DISCUSSION PAPER
SERIES IN
ECONOMICS AND
MANAGEMENT
Task Interdependence between Economic and
Non-economic Goals and the Family Owner’s
Decision to Hire a Family or Nonfamily Manager:
A Multitask Model
Joern Block, Jenny Kragl, Guoqian
Xi
Discussion Paper No. 15-15
GERMAN ECONOMIC ASSOCIATION OF BUSINESS
ADMINISTRATION – GEABA
Task Interdependence Between Economic and Non-economic
Goals and the Family Owner’s Decision to Hire a Family or
Nonfamily Manager: A Multitask Model
Joern Block, Jenny Kragly, and Guoqian Xiz
Preliminary and incomplete - do not cite or circulate.
April 13, 2015
Corresponding author; Universität Trier, Faculty IV, Department of Business Administration, e-mail:
block@uni-trier.de.
y
EBS Universität für Wirtschaft und Recht, Department of Management & Economics, e-mail:
jenny.kragl@ebs.edu.
z
Universität Trier, Faculty IV, Department of Business Administration, e-mail: xgq.natalie@gmail.com.
1
1
Introduction
Family …rms and family owners pursue both economic and non-economic goals, where the noneconomic goals are mostly related to family goals such as family harmony or family reputation
(Astrachan & Jaskiewicz, 2008; Chrisman, Chua, Pearson, & Barnett, 2012). Managers in family …rms need to ful…ll both types of goals. The recruitment of top management team members
in family …rms and the decision to hire a family or a nonfamily manager is therefore often a
complex process and depends on various factors such as the availability of family managers,
the importance of family goals, and the family’s risk attitude towards non-economic (family)
goals (Gómez-Mejía, Haynes, Núñez-Nickel, Jacobson, & Moyano-Fuentes, 2007). So far, however, prior research has not considered how the interdependence between the two types of goals
in‡uences top management recruitment decisions in family …rms.
Our paper makes a …rst step in this direction. We analyze how task interdependence between
economic and non-economic goals in family …rms in‡uences the decision to hire a family or a
nonfamily manager. The tasks of ful…lling economic and non-economic goals in family …rms can
be either substitutes or complements. That is, they can either reinforce or exclude each other.
As an example for the two tasks being substitutes consider the situation where the manager, for
economic reasons, is forced shutting down a factory in the family’s and the family …rm’s home
region. Shutting down the factory and laying o¤ its employees may help the …rm to survive
and ful…ll the family’s economic goals but does harm to the family’s reputation in the public.
Another example is when the manager spends a lot of time training and nurturing a potential
family successor while being busy on expanding the business into a new market. As an example
for the two tasks being complements consider the case where the manager helps to solve a family
con‡ict which was visible in the public contributing to a negative public …rm image and creating
mistrust in the …rm and between its stakeholders. By solving the family con‡ict, the family
harmony is restored, decision-making becomes quicker, and the …rm looks more attractive as an
employer for potential employees.
The manager has limited time and e¤ort that he can put into doing the respective tasks.
The interdependence between both tasks has an in‡uence on the manager’s distribution of his
e¤orts towards the two tasks. Our study aims to understand how the family owner’s decision
to hire a family or a nonfamily manager depends on whether the two tasks are substitutes or
complements.
We use a multitask principal-agent model to answer this research question. In the model,
the family …rm owner (principal) chooses a family or a nonfamily manager (agent). The family
owner values both economic and non-economic goals and the manager has the task to ful…ll
both types of goals. Yet the manager’s work e¤ort is his private information so that a moralhazard problem arises. While the manager’s performance regarding non-economic goals cannot
be objectively assessed, there is a measure of economic performance which the …rm owner uses
in an incentive contract. We model two important characteristics in which the two types of
managers di¤er. First, we assume that the nonfamily manager has a higher ability than the
family manager with regard to economic goals as he is drawn from a pool of suitable candidates
2
(Burkart, Panunzi, & Shleifer, 2003; Pérez-González, 2006). Second, we assume that, in contrast
to the nonfamily manager, the family manager has a personal interest in the pursuit of noneconomic goals (Chrisman, Chua, Pearson, & Barnett, 2012). We argue that the valuation of
non-economic goals is decreasing over the family generation, and the family manager’s valuation
falls, however, below that of the …rm owner. We then analyze how the task interdependence
between ful…lling economic and non-economic goals in‡uences how the manager distributes his
e¤ort between the two tasks and how this a¤ects the family’s utility as an owner.
Our main …ndings are threefold. First, we …nd that the nonfamily manager does not put
any e¤ort into pursuing the family’s non-economic goals if the two tasks are substitutes. The
reason is that any e¤ort the manager would put into non-economic goals not only decreases his
incentive pay for economic performance but moreover impedes his work e¤ort in the latter task.
Hiring the family manager is optimal if the family manager’s valuation of the non-economic
goals is close to that of the …rm owner and/or the family manager’s ability in the economic
task does not di¤er too much from that of the nonfamily manager. Secondly, if the two tasks
are complements, the owner is more likely to choose the family manager, the more aligned the
latter’s valuation of the non-economic goals with the former’s. Intuitively, with complementary
tasks, both types of managers will allocate some e¤ort to both tasks although the non-economic
goal is not explicitly rewarded. This occurs because enhancing non-economic goals at the same
time facilitates raising economic performance and hence increases the expected incentive pay.
However, the family manager moreover has an intrinsic incentive to pursue the non-economic
goals. The stronger this incentive, the more valuable is the family manager to the …rm. Thirdly,
if the two tasks are complements, the owner is more likely to choose the nonfamily manager as
the complementarity of the two tasks increases. This is because strong task complementarities
also induce the nonfamily manager to comprehensively engage for the non-economic goals. When
hiring the nonfamily manager, the …rm owner additionally bene…ts from that manager’s higher
ability in the economic task.
The remainder of the study is structured as follows. The following section presents the model.
We introduce the basic assumptions and then we solve the model for the optimal incentive
contract. The fourth section presents our main …ndings regarding the optimal hiring decision.
Section …ve o¤ers a discussion of our main results, and the …nal section concludes, thereby
highlighting the avenues for further research.
2
2.1
The Model
Assumptions
We model a principal-agent relationship in which the family-…rm owner (principal) selects one
out of two candidates (agents i = F; N ) to manage the …rm. The former has two options;
hiring a family manager (i = F ), that is, a person with family ties to the …rm, or a nonfamily
manager (i = N ), that is, somebody from outside the familiar context of the …rm. All parties
are risk neutral. Managing the …rm requires ful…lling two tasks; enhancing the …rm’s economic
3
performance and the family’s non-economic goals such as preserving and fostering the family’s
reputation. The tasks cannot be split between managers; that is, just one manager will be
hired.1 By e¤ort ei1 we denote all activities manager i undertakes to raise the …rm’s economic
performance xi , e.g., the stock price. E¤ort ei2 in the second task summarizes the manager’s
e¤orts related to achieving the family’s non-economic goals yi . The manager’s exerted e¤ort
levels are not veri…able by the …rm owner, implying a moral-hazard problem. Performance in
the …rst task can, however, be assessed using the veri…able measure of economic performance xi :
xi = ei1 +
1;
1
N (0;
2
1
);
i = F; N;
(1)
where 1 denotes the random shock to economic performance outside the manager’s control. By
contrast, the non-economic outcome yi is not veri…able:2
yi = ei2 +
2;
2
N (0;
2
2
);
i = F; N;
(2)
where similarly 2 denotes the exogenous random term. For simplicity, we assume the random
terms ( 1 , 2 ) to be independent.
The …rm owner o¤ers the manager an incentive contract which speci…es a …xed wage i and
an incentive rate i 0 per unit of economic performance xi .3 Accordingly, manager i’s wage
is given by
wi = i + i xi ; i = F; N:
(3)
The manager is …nancially constrained, hence no negative payment is allowed. When hiring
manager i, the …rm owner’s utility is given by the sum of economic and non-economic outcome
minus wage payments:
wi ; i = F; N:
(4)
i = xi + yi
According to the above speci…cation, for simplicity, we assume the …rm owner to value economic
performance goal as important as the non-economic outcome.4
Manager i’s utility is
Ui =
i
+
i xi
+
i yi
c (ei1 ; ei2 ) ;
i = F; N;
where c (ei1 ; ei2 ) denotes his cost of exerting e¤ort. In the utility function,
(5)
i
denotes manager i’s
1
If the two tasks could be separated, the …rm owner could hire both managers, assigning one task to each of
them, which is, however, not plausible in many management cases. Our interest lies in the understanding of the
…rm owner’s choice when she faces the situation where she is forced to choose one out of two managers to conduct
both tasks.
2
Note that non-economic goals are often hardly objectively measurable. On the one hand, non-economic goals
frequently refer to "soft" criteria such as reputation. On the other hand, e¤orts related to these goals often take
e¤ect only in the future.
3
That is, in line with most real-life cases, we exclude the theoretical possibility of punishing good performance.
4
This assumption greatly simpli…es the exposition of the model. A more general formulation allows for di¤erent
valuations of economic and non-economic goals: i = axi + byi
wi ; i = F; N , where a and b denote the
respective weights the …rm owner assigns to the two goals. While such a model provides further results, assuming
a = b = 1 does not change any of the main results of our paper.
4
personal valuation of the non-economic outcome. We assume that the nonfamily manager does
not bene…t from pursuing non-economic goals, thus N = 0. By contrast, the family manager’s
valuation of the non-economic outcome is positive. Moreover, we assume that his valuation falls
below that of the …rm owner, hence F =: 2 (0; 1).5
Manager i’s e¤ort cost function is given by
c (ei1 ; ei2 ) =
1 2
2Di ei1
+ 12 e2i2 + cei1 ei2 ;
i = F; N;
(6)
where Di 1 denotes manager i’s ability in the task related to economic performance. Specifically, we assume the nonfamily manager to have a higher ability in that task than the family manager.6 Accordingly, we assume DF = 1 and DN =: D > 1. In the cost function,
p1 ; p1
c2
is a measure of task interdependence.7 If c > 0, the two tasks are substitutes,
Di
Di
i.e., the tasks compete for the manager’s attention so that he …nds it harder to engage in one task
when he is already working on the other. By contrast, if c < 0, tasks are complements. In that
case, doing one task reduces the manager’s marginal e¤ort costs for the other task. Obviously,
tasks are independent if c = 0.8
The timing is as follows. First, the …rm owner decides whether to hire the family or the
nonfamily manager. Then she o¤ers that manager an employment (incentive) contract. Third,
the manager decides whether to accept that contract or reject it. In the latter case, the manager
obtains his outside option, which we, for simplicity, set to zero. If the manager accepts the
contract, he chooses the e¤ort levels ei1 and ei2 . Fourth, economic performance xi and the
non-economic outcome yi are realized. Finally, the manager is paid according to the contract.
2.2
First-best Solution
As a benchmark, we …rst determine the e¢ cient e¤ort levels if e¤ort is contractible for both types
of managers. The …rm owner’s optimization problem under the …rst-best solution is maximizing
expected utility so that the manager participates in the contract. In the Appendix, we present
the solution to this problem. The …rm owner’s …rst-best expected utility is given by:
E( ~i ) =
Di (1
2c (1 + i )) + (1 +
2(1 c2 Di )
i)
2
;
i = F; N:
(7)
5
Recall that, by the …rm owner’s utility function, her valuation of non-economic goals is one. We argue that
a family member’s valuation of non-economic goals is decreasing over the family generation.
6
This assumption is justi…ed by previous empirical evidence (see, e.g., the study by Pérez-González, 2006),
and it is in alignment with the theoretical paper by Burkart, Panunzi, & Shleifer (2003). The respective argument
is that nonfamily managers are chosen from a large sample pool of candidates who are thus likely to be superior
than family managers with regard to managerial abilities.
1
c
7
The cost function can be written as c (ei1 ; ei2 ) = 21 eT Ce, where e = (ei1 ; ei2 )T and C = Di
is the
c
1
Hessian matrix. The restriction c 2
p1 ; p1
Di
Di
ensures that the cost function is strictly convex, and the
matrix C is positive de…nite. In the model, we also assume that c > 0 is not too large to exclude the unrealistic
cases of negative e¤ort levels.
8
In our analysis, we will focus on the more interesting cases in which c 6= 0.
5
By inspection of the …rst-best utility function, …rm pro…t is strictly increasing in
when tasks are complements (c < 0).
3
i
and Di
Optimal Incentive Contract
In this section, we analyze the case with non-veri…able e¤ort, hence the moral-hazard problem.
The …rm owner’s maximization problem is given by:
max
ei1 ;ei2 ;
s.t.
i
0
ei1 + ei2
(
i
+
i ei1 )
1 2
+ i ei1 + i ei2 ( 2D
e + 12 e2i2 + cei1 ei2 ) 0;
i i1
1
ei1 ; ei2 = arg max i + i e^i1 + i e^i2 ( 2D
e^i1 + 12 e^i2 + c^
ei1 e^i2 );
i
0 for all xi
i + i xi
i
(8)
The …rst constraint is the participation constraint, the second constraint is the incentivecompatibility constraint, ensuring that the manager maximizes his own expected utility for
any given incentive rate i . The last constraint is the non-negativity constraint, guaranteeing
that negative payments cannot arise. The formal solution to the problem is again relegated to
the Appendix. We assume that ei1 ; ei2 ; i
0, i.e., c is not too large.
Recall, that, for the family manager, it holds that F =
and DF = 1 while, for the
nonfamily manager, it holds that N = 0 and DN = D. Accordingly, the above results yield
the …xed wage, incentive rate and e¤ort levels for the two types of manager under the optimal
incentive contract, respectively. For the family manager, we obtain:
F
= 0;
F
=
eF 1
eF 2
(9)
1 + c(
1)
;
2
1 c(1 + )
=
;
2(1 c2 )
2 + ((1
)c
=
2(1 c2 )
6
(10)
(11)
1)c
:
(12)
For the nonfamily manager, i = N , we have:9
N
N
eN 1
eN 2
= 0;
8
< 1 c if c 0
=
;
2
: 1
if c > 0
2
8
< D(1 c) if c 0
2(1 c2 D)
;
=
:
D
if
c
>
0
2
8
cD(1
c)
<
if c 0
2
2(1 c D)
=
:
:
0
if c > 0
(13)
(14)
(15)
(16)
The following lemma highlights a …rst interesting insight regarding the nonfamily manager’s
e¤ort choice under the optimal incentive contract as formally stated in the above results.
Lemma 1 If the two tasks are substitutes, c > 0, the nonfamily manager does not put any e¤ ort
into pursuing the family’s non-economic goals; eN 2 (D; c > 0) = 0.
The manager’s e¤ort in pursuing the family’s non-economic goals is not monetarily incentivized by the …rm owner. In contrast to the family manager whose name is tied to the family
…rm, the nonfamily manager has no intrinsic motivation to achieve the non-economic goals. If
the two tasks are substitutes, doing a task such as nurturing a potential family successor makes
working in the other task related to produce economic performance more di¢ cult and costly.
Hence, the nonfamily manager would rather focus on the economic goals only.
Using the results above, we calculate the …rm owner’s utility under the optimal incentive
contract. For the family manager ( F = , DF = 1) and the nonfamily manager ( N = 0,
DN = D), the …rm owner’s respective levels of expected utility are given by:
c2 (
1)2
2c( + 1) + 1 + 4
;
4(1 c2 )
8
2
< D(1 c)
if c 0
4(1 c2 D)
E( N ) =
:
:
D
if c > 0
4
E(
F)
=
(17)
(18)
In the following section, we take a closer look at the …rm owner’s utility, depending on the
managers’characteristics ( ; D) and the task interdependence as characterized by c. Then we
derive the optimal hiring decision, depending on the foregoing parameters.
4
Whom to Hire: Family versus Nonfamily Manager
In order to determine which manager the …rm owner should optimally hire, we analyze the
di¤erence in utility between hiring a family and a nonfamily manager. That di¤erence is given
9
We derive
N ; eN 1 ; eN 2
explicitly in the Appendix.
7
by:
E(
F)
E(
N)
=
8
(1
>
>
<
>
>
:
c)2 (1
c2 (
D) + (1 Dc2 )( 2 c2 2 c2 2c + 4 )
4(1 c2 )(1 c2 D)
1)2 2c(1 + ) + 1 + 4
D(1 c2 )
4(1 c2 )
if c
0
:
(19)
if c > 0
We initially consider the case where economic and noneconomic goals are substitutes (c > 0).
Proposition 1 If the two tasks are substitutes, c > 0, the …rm owner’s utility when hiring a
family manager exceeds the utility when hiring a nonfamily manager if > 1 ;where
1
=
p
1
(c
c+
2
c
1) (c + 1) ( 4c + c2 D + 4) + c2
2 :
Proof. See the Appendix.
The result shows that should be su¢ ciently large to ensure the di¤erence of utility to be
positive.10 Moreover, it is easily checked that the di¤erence of utility E( F ) E( N ) is decreasing
in D: Accordingly, we can draw a conclusion for the optimal hiring decision.
Corollary 1 If the tasks are substitutes, c > 0, the family …rm owner might be better o¤ by
choosing the family manager although the nonfamily manager has a higher ability in the task
related to economic goals. That case is more likely to arise if the family manager’s valuation of
non-economic goals is close to that of the …rm owner and/or the family manager’s ability is not
too di¤ erent from that of the nonfamily manager.
The family manager is more likely to be chosen by the …rm owner if his valuation of the
non-economic goals is su¢ ciently large. In our case, this signi…es that the family manager’s goal
is aligned with the …rm owner’s. Family managers who view family reputation or …rm image as
a re‡ection of their own public image exert e¤orts in protecting the family’s non-economic goals
from being harmed. When the manager’s valuation is su¢ ciently strong, the e¤ort he exerts will
be higher, then the …rm owner’s total utility achieving from both economic and non-economic
goals will increase.
Now consider the case where the tasks are complements (c < 0). Inspection of the …rm
owner’s utility di¤erence given in (19) yields the following result.
Proposition 2 If the two tasks are complements, c < 0, the …rm owner’s utility when hiring a
family manager exceeds the utility when hiring a nonfamily manager if > 2 ;where
2
=
(c 1)
4
c D c2
Proof. See Appendix
c+
p
(c2 D
1) (c + 1) (3c2 D + c3 D
10
4) + 2c2 D + c3 D
2 :
Recall that, cannot not exceed 1; as we assume that the family manager’s valuation of the non-economic
goals is smaller than that of the …rm owner, .
8
Similar to the substitute case, the di¤erence of utility is positive if is su¢ ciently large.
Again, E( F ) E( N ) is decreasing in D: Accordingly, we can draw a conclusion for the optimal
hiring decision in the case of task complementarities.
Corollary 2 If the two tasks are complements, c < 0, the family …rm owner is more likely to
choose the family manager the more aligned the latter’s valuation of the non-economic goals with
the former’s.
The family manager has an intrinsic motivation to ful…ll the family’s non-economic goals
even though he does not receive any monetary compensation for this task. The more the family
manager cares about family reputation or family harmony, the more e¤ort he will put into doing
both tasks, hence increasing the …rm owner’s total utility.
We now analyze how the complementarity of the tasks a¤ects the …rm owner’s decision, that
is, how the …rm owner’s utility varies in c:
Proposition 3 If the two tasks are complements, c < 0, the …rm owner’s di¤ erence of utility
E( F ) E( N ) is decreasing in the complementarity of the two tasks.
Proof. See the Appendix.
Based on this …nding, we conclude the following for the …rm owner’s hiring decision.
Corollary 3 If the two tasks are complements, c < 0, the family …rm owner is more likely to
choose the nonfamily manager as the complementarity of the two tasks increases.
Our model shows that, although the family manager personally cares for the non-economic
goals, the …rm owner might favor the nonfamily manager over the family manager if tasks are
complements. This is the case when the complementarity of the tasks is su¢ ciently strong and/or
the nonfamily manager is much better than the family manager at task related to economic
goals. Even though the nonfamily manager does not receive any compensation from the …rm
owner, he will put e¤ort into pursuing the family’s non-economic goals when the two tasks are
complements. The more complementary the two tasks are, the more likely it is that doing one
task reduces the marginal cost of another task, thus the nonfamily manager will put more e¤ort
into both tasks. Hence, the …rm owner’s utility increases.
5
Discussion
Our economic model shows that it can be an optimal and rational choice for family owners
to hire a family manager with a low ability regarding the ful…llment of economic goals. This
situation occurs when the tasks of ful…lling economic and non-economic goals are substitutes and
the non-economic goals are di¢ cult to measure. In such a situation a highly quali…ed nonfamily
manager would rationally choose to put all his e¤orts in the ful…llment of economic goals and
neglect the non-economic goals such as family harmony or family reputation, which the family
cares about.
9
With this result, our paper contributes to prior research about the top management hiring
decisions in family …rms (Chrisman, Memili, & Misra, 2013; Vandekerkhof, Steijvers, Hendriks,
& Voordeckers, in press; Salvato, Minichilli, & Piccarreta, 2012). In contrast to prior research,
our model shows that it can be a rational and utility-maximizing choice of family owners to
recruit a member of their own family into a top management position even though he is less
quali…ed in terms of economic goals than a nonfamily manager drawn from a larger pool of
potential candidates (Burkart, Panunzi, & Shleifer, 2003). It should be noted that the preference
for the family candidate is not due to other reasons such as nepotism (Jaskiewicz, Uhlenbruck,
Balkin, & Reay, 2013), exploitation of minority shareholders (Morck &Yeung, 2003), the family
…rm’s inability to attract good nonfamily candidates (Chrisman, Memili, & Misra, 2013) or
irrational decision making of family owners (Kets de Vries, 1993). Thus, our model o¤ers a new
explanation why family …rms stick to family members as top managers even though they are
not as well quali…ed (in terms of economic goals) than outside nonfamily candidates are.
The situation di¤ers, however, when the tasks of ful…lling economic and non-economic goals
are complements and the ful…llment of one task helps to ful…l the other task. In such a situation,
the hiring decision should be based primarily on the ability of managers to ful…ll economic goals.
The ful…llment of economic goals helps also to ful…ll non-economic (family) goals. In such a
situation, the likelihood that the family manager is the best candidate from the family owner’s
perspective decreases strongly as the family manager is drawn from a much smaller pool of
quali…ed candidates and usually has less outside …rm and industry experience than comparable
nonfamily managers. This result helps to understand why in some industries and some family
contexts the family manager is the preferred and optimal choice whereas in other industry and
family contexts the nonfamily manager is preferred. The more the tasks of ful…lling economic
and non-economic goals are complements and not substitutes, the better the chances of the
nonfamily manager to get hired by a family …rm.
Next to the literature about the top management hiring decisions in family …rms, our paper
also contributes to the discussion how family owner’s economic and non-economic goals interrelate with each other and how this in‡uences family …rm decision making. This point was
raised by Berrone et al., (2012) in their summary of open questions related to the concept of
socio-emotional wealth.
6
Further Research
The model o¤ers several interesting avenues for further research. Our model is about the selection
of a single family or nonfamily manager. The model could be extended to the case of management
teams, where both family and nonfamily managers prevail (Patel & Cooper, 2014). In this case,
the family owner being principal hires two or more managers. Another avenue would be to
extend the model to the case where several principals with di¤erent objectives exist. This case
refers to family …rms with minority nonfamily owners.
10
Appendix
First-best Solution
With contractible e¤ort and in the absence of …nancial constraints, the …rm owner o¤ers manager
i a …xed wage w
~i to be paid i¤ the manager exerts at least the pro…t-maximizing e¤ort levels
e~i1 ; e~i2 . The …rm owner’s maximization problem is given by11 :
max
ei1 ;ei2 0;wi
s.t.
ei1 + ei2
wi +
i ei2
wi
1 2
e + 12 e2i2 + cei1 ei2 )
( 2D
i i1
(20)
0
The constraint to the problem is the participation constraint since it ensures that the manager
accepts the contract. As the …xed wage negatively enters the …rm owner’s objective function,
she will reduce it as much as possible so that the constraint becomes binding at the optimum.
Hence, we obtain:
1 2
e + 21 e2i2 + cei1 ei2
(21)
w
~i = 2D
i ei2 :
i i1
Substituting w
~i into the …rm owner’s utility maximization problem and calculating the …rst-order
conditions yields:
Di (1 c(1 + i ))
; i = F; N;
1 c2 Di
1 + i cDi
e~i2 =
; i = F; N:
1 c2 Di
e~i1 =
(22)
(23)
We assume e~i1 ; e~i2 0, hence c not too large.
The …rm owner’s …rst-best utility becomes:
E( ~i ) =
Di (1
2c(1 + i )) + (
2(1 c2 Di )
i
+ 1)2
;
i = F; N:
(24)
Recall, that, for the family manager, i = F , it holds that i = and Di = 1. Hence, for the
…rst-best e¤ort and …rm pro…t when hiring the family manager, we obtain:
c(1 + )
;
1 c2
1+
c
e~F 2 =
;
2
1 c
1 + (1 + )(1 +
E( ~F ) =
2(1 c2 )
e~F 1 =
1
For the nonfamily manager, i = N , it holds that
11
i
(25)
(26)
2c)
:
(27)
= 0 and Di = D. Hence, for the …rst-best
We assume that i is small enough so that w
~i is non-negative. In other words: We focus on the most plausible
case where the family manager does not enjoy working for non-economic goals so much that he would accept even
a negative wage.
11
e¢ cient e¤ort and …rm pro…t when hiring the nonfamily manager, we obtain:
D(1 c)
;
1 c2 D
1 cD
e~N 2 =
;
1 c2 D
D(1 2c) + 1
E( ~N ) =
:
2(1 c2 D)
(28)
e~N 1 =
(29)
(30)
Comparing the …rm owner’s expected utilities for i = F; N , respectively, veri…es that hiring
the family manager yields higher pro…t if:
(1 + (1 + )(1 +
c2 D) > (1 + D (1
2c)) 2(1
2c)) 2(1
c2 )
(31)
Solution to the Optimal Incentive Contract (Second-best Solution)
Manager i maximizes his expected utility:
max
i
ei1 ;ei2 0
+
i ei1
+
i ei2
1 2
e + 12 e2i2 + cei1 ei2 )
( 2D
i i1
(32)
The …rst-order conditions are given by:
Di ( i c i )
; i = F; N;
1 c2 Di
c i Di
i
i = F; N:
ei2 =
1 c2 Di
ei1 =
(33)
(34)
Hence, the …rm owner’s problem becomes:
max
ei1 ;ei2 ;
s.t.
i
0
ei1 + ei2
(
i
+
i ei1 )
1 2
+ i ei1 + i ei2 ( 2D
e + 12 e2i2 + cei1 ei2 )
i i1
(33); (34)
0 for all xi :
i + i xi
i
0;
(35)
Since we have i 0, the ex-post wage payment as given in the last constraint is continuously
increasing in xi . Accordingly, if the constraint holds for the lowest possible realization of xi , it
holds for all xi . This implies that we must have i 0. As the …xed wage i negatively enters
the …rm owner’s objective function, she will choose it as small as possible so that the constraint
becomes binding in the optimum, hence i = 0. After substituting i , ei1 , ei2 into the …rm
owner’s maximization problem, the …rst-order condition with respect to i is given by:
i
=
1+(
i
1) c
2
12
;
i = F; N:
(36)
Substituting
i
into equations (33),(34) yields the optimal e¤ort levels:
Di (1 (1 + i )c)
; i = F; N;
2(1 c2 Di )
2 i + ((1
1)cDi
i) c
ei2 =
; i = F; N:
2
2(1 c Di )
ei1 =
As before, we assume ei1 ; ei2
0, hence c is not too large. Substituting
owner’s utility under the optimal incentive contract becomes:
E( i ) =
cDi (c(
i
1)2 2( i + 1)) + Di + 4 i
;
4(1 c2 Di )
(37)
(38)
i
, ei1 , ei2 , the …rm
i = F; N:
(39)
Using that F = ; DF = 1; we obtain the optimal …xed wage, incentive rate and e¤ort
levels for the family manager as given in equations (9), (10), (11) and (12). For the nonfamily
manager ( N = 0; DN = D), we get:
eN 1
eN 2
1
c
;
2
D(1 c)
=
;
2(1 c2 D)
cD(1 c)
=
:
2(1 c2 D)
=
N
(40)
(41)
(42)
Note that, by the convexity condition of the cost function, we have 1 c2 D > 0 for all c. First,
consider the case c 0. In that case, we have N ; eN 1 ; eN 2 0, and the solutions N ; eN 1 ; eN 2
are given by the terms above. Now turn to the case c < 0 and …rst consider eN 2 . Observe that
p
D > 1 together with c < 1= D implies 1 c > 0. Hence, for c > 0, the numerator of the fraction
in equation (42) gets negative and, due to the restriction to non-negative e¤ort, the solution to
eN 2 is given by the corner solution eN 2 = 0. Accordingly, for c > 0, the nonfamily manager’s
expected-utility maximization problem becomes
max
eN 1 0
N eN 1
1 2
e
2D N 1
(43)
The …rst-order condition yields
eN 1 =
N D:
(44)
The …rm owner’s expected utility maximization problem then is
max
ND
2
ND
(45)
N
1
D
The …rst-order condition yields N = : This implies eN 1 = D
2 and E( N ) = 4 for c > 0. The
2
complete solution to the second-best contract in the case of hiring the nonfamily manager is
summarized in equations (13), (14), (15), and (16).
13
Proof of Proposition 1
Consider the case where c > 0. Then the …rm owner’s utility di¤erence between hiring a family
and a nonfamily manager becomes:
E(
F)
E(
N)
= f (c > 0; ; D) =
c2 (
The function f (c > 0; ; D) is positive when
1
=
p
1
c+
(c
2
c
1)2
>
1,
2c(1 + ) + 1 + 4
4(1 c2 )
D(1
c2 )
(46)
where
1) (c + 1) ( 4c + c2 D + 4) + c2
2 :
(47)
Proof of Proposition 2
For c < 0, the di¤erence of the …rm owner’s utility between hiring a family and a nonfamily
manager is given by:
E(
F)
E(
N)
= g(c < 0; D; ) =
(1
c)2 (1
D) + (1
4(1
Dc2 )( 2 c2 2 c2
c2 )(1 c2 D)
2c + 4 )
(48)
The …rm owner chooses the family manager when the above function is positive. This is the
case if > 2 , where
2
=
(c 1)
4
c D c2
c+
p
(c2 D
1) (c + 1) (3c2 D + c3 D
4) + 2c2 D + c3 D
2 :
(49)
Proof of Proposition 3
We use a graphical illustration for this proof and set D = 2 for expository purpose. Note that,
by the convexity condition of the cost function, we then have p12 < c < 0. The following …gure
plots the function g(D = 2; c; ) for di¤erent values of c < 0 in the aforementioned range. In
particular, c ranges from 0:1 to 0:6. Recall that 0 < < 1. The solid curve depicts the
di¤erence in utility when c = 0:1, the dashed curve is for c = 0:3, and the dotted curve
depicts the case where c = 0:6:
14
g(c,gamma)
1
-0.2
0.2
0.4
0.6
0.8
1.0
gamma
-1
-2
-3
-4
Impact of a variation in c on g (c; D; )
As c decreases from 0:1 to 0:6, the function g(c; D; ) moves downwards. This implies
that the …rm owner’s utility di¤erence E( F ) E( N ) is decreasing in the absolute value of c
for any 2 (0; 1).
References
[1] Astrachan, J. & Jaskiewicz, P. (2008). Emotional returns and emotional costs in privately
held family businesses: Advancing traditional business valuation. Family Business Review, 21(2), 139-149.
[2] Bennedsen, M., Nielsen, K. M., Pérez-González, F., & Wolfenzon, D. (2007). Inside the
family …rm: The role of families in succession decisions and performance. Quarterly
Journal of Economics, 122(2), 647-691.
[3] Berrone, P., Cruz, C., & Gómez-Mejía, L. R. (2012). Socioemotional wealth in family …rms:
Theoretical dimensions, assessment approaches, and agenda for future research. Family
Business Review, 25(3), 258-279.
[4] Bloom, N. & Van Reenen, J. (2006). Measuring and explaining management practices across
…rms and countries. Quarterly Journal of Economics, 122(4), 1351-1408.
[5] Burkart, M., Panunzi, F., & Shleifer, A. (2003). Family …rms. Journal of Finance, 58(5),
2167-2201.
[6] Chrisman, J. J., Chua, J. H., Pearson, A. W., & Barnett, T. (2012). Family involvement,
family in‡uence, and family-centered non-economic goals in small …rms. Entrepreneurship Theory and Practice, 36(2), 267–293.
[7] Chrisman, J. J., Memili, E., & Misra, K. (2013). Nonfamily managers, family …rms, and
the winner’s curse: The in‡uence of noneconomic goals and bounded rationality. Entrepreneurship Theory and Practice, 38(5), 1103-1127.
[8] Gómez-Mejía, L. R., Haynes, K. T., Núñez-Nickel, M., Jacobson, K. J. L., & MoyanoFuentes, J. (2007). Socioemotional wealth and business risks in family-controlled …rms:
Evidence from Spanish olive oil mills. Administrative Science Quarterly, 52(1), 106.
[9] Jaskiewicz, P., Uhlenbruck, K., Balkin, D. B., & Reay, T. (2013). Is nepotism good or
bad? Types of nepotism and implications for knowledge management, Family Business
Review, 26(2), 121-139.
15
[10] Kets de Vries, M. (1993). The dynamics of family controlled …rm: the good and the bad
news. Organizational Dynamics, 21(3), 59-71.
[11] Morck, R. & Yeung, B. (2003). Agency problems in large family business groups. Entrepreneurship Theory and Practice, 27(4), 367–382.
[12] Patel, P. & Cooper, D. (2014). Structural power equality between family and non-family
TMT members and the performance of family …rms. Academy of Management Journal,
57(6), 1624-1649.
[13] Salvato, C., Minichilli, A., & Piccarreta, R. (2012). Faster route to the CEO suite: Nepotism
or managerial pro…ciency? Family Business Review, 25(2), 206-224.
[14] Vandekerkhof, P., Steijvers, T., Hendriks, W., & Voordeckers, W. (in press). The e¤ect
of organizational characteristics on the appointment of nonfamily managers in private
family …rms: The moderating role of socioemotional wealth.
16