Are Educational Reforms Necessary Growth-Enhancing

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Are Educational Reforms Necessary Growth-Enhancing
Are Educational Reforms Necessary
Growth-Enhancing?
Weak Institutions as the Cause of Policy
Failures
Ivan Lyubimov
14th October 2012
Abstract
We study a developing economy in which the representative …rm’s production function exhibits complementarities between human capital and
the available level of technology. The …rm invests in the acquisition of new
technology, while employees decide how much human capital to acquire.
The speed of human capital accumulation positively a¤ects the growth
rate of the economy, and as a result a reform that improves the educational system can lead to faster growth. Importantly though, if property
rights are weakly enforced, …rms have limited incentives to invest in the
acquisition of new technologies. This might generate limited demand for
the human capital, making an educational reform potentially unsuccessful. If property rights are weakly protected, an educational reform results
in a choice of a higher level of education only if individuals can transfer
their human capital to a di¤erent economy, where the demand for their
skills is higher. We thus conclude that only if an improvement in the
school system is combined with a better property rights enforcement, will
an educational reform unambiguously lead to faster growth.
1
1
Introduction
A vast literature has emphasized the role of human capital as a key determinant
of long-term growth (see, for instance, Mincer, 1984, Lucas, 1988, Stokey, 1991,
Barro and Lee, 1993 and Barro, 2002). Quantitative estimates by Barro (2003)
suggest that one additional year of education for males raises the growth rate
by 1.2% per year.
At the same time, many papers indicate that the provision of educational
services in developing countries operates relatively far away from the e¢ cient
frontier (see, for instance, Hanushek, 1995, Glewwe, 1999a), even if developing
countries spend hundreds of billions dollars every year to support and improve
education (see, for instance Glewwe, 2002). This evidence is con…rmed by the
PISA1 (2009) results which indicate that the vast majority of developing countries perform below the OECD averages as far as scores in reading, mathematics
and sciences are concerned. This implies that there is a signi…cant potential for
improvement in education standards, and much attention has been dedicated in
the literature to these issues. For instance, Glewwe (2002) studies what kind of
cognitive skills are more relevant for individual income growth. The World Bank
(2001) argues that investment in education, which should result in a better educational infrastructure, properly trained teaching sta¤ and equipped classrooms
and laboratories, is a policy priority. Thus, a reform of the educational system
which is aimed at dealing with the variety of inappropriate practices impeding the transfer of knowledge to young generations and at improving education
standards has the potential to be an answer to these problems. In this paper,
we argue though that this type of reform taken in isolation does not necessarily
lead to the desired outcomes and that the results highlighted in the existing
literature are driven by a partial equilibrium focus. To capture the important
interaction between demand and supply of human capital we develop instead
a general equilibrium model, in which we show that the equilibrium level of
education can fail to adjust to the positive changes brought about by the educational reform. This can be the case when an improvement in the quality of the
education system introduced by a reform might not lead to an actual increase
in the demand for education.
1 "PISA is an international study that was launched by the OECD in 1997. It aims to
evaluate education systems worldwide every three years by assessing 15-year-olds’competencies in the key subjects: reading, mathematics and science. To date over 70 countries and
economies have participated in PISA", http://www.oecd.org/pisa/
2
Why can the demand for education be low? In the case of developing economies, the literature has highlighted the role of liquidity constraints, which
make it impossible for individuals to choose their education optimally (see Morley and Coady, 2003 or the World Bank, 2001). In this paper we show that even
if liquidity constraints are not binding, education opportunities might remain
unexploited. We argue that an individual’s demand for education depends implicitly on institutional features, like the quality of property rights protection,
the risk of expropriation, etc. When property rights are weakly protected, returns on investments are low, and …rms tend to acquire less new capital and
technologies. At the same time, since factors of production are complements,
employees prefer to invest less into human capital acquisition. If an economy
is characterized by poor protection of property rights, then higher education
standards can be demanded only if individuals have the opportunity to transfer
their human capital to another economy, where the returns on human capital
are higher. We thus argue that to be successful in bringing about faster growth,
an educational reform should be accompanied by an institutional reform, which
improves the quality of property rights protection.
Our paper, thus, builds on the literature emphasizing the importance of
complementarity between production factors. Following Acemoglu (1994) and
Redding (1996) we argue that the investment into one factor of production
a¤ects a decision to invest into another. Importantly, these papers though
pay limited attention to what can restrain the accumulation of complementary
factors. Our contribution lies instead in modelling the role of corruption as a
key obstacle to the investment into a complementary factor. Our paper is therefore also related to the broad literature which links corruption and the quality
of institutions to investments and growth. For instance, Mauro (1995) and Mo
(2001) provide quantitative estimates of the negative in‡uence of corruption on
growth rates. Works by Clarke (2001) and Keefer and Knack (1997), which
are closer to our paper, show that R&D expenditures increase when the rule
of law improves, and the risk of expropriation declines. Hanushek and Woessmann (2008) provide empirical evidence on the complementarity of skills and
the quality of economic institutions. However, none of these papers provide a
theoretical analysis of how bad institutions and the risk of expropriation a¤ect
human capital accumulation.
To …ll this gap we develop a model which describes how this complementar-
3
ity works. In our setting identical …rms combine technology and human capital
to produce output. Following Redding (1996), we consider a non-overlapping
generations economy where output is shared between …rms’owners and employees. When a new generation arrives, …rms produce output and invest part of
it into the acquisition of a new technology. When young, the employees decide
how to allocate their human capital stock, which they inherit from the previous
generation, between production and investment in human capital. Education
and investment in the new technology result, respectively, in a larger human
capital stock and a higher level of technology, which are used to produce output when the generation becomes old. Firms and employees share the same
information, and thus the employees can perfectly foresee how much output do
the …rms plan to invest in a new technology. When …rms invest more into a
new technology, employees also prefer to allocate a larger share of their existing
human capital to acquire more human capital, since the latter earns a higher
return when it is combined with a more productive technology. The economy
starts by imitating technologies from the leading frontier, and then converges
to a steady-state, where it substitutes imitation with innovation.
Empirical evidence suggest though that convergence did not take place in
the case of many developing countries (see, for instance, Acemoglu, 2008). In
some cases, developing economies grow at relatively low rates and end up in
non-convergence traps (see, for instance, Acemoglu at al, 2006). To incorporate
this possibility, we add imperfect institutions to the baseline model. Following
Shleifer and Vishny (1993), we introduce corruption to the economy and assume
that …rms need to share their pro…ts with bureaucrats every time …rms need
a permit.2 We show that corruption reduces …rms’ incentives to invest in a
new technology, and this a¤ects the economy’s ability to reach the steady-state.
Since production factors are complements, employees reduce their investments
into human capital in response to a slower pace of technological advancement.
We conclude that an educational reform is more likely to be successful if the
government is able to limit on corruption.
We turn then to a particular solution to the corruption problem. Since in
many developing countries corruption is pervasive, it follows that the whole
2 Alternatively, we could assume that managers steal a share of the pro…ts and that the
judiciary is too weak and corrupt to punish them. This argument has been pursued, for
instance, by Boycko, Shleifer and Vishny (1993), Boycko, Shleifer and Vishny (1994), or
Shleifer and Vishny (1997).
4
system of state authority there requires a signi…cant renovation. This implies
that a large share of state o¢ cials will be replaced if an institutional reform is
implemented.3 The corrupt bureaucracy can try to oppose this reform, which is
easier to do when the political power is allocated among independent centers of
authority.4 Granting more political power to a politician who is considered as
a proper candidate to lead the anticorruption campaign can therefore become a
popular response to this problem.5 This kind of situation occurred in some developing economies, where the government was not successful enough in pinning
corruption down and carrying out economic reforms, lost its popularity and, as
a result, failed to consolidate the democratic rule (see, for instance, Svolik,
2011). In response, voters provide a new ruler with greater power, so that the
new regime has enough authority to eradicate corruption, and this authority is
extended if the ruler meets voters’expectations. This political regime is known
as delegative democracy6 (see Hale, 2009). However, this approach su¤ers from
a moral hazard problem: instead of reducing corruption, the regime can focus
on rent-seeking and expropriation (see Acemoglu, Johnson and Robinson, 2005,
and Acemoglu and Robinson, 2006). Besley and Kudamatsu (2007) show that
the ruler’s accountability to a group of individuals on whom the leader depends
to stay in power is of key importance: on average, higher accountability and
turnover of political leadership reduces the moral hazard problem. When accountability is low, there is no stronger power which can discipline the ruling
regime, and the moral hazard problem is aggravated. In case of our model, this
results in a higher risk of expropriation which depresses investment into technology and this, in turn, reduces the incentives to accumulate human capital.
Therefore, we argue that a stronger rule does not necessarily result in better
institutions, faster technological development and human capital accumulation.
3 Mass replacement of old bureaucracy took place in a number of ex-Socialist countries.
The process of lustration, which regulates the participation of former communists, especially
informants of the communist secret police, in the successor political appointee positions or in
civil service, took place in Poland, Czech Republic and ex-GDR.
4 The judiciary, the legislature, the executives power, the federal and regional authorities
5 Not necessarily, bot quite often, people consider military or secret service sta¤ members
as the proper candidates for this role.
6 For instance, in 1999, after almost a decade of devastating corruption, Russian voters
granted their political support to Vladimir Putin and his pursuit to acquire more political
power.. In particular, they did not show any explicit doscontent when Putin was making his
major steps towards the consolidation of political power, like the abolition of the regional
elections.
5
We then show how the government can intervene di¤erently to help the economy move to the steady-state. Aghion and Gri¢ th (2008) mention that after
WWII Mexico, Peru, Brazil, South-east Asian countries, Japan and a number of
European countries were practicing restrictions on competition and favoring the
creation of domestic monopoly, which might have bene…ted them at a particular
stage of development. Thus, under particular circumstances, limited competition and entrenchment can be bene…cial for economic growth. Therefore, the
ruling regime can restrict competition and leave the problem of corruption as
it is. When competition is limited, the pro…ts of a representative …rm increase,
and the …rm’s incentives to invest into a new technology become stronger. As
a result, the steady-state is again attainable, and the economy becomes richer
in the long run. We show that a larger corruption results in larger restriction
on competition, since a …rm needs higher pro…ts to a¤ord paying higher bribes
and continue investing into new technologies at the same time, which requires
a higher level of monopolization. However, since a less competitive economy
produces a smaller output, a higher level of monopolization lowers the level of
production.7 We argue though, that the restrictions on competition can result
instead in a higher level of corruption, which implies that bureaucrats expropriate a signi…cant part of pro…ts and bene…t from monopolization at the expense
of the rest of the population.
Thus, we conclude that an educational reform which aims to expand the
supply of high-quality education can be more successful when an anticorruption
policy is also implemented. The latter is more e¤ective if it is conducted by an
accountable leadership. Alternatively, the government can restrict competition,
although this policy is costly in the short run. It results in a higher investment
level into new technologies and faster human capital accumulation only if the
government constrains the level of corruption. If the opposite situation occurs,
the economy ends up in a non-convergence trap, and it is possible for the educational reform to result in a choice of a higher level of education if individuals
can transfer their human capital to a better developed economy which results in
a larger migration, and not in an increase in the domestic human capital stock.
The remainder of the paper is organized as follows. Section 2 introduces the
7 This
part of the paper is similar to Acemoglu, Aghion and Zilibotti (2006), who consider
a growth model where the government restricts competition to let the economy avoid a nonconvergence trap. An earlier paper by Gerschenkron (1962) also emphasizes that government
intervention can be useful for the investment-based strategy.
6
baseline model. Section 3 extends the model by adding corruption. In Section 4,
possible consequences of the concentration of power for investments into human
capital are considered. Section 5, shows how the consolidation of …rms can help
the economy leave the non-convergence trap. Section 6 provides a summary.
2
The model
2.1
Production
In this section, we present our baseline growth model which builds upon Redding
(1996). Consider a non-overlapping generations economy, where a generation
lives for two periods, j = 1; 2. In period j = 1 a new generation is born,
produces output and makes investment decisions. In period j = 2 the same
generation produces output once again and dies.
Each generation is made up of M employees working for N identical …rms.
Every …rm combines technology and human capital to produce …nal output. In
1
i
each period j = 1; 2, a typical …rm i produces Yt;j
= At;j (ht;j mt )
, so that
each generation produces the following output:
Yt = N
2
X
1
At;j (ht;j mt )
(1)
j=1
where t represents a particular generation, Yt is the level of output which is
produced by generation t, At;j is the level of technology which is identical for
every …rm, ht;j is the amount of human capital per employee, and mt stands
for the number of employees in a …rm, which is also identical for every …rm, as
well as for every period j = 1; 2:8
A …rm has an owner who hires employees to produce output. The owner
provides workers with a technology, and for that he receives a share 0
of the …rm’s output
i
Yt;j
.
1
could be modeled as the result of Nash bargaining.9
Our sharing rule implies that both, the owner and the employees, behave like
stakeholders, so they are interested in having a …rm which keeps growing.
8 We
omit subscript i for all the variables, since their optimal values are identical for every
…rm
9 Workers
need a …rm to combine their human capital with technology, while the manager,
who receives the control rights from the owner, coordinates the production process. The
workers and the manager receive (1
) Ytij . We don’t discuss in this paper how the manager
j
and the workers share (1
) Yti among themselves.
7
Employees decide which …rm to join. They build expectations about each
…rm’s investment decisions, and join those …rms where they expect technological progress to be the fastest. Since all …rms behave identically, all …rms are
equally attractive for the employees, and as a result the labor force is uniformly
distributed among …rms.
Every generation inherits technology and human capital from the previous
one. When a new generation is young, it uses the following technology to produce output:
At;1 = At
where At
1;2
(2)
1;2
is the level of technology the generation t
1 reached in period
j = 2.
We assume that all young members of generation t receive the same share
of the total human capital stock Ht
generation t
1,
which is inherited from the previous
1. Thus, we implicitly assume that wealth distribution is equal
among the employees.10
Finally, there is a storage technology which pays a return r = 0 in j = 2 if
a …rm invests a particular amount in this technology in j = 1. We introduce
the storage technology in the model to capture a possibility of non-convergence
trap. A …rm invests in this asset if investing into the productive technology
provides a negative return. Thus, if the return on investments falls below 0,
the owners stop investing into a new technology, and thus the economy stays
with the same technology until the return on investment into a new technology
becomes at least 0.
2.2
Investment
At the end of the …rst period, j = 1, a …rm chooses whether to improve its
technology or to stay with the old technology. Each …rm can improve upon the
old technology in two di¤erent ways:
At;2 =
8
<
:
( t ) AL
t;1 + (1
( t ) At;1 + (1
( t )) At;1
(3)
) At;1
1 0 This assumption facilitates aggregation of the most important variables in the model.
A di¤erent assumption would complicates aggregation and the whole analysis of the model
without adding any important results.
8
The …rst line of equation (3) re‡ects the possibility of adoption from the
exogenously given leading frontier. We consider technology as a stock of knowledge, which can be extended if a …rm “buys” additional knowledge from the
leading frontier:
At;2 = At;1 + ( t ) AL
t;1
At;1
where AL
t;1 ; representing the state of the leading technology at t; 1, grows at an
exogenously given constant rate g every period,
t
invests into a new technology and 0
1,
( t)
is a share of income a …rm
0
( t ) > 0,
00
( t ) < 0,
(0) = 0.
The second line of equation (3) shows how the technology can be improved
if instead a …rm innovates. Innovation comes with a success probability
An innovation improves …rm’s technology by a factor
00
( t ) < 0,
( t)
1,
0
.
( t ) > 0,
(0) = 1.
We assume that a …rm can not adopt and innovate simultaneously. In other
words, each generation chooses whether to adopt or to innovate. This assumption implies that the level of investment into a new technology is too large to
a¤ord two di¤erent technological projects at the same time. The assumption is
also in line with Acemoglu et al (2006), who argue that adoption is more bene…cial whenever the distance to the technological frontier is su¢ ciently large.
Before the distance to frontier declined to a particular threshold, …rms prefer
to invest more into adoption, but after this …rms’ priorities change towards
innovations.
One can notice that using a share of output
t
as the only determinant of
the speed of technological progress is a strong assumption. If
t
is a very small
number, then a …rm can still improve its technology. However, a more natural
assumption is that investments into a new technology are not perfectly divisible,
since, to be completed, a project normally requires a minimal amount of input.
However, we overcome this di¢ culty by introducing a minimum share
,
such that:
( t) =
and
8
<
:
( t) > 0
( t) = 0
9
if
t
t
(4)
<
( t) =
Given this restriction on
8
<
:
t,
( t) > 1
if
( t) = 1
t
t
(5)
<
we make sure that technological progress re-
quires larger and larger amount of inputs. If …rms …nd it bene…cial to invest
of Yt;1 .
in a new technology, then every time they need to invest at least
Since Yt;1 is getting larger and larger over time because of technological proYt;1 is getting larger as well. Thus,
gress and human capital accumulation,
every subsequent improvement in technology requires more and more resources.
As for the threshold value
itself, it can characterize di¤erent features of
the economy. For instance, a high value of
can re‡ect lack of infrastructure,
adverse natural conditions, etc. We will discuss
A …rm invests
t Yt;1
later.
into technology in period j = 1, and the returns are
realized in period j = 2. The owner receives (1
j = 2. Since Ytj = At;j (ht;j mt )
1
t)
Yt;1 in j = 1 and Yt;2 in
, j = 1; 2, the owner’s payo¤ can be written
as:
Wo = (1
t)
Employees receive instead (1
We = (1
1
At;1 (ht;1 mt )
1
+ At;2 (ht;2 mt )
) Yt;1 in j = 1 and (1
) At;1 (ht;1 mt )
1
+ (1
(6)
) Yt;2 in j = 2:
) At;2 (ht;2 mt )
1
(7)
Employees can invest a fraction 't of their human capital endowment to
augment their human capital stock. For simplicity, we assume that human
capital is created according to a one-to-one technology, so in period j = 2
an employee gets (1 + 't ) ht;1 if she invests 't ht;1 in j = 1:11 Allowing for
investment into human capital by the employees, equation (7) becomes:
We = (1
) At;1 (ht;1 (1
1
't ) mt )
+ (1
1
) At;2 (ht;1 (1 + 't ) mt )
(8)
At the beginning of period j = 1, …rms and employees decide how much
to invest. Di¤erentiating (8) with respect to 't gives the following …rst order
1 1 A di¤erent assumption would cost us algebraic and geometric convenience, including explicit algebraic solutions and their geometric counterparts, without producing any tangible
bene…ts and additional insights.
10
condition:
1 + 't
At;2
=
1 't
At;1
(9)
or
't =
At;2 At;1
At;2 + At;1
(10)
The right-hand side of equation (10) is obviously less than one and becomes
smaller as At;2 gets closer to At;1 :12 Similarly, the fraction of human capital 't
is higher the larger is At;2 . In the case of adoption, as we will see shortly, At;2
is larger the further away the local technology is from the leading frontier.
If the …rm innovates, we can derive from (10) that 't =
We will see shortly that if the …rm innovates,
that 't is a constant as well. Since
t
At;2 At;1
At;2 +At;1
=
i(
i(
(
(
t)
t)
1)
1)+2 .
is a constant, which implies
and 't are both time invariant, the
t
economy reaches the steady-state immediately when …rms start to innovate.
The owner maximizes instead (6), choosing the optimal level of adoption or
innovation. The corresponding …rst order conditions are given by:
0
(
t)
0
1
=
(
(11)
AL
t;1
At;1
t)
=
1
1
(12)
i
See Appendix I for the detailed derivation of (9), (11) and (12). Given
that a …rm can improve its technology in two ways, it needs to make a choice
between adoption and innovation? It is easy to show that when the distance
to the frontier is large enough, a …rm chooses to invest in adoption. As soon
as this distance reaches a threshold level, a …rm …nds it more bene…cial to
innovate.13 Alternatively, if innovations provide a return that is too low, a …rm
keeps adopting technologies forever. We focus on the former case in this paper,
which implies that in our model the steady-state corresponds to the innovation
stage. This assumption is in line with the literature on technological progress
and productivity growth (see, for instance Acemoglu et al, 2006). At the earlier
12 '
A
+A
2A
2A
t;1
t;1
= t;2A t;1
= 1 A +A
which is going to 0 as soon as At;2 is getting closer
t;2 +At;1
t;2
t;1
to At;1 , and it is approaching 1 when At;2 is signi…cantly larger than At;1 .
1 3 This thresholt exists if
is large enough, and g is small enough
t
11
stages of development an economy bene…ts more from the state of the world
technology, while at a more technologically mature stage, when the economy is
relatively close to the world technological frontier, innovations become relatively
more important.
We are now ready to formulate our …rst result.
Proposition 1 The economy converges to a unique steady-state. Furthermore, the relative distance
AL
t;1
At;1
to the leading frontier, the measure of
importance of technology for output growth , and the probability of a successful innovation
, all have a positive e¤ ect on the level of investment
into new technologies and human capital acquisition.
, the threshold share
of income, has instead a negative e¤ ect on investment.
Proof. We …rst establish uniqueness: from (11) we know that At;1 is a
function of
t 1,
and the more the previous generation invested into technology,
the higher is At;1 . From equation (11) it follows that
It also follows from (11) that
f
t
> 0 when
t 1
t 1
is a monotonically decreasing function, and
t 1
equation (11) intersects
t
=
t 1,
a¤ects
t negatively.
= 0. This implies that
t
t
=
= f (0) > 0. Then,
which represents all possible steady-state
levels of , at a single point, and thus, there is a unique steady-state .
We can now characterize this steady-state. From the denominator of the
right-hand side of equation (11) it follows that in the steady-state the technology is growing at the same rate as the leading frontier. As a result, along the
balanced growth path a …rm’s technology should also develop at rate g. Using
equation (10) we can show that in the steady-state investment into human capital is given by ' =
Since
i
and
g
2+g .
If a …rm innovates, then
t
depends on
i
and .
are both constants, the unique steady-state is reached immedi-
ately, which implies that ' also reaches the steady-state immediately.
The proof of the second part follows directly from equations (4), (5), (11) and
(12).
We can illustrate this argument with a graph. To this end, we compare the
payo¤ from investing into a new technology, and the payo¤ from the storage
technology. These two payo¤s are the same when
(1
'(
1
t ))
1
t
12
+
1 + '(
1 '(
t)
t)
=2
(13)
Figure 1. Steady-state level of investments in the economy without corruption
and expropriation.
On the Figure, the share
t
is placed along the horizontal axis. R, which
re‡ects a value of the left-hand side or the right-hand side of equation (13), is
placed along the vertical axis. The curve which we call the adoption function, corresponds to the left-hand side of equation (13), which re‡ects the
payo¤ from investing
into a newi technology. We show in Appendix I that
h
1+'( t )
1
(1 '( t ))
1
t + 1 '( ) is a monotonically increasing function of t .
t
As we know form (11), the larger is the distance to the leading frontier, which
is captured by
is larger when
AL
t;1
At;1 ,
t
distance to frontier
the larger is
t.
Since the left-hand side of equation (13)
is higher, the left-hand side of (13) is also larger when the
AL
t;1
At;1
is larger. As a result, as the distance to the leading fronh
i
1+'( t )
1
tier declines, so does (1 '( t ))
1
t + 1 '( ) . Thus, the upper-right
t
part of the adoption function re‡ects a lower stage of technological develop-
ment, when the economy if relatively far away from the leading frontier. On
the contrary, the lower-left part of it corresponds to a higher level of technology,
which is closer to the leading technological frontier. Thus, the adoption function
represents the development path. When
t
= 0, '(
t)
= 0 as well, and in this
case the left-hand side of equation (13) is equal to 2. The horizontal line which
13
re‡ects the payo¤ from the storage technology, intersects the vertical axis at
R = 2. Thus, the payo¤ from the storage technology is always below the payo¤
from investments into a new technology as long as
t
> 0. Since
the transitional path, from equation (11) it follows that
equation (12) it follows that
t
t
AL
t;1
At;1
> 1 on
is positive, and from
is also positive along the balanced growth path.
Thus the payo¤ from investment into a new technology is always larger than the
payo¤ from the storage technology. The vertical line, which re‡ects equation
(12),
represents the steady-state , which is derived from (12). It intersects with
the adoption function in the steady-state point.
Recall that the economy can fail to switch from adoption to innovation if
is too high. For instance, if …rms need to pay high costs because of poor
infrastructure, then only the most pro…table projects can be completed. Equation (11) points out that new projects are more pro…table when the economy
is far from the technological frontier. Thus, if the level of infrastructure is low
which implies a high value of , a …rm invests into a new technologies only when
the gap between the leading frontier and the level of local technology remains
su¢ ciently large. As soon as this economy reaches a threshold level of
AL
t1
At1 ,
it
neither adopts new technologies, nor it invests into human capital. The latter
result follows from equation (9), since if At;1 = At:2 , then 't = 0.
In the rest of the paper we will focus on a value for
which is su¢ ciently
low as to let …rms switch from adoption to innovation.
3
Corruption
In this section, we introduce corruption into the model by assuming that a
…rm is required to pay a share of its pro…t in order to receive a license, a
permit, etc. This assumption is built on the broad literature in corruption (see
Mauro, 1995, Shleifer and Vishny, 1993 and Reinikka and Svensson, 2005). We
consider an extreme case of corruption, where a bureaucrat avoids prosecution
for taking a part of the …rm’s pro…t away. The diverted pro…t is not invested
into a new technology. Corruption reduces the owner’s incentives to undertake
an investment, and the employees respond by reducing investment into human
capital. With smaller investments, a …rm has less chances to transit into the
14
innovation stage and is more likely to end up in a non-convergence trap.14
3.1
The model with corruption
Assume now that a part of the …rm’s pro…t can be taken away at no cost. This
stylized model describes the working of an economy with weak legal protection
of shareholders. Assume also that the pro…t can be diverted only if a …rm runs
an investment project. In other words, if a …rm does not adopt or innovate,
then pro…ts can not be taken away. A state o¢ cial can take a share 0 <
of the pro…t, and the owner receives the remaining share 1
<1
. Thus, the owner
receives the following payo¤:
Wo = (1
) (1
t)
1
At;1 (ht;1 mt )
+ (1
) At;2 (ht;2 mt )
1
(14)
To start a project, the owner needs to be sure that the project provides a
higher pay o¤ than investing in the storage technology, and this is true if and
only if the following inequality holds (see Appendix II.a for more details):
1
(1
'(
t ))
1
2
h
1
t
+
1+'(
1 '(
t)
t)
i
(15)
In Appendix II.a we show that the denominator of the right-hand side of
inequality (15) increases with
t.
case of no corruption, where
= 0. Whenever
satis…ed for relatively low values of
In the previous section, we considered the
> 0, condition (15) is not
t . Thus, in general, shareholders are less
willing to invest if corruption can occur.
The maximum feasible share of corruption is given by:
1 4 Alternatively, we can consider the case of pro…ts diversion. Managers receive rights from
the owners to run a …rm, however, their interests are often di¤erent from those of the owners.
Managers tend to divert pro…ts from shareholders in developing and transitional economies,
where owner’s rights are more weakly protected, and powerful managers are able to follow their
own interests at the expenses of those of shareholders (see, for instance Boycko, Shleifer and
Vishny (1993), Boycko, Shleifer and Vishny (1994), or Shleifer and Vishny (1997), and Black
(1998)). However, pro…t diversion is far from being uniquely a developing country feature.
Even in the richer parts of the world, pro…ts diversion and, in some cases, pro-managerial
biasedness of the courts, also constitute signi…cant problems. For instance, Enriques (2002)
concludes that Italian courts are often ine¤ective in protecting shareholders, since judges are
incompetent when it comes to business disputes and/or sometimes have good relations with
particular executives. Johnson et al (2000) describe three legal cases from Continental Europe
where expropriation was approved by courts.
15
bt = 1
(1
'(
t ))
1
h
2
1
t
+
1+'(
1 '(
Since the denominator of (16) is increasing with
with
t.
From equation (11) we know that
t
t,
t)
t)
i
(16)
bt is also increasing
is larger when the distance to
the leading technological frontier is larger.
We can conclude that bt is a positive function of the distance to frontier :
AL
t;1
At;1
bt = f
!
(17)
This is a remarkable result, since if the distance to the technological frontier can serve as a measure of development, then this result says that in less
developed countries the maximum feasible level of corruption is higher than in
more developed ones. At a lower level of development projects are relatively larger with respect to the amount of investment and returns, and thus state o¢ cials
can distort proportionally more. This result is summarized in the following:
Proposition 2 The lower is the level of technological development, the higher
is the maximum feasible level of corruption bt .
Proof. From equation (11) it follows that a larger
and from (16) it follow that a higher
t
AL
t;1
At;1
leads to a larger
t,
positively a¤ects bt .
Corruption, similarly to a high value of , can reduce the pace of technological advancement. For instance, let us assume that the corruption parameter
=
> 0. It can happen that b < , i.e. the maximum level of corruption at
which owners prefer to start a new technological project, is less than the actual
level of corruption. In that case, the owner does not start a new project. If this
occurs when the economy is on the transitional path, then the economy can fail
to reach the steady-state.
When a …rm does not start a project, from equation (9) it follows that
't = 0, so employees also do not invest in human capital. Thus, corruption
negatively a¤ects all kinds of investments in the economy.
As a result, with corruption the economy can get into a non-convergence
trap. When this is the case, a …rm does not switch from adoption to innovation,
and it the distance to the leading technological frontier stays relatively large.
16
In particular, the larger is the average rate of corruption , the higher is the
distance between technological frontier and domestic technology.
We can illustrate this idea with a picture:
Figure 2. A non-empty non-convergence set in the economy with corruption.
This picture is almost identical to Fig 1. The only di¤erence here is that
1
scales the adoption function down.
To reach this result analytically, we need to multiply the left-hand side of
equation (13) by 1
. Unlike the case of no corruption, the set of
t
for
which the storage technology provides a higher payo¤ than investing into a
new technology is non empty now. From Figure 2 we can see that there is a
set of
t
0 (represented by a bold section of the horizontal axis) for which
the horizontal line, which represents the payo¤ from the storage technology, is
located strictly above the adoption function, which represents the payo¤ from
investing into a new technology. Whenever
t
belongs to this set, which we
call the non-convergence set, a …rm prefers to invest into the storage technology
rather than investing into the new technology. Thus, if the innovation steadystate level
belongs to this set, this implies that this steady-state can not be
reached. In the example presented by Figure 2, the level of , which is de…ned
by the intersection between the vertical line and the adoption function, belongs
to this non-convergence set, which implies that this steady-state will not be
17
attained by this economy. Instead, the economy will attain the level of
which
is de…ned by the intersection of the adoption function and the horizontal line.
In fact, from equation (16) we know that a higher value of
a larger value of
t.
According to equation (11), a higher
AL
t;1
At;1 .
larger distance to the leading frontier
t
into a new technology, and
t
t
corresponds to
corresponds to a
Assume that a generation t invests
satis…es equation (16). As we know from
Proposition 1, the next generation will invest a value
t+1
which is less than
t . This is because the economy is converging to the technological frontier, and
it follows from (11) that investing
value of
is not optimal in t + 1. However, if the
t
does not decline in t+1 and stays the same as in t, then
satisfy equation (16). Given the optimal
t+1 ;
t+1
does not
which is de…ned from (11), and
the level ; the payo¤ from investing into the storage technology becomes larger
than the payo¤ from investing into a new technology, which implies that the
actual value of
t+1
will be equal to zero. The actual investment level becomes
positive again as soon as the optimal
distance to the frontier
AL
t;1
At;1
t
satis…es (16). The latter is true when the
is su¢ ciently large. From this discussion, it follows
that the economy does not converge to the technological frontier, which implies
that on average the level of technology is growing at rate g. From equation
(10) it follows that on average the level of investment in human capital is also
constant at a level ' =
g
2+g .
Whenever
t+1
= 0, '(0) also equals to zero,
which implies that the employees do not acquire human capital.
Corruption creates a negative externality for the economy. Because of corruption, the economy is under risk to stay in the adoption stage. This is costly
for the future generations, since income per capita in this kind of economy is
lower than in the economy which switches to innovations.
We can now show why an educational reform can have a limited success.
Through the previous part of the paper we have assumed that an employee
can attain an education level which corresponds to 't . Apart from 0
't
1;
there are no limits on 't , which implies that the supply of education services can
perfectly satisfy any demand. However, it is more natural to assume that supply
of education services is limited, since education systems can have a limited scale.
This can be speci…cally the case for developing countries, which have relatively
less developed education systems. For instance, a country can have a poorly
trained teaching sta¤, a limited number of universities, etc.
Many papers argue that the quantity of education, measured in terms of the
18
average years of schooling (see, for instance, Hanushek and Woessmann, 2007),
or adult literacy rate (see Durlauf and Johnson, 1995) have positive e¤ect on
economic growth. Other papers, for instance Hanushek and Kimko (2000) and
Hanushek and Kim (1995), report a strong and robust in‡uence of the quality
of education on economic growth. Thus, if an economy is characterized by a low
level of ht;1 , this can lead to a conclusion that growth can be accelerated if, for
instance, the most limiting constraints on education capacities can be removed.
In this case, an education reform comprising technical and …nancial assistance
which aims to improve education standards can look promising.
This can be correct, indeed, if ', the supplied education, is less than 't ,
which is de…ned by equation (10). However, it can be the case that 't
'
i.e. the supplied education can satisfy the existent demand for education. This
is more likely to occur when 't is low, which is the case when At;2 is close to
At;1 , as we know from equation (10). In case of corruption, the demand for
education can be low, and thus educational reform can have a limited e¤ect
on growth. The educational reform has a stronger potential to be successful
if the educational reform is carried out together with a reform of institutions.
The latter reduces , so the curve on Figure 2 shifts up, the non-convergence
set reduces and the level of technology converges to the leading frontier. The
employees acquire 't > 0 according to equation (10).
In the following section, we would like to discuss what kind of policy a
government can implement to help the economy reach the stead-state.
4
Expropriation
In this section, we discuss a solution to the corruption problem. We assume
that the government is granted more political power, so it can control the judiciary to reduce the level of corruption. We assume that a political reform,
which redistributes political power in favor of state o¢ cials, precedes the anticorruption campaign. Then, we use the framework of Acemoglu, Robinson and
Johnson, (2005) who discussed why the political Coase theorem fails to work
when political power is signi…cantly redistributed in favor of a speci…c group.
This is because there is no stronger power which can enforce a contract among
political players. In this situation, property rights are not well protected, and
we show that this leads to a Pareto ine¢ ciency.
19
Such a situation is likely to occur in a non-consolidated democracy15 . Svolik
(2011) argues that in non-consolidated democracies, the reputation and popularity of democratic rule strongly depends on economic performance of political
leadership. If a democratic regime fails to improve economic conditions, and,
moreover, if democratic leadership gets bogged down in corruption, people can
appeal to a "strong hand", for instance, the military, who can reduce corruption and improve institutions. This is consistent with Hale (2009) who surveyed
Russian voters and concluded that voters in Russia prefer delegative democracy
over autocracy or conventional democracy. O’Donnell (1994) describes a similar historical situation for Chile and Uruguay. Delegative democracy implies
that voters grant almost unlimited power to the ruler, however they extend this
political mandate only if the regime meets their expectations with respect to
economic performance. At the same time, delegative democracy is risky. First
of all, if a political regime does not meet voters’expectations, it can use political power to extend its rule. Second, the regime can use power to extract rents
instead of reducing corruption. When power is concentrated in the hands of
a group of state o¢ cials, then it is more di¢ cult for that group to commit not
to expropriate pro…ts or assets. Since it is di¢ cult to make a commitment in
this case, the level of investment is smaller and the economy operates below its
potential. This situation occurs when the ruler is not accountable to a group of
individuals on whom his hold onto power depends (see Besley and Kudamatsu,
2007). Therefore, there is no arbitrageur who can enforce property rights if
the ruler breaks his commitment.16 In the context of our model, this leads to
underinvesting in technology, and, as a result, to lower investment into human
capital.
1 5 I.e.
in a democratic regimes where a reversal to autocracy is possible
developing nations are characterized by bad institutions. At the same time, as
Acemoglu (2003), and Acemoglu, Johnson and Robinson (2005), Acemoglu and Robinson
(2008) show, institutions play a major role on long-run economic growth. Technological and
economic backwardness is more likely to occur in those countries where politically powerful
elites create economic institutions which are detrimental for economic growth. Growth rates
are lower in those economies where property rights are weakly protected, as it is stressed in
Acemoglu and Johnson (2005). Li (2009) concludes that on average expropriation is a more
likely outcome in autocratic regimes.
1 6 Many
20
4.1
The model with expropriation
Assume that in response to the corruption problem, people grant the ruling
regime with greater political power. If the ruler is accountable, then an anticorruption policy is implemented and
reduces. As a result, the level of technology
in the economy approaches the leading technological frontier. However, an unaccountable regime can instead use larger political power to expropriate …rms.
Assume that o¢ cials have no skills to run a company pro…tably. Thus, whenever
they expropriate a company, they keep the owner’s share 1
put
Ytj ;
of the …rm’s out-
j = 1; 2 and then shut the …rm down. Under this assumption, they
never expropriate a …rm in the …rst period, j = 1, since if they do that in j = 2,
they will get at least as much as they get in the …rst period.
Assume that there is an exogenous probability p of expropriation. In case of
expropriation, the payo¤ function (8) can be rewritten as:
Wo =
(1
t ) At;1
(ht;1 (1
't ) mt )
1
1
+ (1
p) At;2 (ht;1 (1 + 't ) mt )
(18)
The maximization of (18) with respect to
t
gives, respectively, the following
versions of equations (11) and (12):
0
(
t)
0
1
=
(1
(
t)
=
p)
(19)
AL
t;1
At;1
1
1
(1
p)
(20)
i
It follows that a higher p reduces the size of the investment into a new
technology. In the steady-state the level of investment is also lower, and can
be derived from equation (19)
17
. From equation (20) we can see that
is
smaller exactly when p is larger. If the economy reaches the innovation stage,
1 7 We agreed that the steady-state corresponds to the innovation stage. If we allow for a
steady-state at the adoption stage, then equation (19) implies that the the gap between the
leading technology is permanently wider than in the case of no expropriation. For the steadstate, this result can be derived from the fact that in the steady-state the domestic technology
is growing at the same pace as the leading technology does:
!
AL
At1
t1
( )
=g
(21)
At1
From equation (21) it follows that when
is smaller in the steady-state, then AL
t1
should be larger, which implies a higher technological backwardness.
21
At1
it develops slower in the steady-state than an economy with p = 0.
Furthermore, it is more di¢ cult to reach the innovation stage. Since the key
ingredient of growth is technological development, then a …rm switches from
adoption to innovations if the following condition holds:
(
(p; )
1) > g
(22)
From (22) it follows that expropriation reduces the rate of growth at the
innovation stage, and the larger is p, the less likely it is that (22) holds. If
the economy reaches the innovation stage, it develops slower in the steady-state
than an economy with p = 0.
Reaching the steady-state is less easy also because the riskless alternative is
more bene…cial now. If a …rm invests into the storage technology, it receives the
following payo¤:
(1
) At;1 (ht;1 Kmt )
1
+ (1
) (1
1
p) At;1 (ht;1 Kmt )
(23)
A …rm is indi¤erent between investing into a new technology or investing
into the storage technology when the following equality holds:
(1
'(
t ))
1
1
t
+ (1
p)
In Appendix III.a we show that when
respect to
t.
t
1 + '(
1 '(
t)
t)
=2
p
(24)
< p, then (24) is decreasing with
If p is large, which means that o¢ cials are powerful, then the
owners invest in new technology only if
t
is also large enough.
Proposition 3 Expropriation results into a non-empty non-convergence set.
Proof. From equation (24) it follows that when p > 0, then for some values
of
t,
a …rm prefers to invest in the storage technology. We can see from equa-
tion (24) that when
t
= 0the left-hand side of this equation is equal to 2
p.
The minimum of the left-hand side of equation (24) is equal to the right-hand
side of (24) only when p = 0. This case corresponds to the expropriationfree economy which we discussed in the second sections. Whenever p > 0,
the minimum point ish less than 2
1
1
III.a, (1 '( t ))
t + (1
p. This isi since, as we show in Appendix
1+'( )
p) 1 '( t ) is not a monotonically increast
ing function any longer when p > 0. It follows that for some values of
22
t
a
…rm will prefer not to invest in a new technology. At the same time, in the
expropriation-free case, the non-convergence set was empty.
Figure 3. Steady-state level of investments and the non-convergence set in the
economy with expropriation.
Again, we can illustrate this situation with a picture. The adoption function
looks di¤erently now. As we show in Appendix III.a, it has a minimum point at
t
= p > 0. As we can see, a part of the curve is located below the horizontal
line, which was not the case in the expropriation-free economy.
Furthermore, according to (12) and (20) the steady-state
case of expropriation than
is smaller in the
in both, corruption and no corruption cases, since
the vertical line is shifted more to the left. As a result, there is large chance
to be trapped and not to converge to the steady-state. The non-convergence
set, which is again depicted with a bolder part of the horizontal axis, is located
between two values of
, one is zero, and the other one corresponds to the
intersection between the adoption function and the horizontal line.
We can again use equation (10) to show that expropriation also reduces the
rate of accumulation of human capital. Since expropriation reduces investment
into a new technology, employees will reduce their investments into human capital as well.
23
In section 3 we concluded that a reform which aims at improving education
standards has more potential to become a success if a reform of institutions
also takes place. We can follow the same logic in case of expropriation. Since a
positive p reduces the
t,
it also a¤ects '(
t)
negatively. If '(
t)
< ' before
the reform takes place, where ' re‡ects is the supply of education, then an
educational reform which increases ' will not result into a higher ht;1 . In some
particular cases the result can even be the opposite. For instance, suppose that
people can transfer their human capital to an economy where p is smaller, and
thus At;2 and 't are larger. Suppose there are two economies, A and B, which
di¤er with respect to p. Assume that in A the expropriation risk is higher than
in B, so pA > pB . Assume also that initially these two economies are equally
populated. Finally, assume for convenience that these two economies are able
to reach the respective steady-states levels of . Thus, if labor mobility between
these two countries is perfect, then labor incomes in both economies should be
the same. This implies that the following result holds in the steady-state:
AB
t;2
AA
t;2
!
hB
t;1
hA
t;1
!1
2+
2+ ( (
B
A)
1
1)
!
=
mB
mA
Since pA > pB by assumption, then, according to equation (20),
(25)
B
t
>
A
t ,
and this implies a slower growth along the balanced path in country A. A slower
B
A
B
growth rate leads to a divergence between AA
t;2 and At;2 , ht;1 and ht;1 . From this
we can conclude that mB > mA . This means that employees tend to migrate
to an economy with a lower expropriation risk, and, consequently, with a faster
technological progress. Thus, individuals can acquire the desired level of human
capital in A, and then migrate to country B to apply their human capital in the
faster growing economy.
5
Consolidation
Is there an alternative policy the government can introduce in order to reduce
the negative e¤ects of corruption?18 One possibility is to provide …rms with
a subsidy, which reduces the cost of the investment for the …rm and thus, increases the pro…tability of a project. But if tax revenues are insu¢ cient to
implement this policy, which is likely to be the case for many developing coun1 8 Or
corporative corruption
24
tries, an alternative solution is to restrict competition (see Acemoglu, Aghion
and Zilibotti, 2006).
Today, restrictions on competition are widely considered to be an impediment for economic growth. However, Aghion and Gri¢ th (2008) mention that
after WWII Mexico, Peru, Brazil, South-east Asian countries, Japan and a
number of European countries were practicing restrictions on competition and
favoring the creation of domestic monopoly, which might have bene…ted them at
a particular stage of development. Thus, under particular circumstances, limited competition and entrenchment can be bene…cial for economic growth. As
Acemoglu, Aghion and Zilibotti (2006), following Gerschenkron (1962), show,
middle-income countries …rst go through a stage of imitation and factors accumulation, where limited competition is helpful.
In this section we show how restricted competition can help to escape from
the non-convergence trap. We argue though, that this recipe can work only if
corruption does not increase. In the opposite case the economy stays in the
non-convergence trap.
Before continuing, we have to answer the following questions: why is state interference a necessary way out? Why can’t …rms voluntarily merge to overcome
the corruption problem?
To answer this question, assume that K …rms were to merge to create one
large …rm with K shareholders. We assume that if the number of …rms decreases
twofold, then the number of employees at each …rm doubles. This means that,
whenever two …rm merge, the bigger …rm employs everyone from the two smaller
…rms. It is easy to check that (16) holds again in that case. Intuitively, if
corruption a¤ects the incentives of N di¤erent owners who own N small …rms,
then it also a¤ects the incentives of N shareholders who own one large …rm which
is N times larger than a small …rm with respect to the number of employees.
Then, if the number of owners stays the same, a voluntary merger can not lead
to an improvement here.
Thus, the remaining way out is to have less owners. To reduce the number
of owners, the government can increase licensing standards, or nationalize …rms,
etc. We assume that the government does not limit competition unconditionally:
if it does not observe investment being realized at the end of period j = 1, then
it does not limit competition any longer. In that case, equation (16) can be
rewritten as follows:
25
bt = 1
h
1
Ki1
1+'( t )
1 '( t ) (1
1+
1
t
+
'(
t ))
(26)
1
, where K > 1 is the number of …rms which were converted into one large …rm.
For the derivation of equation (26), see Appendix II.b.
From (26) it follows that now the threshold level of corruption bt is higher
for every level of
t.
Even when
t
= 0, a …rm can still tolerate some corruption
which was not the case before the reduction in the number of …rms took place.
Recall that the government limits competition to let the economy reach
the innovation stage. We also know that the innovation stage corresponds to
the economy’s balanced growth path. The balanced growth path, in turn, is
characterized by , which is the probability of successful innovation. The larger
is
, the larger is the steady-state levels of investment into a new technology
and human capital. From (12) it follows that a smaller
leads to a smaller
t.
We are now ready to formulate the following proposition:
Proposition 4 Assume that the government restricts competition such that the
economy reaches the steady-state. Then, if the level of corruption in the economy
is large, restrictions on competition are also larger.
Proof. Assume that bt < , where
is the average level of corruption in
the economy. Then, for (26) to be satis…ed,
1
K1
should become smaller. The
latter means that we need to have a larger K.
A larger K implies larger …rms in the economy, since K re‡ects the number
of …rms which were merged to make a bigger …rm. However, a …rm which is
K times larger than a smaller …rm, produces less than K smaller …rms. This
is since we have diminishing returns to labor, so a large …rm can’t produce
the same amount of output as a group of smaller …rms produces. A larger
implies that a bureaucrat takes away a larger share from the owner, so the
owner receives less when he invests into a new technology. Since it is necessary
to absorb more …rms to compensate these losses, a larger
and this, consequently, leads to a larger loss in output.
26
leads to a larger K,
Figure 4. Steady-state level of investments in the economy with corruption and
limited competition.
This picture inherits all the traits of the previous pictures. An opportunity
to own a larger …rm makes investment into the storage technology less bene…cial.
This is since now, instead of 2 on the right-hand side of condition (15), which
re‡ects the return on the storage technology, we now have 1 +
1
K1
;which is
less than 2 whenever K > 1:That’s why the horizontal line is shifted down,
and thus the non-convergence set, which is again depicted with a bolder section
of the horizontal axis, becomes smaller. The horizontal line shifts down nonarbitrarily. It intersects the adoption function exactly at the same point, where
the adoption function itself intersects with the vertical line. This is because to
minimize costs, the government should select K exactly such that the economy
can reach the steady-state.
5.1
The cost of state intervention
Let’s compare an economy with a smaller number of …rms and one with a larger
number of …rms. Assume that these two economies use the same technology
and have the same level of human capital at time j = 1.
27
We want to compare the level of output when competition is restricted with
the output which is produced when there are no restrictions on competition.
After some manipulations, we reduce this comparison to the following two expressions:
YtR = (1
'(
t ))
1
1
t
+
1 + '(
1 '(
t)
(27)
t)
and
YtN R = 2K
(28)
where YtI denotes the owner’s normalized payo¤ when competition is restricted, and YtN R denotes the owner’s normalized payo¤ when there are no
restrictions on competition. For derivation of (27), see Appendix II.c.
If
t
= 0, which means that a large …rm does not invest in a new technology,
the right-hand side of equation (27) reduces to 2. Since K > 1, then 2 <
2K , which means that a larger …rm produces a smaller output than K smaller
…rms do. The di¤erence between 2 and 2K re‡ects the output loss in the
economy caused by the reduction of the number of …rms. Thus, the larger is
K, the higher is the loss in output. Intuitively, since the returns to labor are
diminishing, a large …rm with M employees produces less than K identical …rms,
M
K
each employing
workers. Thus, if the number of …rms becomes smaller, the
output declines.
These losses can be compensated when
t
> 0. Since the economy with lim-
ited competition is investing into a new technology faster than the economy with
free competition, then as time passes, the technological divergence between the
two economies widens. This fact can be summarized in the following expression:
Ant;1
Act;1
!
hnt;1
hct;1
!1
(1
'(
t ))
1
1
t
+
1 + '(
1 '(
t)
t)
2K
(29)
where Ant;1 and hnt;1 denote technology and human capital in the less competitive environment and Act;1 and hct is technology and human capital in the
more competitive environment. For derivation of (29) see Appendix II.c.
In comparison to (27), now we have an additional scalar,
An
t;1
Act;1
hn
t;1
hct;1
1
,
which is larger whenever a less competitive environment generates faster tech28
nological progress and leads to a faster accumulation of human capital. As we
showed in section 3, a competitive economy may not reach the steady-state,
since it may stay in the adoption stage forever. With respect to technological
development, this kind of economy totally depends on adoption, which implies
that it grows at rate g. At the same time, since a less competitive economy can
reach the innovation stage, it develops the level of technology faster than the
leading frontier.19 Thus, this kind of economy reaches higher levels of technological development and human capital than a less monopolized one.
We can conclude that the positive e¤ect of having restricted competition
is stronger when the economy is able to switch to innovations relatively fast.
Assume that initially the economy stays in a non-convergence trap. Then, the
government restricts competition. If after this the economy can switch to innovations fast, then it means that the economy was trapped at a point which
is relatively close to the point where transition from adoption to innovations
takes place, i.e. it was close to the steady-state point. At such a point,
t
is
relatively large. Here, we explain why. Since the economy is approaching the
technological frontier,
AL
t;1
At;1
can conclude that
is declining, and, respectively, growth is getting slower.
t
is getting smaller, and, thus, from equation (11) we
As soon as the economy reaches the innovation stage, or the steady-state,
t
behaves according to equation (12) and, thus, it is a constant. When the government restricts competition, the economy can move from a non-convergence trap
to its steady-state. If the way from the non-convergence trap to the steady-state
is relatively short, then because of a short transition,
decline signi…cantly, and thus the steady-state
If the steady-state
t
does not have time to
is relatively high.
is relatively high, then from equation (26) we conclude
that K should be relatively small, which implies that the government does not
need to restrict competition signi…cantly. This, in turn, means that output
does not decline signi…cantly when the government limits competition to let the
economy transit from adoption to innovation. But if the economy is trapped far
away from the steady-state, which implies that the steady-state
is low, then
one can see from equation (26) that in that case competition should be limited
signi…cantly, which implies that K should be large. The larger K is, the more
signi…cantly the output is reduced when the government limits competition.
1 9 This is because the leading frontier is growing at g, which, by assumption, is slower than
the growth rate of an innovating economy
29
This result is in line with the view that competition should be limited only if
the economy can reach the leading technological level su¢ ciently fast, otherwise
the welfare loss are too large, and it takes a lot of time to restore the initial
level of output. Moreover, this approach works only when the restrictions on
competitions do not result in a higher level of corruption. Assume that the
level of corruption increases. This leads to a downward shift of the adoption
function, and as a result the non-convergence set increases and the economy can
not reach the innovation stage again. Therefore, the bureaucracy bene…ts from
more restricted completion at the expense of the rest of the economy.
6
Conclusion
In this paper, we consider an economy with technological progress and accumulation of human capital. To grow, the economy …rst adopts technology from the
leading frontier, and later, when the distance to frontier becomes su¢ ciently
small, it arrives at the steady-state and substitutes imitation with innovations.
The pace of technological advancement a¤ects the speed of human capital accumulation, since the employees bene…t from technological progress more when
they invest in human capital.
Thus, factors which slow down the pace of technological development also
a¤ect the speed of human capital accumulation negatively. Since many developing countries su¤er from corruption, we incorporate it into our model. We
show that, because of corrupt bureaucracy, the economy can fall into a nonconvergence trap, since owners have lower incentives to invest in a new technology. In response, employees adjust their investments into human capital by
acquiring less education.
To help the economy to leave this trap and to continue to grow, politicians
can interfere and limit competition. However, this is costly, since with limited
competition output declines in the short run. But if the economy switches to
the innovation regime relatively fast, then output restores sooner, and the economy continues growing at a constant rate. As soon as the level of competition
decreases, it is important though to prevent corruption from growing. If the
latter occurs, then the rents from restricted competition are not invested, but
instead expropriated by the bureaucracy.
An alternative solution is to grant the ruler with more political power, such
30
that he can start an anticorruption campaign. However, there is a moral hazard problem: the regime in power can use its authority to extract rents instead
of improving the quality of institutions. If the ruler is not accountable to any
group of individuals, whether this group is the entire electorate, or a shadow elite
group, there is no stronger power which can solve this moral hazard problem,
property rights are weakly de…ned, and Pareto optimum can not be attained.
We show that expropriation reduces incentives to invest in a new technology.
Slower technological development, in turn, erases incentives to accumulate human capital.
We conclude that the reason for low human capital stock should be investigated carefully, and if weak institutions contribute to low incentives of individuals
to invest in their human capital stock, then an educational reform should be
accompanied with an institutional reform. Otherwise, the educational reform
can result into human capital loss if individuals can transfer their human capital
to an economy with a higher level of technology.
31
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35
Appendix I
Each owner maximizes his net income
Wo = (1
t)
by choosing
We = (1
t,
1
At;1 (ht;1 (1
1
't ) mt )
+ At;2 (ht;1 (1 + 't ) mt )
while employees maximize their labor income
) At;1 (ht;1 (1
't ) mt )
1
+ (1
) At;2 (ht;1 (1 + 't ) mt )
1
with respect to 't .
The respective FOCs are:
1
At;1 (ht;1 (1
(1
't ) mt )
h
) At;1 (ht;1 (1
) (1
At;2 1
+
't ) mt )
@At;2
1
(ht;1 (1 + 't ) mt )
@ t
ht;1 mt
=0
At;2 (ht;1 (1 + 't ) mt )
i
ht;1 mt = 0
or, after rearranging
At;1
@At;2
=
@ t
At;2
1 + 't
=
At;1
1 't
One can use (3) to derive (11) and (12) from
At;2
At;1
derived from
=
To show that (1
1+'t
1 't .
1
't )
we …rst rewrite it as follows:
At;2 +At;1
At;1
t
h
2At;1
At;2 +At;1
1
t
+
1+'t
1 't
i
1
2At;1
At;2 +At;1
1
(1
=
At;1
. (10) can be
is increasing with respect to
t,
1
and then di¤erentiate it with respect to
1
@At;2
@ t
)
2At;1
At;2 +At;1
36
t:
2At;1
At;2 +At;1
At;1
(At;2 +At;1 )
At;2 +At;1
At;1
t
=
=
1
1
2At;1
At;2 +At;1
1
At;1
t At;2 +At;1
>0
Appendix II.a
In case of corruption, we consider the following inequality:
(1
) (1
At;1 (ht;1 mt )
t)
1
At;1 (ht;1 (1
+ At;1 (ht;1 mt )
which reduces to
(1
h
1
1
) (1
't ) mt )
't )
t
+
1
1
+ At;2 (ht;1 (1 + 't ) mt )
1
1+'t
1 't
i
2
From this (15) follows immediately.
Appendix II.b
b should hold for the following expression
(1
b) (1
t)
At1 (ht;1 (1
1
(1 + r) At;1 (ht;1 Kmt )
(1
b) (1
t ) At;1
(ht;1 (1
b) K
(1
+ At;2 (ht;1 (1 + 't ) Kmt )
1
=
1
't ) Kmt )
1
1
+ At;2 (ht;1 (1 + 't ) Kmt )
=
1
(1 + r) At;1 (ht;1 Kmt )
(1
1
+ At;1 (ht;1 mt )
1
1
't ) Kmt )
't )
1
+A
h t;1 (ht;1 mt )
1
t
1+'t
1 't
+
From this (26) follows immediately
i
= K1
(1 + r) + 1
Appendix II.c
At;1 (ht;1 (1
1
't ) Kmt )
2KAt;1 (ht mt )
K1
( (1
t)
+ (1
1
))+At;2 (ht;1 (1 + 't ) Kmt )
1
(1
t)
+ (1
)+
1+'t
1 't
2K
and we arrive at (27).
Consider the following inequality again:
At;1 (ht;1 (1
't ) Kmt )
1
( (1
t)
+ (1
1
))+At;2 (ht;1 (1 + 't ) Kmt )
1
2KAt;1 (ht mt )
Let Ant;1 and hnt;1 denote technology and human capital in the less competitive environment and Act1 and hct is technology and human capital in the more
competitive environment, Ant;1 6= Act;1 ; and hnt1 6= hct . If we substitute Ant;1 and
hnt;1 into the left-hand side of the inequality, and Act;1 and hct into its right-hand
side. Then, after some manipulations, we arrive at (29)
37
Appendix III.a
To conclude what an owner prefers to do - to invest in a new technology or to
buy a risk-free asset - we need to
h compare the following
i two expressions:
1
1+'t
(2 + r p) and (1 't )
1
+
(1
p)
t
1 '
t
Since k and r are constants, the …rst expression is the constant. The second
expression reduces to 2 (1
behaves when
t
) when
t
= 0. To understand how this function
> 0 , we need to take a derivative of it with respect to
This derivative is equal to
1
1
2A0
A1 +A0
1
A0
A1 +A0
which is more than 0 when
t p
1 p
t
,
> p, and is non-positive when
38
t
p.
t.

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