Lack of skilled labour and the size and productivity of
firms in Latin America
Pedro Gomes∗
Zoë Kuehn†
This version: June 2013
Abstract
Large firms in most Latin American countries are on average smaller and less productive than large firms in the US or in other OECD countries. For a firm in order
to grow and expand its operations it must establish hierarchies and thus its growth
prospects depend on the availability of skilled workers to take the role of middle managers. We provide empirical evidence for the lack of skilled workers in Latin America
stemming from: i) few university graduates and ii) large public sectors that predominantly hire more educated individuals. We set up a model economy with private firm
formation where unskilled labor and skilled labor are complements in production. We
calibrate our model to the United States and test how much of the difference in the
size of large US and Latin American firms can be accounted for by a lack of middle
managers. We also use our model to evaluate the impact of government hiring on TFP
and firm size. Our model also has testable implications regarding the skill premium
for university graduates or the predominance of small scale entrepreneurship in Latin
America.
∗
[email protected] · Universidad Carlos III de Madrid · C/Madrid 126 · 28903 Getafe (Madrid) ·
Spain. Pedro Gomes acknowledges financial support from the Bank of Spain’s Programa de Investigación de
Excelencia.
†
[email protected] · Universidad Autónoma de Madrid· Departamento de Análisis Económico: Teorı́a
Económica e Historia Económica · Campus de Cantoblanco · 28049 Madrid · Spain.
1
1
Introduction
Latin America’s business landscape is characterized by many small, informal, and less productive establishments and few large formal firms. In addition, large formal Latin American
firms tend to be smaller than their counterparts in the US, other OECD countries, and even
other developing countries (see IDB [2010] or Lora et al [2001]). These differences in firm size
and firm productivity have negative implications for aggregate productivity in the region.
Research by the IDB [2010] suggests that “ in Latin America, reallocating resources could
increase aggregate productivity by approximately 50-60 percent (pg 77).1 ” Hence, analyzing
these differences in firm size and productivity and their possible causes is essential for being
able to make policy recommendations for improvements in aggregate productivity, aggregate
output, and ultimately citizens’ welfare.
We propose a novel mechanism that can contribute to explain firm size differences between
Latin America and the US. We argue that a lack of educated individuals, under a certain
degree of complementarity between unskilled and skilled workers, limits the growth of firms.
An important strand of literature on the theory of the firm has micro-founded managerworker complementarities, by focussing on managerial layers; for instance, Rosen [1998],
Garicano [2000], Antras, Garicano and Rossi-Hansberg [2008] and further developed by
Caliendo and Rossi-Hansberg [2012]. Fewer skilled workers reduce the availability of middle
managers. As middle managers we define a layer of management that is responsible for
monitoring workers and that reports to the upper management (i.e. general managers, department managers, branch managers). As productive firms want to expand their operations
and face a shortage of middle managers their growth is restrained.
While we do not model a firm’s managerial layers explicitly, we introduce this concept into a
typical Lucas [1978]’s span-of-control model. Agents in our model economy are endowed with
managerial ability as well as a skill type (high, low). According to their managerial ability
agents decide to become entrepreneurs or employees. Production requires capital, unskilled,
and skilled labor aggregated in a CES production function as in Krusell et al [2000]. Both
types of labor are complements in production. We assume that the entrepreneur himself can
1
Regarding manufacturing only the gains in productivity would be even more impressive as matching
the US firm size distribution for manufacturing without altering individual firms’ productivity would almost
double manufacturing productivity for many Latin American countries (pg. 6)
supply some skilled and unskilled labour to its own firm, which create some non-convexities
in the problem. It implies that some entrepreneurs will be self-employed, other will hire only
unskilled workers, while only the most productive will also hire skilled labour.
Since Lucas [1988], the idea that education matters for economic growth has received a lot of
attention. Our model proposes one possible micro channel through which education matters
for productivity and hence growth. The fact that high skilled employees are scare makes it
hard for more productive firms to grow and thus a lack of middle managers leads to a large
population of small low productive firms. The reasons for the shortage of skilled workers
stem from two facts: i) the shortage of university graduates in Latin America and ii) large
public sectors that predominantly hire more educated individuals. Our paper is related to
Hamermesh [1996] (Chapter Ten) who argues how public sector employment biased towards
more educated individuals can hinder economic development.2 However, while his argument
and most of the related existing literature rely on capital-skill complementarity for a lack of
skilled workers to lead to a reduction in overall employment via a reduction in capital, we
suggest another channel through the size distribution of firms.
The large part of the literature regarding the business landscape in Latin America studies
the formation of small and less productive units with a clear focus on informality. Empirical
works suggest that in Latin America access to credit, labor market regulations, corruption, and entry costs influence informality positively and hence firm size negatively (see
Loayza [1997], Chong and Gradstein [2007], or Johnson et al [1998] ). Models of informality
by Antunes and Cavalcanti [2007] or Amaral and Quintin [2006] also highlight the formation
of small units. A comparison of Latin America and the US or other developed countries
regarding differences in the size of large firms, on the other hand, has received less attention.
The current paper suggest to focus in particular on differences in large formal firms and
to consider a novel obstacle to firms’ growth prospects, stemming from a lack of university
graduates and the complementarity of managers and workers in production. Manager-worker
complementarity hence represent a novel factor of influence on the distribution of firm size.
Most of the literature on the determinants of firm size has focused on questions of capital
constraints as Cabral and Mata [2003] or policy aspects as Guner et al [2008]. Hsieh and
2
The author also points out that a large tourism sector or other enclave establishments could have a
similar negative effect on employment and economic development, a variant that we do not consider in this
paper.
2
Klenow [2009] consider how distortions affecting marginal products of labor and capital can
lead to a departure from the efficient firm size distribution. Our paper is also related to the
strand of literature concerned with the effect of public sector hiring on private sector outcomes. While there are some papers that consider the effects of homogeneous employment
(see for example Finn [1998] in an RBC model or Gomes [2010] in a search and matching
model), only few focus on the distinct effects across skill levels. For instance, Malley and
Motos [1996] show that for Sweden, good quality lower educated individuals from the formal
sector (workers) are selected into public employment. Domeij and Ljungqvist [2006] find
that, also for Sweden, the expansion of the public sector that hires more low-skilled workers, can explain the different evolution of the skill premium between the United States and
Sweden.
Much of our hypothesis relies on the complementarity between managers and workers. While
capital-skill complementarity has received great attention in the literature, from the pioneering work by Griliches [1969] to empirical tests of capital-skill complementarity (Duffy
et al [2004]) to further implications of capital-skill complementarity on inequality (Fallon
and Layard [1975] or Krusell et al [2000]), skilled-unskilled complementarities on the other
hand have been considered only marginally.3 However, the limited existing evidence strongly
supports our hypothesis. Dinopoulos et al [2011] using Mexican firm data find that production and non-production workers are gross complements. The authors obtain estimates of
the elasticity of substitution between skilled and unskilled labor that are very similar to the
ones found for the US by Krusell et al [2000] or Unel [2010]. Behar [2008] studies labor
demand elasticities in South Africa and finds skilled and unskilled labor to be complements
while semi-skilled and unskilled labor turn out to be substitutes.4 Similar to our intentions,
Nikolowa [2010] tests how the supply of skilled labor affects firm’s organizational decisions.
The remainder of this paper is organized as follows. The next section presents some empirical
evidence regarding a lack of skilled labor in Latin America due to few university graduates
as well large public sectors that predominantly hire more educated individuals. Section 3
includes our model and a preview of its explanatory power. Section presents 4 our calibration
strategy. In Section 5 we present and discuss our results and Section 6 includes our policy
3
There is also a vast literature on technology-skill complementarity, see for instance Acemoglu [1998].
Hamermesh [1996], Chapter 3 presents a non-conclusive summary of studies of substitution elasticities
between skilled and unskilled labor. As the author points out, most studies rely on household surveys rather
than establishment data, making it difficult to interpret these elasticities.
4
3
experiments. Section 7 concludes.
2
Empirical Evidence
According to Lora et al [2001] it is puzzling that in a region of abundant labor as Latin
America, large firms hire much fewer employees compared to large US firms. On the other
hand, cross-country differences in large firms’ capital stocks are less pronounced. However,
while labor in Latin America might be abundant, qualified labor might not be. As firms
grow, tasks have to be delegated to middle managers. For most individuals in order to
be able to handle managerial tasks additional qualifications obtained at higher education
institutions are essential. However, most Latin American countries have fewer university
graduates compared to the US or many other OECD countries (see Table2.1). In most Latin
American and Caribbean countries, with the exception of Peru and Panama, fewer than 14%
of the population above 25 hold a university degree while in the US, Australia, Canada, and
Japan the fraction of university graduates among those 25 and older is 20% or higher.
Figure 2.1: Share of Population age 25 and older with university completed-2010
Japan
Australia
Canada
USA
Sweden
Peru
Netherlands
Panama
Norway
United Kingdom
Mexico
Costa Rica
Germany
Chile
France
Ecuador
Nicaragua
Bolivia
El Salvador
Colombia
Uruguay
Brazil
Venezuela
Argentina
Paraguay
Guatemala
0
5
10
15
20
25
30
Data: Barro and Lee [2010]
In addition, many Latin American countries still have bigger public sectors than the US or
the average OECD country. While the average OECD country had around 15% of its work4
Table 2.1: Educational attainment and the size of public sector
Educational
Secondary of
higher
Bolivia
37.2
Brazil
21.0
Chile
36.8
Colombia
29.1
Costa Rica
28.4
Ecuador
23.3
Guatemala
9.2
Honduras
15.0
Mexico
25.0
Nicaragua
16.8
Panama
33.4
Paraguay
19.9
Peru
40.9
Dominican Republic
11.1
El Salvador
16.8
Uruguay
21.5
Venezuela
7.3
Latin American Countries 23.1
United States
56.6
Attainment
Tertiary
All
Public sector employment (% of total)
Men
Men
Women
Women
High skill Low skill High skill Low skill
5.3
11.8
24.0
3.2
36.3
3.3
3.8
14.1
23.6
6.2
38.0
10.9
8.3
8.7
10.5
3.7
19.2
4.4
8.6
9.4
17.3
2.3
23.1
5.7
9.7
16.4
30.6
6.5
49.3
6.4
7.0
9.8
21.4
3.6
25.5
2.9
1.7
6.2
22.8
3.5
28.8
2.4
2.5
8.9
23.7
3.4
36.7
4.3
8.4
14.6
27.1
7.8
44.6
7.0
6.5
20.1
40.1
13.5
57.1
14.3
12.5
21.9
25.1
12.5
40.0
13.3
4.6
4.1
25.2
1.3
26.5
0.7
13.1
12.0
18.5
3.6
22.8
2.3
2.9
14.4
20.7
9.5
32.7
10.8
5.6
12.3
27.6
8.3
33.9
2.0
6.1
54.2
50.3
51.6
51.5
64.0
3.0
16.1
22.1
7.3
34.4
15.7
6.4
15.0
25.3
8.7
35.3
10.0
26.4
15.8
5.7
11.0
20.3
7.2
$
$
$
16.4
23.6
33.5
13.7$
Notes: Educational attainment data is from Barro and Lee dataset, for the year 2000. The data of
the public sector in Latin America is taken from Panizza (2000), which is based on household surveys
for 17 Latin American and Caribbean countries that have uniform coding in their questions on human
capital investment and labor market participation. All surveys refer to the years 1996 to 1998 except for
Mexico and Nicaragua which refer to 1993 and 1994. For the Latin American countries, high skilled refer
to people with completed secondary education or higher. The data for the United States is taken from
the Current Population Survey, from January 1998. $ considers high skilled to have tertiary education
completed.
force employed by the public sector, in countries like Venezuela, Uruguay, Argentina, Costa
Rica, and Panama more than 20% of the labor force worked in the public sector. In particular
high-skilled individuals, among those many university graduates work in the public sector.
Average years of education in Latin American public sectors tend to be 3 to 6 years higher
compared to the private sector. According to a tentative measure up to 30% of aggregate
education is absorbed by the public sector in many Latin American countries.5 While this is
5
We construct our tentative measure by calculating the aggregate total years of education of the labor
force for some Latin American countries, the US, and some OECD countries. In a second step we calculate
the fraction of years of education hired by the public sector by multiplying the average years of education
of employees in the public sector with the number of public employees (see Tables A.2 and Table A.3 of
the Appendix). The measure is tentative as data is not completely comparable given fraction of labor force
participation rates for individuals of age 15 to 64 and average years of education for individuals of age 15
and older, including those of age 64 and above.
5
similar in OECD countries, it seems more perverse in Latin American countries. Given that
university graduates are scarce and many of them work in the public sector, private sector
entrepreneurs may face limitations when trying to hire qualified labor - middle managers in order to expand their operations, limiting firms’ growth prospects.
There is also some direct evidence that entrepreneurs in Latin America seem to have difficulties finding qualified personnel. Lora and Maquéz [1998] find that on average entrepreneurs
in Latin America have a more difficult time finding qualified personnel than Asian entrepreneurs. In particular, in Venezuela, Peru, Mexico, Columbia and Brazil entrepreneurs
find that it is not easy to hire qualified employees. According to the Global Competitiveness Report [2010] entrepreneurs in Peru, Bolivia, Nicaragua, Paraguay, Chile, and Panama
complain more frequently about a low educated workforce than entrepreneurs in the US. In
addition, the average skill premium for tertiary education compared to secondary education
across Latin America of 85% (IDB [2003]) was clearly higher than the college graduate wage
premium in the US of around 60% (Goldin and Katz [2007]), which can be interpreted as an
additional indicator for the scarcity of university graduates.
Figure 2.2: Share of Labor Force working in Public Sector
35%
30%
25%
20%
15%
10%
Data: Latin American countries: IDB [2011] Rest: OECD [2011]
6
Norway
Venezuela
Sweden
Uruguay
Panama
France
Costa Rica
Argentina
Peru
Paraguay
United Kingdom
Brazil (IDB)
Canada
Australia
OECD32
United States
El Salvador
Chile (IDB)
Nicaragua
Netherlands
Columbia
Guatemala
Germany
Chile (OECD)
Mexico (OECD)
Brazil (OECD)
0%
Japan
5%
3
Model
We build a model economy à la Lucas [1978]. There is a single representative household and
a government in this economy. The household is made up of a continuum of members with
different managerial abilities.6 According to their managerial abilities, household members
either become employees or entrepreneurs. There are two skill types of employees in the
economy. There is a fraction s of individuals who are skilled and (1 − s) individuals who
are unskilled. Entrepreneurs produce a homogenous good by using low skilled labor, high
skilled labor, capital and their ability as inputs. Given incomes of all household members,
the household decides jointly about consumption and savings.
Household The household is composed of a continuum of members. Its total size is
normalized to unity. The household lives forever and maximizes the infinite sum of discounted
utilities given by
∞
X
β t log(Ct ),
(3.1)
t=0
where Ct denotes total household consumption at time t and β ∈ (0, 1) is the discount factor.
Endowments Each household member has one unit of productive time that he supplies
inelastically. Household members differ in their managerial abilities (z) as well as in their
skill type. There are two types: low skilled workers (n) and high skilled workers (m). For
each individual managerial ability is distributed in Z = [0, z] with cdf F (z) and density f (z).
The household assigns occupations to its members depending on their abilities and employee
types. They can become workers, middle managers, or entrepreneurs.
Production All entrepreneurs have access to the same technology. They hire workers
and middle managers, rent capital, and produce a single output used for consumption and
investment, according to the following CES production function as in Krusell et al [2000]
(1−γ)
yi = zi
σ
γ
[µ(ni + ¯i n )σ + (1 − µ)[λkiρ + (1 − λ)(mi + ¯i m )ρ ] ρ ] σ ,
6
(3.2)
By assuming a single representative household we abstain completely from any effects of occupational
choice on the distribution of income but focus on the effects on firm set-ups.
7
where σ is the elasticity of substitution between workers and middle managers. Note that
γ ∈ (0, 1) is the span-of-control parameter. The scale of production is increasing in the
enhanced span-of-control , i.e. the entrepreneur’s ability, z. The only difference relative to
Krusell et al [2000] are the variables ¯i n and ¯i m that reflect the fact that once an entrepreneur
sets up his firms he decides to already supply some labor, both skilled and unskilled. These
decisions introduce some non-convexities into the problem.
Entrepreneurs Entrepreneurs choose the optimal numbers of workers, middle managers,
and capital in order to maximize their profits. They also choose ¯i n and ¯i m , i.e. how much
unskilled and skilled labor to supply. While entrepreneurs always choose a strictly positive
amount of capital for production, they might however decide not to hire any middle managers
or even any workers and to thus work on their own. Given a wage rate for workers (wtn ), a
pay for middle managers (wtm ), and a rental rate for capital(rtk ) the entrepreneurs’ problem
is given by
max
{ni ,mi ,ki ,¯i n }
Πi = yi − wn ni − wm mi − rk ki
(3.3)
subject to:
(1−γ)
yi = zi
σ
γ
[µ(ni + ¯i n )σ + (1 − µ)[λkiρ + (1 − λ)(mi + ¯i m )ρ ] ρ ] σ ,
mi ≥ 0
ni ≥ 0
¯i n ≥ 0
¯i m = 1 − ¯i n
Hence, there are three different cases. In the first case, where none of the non-zero constraints
is binding, the entrepreneurs hire both workers and middle managers for production. In this
case the first-order conditions of the entrepreneur’s problem are as follows:
(1−γ)γ/σ 1−σ/γ
yi
µγ(ni
wn = zi
(1−γ)γ/σ 1−σ/γ
yi
γ(1
wm = zi
(3.4)
σ
− µ)[λkiρ + (1 − λ)(mi + ¯i m )ρ ] ρ −1 (1 − λ)(mi + ¯i m )ρ−1
(1−γ)γ/σ 1−σ/γ
yi
γ(1
rk = zi
+ ¯i n )σ−1
σ
− µ)[λkiρ + (1 − λ)(mi + ¯i m )ρ ] ρ −1 λkiρ−1
8
(3.5)
(3.6)
σµ(ni + ¯i n )σ−1 = σ(1 − λ)(1 − µ)(mi + (1 − ¯i n ))σ−1 [λkiρ + (1 − λ)(mi + (1 − ¯i n ))ρ ]σ/ρ−1 (3.7)
The last first order condition implicitly defines the entrepreneur’s choice of his own relative
labor supply. His optimal decision is such that it equalizes marginal productivities of his
own unskilled and skilled labor. Combining the second and third first order conditions of
this maximization problem, the optimal skilled labor-capital ratio for entrepreneurs is given
by
1
mi + ¯i m
λ wm ρ−1
=[
] ,
k
ki
1−λ r
(3.8)
which is decreasing in the weight of capital in production λ, and in the pay for middle
managers (wtm ). Similarly, and using the above expression we can derive the optimal unskilled
labor-capital ratio
ρ
1
ni + ¯i n
λ wm ρ−1
wn λ
σ/ρ−1 σ−1
]
= [ k (1 − µ)[λ + (1 − λ)[
]
]
,
ki
r µ
1 − λ rk
(3.9)
which is decreasing in the weight of unskilled labor in production µ, and in the wage rate
for workers (wtn ).
In a second case, where it is optimal for the entrepreneur to rent capital, hire low skilled
workers but to not hire any middle managers, his problem looks as follows:
(1−γ)
max πi = ỹi −wn ni −rkk = zi
{ni ,ki }
σ
γ
[µ(ni + ¯i n )σ +(1−µ)[λkiρ +(1−λ)(¯
i m )ρ ] ρ ] σ −wn ni −rk k.
(3.10)
Substituting yi = ỹi , into the first and third first order conditions and setting mi = 0 in the
fourth condition, give the optimality conditions for this case.
There is a third case in which the entrepreneur hires capital but works by himself.
(1−γ)
max πi = ŷi − rk k = zi
{ki }
σ
γ
[µ(¯
i n )σ + (1 − µ)[λkiρ + (1 − λ)(¯
i m )ρ ] ρ ] σ − rk k.
(3.11)
Substituting yi = ŷi , into the third first order condition and setting mi = 0 and ni = 0 in
the fourth condition, gives the optimality condition for this case.7
7
We rule out the case where the entrepreneurs only hires high skilled workers and not low-skilled workers.
This is always the case under reasonable parametrization.
9
The skill premium ψ = wm /wn in this economy is defined as follows
ψ=
ki
(1 − µ)(1 − λ) (ni + ¯i n ) 1−σ
[
] [λ(
)ρ + (1 − λ)]σ/ρ−1
m
m
µ
(mi + ¯i )
(mi + ¯i )
The skill premium is thus increasing in the use of unskilled labor in production as long as
σ < 1. Under this assumption the skill premium is also decreasing in the use of skilled labor
for production as long as ρ > 0 and σ/ρ > 1 or ρ < 0 and σ > 0. For the same range of
parameter values, the skill premium is also increasing in the use of capital in production,
ki . A situation where more capital in production raises wages of skilled workers more than
wages of unskilled workers is driven by capital-skill complementarity. Hence, a necessary
conditions for choosing parameters of the production function is that σ > ρ.
The Household’s problem The household chooses sequences of consumption and savings, and the optimal occupation for each household member. Formally the household
chooses {Ct , Kt+1 , z ∗ , z ∗∗ } in order to maximize Equation 3.1 subject to
Ct + Kt+1 = rt Kt (1 − τ ) + (1 − δ)Kt + (1 − τ )[(1 − s)wn F (z ∗ ) + swm F (z ∗∗ ) +
Z z
Z z
+s
πt (z, .)f (z)dz + (1 − s)
πt (z, .)f (z)dz]
z ∗∗
z∗
and
K0 > 0.
where π are firms’ before-tax profits. The income of the household includes the capital
income, the wage income of the skilled and unskilled members and the profits of the low
and high skilled members that became entrepreneurs. All income is taxed at rate τ used to
finance the government wage bill. Although we set up the dynamic problem, the analysis is
going to be in steady-state. The solution to the household’s problem is characterized by the
following first order conditions evaluated at steady-state:
rk =
1
1
( − 1 + δ),
(1 − τ ) β
(3.12)
wn = πte (z ∗ , .),
(3.13)
wm = πte (z ∗∗ , .).
(3.14)
10
Condition (3.12) is the standard Euler equation for optimal capital accumulation evaluated
at steady-state which determines the equilibrium interest rate. Conditions (3.13) and (3.14)
are similar to Lucas’ [1978] condition for the ‘marginal’ entrepreneur. An unskilled household member with managerial ability z ∗ and a skilled household member with managerial
ability z ∗∗ are indifferent between working or setting up a firm. Wage payments of both have
to equal the profits they expects to make as entrepreneurs.
Government The government in this economy hires unskilled and skilled workers to produce the government consumption good. It collects taxes on wages, profits and capital
income. Government revenues are used to finance the wage bill of the public sector. Each
period the government has to fulfill the following constraint
ϕlg wm + (1 − ϕ)lg wn = τ [rk K + wn F (z ∗ )(1 − s) + wm F (z ∗∗ )s +
Z z
Z z
(1 − s)
π(z, .)f (z)dz + s
π(z, ; )f (z)dz],
z?
(3.15)
z ??
The government chooses the level of public sector employment lg and the fraction of skilled
workers ϕ.
Equilibrium In equilibrium, all four markets must clear, i.e. unskilled and skilled labor,
capital and goods. Denote by ni (zi , wn , wm , rk ), mi (zi , wn , wm , rk ) and ki (zi , wn , wm , rk )
demands for unskilled and skilled labor services and capital by an entrepreneur of ability zi .
Then for the unskilled labor market to clear we need the following to hold
z
Z
∗
n
N ≡ F (z )(1−s) = (1−s)
m
z
Z
k
n(z, wn , wm , rk )f (z)dz+(1−ϕ)lg .
n(z, w , w , r )f (z)dz+s
z∗
z ∗∗
(3.16)
Aggregate unskilled labor supply Nt has to equal the sum of labor demands by all entrepreneurs and the government. For the skilled labor market to clear we need
∗∗
Z
z
M ≡ F (z )s = (1 − s)
n
m
Z
k
z
m(z, w , w , r )f (z)dz + s
z∗
m(z, wn , wm , rk )f (z)dz + ϕlg .
z ∗∗
(3.17)
11
Again, aggregate skilled labor supply M has to equal the sum of labor demands by all
entrepreneurs and the government’s demand of skilled labor.
Z
z
n
K = (1 − s)
m
Z
k
z
k(z, w , w , r )f (z)dz + s
z∗
k(z, wn , wm , rk )f (z)dz.
(3.18)
z ∗∗
With y(z, wn , wm , rk ) being the supply of goods by any entrepreneur of ability z, for market
clearing in the goods market we require
Z
z
(1 − s)
n
m
k
Z
z
y(z, wn , wm , rk )f (z)dz = C + δK.
y(z, w , w , r )f (z)dz + s
z∗
(3.19)
z ∗∗
We can now define a competitive equilibrium for the model economy in steady-state. Given
a government policy {τ, lg , ϕ} and a sequence of prices for labor and capital {wn , wm , rk }, a
competitive equilibrium is a collection of cut-offs {z ∗ , z ∗∗ }∞
0 and allocations N, M, K and C.
such that:
1. {z ∗ , z ∗∗ }∞
0 solves the household’s problem;
2. interest rate is determined by the Euler equation (3.12)
3. all four markets, for goods, capital unskilled and skilled labor clear for , i.e. equations
(3.16)- (3.19) hold;
4. the tax rate τ is such that government budget constraint is fulfilled, i.e. equation (3.15)
holds.
Absent any exogenous growth, there will be a steady state.
3.1
Illustration of the effects of skill shortage
In order to illustrate the main mechanism of the model we simulate our model maintaining
wage payments for skilled and unskilled employees fixed.8 Figure 3.3 displays firms size
along different levels of entrepreneurial talent in terms of capital, labor, and profits for two
different wages for high skilled employees: low (blue line) and high (dotted green line). First,
we can look at the non-convexities of the problem.
8
We assume the following values for our parameters µ = 0.3, λ = 0.15, θ = (1 − γ) = 1,γ = 0.89;
w = 0.11; rk = 0.04; σ = 0.401; ρ = −0.495; ¯m = 0.25; ¯n = 0.125; Note that
we used a slightly different
σ γ
production function:yi = ziθ [µ(ni + ¯i n )σ + (1 − µ)[λkiρ + (1 − λ)(mi + ¯i m )ρ ] ρ ] σ .
n
12
Figure 3.3: Sizes of firms, with capital for 2 different skilled wages
Capital
Unskill labour
45
60
40
50
35
30
40
%
%
25
30
20
15
20
10
10
5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0
0.8
0
0.1
0.2
0.3
0.4
z
0.5
0.6
0.7
0.8
z
Skill labour
Optimal Profits
35
2.5
30
2
25
1.5
%
%
20
15
1
10
0.5
5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0
0.8
0
0.1
0.2
0.3
0.4
z
0.5
0.6
0.7
0.8
z
Capital−Output ratio
Skilled−Unskilled ratio
10
0.7
9
0.6
8
0.5
7
0.4
%
%
6
5
0.3
4
0.2
3
0.1
2
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0
0.8
z
0
0.1
0.2
0.3
0.4
z
13
0.5
0.6
0.7
0.8
If an entrepreneur has a productivity lower than 0.28, he will be self employed and he will
not hire anyone. If he is more productive, he will hire unskilled worker first and only if his
productivity is above 0.43 he will also hire skilled labour. As the high skilled wage increase
we observe two effects. The first effect is due to the capital-skill complementarity and it implies that a higher wage for skilled labor reduces capital per firm for firms that were already
hiring skilled workers.
In the bottom-left panel of the figure we can see how the capital-output ratio changes as
high-skilled wages increase. The second effect, and the one we want to highlight in this paper
concerns the firm distribution. Increasing the high-skilled wage, many firms now chose not to
hire any skilled workers and hence given skilled-unskilled complementarity, they also reduce
the number of low-skilled workers. Given a low skilled wage of 0.11, there will always be a
mass of self-employed who produce by only hiring capital and without hiring unskilled or
skilled employees. Entrepreneurs with higher talent start hiring unskilled workers. There
exists a second threshold in entrepreneurial talent that divides firms producing with capital
and unskilled labor and those producing with all three available input factors, skilled labor,
unskilled labor and capital. Hence, Figure 3.3 clearly illustrates the three cases described
before. In order to assess the quantitative explanatory power of our model we calibrate it to
US data and perform policy experiments altering the relative amount of skilled and unskilled
labor in the economy as well as the fraction of skilled labor hired by the government.
4
Calibration
We fix some parameters of the model a priori based on available evidence and we calibrate
the model’s remaining parameters by matching certain moments of US data. Table 4.2 displays the chosen parameter values. We fix the discount factor β to 0.96 and the depreciation
rate δ to 8%, following Kydland and Prescott [1982]. We take parameter values for σ and
ρ of 0.401 and −0.495 respectively from Krusell et al [2000]. Using 3-digit industry data,
Burnside et al [1995] estimate returns to scale in production to lie between 0.81 and 0.92.
We choose the midpoint of their values of 0.865. According to data by the OECD [2011],
around 15% of the US labor force is employed by the public sector. And public sector hiring
is clearly biased towards skilled labor. According to Gregory and Borland [1999] 40% of
public labor is skilled labor; i.e college graduates. We also set the fraction of skilled labor
14
in the population to 30%, following Autor et al [1998] who provide data for the fraction of
college graduates in the US labor force.9 Hence, almost one fourth, 22.5% of skilled labor is
employed by the public sector.
Table 4.2: Parameters
Discount Factor (γ)
Annual Depreciation Rate (δ)
Scale of Input Factors (σ)
Scale of Capital and Skilled Labor (ρ)
Span-of-Control (γ)
Fraction of Public Labor (LG )
Fraction of Skilled Labor (s)
Fraction of Skilled Labor in Public Sector (g m )
Mean Log Entrepreneurial Talent (µz )
Dispersion in Log Talent(σz )
Highest Managerial Ability Level (zmax)
Mass Highest Managerial Ability Level (f max)
Weight of Unskilled Labor in Production (µ)
Weight of Capital in Production (λ)
Tax Rate (τ )
0.96
0.08
0.401
-0.495
0.865
0.15
0.3
0.4
1.75
2.15
15.000
0.055
0.46
0.6
0.115
Even though in a general equilibrium model all parameters affect all targets, we discuss
briefly the data moments that each parameter is most likely to determine. We choose the
capital share in production, the parameter λ to target a private capital-output ratio for
a closed economy US of 1.4. We use data from the Bureau of Economic Analysis on the
equivalent of capital in our model, i.e. private fixed assets less residential structures and
divide it by GDP plus net exports. This gives us an average private-capital/closed economy
output share over 1990-2011 of 1.43. We set the weight of unskilled labor in production,µ
to 0.46 to target a skill premium of 60% (Goldin and Katz [2007]) . Between 1984 and
2006 the average wage compensation as part of output made up around 57% and corporate
profits together with proprietors’ income were equal to 16% of GDP (see Nalewaik [2010].
Finally we set the tax rate (τ ) to , to balance the budget. All tax revenues are used to
pay public employees. We also have to calibrate the parameters related to the distribution
of entrepreneurial talent. We assume that managerial ability is distributed according to a
(truncated) log-normal distribution, with mean µz and variance σz2 . As the focus of this
9
Note that this number is larger than the one by Barro and Lee [2010] displayed in Figure 2.1 that refers
to share of college graduates in the population and not in the labor force.
15
paper is on the size and productivity of large firms, we follow Guner et al [2008] and impose
that this distribution only accounts for a mass of (1 − fm ax). To account for the remainder
of the distribution of establishments, we choose a top value for managerial ability, zmax and
its corresponding fraction, f max. We target a fraction of entrepreneurs of 9.80% following
Fairlie [2004] who explicitly includes the group of the incorporated self-employed into the
calculations using data from the US Micro-Census. According to data from the US Census
Bureau [2007], in 2007 around 74% of all establishments did not have any employees, so
called non-employers. The same data source provides information on additional business
statistics that we use for calibration. Establishments with more than 100 employees make
up 5.4% of all establishments. We set parameters, µz , σz2 , zmax, and f max to 1.75, 2.15,
15.000 and 0.0055 in order to match these targets.
5
Results
Our model matches the data fairly well. Table 5.4 displays calibration targets next to model
values. Our model matches fairly well the skill premium and the fraction of profits in GDP.
We somewhat underestimate the fraction of non-employers as well as the biggest firms and
the private capital to closed economy GDP ratio.
Table 5.3: Calibration Targets and Model Values
Fraction of Entrepreneurs
Establishment share of self-employed (no employees)
Establishment share of large firms (> 100 employees)
Capital-output ratio
Profits to GDP
Skill Premium
Government’s Budget
Data
9.80%
74%
5.37%
1.43
16%
60%
0
Model
12.5%
69%
4.40%
1.36
17%
63%
0.56%
However, in order to judge the predictive power of our model, we need to consider moments
not targeted. Table ?? displays some of these moments from the data next to the ones produced by our model. The economy’s wage bill is in line with data on employee compensation
over GDP in the US by the Buerau of Economic Analysis. Average Firm Size according to
the US Census Bureau [2007] was 4.2 (when considering establishments and 4.4 considering
16
firms). In our model this number is a little higher: 5.8. Regarding establishments that hire
workers, average establishment (firm) size was 15.9 (20.4) in the data, while in our model it is
18.6. This mismatch is explained for the missing middle in the model’s firm size distribution.
Wile in the data 4.61% of firms hire between 10 and 99 employees, in the model only 0.27%
of firms do so. On the other hand, there are more micro firms in the model than in the data;
24.5% versus 16%.
Table 5.4: Un-targeted Moments
Establishment share of micro firms (> 0 − 9 employees)
Establishment share of small firms (10 − 99 employees)
Employment share of large firms (> 100 employees)
Employee Compensation to GDP
Average Establishment Size Employers
Average Establishment Size Total
6
Data
16%
4.61%
64.96%
57%
15.9
4.2
Model
24.5%
0.27%
94.9%
65%
18.6
5.8
Policy Experiments
We run three different policy experiments. The first experiment increase public employment,
the second raises the fraction of public high-skilled employment and the last experiment
considers a situation with skilled workers, i.e. fewer graduates. Table 6.5 displays the
moments model’s for each experiment next to moments from the Benchmark model. The first
experiment consists of enlarging the public sector to 25% of the work force, while maintaining
the share of public sector employees constant at 40%. Increasing public employment by 10
percentage points leads to a large government deficit. Given that the public sector hires
high skilled more than proportionally to their representation in the economy, the increase in
public employment leads to an increase in the skill premium. Firms thus higher fewer skilled
employees and they have to operate on an overall smaller scale. Average firm size is lower
compared to the Benchmark case and there are slightly more micro firms and fewer small
firms. Hence, the capital output ratio and profits relative to GDP both fall. The increased
skill premium on the other hand leads to a rise in employee compensation to GDP.
Our second experiment considers maintaining public sector employment at 15% but increas17
Table 6.5: Three Policy Experiments
Entrepreneurs
Share of self-employed
Micro firms (> 0 − 9 employees)
Small firms (10 − 99 employees)
Large firms (> 100 employees)
Employment large firms
Capital-output ratio
Wage Bill to GDP
Profits to GDP
Skill Premium
Establishment Size (Employers)
Establishment Size (Total)
Government’s Budget
Benchmark
12.5%
69%
24.5%
0.27%
4.40%
94.9%
1.36
65%
17%
63%
18.6
5.8
0.56%
Larger
Public Sector
LG = 0.25
12.5%
69%
26.3%
0.21%
4.41%
94.8%
1.30
67%
16%
70%
16.2
5.0
42.19%
More public
skilled jobs
g m = 0.6
12.5%
54%
41.1%
0.27% 3.7%
4.41% 0
94.1%
1.27
66%
17%
84%
12.7
5.8
12.61%
Fewer
Graduates
s = 0.1
15.5%
0
96.3%
0
1.08
65%
20%
388%
4.5
4.5
43.72%
ing the share of skilled labor in public employment to 60%. Again the government’s budget
deficit rises, as high skilled public employees are paid higher wages. This has caused the
increase of 20 percentage points in the skill premium relative to the Benchmark economy.
As wages of unskilled are relatively lower, fewer firms operate without any employees and
there are more small firms. Hence, overall firms size remains the same while employer firms
are smaller than in the Benchmark economy. Some of these firms have substituted capital
with unskilled labor, leading to a lower capital output ratio. On the upper end of the firm
size distribution nothing changes.
Our last experiments consider a situation in which skilled labor is more scarce. Instead of
30%, we consider that only 10% of the population is skilled. This extreme reduction in the
number of skilled workers raises the skill premium more than five fold. Given a fixed number
of skilled public sector workers, this increase leads to a large budget deficit. Low wages of
unskilled workers make running a business without employees unprofitable. All firms higher
some workers. However, on average firms are smaller than before as the firm size distribution
is now limited to micro and small firms. There are no large firms hiring 100 employees or
more. Too few skilled workers and their high wage premium make it too costly to run large
firms that require more managers. More individuals decide to set up a firm given hat as low
skilled their alternative implies a low wage, this is why he ratio of profits to GDP increases
18
relative to the Benchmark model. On average smaller firms operate with less capital, and
hence the capital output ratio falls.
7
Conclusion
Alternative explanations have been proposed to explain why Latin America’s business landscape is characterized by many small, informal, and less productive establishments and few
large formal firms. We present a novel mechanism that combines two factors: i) few university graduates and ii) large public sectors that predominantly hire more educated individuals.
In our model economy with private firm formation unskilled labor and skilled labor are complements in production. Calibrating our model to the United States, we then run three
experiments that increase public employment, increases the fraction of public high-skilled
employment and reduce the number of graduates. We find that each leads to increases in the
skill premium. In particular, fewer graduates lead to smaller average firm size, lower capital
output ratios, and a lack of large firms.
We thus show that public policies may also be unintentionally affecting firm size. Our model
allows us to measure effects of public sector hiring that go beyond the ones already pointed
out by the literature, like queuing. Further empirical studies regarding complementarities
between skilled and unskilled labor are needed to advance in this field.
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A
Appendix
23
Table A.1:
Countries
Years of education
Public Sector
Private sector
Argentina
13.1
10.6
Bolivia
14.6
9.5
Brazil
11.6
8.5
Chile
13.5
11.2
Colombia
15.3
9.0
Costa Rica
13.2
9.3
El Salvador
13.7
8.4
Honduras
12.1
7.1
Panama
13.8
10.8
Paraguay
13.0
8.9
Uruguay
11.7
9.1
Data from Table 1 in Mizala et al [2010]
Table A.2:
Countries
For Population 15 and older
Average Years
Population 15 and older
Share in
Total Years of Education
of Schooling
(in thousands)
Labor Force
of Labor Force
Argentina
9.3
30,538
65%
185,511,326
Bolivia
9.9
6,440
72%
45,880,385
Brazil
7.5
145,288
71%
774,405,918
Chile
10.2
13,319
57%
77,717,540
Colombia
7.7
34,853
59%
157,130,952
Costa Rica
8.7
3,463
63%
18,844,939
El Salvador
8.0
5,076
60%
24,223,551
Honduras
7.5
5,087
60%
22,816,477
Panama
9.6
2,492
65%
15,422,674
Paraguay
8.5
4,428
72%
27,151,185
Uruguay
8.6
2,737
64%
15,005,353
Data on Education by Barro and Lee [2010] and Labor Force Participation Rates from Worldbank [2011]
24
Table A.3:
Countries
For Population 15 and older
Labor Force in Public Sector
Years of Education
% of years of education
(in thousands)
in Public Sector
hired by the public sector
Argentina
4,087
53,540,397
28.9%
Brazil (IDB)
17,914
207,803,869
26.8%
Brazil (OECD)
8,792
101,991,346
13.2%
Chile (IDB)
1,084
14,630,136
18.8%
Chile (OECD)
692
9,338,847
12.0%
Colombia
2,267
34,685,838
22.1%
Costa Rica
454
5,990,185
31.8%
El Salvador
444
6,081,656
25.1%
Panama
356
4,909,666
31.8%
Paraguay
576
7,491,321
27.6%
Uruguay
375
4,392,709
29.3%
Data on Education by Barro and Lee [2010] and Labor Force Participation Rates from Worldbank [2011]
25