, top manager’s productive effort level increases gradually. Here the incentive strength is up to ECG, so CEO can promote top managers to compete with others and work harder by enlarging ECG.
Analysis Results
Considering the assumption of CEO’s being risk neutral, the model gets his expectation utility (UCEO)
by subtracting two members’ rewards (C1C2) from the sum of team expectation output (Y Py1y2)
and private benefit of each top manager(P[b1()b2()]).
)] ( )] ( ) ( [
[Py1y2 Pb1 b2 C1 C2 E
UCEO
) ( ] 2 2 2 [ ) )(
( 1 2
2 2 2 1 2 2 1 1 2 C C T e T e PTR P e S e S
PT
(8) Due to information asymmetry, firm CEO can not observe top managers’ effort degree, and it is impossible to use enforcement contract under information symmetry. Generally speaking, firm CEO hopes to make use of incentive contract to induce top manager to choose the behavior as firm CEO wishes. The mission of firm CEO is to choose an incentive contract satisfying top managers’ participation constraints and incentive compatible constraints in order to maximize the expectation utility function of the firm. Therefore, firm CEO needs to solve the maximization problem of Eq.(9).
) )( (
{ 2 1 1 2 2
, , , ,
,
, 2 1 2 1 2 1 2 1 e S e S PT U
Max
Max
C C e e CEO C C e e ] ( ) 2 2 2[ 1 2
2 2 2
1 C C
T e T e PTR
P
) ( ] 0 , 2 [ . . 1 2 1 2 1 1 IC T e PTR C CL Max e t
s
) ( ] 0 , 2 [ 2 2 2 2 2 2 IC T e PTR C CL Max
e
) ( 0 2 1 2 1 2 1 IR T e PTR C
CL
) ( 0 2 2 2 2 2 2 IR T e PTR C
CL
) ( 0
2
1 C LL
C
(9)
Substituting Eq.(7) into Eq.(9) under the assumption of S1S2 S, we can simplify Eq.(9) as follows,
PT S PT Sg C
U
Max
Max
CEO { 2 (0) 2 2 4)
(
2
)
0
(
) , ( 2
) 0 ( )
0 ( .
. 1 2
2 2
2 IC IC
T C g PTR C C G t
s
(10) Because G(x) is a symmetric probability distribution function, G(0)=1/2. It can be concluded that,
PTR C g
T C
C
2 1 ) 0 ( 2
1 2 4 2 2
(11)
Substituting Eq.(11) andC1C2C into Eq.(10), we get,
R T P Cg S PT S PT
U
Max
Max
C CEO C
2 2 3
2 2
2 ) 0 ( 2
{
} 2 ) ( 2 4 2
PTR o
g T
C
(12)
To differentiate W of Eq.(12), there is
) 0 ( 2
) 0 (
2PST3g T4 Cg2 C
UCEO
(13) To set the first-order condition of Eq.(13) equal zero, the model can determine the optimal ECG,
) 0 (
Tg PS C
(14) The model shows that CEO power and ECG is positively related, and such an effect of CEO power on ECG would be moderated by CEO tenure to a large degree.
Conclusions
The research introduces CEO power into traditional tournament model, and constructs a new team tournament model based on CEO power which discusses the relationship among CEO power, ECG and firm performance. The main research conclusions are shown as follows. ① CEO power has positive effect on ECG. ② CEO tenure can negatively moderate the positive effect of CEO power on ECG. New CEO intends to choose a larger ECG than senior CEO given the same arrangement of CEO power out of firm-friendly motivations.
The above conclusions are helpful to understand the determining mechanism of ECG, and to some extent, they can be used as the tools guiding the practice of TMT operation in modern firms. The shareholders and the board should keep more vigilant eyes on senior CEO, while empower more discretion to new CEO. However, all the conclusions are the results of mathematical calculations and logical inferences based on theoretical model, and their validity still needs further empirical tests.
Acknowledgements
This research was supported by Projects of the National Social Science Foundation of China under the Grant "15BGL109", the Scientific Research Foundation of Ministry of Education of the PRC in Humanities and Social Sciences under Grant “14YJA630089”, and Shaanxi Social Science Foundation under Grant “2014P04”.
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