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SCHOOL
White Paper on Economic Analysis
THE PETER AND DILBERT PRINCIPLES
Abstract: The paper discusses how the Peter and Dilbert Principles can occur and what
are the consequences for a profit maximizing firm. A competence frontier is constructed
as a linear combination of the maximum levels of technical and social skills that are
difficult to measure and evaluate. The Peter Principle holds when managers are chosen
from workers that are in the competence frontier and the Dilbert Principle when they are
below the competence frontier. It is shown that the profitability under the Dilbert
Principle is less than under the Peter Principle. The introduction of new technologies is
one form to avoid the Dilbert Principle.
I. Introduction
Lifetime jobs are a common feature of developed economies. A great part of the work
force experiences a long-term employment relationship with their current employers
1
.
Workers in such lifetime jobs expect to make a career within the firms that are currently
employing them. Workers try to rise through the ranks in their firms via promotions. As
their employers share these expectations, firms set some rules to encourage workers to
maximize their effort and, as a result, firms' profits.
The seminal study of Doeringer and Piore (1971) have identified several key
regularities - long-term employment relationships among them - that shaped the concept
of internal labor market. An internal labor market operates with limited ports of entry for
hiring, career paths within the firm and promotions
2
. These characteristics make it
3
difficult to apply the competitive model of labor market, mainly based on the human
capital theory, to understand the workings of the internal labor market (Lazear, 1995).
Some of the outcomes of the internal labor market are explained through models of
agency theory. Using a mix of uncertainty, asymmetric information and opportunism,
these models show that some of the main features of the internal labor market can be
construed as second best solutions to contracting problems under incomplete information
(e.g., Milgrom and Roberts, 1992; Gibbons, 1998; and Lazear, 1998).
The issue tackled in this paper concerns the role of promotions to managers and its
impacts on the firm behavior
3
, assuming an internal labor market structure. Efficient
incentives aim to extract the maximum effort from workers
4
. One of the tools to achieve
it is the use of promotions to higher ranks of the firm, such as managerial positions. Some
firms try to avoid rent-seeking workers, the ones that spend so much time advertising
themselves and politicking to get promoted
5
, by imposing simple rules of promotions,
based on seniority and past performance. One shortcoming of this selection process is
that people can be placed in important jobs for which they are ill qualified. That is, the
Peter Principle
6
can be an outcome of this process, where people are promoted to their
levels of incompetence. A slightly different restatement of the Peter Principle is that
people are promoted out of jobs for which they are overqualified until they reach ones
where the job demands are suited to maximum individual ability levels. That is, they are
on the edge of their competence, so they cannot achieve anything more than what they
had already achieved.
Another serious possible outcome of the promotion system occurs when incompetents
are promoted to management. This is the Dilbert Principle. The Dilbert Principle stands
4
that "the incompetent workers are promoted directly to management without ever passing
through the temporary competence stage" (Adams, 1996, P.12). That is, the Dilbert
Principle is a sub-optimal version of the Peter Principle.
This paper develops a unified model that shows how the Peter and Dilbert Principles
can occur and explores their implication for the behavior of a profit maximizing firm.
The paper is structured as follows. Next section presents the concept of competence
frontier. The basic model appears in section three, and has two possible outcomes, the
Peter and the Dilbert Principles. Section four discusses the implications of the Peter and
Dilbert Principles, showing that the Dilbert Principle is a sub-optimal version of the Peter
Principle. Section five examines two alternative incentive schemes to avoid the Dilbert
Principle and, finally, the concluding remarks appear in section six.
II. Managerial Skills: Idiots and Jerks.
It is assumed, along the lines of Mehta (1998) and Faria (2000), that the manager
performs two basic functions: monitoring and coordination. In order to monitor, the
manager has to have some technical skills. In the same vein, to coordinate, the manager
has to have some communication or social skills. Both skills can be acquired through on-
the-job training, however, this is not vital to our analysis
7
. What is essential to assume is
that a manager is promoted out of a set of relatively homogeneous workers. That is, the
worker promoted to a managerial position comes from a set of workers with similar
qualities. It is well known that returns to the time spent on tasks are usually greater to
workers who concentrate on a narrower range of skills (e.g. Becker and Murphy, 1995).
5
In the present case we deal with two types of skills: technical and social. The workers'
productivity is bounded by a combination of these skills. Naturally the workers can differ
in the amount of these skills. Some are endowed with better technical skills, while others
have more social skills.
Figure 1 shows how technical (T), and social (H) skills bound workers productivity. It
is assumed that technical and social skills have a maximum level [ T , and H ]. The
productivity boundary is given by a linear combination of maximum skill levels and is
called the competence frontier.
[INSERT FIGURE 1 HERE]
The rationale for the existence of the competence frontier is simple. There is an
implicit trade off between the skills. A worker that spends most of his time developing
his technical skills don't have too much time to spend in acquiring and developing social
skills, and vice-versa. As managers are chosen from workers, the managerial performance
will also be limited by the maximum competence levels that managers have as workers.
The firm can choose a worker to be a manager from two different positions. The firm
can choose a worker that is on the competence frontier or below it. Imagine that the firm
chooses a worker on the competence frontier, specifically, it chooses the best technician
to be the manager. If he is the best technician, he has no social skills at all. As a manager
he is able to be an excellent monitor, but will be an appalling coordinator. If the firm
chooses the worker that has the better social skills and no technical knowledge, he will be
a good coordinator and a dreadful monitor. Finally, if the firm chooses a worker that has
some technical and social skills [and is on the competence frontier], he will not be a good
6
monitor as the first, neither a good coordinator as the latter. This first case illustrates the
Peter Principle, where the workers are on the limit of their competence.
The firm can choose a worker that is not on the maximum level of competence, that
is, he is not on the competence frontier, actually he is below it. No matter how close he is
from the competence frontier, his performance as a manager will be worse than the ones
on the frontier. This second situation illustrates the Dilbert Principle.
An interesting feature of the competence frontier as displayed above is that every
worker is an idiot
8
. In this two dimensional world, if the worker has the highest amount
of technical skills, he has no social skills. So he is an idiot from the social skill viewpoint.
Now, considering the worker with the best social skills, as he has no technical ability, he
is an idiot from the technical point of view. Looking from the viewpoint of technical
skills one can say: "Well, he can't write code, he can't design a network, and he doesn't
have any sales skill. But he has very good hair. " (Adams, 1996, p. 14). This is true
whatever the workers' skills. In the end of the day, the model precludes the manager to
have excellency in both traits. The manager, even when the Peter Principle holds, is an
idiot. In the case of the Dilbert Principle, he is more than an idiot, he is a jerk
9
.
How and why a profit maximizing firm would choose a worker that is not at the
maximum competence level? There are many possible stories that can explain this
possibility
10
.
One of them is that workers and firms do not know exactly the amount of
skills workers have. Technical skills can be a type of knowledge difficult to measure
11
.
Social skills are even more complicated to quantify. Characteristics such as honesty,
communication, sympathy, loyalty, good manners, etc, despite being easy to observe, are
hard to measure
12
.
Firms try to extract this information by observing the worker and
7
using some proxies to measure his abilities. However, the proxies can be imperfect and
drive workers to put more emphasis in the proxies than in the skills, and the selection
process can lead to a choice of a worker that is not at the frontier of competence.
III. The Model
From the discussion in the past section, the productivity of a manager (M) is an
increasing function of technical skills (T), and social skills (H):
M = M (T, H ), M
T
> 0, M
H
> 0. Managerial productivity is bounded from above by the
maximum skills one worker can have, given by the competence frontier:
M (T , H ) s ìM (T , 0) + (1÷ ì) M (0, H ), ìe [0,1] (1)
The representative firm is a monopolistic competitor in the goods market. The firm
chooses the structure of promotions (x), workers' wage (w), manager's wage (W), the
number of workers
, technical (T) and social skills (H) to maximize the discounted
profit over an infinite horizon:
·
Max }[P( y) y ÷
x . w , n , W , H ,T 0
wn ÷ c (H ) ÷ t (T ) ÷ O ( x,W )]exp (÷ rt) dt (2)
Where y is the firm's output, it depends on the managers' productivity, workers' effort
(e), and the number of workers: y = y (M (T , H ), e, n) . The term in the brackets captures
total revenue less total costs. c(H) stands for the coordination costs, t (T ) represents the
monitoring costs, and O ( x,W ) are the promotion costs, r is the interest rate.
The firm faces the following constraint, which accounts for the evolution of workers'
effort:
8
•
e = f (T , H , w ÷ w ,W ÷ w, x, e) (3)
This dynamic restriction describes how workers' effort reacts to the incentives set by the
firm. There are wage incentives, such as the wage differential between actual wage and
the reservation wage ( w ÷ w ) , and the wage differential between the prospective
manager's wage and actual wage (W ÷ w) . Promotions (x) also have a positive role in
stimulating workers' effort. Finally, as discussed above, workers effort depends on the
workers' skills. Equation (3) captures elements of an optimal contract, such as the
reservation utility and incentive compatibility constraints. One can think of it as workers'
response to wage and careers incentives.
The representative firm maximizes (2) subject to equations (1) and (3)
state equilibrium is given by the following system of equations:
13
.
The steady
O
x
=u f
x
O
W
= u f
W
÷ w
u [ f
W
÷
w
÷ f
w
÷
w
] = n
y
n
[1+ c] = w
y
M
M
H
[1+ c] + u f
H
= c
H
+ · M
H
y
M
M
T
[1+ c] + u f
T
=t
H
+ · M
T
u [r ÷ f
e
] = y
e
[1+ c]
e = e (T , H , w ÷ w , W ÷ w , x )
· [ìM (T , 0) + (1÷ ì) M (0, H )] = 0
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
9
Where u is the co-state variable associated with e, · is the lagrange multiplier
associated with the inequality (1), and c = P' ( y) y
is
the inverse of price elasticity of
P( y )
demand.
Equations (4) and (5) balance the marginal cost of setting a career structure [with
promotions and wages to managerial positions] with the value of its effects on workers'
effort. Equations (6) and (7) concern the employment of n workers with a wage w. Given
the number of workers, the firm sets the wage according to their marginal productivity
[eq. (7)]. Notice, however, that the marginal productivity of workers' is affected by
managerial productivity and workers' effort. These are characteristics of an efficiency
wage. On the other hand, given the workers' wage, the firm decides to employ a number
of workers attracted by the wages differentials structure [eq. (6)]. Equations (8) and (9)
balance the benefits of skills in terms of output and effort with their costs, taking into
account the position of these skills relative to the competence frontier. Equation (10) is
the steady state Euler equation for workers' effort, and equates the interest rate with the
marginal revenue of effort in terms of output and effort incentives. Equation (11) is the
steady state equilibrium for labor effort. It shows that in the steady state, workers' effort
is positively related to workers' skills, wage differentials and career incentives. Finally
equation (12) are the bounded controls conditions for H and T to be maximizing.
From equation (12) one can analyze the two principles: i) The Peter Principle:
when · > 0 ; and ii) the Dilbert Principle: when · = 0 .
10
IV. The Dilbert and Peter Principles
When · > 0 , the Peter Principle holds. From equations (1) and (12), we
have: M (T , H ) = ìM (T , 0) + (1÷ ì) M (0, H ) . Depending on the value of ì , the
equilibrium values of T and H can be determined. There are basically three interesting
cases: 1) When ì= 0 , we have: M (T , H ) = M (0, H ) , so T = 0 and H = H ; 2) When
ì=1, we have: M (T , H ) = M (T , 0) , so T = T and H = 0 ; and 3) When ìe (0,1) , we
have: M (T , H ) = ìM (T , 0) + (1÷ ì) M (0, H ) . A further mathematical assumption is
useful here. Let us assume that function M is a linear function such that:
M (T , H ) = M
1
(T ) + M
2
(H ) , and M
1
(0) = M
2
(0) = 0 . Therefore, this third case
yields:
M (T , H ) = M (ìT , 0) + M (0, (1÷ ì) H ) = M
1
(ìT ) + M
2
((1 ÷ ì) H ) = M (ìT , (1 ÷ ì) H ) ,
so: T = ìT and H = (1÷ ì)H .
Given the equilibrium values of T and H are determined as above, two equations
out of the system of equations (4)-(11) become redundant. The system (4)-(9) determines
simultaneously the optimal values of x, w, W, e, n, and u . The workings of this optimal
solution are very simple. When the Peter Principle holds, the firm chooses a combination
of maximum skills available from the competence frontier it wants its manager to have.
Then it sets the wage and career incentives in order to extract the workers' effort and
maximize profits.
By considering the Dilbert Principle case, that happens when · = 0 , we have,
from equations (1) and (12): M (T , H ) < ìM (T , 0) + (1÷ ì) M (0, H ) which implies,
11
M (T , H ) < M (ìT , 0) + M (0, (1÷ ì) H ) = M (ìT , (1÷ ì) H ) . An important implication
is that the optimal values of T and H are below the maximum competence
D
levels. T < ìT , and H
D
< (1 ÷ ì) H , for any value of ìe [0,1]
14
.
Furthermore, equations (8) and (9) become:
y
M
M
H
[1+ c] + u f
H
= c
H
(8')
y
M
M
T
[1+ c] + u f
T
=t
H
T (9')
The system of equations (4), (5), (6), (7), (8'), (9'), (10) and (11) determines
simultaneously the equilibrium values of x, w, W, e, H, T , n, and u . Therefore, when
the Dilbert Principle holds, firms cannot choose clearly the amount of skills of their
managers from the competence frontier. So they set the career incentives, wage
differentials and the levels of skills simultaneously, hoping for the best outcome possible.
In order to compare the effects of both Principles on firms behavior, notice that
managerial productivity and workers' effort are increasing functions of workers' skills. As
the skills under the Peter Principle are higher than under the Dilbert principle, so
managerial productivity and workers' effort are higher under the Peter Principle than
under the Dilbert Principle. Higher managerial productivity, and workers' effort imply
higher output, and other things constant, imply higher profits. In this sense, the Dilbert
Principle is in fact a sub-optimal solution relative to the Peter Principle. The problem,
then, is how to avoid the Dilbert Principle and to achieve the Peter Principle. Two
alternative incentive schemes are discussed in the next section.
12
V. Alternative designs
One can think of different ways to avoid the Dilbert Principle, here I discuss just
two alternative designs. Firstly, the firm can divide the number of workers in N teams,
with a span of control of size s . By controlling N and s the firm wants to select the skill
levels of its managers. The manager has to monitor a span of s workers and keep their
work in line with the remaining (N-1) teams by coordination. The firm assumes that T is
a function of s and H is a function of N. The objective of the firm is to identify if the
prospective manager is a worker that is in the competence frontier. However, this new
incentive devise is plagued with the old problems. Basically, the trade off between skills
remains, because there is a trade off between the number of teams and the span of
control. More workers to monitor allow less time to coordinate, and more teams to
coordinate with allow less time to monitor. For that reason, the identification of workers
as idiots or jerks remains a problem.
The second alternative design of incentives is the introduction of technological
innovations. Imagine that new technologies demand more on-the-job training from
workers. This can push the competence frontier forwards. If new technologies demand
more time for on-the-job training and a further development to acquire skills, it becomes
costly for workers that are not in the initial competence frontier. Then, initial small
differences in skills among workers can be widened through the introduction of new
technologies, making it easier to separate workers on the edge of the competence frontier
from the ones behind it.
13
VI. Concluding Remarks
The paper has discussed how the Peter and Dilbert Principles can occur and what
are the consequences for a profit maximizing firm. The departure point is the competence
frontier, which is constructed assuming that prospective managers are chosen out of a set
of relatively homogeneous workers. Workers have two different characteristics, technical
and social skills, that are difficult to measure and evaluate. The competence frontier is the
linear combination of the maximum levels of skills. It implicitly assumes that there is a
trade off between the skills. So if a worker is good in one skill he is bad in the other.
Therefore, every worker on the competence frontier is an idiot. Workers below the
competence frontier are jerks.
The Peter Principle holds when managers are chosen from workers that are on the
competence frontier. The Dilbert Principle applies to the cases in which the manager is
chosen from workers that are below the competence frontier. The Dilbert Principle is
clearly a sub-optimal version of the Peter Principle. Under the Peter Principle the best
policy followed by the firm, given that its managers are on the competence frontier, is to
set the wages and career incentives in order to extract the workers' effort and maximize
profits. Under the Dilbert Principle, the firm cannot choose clearly the amount of skills of
its managers from the competence frontier. So the firm sets the career incentives, wages
differentials and the levels of skills simultaneously, hoping for the best outcome possible.
Nevertheless, the profitability under the Dilbert Principle is less than under the Peter
Principle. The problem, then, is how to achieve the Peter Principle and to avoid the
Dilbert Principle
14
Finally two different incentive schemes to avoid the Dilbert Principle are
discussed. If the firm, by controlling the number of teams and the span of control of its
workers, aims to select and maximize the ability of its managers, it will find the same sort
of problems as before. Basically this design will not work because the trade-off between
skills are reinforced by the implicit trade-off one manager has between monitor s workers
and coordinate its team with other N-1 teams. Another alternative design examined was
the introduction of new technologies. New technologies push forward the competence
frontier and make it easy to identify and separate workers that were initially close to the
competence frontier but that are left behind after the introduction of new technologies.
15
References:
Adams, S. (1996) The Dilbert Principle, Harper, New York.
Baker, G.; M. Gibbs, and B. Holmstrom (1994) The internal economics of the firm:
Evidence from personnel data, Quarterly Journal of Economics 109, 881-919.
Becker, G. S. and K. M. Murphy (1995) The division of labor, coordination costs, and
knowledge, In R. Febrero and P.S. Schwartz (Eds.) The Essence of Becker, Hoover
Institution Press, Stanford, 608-630.
Burgess, S. and H. Rees (1997) Transient jobs and lifetime jobs: Dualism in the British
labour market, Oxford Bulletin of Economics and Statistics 59, 309-328.
Doeringer, P. and M. Piore (1971) Internal Labor Markets and Manpower Analysis,
Heath, Massachussets.
Demougin, D. and A. Siow (1994) Careers in ongoing hierarchies, American Economic
Review 84, 1261-1277.
Farber, H.S. (1995) Are lifetime jobs disappearing ? Job duration in the United States:
1973-1993, Princenton University, Industrial Relations Section, Working Paper: 341,
January.
Faria, J.R. (1998) The economics of witchcraft and the big eye effect, Kyklos 51, 537-
546.
Faria, J.R. (2000) Supervision and effort in an intertemporal efficiency wage model: The
role of the Solow condition, Economics Letters, forthcoming.
Gibbons, R. (1998) Incentives in organizations, Journal of Economic Perspectives 12,
115-132.
Goldsmith, A.H., J. R. Veum and W. Darity Jr. (1999) Motivation and labor market
outcomes, Research in Labor Economics, Forthcoming.
Gordon, D.M. (1990) Who bosses whom ? The intensity of supervision and the discipline
of labor, American Economic Review 80, 28-32.
Hall, Robert (1982) The importance of lifetime jobs in the U.S. economy, American
Economic Review 72, 716-724.
Kessler, A. S. (1998) The value of ignorance, Rand Journal of Economics 29, 339-354.
16
Landers, R.M.; J.B. Rebitzer and L.J. Taylor (1996) Rat race redux: Adverse selection in
the determination of work hours in law firms, American Economic Review 86, 329-348.
Mehta, S. R. (1998) The law of one price and a theory of the firm: A Ricardian
perspective on interindustry wages, Rand Journal of Economics 29, 137-156.
Milgrom, P. (1988) Employment contracts, influence activities and efficient organization
design, Journal of Political Economy 96, 42-60.
Milgrom, P. and J. Roberts (1992) Economics, Organization and Management, Prentice
Hall, New Jersey.
Lazear, E. P. (1995) A jobs-based analysis of labor markets, American Economic Review
85, 260-265.
Lazear, E.P. (1998) Personnel Economics for Managers, John Wiley & Sons, New York.
Prendergast, C. (1993) A theory of "yes men", American Economic Review 83, 757-770.
Ureta, M. (1992) The importance of lifetime jobs in the U.S. economy, revisited,
American Economic Review 82, 322-335.
17
FIGURE 1: The Competence Frontier
H
H
Competence Frontier = ìT + (1÷ ì)H , ìe [0,1]
T T
18
NOTES:
1
For empirical evidence, see Hall (1982), Ureta (1992) and Farber (1995) for USA , and
Burgess and Hedley (1997) for the UK.
2
See Baker, Gibbs and Holmstrom (1994) for more recent evidence on internal labor
market.
3
Gordon (1990) shows that the ratio within the firm's hierarchy of supervisors to
production-workers inputs has increased from 1960 to 1990 for the major economies in
the world.
4
See Goldsmith et al. (1999) for a study of motivation in a human capital model.
5
See Milgrom (1988).
6
See Milgrom and Roberts (1992).
7
For a general model of on-the-job training, see Demougin and Siow (1994).
8
This is in line with the general principle of Adams (1996, p. 2): "I have developed a
sophisticated theory to explain the existence of this bizarre workplace behavior: People
are idiots".
9
If the politically corrected reader find those designations offensive, I suggest them to
think of idiots as limited people and jerks as limited and ignorant people.
10
See, for example, Landers et al. (1996) and Kessler (1998).
11
If you are an economist, try to answer the following question: how can you compare
two leading economists and say that one knows more economics than the other ? You are
going to use some proxies as publications, citations, etc, but you will never be sure that
these proxies actually give you a correct answer.
12
Prendergast (1993) shows that firms may optimally eschew the use of incentive
contracts to retain workers' incentives for honesty. See Faria (1998) for an analysis of
envy on team work.
13
An important caveat should be done here. One can ask if the managers are themselves
idiots and they are in control of the firm, then why are they going to maximize profits
under such scheme ? The point here is that the higher control of the firm is safe from the
sort of problems analysed here. That is, the higher hierarchy of the firms is idiot-free. It
would be an interesting exercise to explore the implications of the Peter and Dilbert
principles when the control of the firm is on the hands of limited people. But it is left for
further research.
14
One can raise the question that what would happen in the model if ìe [a, b] , where 0
< a < b < 1. That is, if there are further constraints on the amount of skills, firms wish to
select. The qualitative results of the model are not altered by it.
doc_719770668.docx
Transport or transportation is the movement of people, animals and goods from one location to another. Modes of transport include air, rail, road, water, cable, pipeline and space.
SCHOOL
White Paper on Economic Analysis
THE PETER AND DILBERT PRINCIPLES
Abstract: The paper discusses how the Peter and Dilbert Principles can occur and what
are the consequences for a profit maximizing firm. A competence frontier is constructed
as a linear combination of the maximum levels of technical and social skills that are
difficult to measure and evaluate. The Peter Principle holds when managers are chosen
from workers that are in the competence frontier and the Dilbert Principle when they are
below the competence frontier. It is shown that the profitability under the Dilbert
Principle is less than under the Peter Principle. The introduction of new technologies is
one form to avoid the Dilbert Principle.
I. Introduction
Lifetime jobs are a common feature of developed economies. A great part of the work
force experiences a long-term employment relationship with their current employers
1
.
Workers in such lifetime jobs expect to make a career within the firms that are currently
employing them. Workers try to rise through the ranks in their firms via promotions. As
their employers share these expectations, firms set some rules to encourage workers to
maximize their effort and, as a result, firms' profits.
The seminal study of Doeringer and Piore (1971) have identified several key
regularities - long-term employment relationships among them - that shaped the concept
of internal labor market. An internal labor market operates with limited ports of entry for
hiring, career paths within the firm and promotions
2
. These characteristics make it
3
difficult to apply the competitive model of labor market, mainly based on the human
capital theory, to understand the workings of the internal labor market (Lazear, 1995).
Some of the outcomes of the internal labor market are explained through models of
agency theory. Using a mix of uncertainty, asymmetric information and opportunism,
these models show that some of the main features of the internal labor market can be
construed as second best solutions to contracting problems under incomplete information
(e.g., Milgrom and Roberts, 1992; Gibbons, 1998; and Lazear, 1998).
The issue tackled in this paper concerns the role of promotions to managers and its
impacts on the firm behavior
3
, assuming an internal labor market structure. Efficient
incentives aim to extract the maximum effort from workers
4
. One of the tools to achieve
it is the use of promotions to higher ranks of the firm, such as managerial positions. Some
firms try to avoid rent-seeking workers, the ones that spend so much time advertising
themselves and politicking to get promoted
5
, by imposing simple rules of promotions,
based on seniority and past performance. One shortcoming of this selection process is
that people can be placed in important jobs for which they are ill qualified. That is, the
Peter Principle
6
can be an outcome of this process, where people are promoted to their
levels of incompetence. A slightly different restatement of the Peter Principle is that
people are promoted out of jobs for which they are overqualified until they reach ones
where the job demands are suited to maximum individual ability levels. That is, they are
on the edge of their competence, so they cannot achieve anything more than what they
had already achieved.
Another serious possible outcome of the promotion system occurs when incompetents
are promoted to management. This is the Dilbert Principle. The Dilbert Principle stands
4
that "the incompetent workers are promoted directly to management without ever passing
through the temporary competence stage" (Adams, 1996, P.12). That is, the Dilbert
Principle is a sub-optimal version of the Peter Principle.
This paper develops a unified model that shows how the Peter and Dilbert Principles
can occur and explores their implication for the behavior of a profit maximizing firm.
The paper is structured as follows. Next section presents the concept of competence
frontier. The basic model appears in section three, and has two possible outcomes, the
Peter and the Dilbert Principles. Section four discusses the implications of the Peter and
Dilbert Principles, showing that the Dilbert Principle is a sub-optimal version of the Peter
Principle. Section five examines two alternative incentive schemes to avoid the Dilbert
Principle and, finally, the concluding remarks appear in section six.
II. Managerial Skills: Idiots and Jerks.
It is assumed, along the lines of Mehta (1998) and Faria (2000), that the manager
performs two basic functions: monitoring and coordination. In order to monitor, the
manager has to have some technical skills. In the same vein, to coordinate, the manager
has to have some communication or social skills. Both skills can be acquired through on-
the-job training, however, this is not vital to our analysis
7
. What is essential to assume is
that a manager is promoted out of a set of relatively homogeneous workers. That is, the
worker promoted to a managerial position comes from a set of workers with similar
qualities. It is well known that returns to the time spent on tasks are usually greater to
workers who concentrate on a narrower range of skills (e.g. Becker and Murphy, 1995).
5
In the present case we deal with two types of skills: technical and social. The workers'
productivity is bounded by a combination of these skills. Naturally the workers can differ
in the amount of these skills. Some are endowed with better technical skills, while others
have more social skills.
Figure 1 shows how technical (T), and social (H) skills bound workers productivity. It
is assumed that technical and social skills have a maximum level [ T , and H ]. The
productivity boundary is given by a linear combination of maximum skill levels and is
called the competence frontier.
[INSERT FIGURE 1 HERE]
The rationale for the existence of the competence frontier is simple. There is an
implicit trade off between the skills. A worker that spends most of his time developing
his technical skills don't have too much time to spend in acquiring and developing social
skills, and vice-versa. As managers are chosen from workers, the managerial performance
will also be limited by the maximum competence levels that managers have as workers.
The firm can choose a worker to be a manager from two different positions. The firm
can choose a worker that is on the competence frontier or below it. Imagine that the firm
chooses a worker on the competence frontier, specifically, it chooses the best technician
to be the manager. If he is the best technician, he has no social skills at all. As a manager
he is able to be an excellent monitor, but will be an appalling coordinator. If the firm
chooses the worker that has the better social skills and no technical knowledge, he will be
a good coordinator and a dreadful monitor. Finally, if the firm chooses a worker that has
some technical and social skills [and is on the competence frontier], he will not be a good
6
monitor as the first, neither a good coordinator as the latter. This first case illustrates the
Peter Principle, where the workers are on the limit of their competence.
The firm can choose a worker that is not on the maximum level of competence, that
is, he is not on the competence frontier, actually he is below it. No matter how close he is
from the competence frontier, his performance as a manager will be worse than the ones
on the frontier. This second situation illustrates the Dilbert Principle.
An interesting feature of the competence frontier as displayed above is that every
worker is an idiot
8
. In this two dimensional world, if the worker has the highest amount
of technical skills, he has no social skills. So he is an idiot from the social skill viewpoint.
Now, considering the worker with the best social skills, as he has no technical ability, he
is an idiot from the technical point of view. Looking from the viewpoint of technical
skills one can say: "Well, he can't write code, he can't design a network, and he doesn't
have any sales skill. But he has very good hair. " (Adams, 1996, p. 14). This is true
whatever the workers' skills. In the end of the day, the model precludes the manager to
have excellency in both traits. The manager, even when the Peter Principle holds, is an
idiot. In the case of the Dilbert Principle, he is more than an idiot, he is a jerk
9
.
How and why a profit maximizing firm would choose a worker that is not at the
maximum competence level? There are many possible stories that can explain this
possibility
10
.
One of them is that workers and firms do not know exactly the amount of
skills workers have. Technical skills can be a type of knowledge difficult to measure
11
.
Social skills are even more complicated to quantify. Characteristics such as honesty,
communication, sympathy, loyalty, good manners, etc, despite being easy to observe, are
hard to measure
12
.
Firms try to extract this information by observing the worker and
7
using some proxies to measure his abilities. However, the proxies can be imperfect and
drive workers to put more emphasis in the proxies than in the skills, and the selection
process can lead to a choice of a worker that is not at the frontier of competence.
III. The Model
From the discussion in the past section, the productivity of a manager (M) is an
increasing function of technical skills (T), and social skills (H):
M = M (T, H ), M
T
> 0, M
H
> 0. Managerial productivity is bounded from above by the
maximum skills one worker can have, given by the competence frontier:
M (T , H ) s ìM (T , 0) + (1÷ ì) M (0, H ), ìe [0,1] (1)
The representative firm is a monopolistic competitor in the goods market. The firm
chooses the structure of promotions (x), workers' wage (w), manager's wage (W), the
number of workers
, technical (T) and social skills (H) to maximize the discounted profit over an infinite horizon:
·
Max }[P( y) y ÷
x . w , n , W , H ,T 0
wn ÷ c (H ) ÷ t (T ) ÷ O ( x,W )]exp (÷ rt) dt (2)
Where y is the firm's output, it depends on the managers' productivity, workers' effort
(e), and the number of workers: y = y (M (T , H ), e, n) . The term in the brackets captures
total revenue less total costs. c(H) stands for the coordination costs, t (T ) represents the
monitoring costs, and O ( x,W ) are the promotion costs, r is the interest rate.
The firm faces the following constraint, which accounts for the evolution of workers'
effort:
8
•
e = f (T , H , w ÷ w ,W ÷ w, x, e) (3)
This dynamic restriction describes how workers' effort reacts to the incentives set by the
firm. There are wage incentives, such as the wage differential between actual wage and
the reservation wage ( w ÷ w ) , and the wage differential between the prospective
manager's wage and actual wage (W ÷ w) . Promotions (x) also have a positive role in
stimulating workers' effort. Finally, as discussed above, workers effort depends on the
workers' skills. Equation (3) captures elements of an optimal contract, such as the
reservation utility and incentive compatibility constraints. One can think of it as workers'
response to wage and careers incentives.
The representative firm maximizes (2) subject to equations (1) and (3)
state equilibrium is given by the following system of equations:
13
.
The steady
O
x
=u f
x
O
W
= u f
W
÷ w
u [ f
W
÷
w
÷ f
w
÷
w
] = n
y
n
[1+ c] = w
y
M
M
H
[1+ c] + u f
H
= c
H
+ · M
H
y
M
M
T
[1+ c] + u f
T
=t
H
+ · M
T
u [r ÷ f
e
] = y
e
[1+ c]
e = e (T , H , w ÷ w , W ÷ w , x )
· [ìM (T , 0) + (1÷ ì) M (0, H )] = 0
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
9
Where u is the co-state variable associated with e, · is the lagrange multiplier
associated with the inequality (1), and c = P' ( y) y
is
the inverse of price elasticity of
P( y )
demand.
Equations (4) and (5) balance the marginal cost of setting a career structure [with
promotions and wages to managerial positions] with the value of its effects on workers'
effort. Equations (6) and (7) concern the employment of n workers with a wage w. Given
the number of workers, the firm sets the wage according to their marginal productivity
[eq. (7)]. Notice, however, that the marginal productivity of workers' is affected by
managerial productivity and workers' effort. These are characteristics of an efficiency
wage. On the other hand, given the workers' wage, the firm decides to employ a number
of workers attracted by the wages differentials structure [eq. (6)]. Equations (8) and (9)
balance the benefits of skills in terms of output and effort with their costs, taking into
account the position of these skills relative to the competence frontier. Equation (10) is
the steady state Euler equation for workers' effort, and equates the interest rate with the
marginal revenue of effort in terms of output and effort incentives. Equation (11) is the
steady state equilibrium for labor effort. It shows that in the steady state, workers' effort
is positively related to workers' skills, wage differentials and career incentives. Finally
equation (12) are the bounded controls conditions for H and T to be maximizing.
From equation (12) one can analyze the two principles: i) The Peter Principle:
when · > 0 ; and ii) the Dilbert Principle: when · = 0 .
10
IV. The Dilbert and Peter Principles
When · > 0 , the Peter Principle holds. From equations (1) and (12), we
have: M (T , H ) = ìM (T , 0) + (1÷ ì) M (0, H ) . Depending on the value of ì , the
equilibrium values of T and H can be determined. There are basically three interesting
cases: 1) When ì= 0 , we have: M (T , H ) = M (0, H ) , so T = 0 and H = H ; 2) When
ì=1, we have: M (T , H ) = M (T , 0) , so T = T and H = 0 ; and 3) When ìe (0,1) , we
have: M (T , H ) = ìM (T , 0) + (1÷ ì) M (0, H ) . A further mathematical assumption is
useful here. Let us assume that function M is a linear function such that:
M (T , H ) = M
1
(T ) + M
2
(H ) , and M
1
(0) = M
2
(0) = 0 . Therefore, this third case
yields:
M (T , H ) = M (ìT , 0) + M (0, (1÷ ì) H ) = M
1
(ìT ) + M
2
((1 ÷ ì) H ) = M (ìT , (1 ÷ ì) H ) ,
so: T = ìT and H = (1÷ ì)H .
Given the equilibrium values of T and H are determined as above, two equations
out of the system of equations (4)-(11) become redundant. The system (4)-(9) determines
simultaneously the optimal values of x, w, W, e, n, and u . The workings of this optimal
solution are very simple. When the Peter Principle holds, the firm chooses a combination
of maximum skills available from the competence frontier it wants its manager to have.
Then it sets the wage and career incentives in order to extract the workers' effort and
maximize profits.
By considering the Dilbert Principle case, that happens when · = 0 , we have,
from equations (1) and (12): M (T , H ) < ìM (T , 0) + (1÷ ì) M (0, H ) which implies,
11
M (T , H ) < M (ìT , 0) + M (0, (1÷ ì) H ) = M (ìT , (1÷ ì) H ) . An important implication
is that the optimal values of T and H are below the maximum competence
D
levels. T < ìT , and H
D
< (1 ÷ ì) H , for any value of ìe [0,1]
14
.
Furthermore, equations (8) and (9) become:
y
M
M
H
[1+ c] + u f
H
= c
H
(8')
y
M
M
T
[1+ c] + u f
T
=t
H
T (9')
The system of equations (4), (5), (6), (7), (8'), (9'), (10) and (11) determines
simultaneously the equilibrium values of x, w, W, e, H, T , n, and u . Therefore, when
the Dilbert Principle holds, firms cannot choose clearly the amount of skills of their
managers from the competence frontier. So they set the career incentives, wage
differentials and the levels of skills simultaneously, hoping for the best outcome possible.
In order to compare the effects of both Principles on firms behavior, notice that
managerial productivity and workers' effort are increasing functions of workers' skills. As
the skills under the Peter Principle are higher than under the Dilbert principle, so
managerial productivity and workers' effort are higher under the Peter Principle than
under the Dilbert Principle. Higher managerial productivity, and workers' effort imply
higher output, and other things constant, imply higher profits. In this sense, the Dilbert
Principle is in fact a sub-optimal solution relative to the Peter Principle. The problem,
then, is how to avoid the Dilbert Principle and to achieve the Peter Principle. Two
alternative incentive schemes are discussed in the next section.
12
V. Alternative designs
One can think of different ways to avoid the Dilbert Principle, here I discuss just
two alternative designs. Firstly, the firm can divide the number of workers in N teams,
with a span of control of size s . By controlling N and s the firm wants to select the skill
levels of its managers. The manager has to monitor a span of s workers and keep their
work in line with the remaining (N-1) teams by coordination. The firm assumes that T is
a function of s and H is a function of N. The objective of the firm is to identify if the
prospective manager is a worker that is in the competence frontier. However, this new
incentive devise is plagued with the old problems. Basically, the trade off between skills
remains, because there is a trade off between the number of teams and the span of
control. More workers to monitor allow less time to coordinate, and more teams to
coordinate with allow less time to monitor. For that reason, the identification of workers
as idiots or jerks remains a problem.
The second alternative design of incentives is the introduction of technological
innovations. Imagine that new technologies demand more on-the-job training from
workers. This can push the competence frontier forwards. If new technologies demand
more time for on-the-job training and a further development to acquire skills, it becomes
costly for workers that are not in the initial competence frontier. Then, initial small
differences in skills among workers can be widened through the introduction of new
technologies, making it easier to separate workers on the edge of the competence frontier
from the ones behind it.
13
VI. Concluding Remarks
The paper has discussed how the Peter and Dilbert Principles can occur and what
are the consequences for a profit maximizing firm. The departure point is the competence
frontier, which is constructed assuming that prospective managers are chosen out of a set
of relatively homogeneous workers. Workers have two different characteristics, technical
and social skills, that are difficult to measure and evaluate. The competence frontier is the
linear combination of the maximum levels of skills. It implicitly assumes that there is a
trade off between the skills. So if a worker is good in one skill he is bad in the other.
Therefore, every worker on the competence frontier is an idiot. Workers below the
competence frontier are jerks.
The Peter Principle holds when managers are chosen from workers that are on the
competence frontier. The Dilbert Principle applies to the cases in which the manager is
chosen from workers that are below the competence frontier. The Dilbert Principle is
clearly a sub-optimal version of the Peter Principle. Under the Peter Principle the best
policy followed by the firm, given that its managers are on the competence frontier, is to
set the wages and career incentives in order to extract the workers' effort and maximize
profits. Under the Dilbert Principle, the firm cannot choose clearly the amount of skills of
its managers from the competence frontier. So the firm sets the career incentives, wages
differentials and the levels of skills simultaneously, hoping for the best outcome possible.
Nevertheless, the profitability under the Dilbert Principle is less than under the Peter
Principle. The problem, then, is how to achieve the Peter Principle and to avoid the
Dilbert Principle
14
Finally two different incentive schemes to avoid the Dilbert Principle are
discussed. If the firm, by controlling the number of teams and the span of control of its
workers, aims to select and maximize the ability of its managers, it will find the same sort
of problems as before. Basically this design will not work because the trade-off between
skills are reinforced by the implicit trade-off one manager has between monitor s workers
and coordinate its team with other N-1 teams. Another alternative design examined was
the introduction of new technologies. New technologies push forward the competence
frontier and make it easy to identify and separate workers that were initially close to the
competence frontier but that are left behind after the introduction of new technologies.
15
References:
Adams, S. (1996) The Dilbert Principle, Harper, New York.
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Institution Press, Stanford, 608-630.
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labour market, Oxford Bulletin of Economics and Statistics 59, 309-328.
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Demougin, D. and A. Siow (1994) Careers in ongoing hierarchies, American Economic
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January.
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Faria, J.R. (2000) Supervision and effort in an intertemporal efficiency wage model: The
role of the Solow condition, Economics Letters, forthcoming.
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115-132.
Goldsmith, A.H., J. R. Veum and W. Darity Jr. (1999) Motivation and labor market
outcomes, Research in Labor Economics, Forthcoming.
Gordon, D.M. (1990) Who bosses whom ? The intensity of supervision and the discipline
of labor, American Economic Review 80, 28-32.
Hall, Robert (1982) The importance of lifetime jobs in the U.S. economy, American
Economic Review 72, 716-724.
Kessler, A. S. (1998) The value of ignorance, Rand Journal of Economics 29, 339-354.
16
Landers, R.M.; J.B. Rebitzer and L.J. Taylor (1996) Rat race redux: Adverse selection in
the determination of work hours in law firms, American Economic Review 86, 329-348.
Mehta, S. R. (1998) The law of one price and a theory of the firm: A Ricardian
perspective on interindustry wages, Rand Journal of Economics 29, 137-156.
Milgrom, P. (1988) Employment contracts, influence activities and efficient organization
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Lazear, E. P. (1995) A jobs-based analysis of labor markets, American Economic Review
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Ureta, M. (1992) The importance of lifetime jobs in the U.S. economy, revisited,
American Economic Review 82, 322-335.
17
FIGURE 1: The Competence Frontier
H
H
Competence Frontier = ìT + (1÷ ì)H , ìe [0,1]
T T
18
NOTES:
1
For empirical evidence, see Hall (1982), Ureta (1992) and Farber (1995) for USA , and
Burgess and Hedley (1997) for the UK.
2
See Baker, Gibbs and Holmstrom (1994) for more recent evidence on internal labor
market.
3
Gordon (1990) shows that the ratio within the firm's hierarchy of supervisors to
production-workers inputs has increased from 1960 to 1990 for the major economies in
the world.
4
See Goldsmith et al. (1999) for a study of motivation in a human capital model.
5
See Milgrom (1988).
6
See Milgrom and Roberts (1992).
7
For a general model of on-the-job training, see Demougin and Siow (1994).
8
This is in line with the general principle of Adams (1996, p. 2): "I have developed a
sophisticated theory to explain the existence of this bizarre workplace behavior: People
are idiots".
9
If the politically corrected reader find those designations offensive, I suggest them to
think of idiots as limited people and jerks as limited and ignorant people.
10
See, for example, Landers et al. (1996) and Kessler (1998).
11
If you are an economist, try to answer the following question: how can you compare
two leading economists and say that one knows more economics than the other ? You are
going to use some proxies as publications, citations, etc, but you will never be sure that
these proxies actually give you a correct answer.
12
Prendergast (1993) shows that firms may optimally eschew the use of incentive
contracts to retain workers' incentives for honesty. See Faria (1998) for an analysis of
envy on team work.
13
An important caveat should be done here. One can ask if the managers are themselves
idiots and they are in control of the firm, then why are they going to maximize profits
under such scheme ? The point here is that the higher control of the firm is safe from the
sort of problems analysed here. That is, the higher hierarchy of the firms is idiot-free. It
would be an interesting exercise to explore the implications of the Peter and Dilbert
principles when the control of the firm is on the hands of limited people. But it is left for
further research.
14
One can raise the question that what would happen in the model if ìe [a, b] , where 0
< a < b < 1. That is, if there are further constraints on the amount of skills, firms wish to
select. The qualitative results of the model are not altered by it.
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