Chapter 2

Allocation of Managerial Ability
and Entrepreneurial Ability
2.1

Introduction

What does a manager do?

How much does a manger’s decisions change the fate of afirm? Is it worth paying a talented manger $1,000,000? Although everybody agrees on
the importance of a manager’s ability in a firm, traditional economics is quite silent about
the role of the manger in a firm.
This paper surveys theories and empirical studies about managerial ability. In particular, I am interested in the economic impact of the allocation pattern of managerial talent.
Through this survey I will ask following specific questions.
1. What is the diﬀerence between entrepreneurial ability and managerial ability?
2. What is the predicted allocation pattern of entrepreneurial ability and managerial
ability? Do data support these allocation patterns?
3. Does allocation of these abilities increase productivity?
4. How do the barriers to allocate these abilities into productive positions aﬀect economic3

welfare, economic growth and inequality?
5. How does IT change these allocation patterns?

2.2Managerial Ability and the Size of a Firm

What determines the optimal size of a firm? Kaldor (1934) wrote,“In order to determine, therefore, the optimum size of combination, it is necessary to assume that the supply of at least one of the factors figuring in the production function should
be fixed, in which case the ‘optimum size’ becomes determinate as a result of operation of
the law of non-proportional returns.”
If one unit of labor and one machine produces an output of N , then 2 units of laborand 2 machines must produce at least an output of 2N , since we can always establish two
identical plants. That is, a natural assumption for a production function should be constantreturns to scale or more. But if it is so, we cannot determine the optimal size of a firm.
If there is a profit of $1 with 1 unit of labor and1 machine, a firm can make more than orequal to a profit of $m with m units of labor and m machines. In order to determine theoptimal size of a firm, at least one input must be a fixed component.
Classical discussions, Kaldor (1934), Robinson (1934) and Coase (1937), reached thesame conclusion: a manager’s ability must be the fixed component of a firm and it limits
the size of the firm. This intuition is clearly formalized by Lucas (1978). In Lucas (1978),what he called “talent for managing” is a fixed factor of production. I want to call Lucas’s“talent for managing,” managerial ability. I will denote it by hm . Assuming heterogeneous
managerial ability in society, Lucas derived the distribution of firm size.
Rosen (1982) and Oi (1983) can be interpreted as a variant of Lucas (1978).

Rosen(1982) explicitly modeled hierarchy, which is implicitly inferred in the Lucas model, andexplains an observable relationship between firm size and earnings. Oi (1983) divided anentrepreneur’s task into two parts according to Kaldor (1934): coordination and supervision.
Since time spent doing a supervisory task is proportional to the number of workers employed,4in order to reduce the time for a supervisory task, an entrepreneur must try to substitutemachines for workers.

Oi (1983) claimed that this explains why a large firm has more

capital/worker. These span of control models have several common assumptions:
1. There exists a exogenous distribution of managerial ability, hm .
2. The production function F is increasing in hm and exhibits decreasing returns to0scale in inputs x, that is, F (h0m , x) ≥ F (hm , x) for any hm ≥ hm , and F (hm , λx) ≤λF (hm , x) for any λ ∈ R.
3. Managerial ability hm is complementary to every input.
Assumptions 1 and 2 provide the heterogeneity of firm size in an industry. If assumption
1 is violated, it is optimal to distribute the same amount of resources to each firm. Hence,
every firm must be of identical size. If Assumption 2 is violated, it is optimal to distributeall resources to the most talented manager.
Assumption 3 is a simple description of the hierarchy in a firm.

Since a manager ispositioned at the top of the hierarchy, his decisions aﬀect all inputs. Hence a market assigns
the most talented person to a large firm by paying an extremely high wage for his talent.
A large firm has an incentive to pay such a high wage, since the benefits from additional
talent are higher than cost. This is the nature of complementarity.
These observations are consistent with the following stylized facts, which are summarized
by Rosen (1982).
1. The distribution of firms by size within an industry is skewed to the right.

Therelative distribution of firm size exhibits a remarkable degree of stability over time.
2. The distribution of earnings, both within and across firms, is also quite stable andhighly skewed. In fact, firm size and earnings distributions have similar functional
forms and exhibit similar general appearances.
3. The earnings of top executive oﬃcers of large firms are enormous in magnitude and are
positively correlated with firm size. The statistical relation between top executive pay
5and sales is log linear and the elasticity is approximately .03 irrespective of industry
and time period.
4. Earnings within firms are closely associated with rank, that is, compensation tends
to rise with positions of greater authority and control within the organization.
These observations are repeatedly mentioned by researchers. Murphy (1998) surveyed
the literature on CEO compensation. He notes a remarkable stable relation between thescale of firms and CEO compensation over time, across industries and across countries.

2.3

Entrepreneurial Ability and Managerial Ability

Diﬀerent strands of literature emphasize diﬀerent aspects of manager’s ability. Based onrich empirical studies, Schultz (1975, 1980) emphasized that education raises the ability“to interpret new information and to decide to reallocate their resources to take advantageof new and better opportunities”1 He calls it entrepreneurial ability. He claims that thedemand for entrepreneurial ability is a function of disequilibria.
His point is consistent with several pieces of empirical evidence: a firm environmentthat changes demands that the manager be more educated.

Welch (1970) found that

1) the rate of flow of new inputs increases the marginal productivity of education in the
agricultural sector and 2) the availability of information about new inputs decreases themarginal productivity of education in the agricultural sector.

Similar evidence was also

observed in the manufacturing sector. Bartel and Lichtenberg (1987) found that the relative
demand for educated workers declines as the age of plant and particularly of equipment
increases, especially in R&D intensive industries.
There is other evidence that implies the importance of entrepreneurial ability. Ree andShah (1986) showed that education increases the probability of self-employment. Bates(1990) showed that highly educated entrepreneurs are most likely to survive. In the CEO
compensation literature, Smith and Watts (1992) and Gaver and Gaver (1993) found that1

Schultz (1980).

6

growth firms pay significantly higher levels of cash compensation to their executives andhave a significantly higher incidence of stock option plans than non-growth firms.
Although there is plenty of evidence that emphasizes the importance of entrepreneurial
ability, it is rare to find a model of it2 . In fact, what is the main diﬀerence between
managerial ability and entrepreneurial ability?

The distinction between entrepreneurial

ability and managerial ability may have a clear connection with the ”allocative eﬀect” andthe “worker eﬀect” of education discussed in Welch (1970).
“It seems plausible that the productive value of education has its roots in two distinct
phenomena. Increasing education simply may permit a worker to accomplish more withthe resources at hand. This ’worker eﬀect’ is the marginal product of education as marginal
product is normally defined, that is, holding other factor quantities constant. On the other
hand, increased education may enhance a worker’s ability to acquire and decode information
about costs and productive characteristics of other inputs. As such, a change in education
results in a change in other inputs including, perhaps, the use of some ’new’ factors that
otherwise would not be used. The return to education is therefore considered as consistingof two eﬀects: a ’worker eﬀect,’ and an ’allocative eﬀect’.”Formally we want to distinguish entrepreneurial ability, he , and managerial ability, hm ,as follows:
V (hm , he ) =

XX
s

z

[F (z, hm , l (s; he , hm )) − wl (s; he , hm )] q (s|z; he ) p (z)where l (s; he , hm ) = arg maxx∈Xγ (z|s; he ) =Xz[F (z, hm , l) − wl] γ (z|s; he )q (s|z; he ) p (z)z q (s|z; he ) p (z)Pwhere z is a random shock, s is a signal, which the entrepreneur can observe, w is the vectorof input price, l is the vector of input, F (z, hm , l) is the production function, p (z) is theprobability of realization of z and q (s|z; he ) is the likelihood function of a signal s given z.
Hence γ (z|s; he ) is a simple posterior probability given s, and l (s; he , hm ) is a manager’s
2

One exception is Holmes and Schmitz (1990). They empasized the division of labor between a manager

and an entrepreneur.

7

best response given a signal s.
I simply assume that V (hm , he ) is an increasing function of hm and he . This meansthat managerial ability is the ability to increase the productivity of the production function;
entrepreneurial ability is the ability to select an accurate likelihood function to predict
profitability z. Hence entrepreneurial ability allows a manager to allocate resources towards
more profitable uses.
Notice that the essence of managerial ability in Lucas (1978) can be captured in hm
when we assume that F exhibits decreasing returns to scale in l: hm limits a firm’s size.
On the other hand, he cannot limit a firm’s size.

Although we can assume that he is a

fixed component of a firm, it has nothing to do with the shape of the production function.

2.4

Accurate information, Risk and Flexibility

If entrepreneurial ability can be formalized as the ability to know what is accurate information about unknown parameters, the literatures on stochastic optimal decision problems
may give us some hint about how to investigate the property of entrepreneurial ability.
According to the Blackwell theorem (1953), for any function F and density p (z),V (Am , Ae ) ≥ V (Am , A0e ) if and only if there exists φ (s0 |s) such that¡q s0 |z; A0e
X
s0

¢

¡ 0 ¢

φ s |s

=

X
s

¡

¢

φ s0 |s q (s|z; Ae ) , ∀s0 , z= 1, ∀s

Several economists have used this condition to analyze the demand for information. Oneof the first applications was Kihlstrom (1974, 1975). He showed that the demand for information is negatively correlated with the price of information.
Although the Blackwell theorem is powerful enough to apply to any production function,in the specific context, a more tractable measure is attractive. Nelson (1961) provided justsuch a measure. He defined a measure of accurate information as follows:
H (he ) = 1 −RRR(z − zγ (z|s; he ) dz)2 q (s|z; he ) p (z) dsdz
RR(z − zp (z) dz)2 p (z) dz
8Now H (he ) is an increasing function of he .
Nelson (1961) showed that the accuracy of information is complementary to risk andflexibility.

This indicates that the allocation pattern of entrepreneurial ability might bediﬀerent than that of managerial ability.

I will actually derive the diﬀerent allocation

pattern of entrepreneurial ability in the next chapter.
But here let me ask two diﬀerent questions: how robust is this complementarity?

Isthe data consistent with the complementarity assumption?

Entrepreneurial ability and Risk:Risk demands accuracy of information. If we agree
that a new environment creates a huge risk, as I showed in the previous section, we can findseveral pieces of empirical evidence that support this hypothesis. But, in fact, theoretically
it is not so obvious. Gould (1974) showed that it is not generally true that risk increases
the value of information.

So any analysis must rely on a particular functional form.

Kihlstrom (1974) showed that risk increases the demand for information that is distributed
normally when there agents have CES utility functions. Bandit problems like in Miller(1984) typically show that an agent prefers to experiment with a risky bandit first since it
provides a learning opportunity.

This is one of the questions that demands much moretheoretical work.

Entrepreneurial Ability and Flexibility: Jones and Ostroy (1984) found a very generalcondition under which a person with accurate information prefers to stay in a more flexible
position in a two period framework. Demers (1989) showed that a person who expects tohave more accurate information reduces investment if investment is irreversible. Irreversible
investment is a particular form of inflexibility.

This is quite intuitive. Even though you

have great information, if you cannot change your decision, you cannot take advantage ofthis information.

9

Although theory shows a quite robust relationship between accurate information and aflexible position, there is no empirical investigation of this claim.

This is one area thatneeds to be seriously considered.

2.5

Allocation of Manager’s Talent and a Firm’s Productivity

We showed that diﬀerent specifications of talent might yield diﬀerent types of allocation
patterns. But how important is the allocation pattern?
Little work has been done in this area, but there is some research.

Baldwin (1993)

showed that turnover increases the level of eﬃciency. Caves (1998) reviewed the literatureand concluded that productivity growth for an industry as a whole depends to an important degree on the redistribution of shares towards more productive units.

Davis andHaltimanger (1999) documented that 60% of a 10-year increase in multifactor productivity
for the average manufacturing industry can be accounted for by eﬀects that involve thereallocation of output across production sites. Thus the empirical literature supports theimportance of resource allocation for productivity improvement.
Several papers have more directly examined the eﬀect of managerial turnover on productivity. Lichtenberg and Siegel (1987) found that
1. A low level of TFP increases the likelihood of ownership change.
2. There has been improvement in the TFP of manufacturing plants after changes incorporate ownership.
They interpret their results using a matching model between a manager and plant: if amatch is bad, then TFP is low. This will attract ownership change. The new match will
most likely be better than the previous match.
On the other hand, Mcguckin and Nguyen (1995) found that10

1. Ownership change is generally associated with the transfer of plants with above average TFP.
2. Transferred plants experience improvements in productivity.
They interpret their results using a synergy theory. If both firms have some complementary input, there is incentive to merge.
Both Mcguckin and Nguyen (1995) and Lichtenberg and Siegel (1987) found a positiveeﬀect of ownership change on TFP improvement.

This implies that ownership change

allocates entrepreneurial talent to a more suitable position. But there is little consistency
in results on the productivity of firms before ownership.

Mcguckin and Nguyen (1995)

argued that the diﬀerent results come from the use of diﬀerent datasets. Actually, the Data
in Lichtenberg and Siegel (1987) covered mainly very large firms; Mcguckin and Nguyen(1995) covered all sizes of firms. In fact, Mcguckin and Nguyen (1995) found a negative
correlation between initial TFP level and the likelihood of ownership change when they
restrict their dataset to only large firms.
Although all empirical literatures focus on the eﬀect of turnover on productivity, as I
will show later, entrepreneurial ability does not necessarily increase productivity, although
this can be the case. Even if it is the case, what is the proper estimate of entrepreneurial
ability? I will answer this question in chapter 4.

2.6

Allocation of Entrepreneurial Ability and Economic
GrowthAllocation of talent may have a larger significance than an increase in productivity. Baumol(1990) investigated historical evidence and provided the following three hypotheses:
1. The social system, which determines the relative payoﬀs to diﬀerent entrepreneurial
activities, changes over time and across regions.
2. Entrepreneurial behavior changes according to variations in the social system.
11

3. The allocation of entrepreneurship between productive and unproductive activities
has a large eﬀect on the innovation of technology and dissemination of technologicaldiscoveries.
Murphy, Shleifer and Vishny (1991) provided one type of formal model that clarifies
Baumal’s hypotheses. It shows that 1) if a talented manager is misallocated to a declining
industry, this reduces the growth rate and rent seeking rewards and also prevents a talented
person from becoming an entrepreneur. They also provided evidence that countries with ahigher proportion of engineering college majors grow faster, whereas countries with a higher
proportion of students concentrating in law grow more slowly.
Hall and Jones (1999) also provided some additional evidence that supports these hypotheses: the diﬀerences in capital accumulation, productivity and therefore output per
worker are driven by diﬀerences in social infrastructure: institutions and government policies that provide incentives for individuals and firms in an economy.
Diﬀerent types of literature support a similar conclusion. Parente and Prescott (1994)
claimed that barriers to the adoption of new technology considerably hamper a country’s
growth rate. Parente and Prescott (1999) showed that monopoly may be one such barrier.

2.7

Information Technology and Entrepreneurial Ability

Information technology changes the demand for skills. Many labor economists have documented that information technology and organizational change increase the skill premium.
They might provide diﬀerent assignment structures for ability.
Krueger (1993) investigated the direct impact of computers on wages. He found 1) thatworkers who use computers on the job earn 10 to 15 percent higher wages and 2) that the
expansion in computer use in the 1980s can account for one-third to one half of the increasein the rate of return to education.

Autor, Katz and Krueger (1998) also found that therate of skill upgrading has been greater in more computer intensive industries.
Corresponding to Krueger (1993), DiNardo and Pischke (1997) argued that the corre-

12

lation between higher wages and computer use just reflects that higher wage workers use
computers on their jobs, since the wage diﬀerential is associated not only with computer use
but also with the use of pens. Doms Dunne and Troske (1997) support this view. They
found that plants that adopt a large number of new technologies employ high wage workers
both pre and post adoption.
What kind of skills does computer use demand? Bresnahan (1997) showed that
1. Computer decision making is a substitute for low- and middle-skill white collar work,
but the computer is not a substitute for a high-skilled worker’s job.
2. IT demands organizational change, so that it creates an organizational complementarity between IT and high-skilled workers (i.e., cognitive skill).
3. This organizational change demands interpersonal skills.
Murnane, Levy and Autor (1999) found that computers substitute mainly for routine
tasks.
It seems that a person who has entrepreneurial ability demands information technology more than a person who has managerial ability.

The intuition is that if you know

which information is more important, you have more incentive to collect this information.
Empirical studies also suggest that IT requires broad organizational change.

This mayalso be consistent with the idea that accurate information is complementary with flexible
organization.
Again, there is no clear evidence and theory. This is one field that needs more work.

2.8

Conclusion

In this chapter, I surveyed a number of diﬀerent literatures’ views on managerial talent. I
have shown that there is a distinct diﬀerence between managerial ability and entrepreneurial
ability. Managerial ability can be formalized as the ability to increase the productivity of13

a firm, which limits the size of the firm; entrepreneurial ability can be formalized as theability to know accurate information given unknown shocks.
I have also shown that these diﬀerent abilities might have diﬀerent allocation patterns.
The aforementioned literatures focus on managerial ability and conclude that a talented
person will be assigned to a large firm. But stochastic decision theory indicates that entrepreneurial ability should be allocated to a diﬀerent firm, like a risky firm or a flexible
firm. Clarification of this point is the main purpose of the next chapter.
I also show that the allocation of talent may have a huge impact on the productivityof firms, industries and economic growth. But I will also suggest that we need a clearer
estimate of entrepreneurial ability. This is the main purpose of chapter 4.
Finally I will claim that the IT revolution changes the demand for skills. This is oneof the next topics that needs to be investigated.

14