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THEHS

’ZC‘CI

 

This is to certify that the

dissertation entitled

Essays on Economic Development and Institutions

presented by

Fabio Mendez

has been accepted towards fulfillment
of the requirements for

Ph.D. Economics

degree in

 

 

Came... ._

Major professor

Date 1/ka /3,1_)¢0C7

MS U is an Affirmative Action/Equal Opportunity Institution 0-12771

 

LIBRARY

Michigan State
University

 

 

 

 

 

 

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_ —__.._.

PLACE IN RETURN BOX to remove this checkout from your record.
To AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE

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11/00 chIRCJDateDtnpes-p.“

A

 

ESSAYS IN ECONOMIC DEVELOPMENT AND INSTITUTIONS
By

Fabio Méndez

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Economics

2000

ABSTRACT
ESSAYS IN ECONOMIC DEVELOPMENT AND INSTITUTIONS
By

Fabio Mendez

Recent economic literature has suggested that institutional elements like
corruption, bureaucratic inefficiency, and monopolistic industries constitute an important
restraint for the economic development of poor nations. My dissertation analyses the
macroeconomic impact of some of these elements. First, it studies the effects of
corruption and bureaucratic regulations on both the creation and the distribution of
wealth. Second, motivated by the recent developments in several energy and
telecommunication markets, it studies the benefits of privatization and deregulation of
intermediate industries that have been traditionally controlled by public monopolies.

The first chapter of my dissertation, “Corruption and Growth: Theory and
Evidence” analyzes the effects of corruption on the rate of income growth. Using a
dynamic general equilibrium model in which private investors are able to bribe corrupt
public officials in order to circumvent a set of government regulations, the model shows
that the growth-maximizing level of corruption can be greater than zero. This result is
then corroborated by an empirical analysis of the relationship between the ICRG
corruption index and the rate of GDP growth for a cross section of countries following
the growth accounting literature. The empirical findings remain robust under several

specifications, including regressions in first differences and a Granger causality test.

The second chapter, “Regulations, Corruption and Income Distribution”, develops
a variant of the overlapping generations model in which the investors face costly
bureaucratic regulations that can be avoided by paying a bribe. Here, the individuals are
endowed with a different amount of effective labor according to a probability function
and the rents from corruption are determined by an exogenous parameter that varies how
unequal the allocation of these rents is. After solving the model and running
computational simulations, the model suggests that the combination of cumbersome
regulations and widespread corruption increase income inequality. Furthermore, the
model points to the distribution of corruption rents as the most important channel through
which corruption affects the overall income distribution and highlights the role of
government regulations in determining the level of corruption.

The third chapter, “Privatization, Deregulation and Capital Accumulation”
presents a model of capital accumulation with one consumption good and an intermediate
good used in the production of final goods only. The model is solved under three
alternative scenarios: one where the intermediate sector is composed of a public
monopoly under government control, one where the intermediate sector is dominated by
a private monopoly, and one with a competitive intermediate sector. The comparison of
these models suggests that the income benefits of state-to-market transitions are mostly
due to increased competition in the deregulated market and that the privatization of state
enterprises alone is not likely to generate significant changes in the economy. In fact, the
model predicts that for high enough levels of public investment, a public monopoly
would be preferred to a private monopoly in terms of the resulting aggregate income

level.

Dedicada a mis Padres.

iv

 

 

 

ACKNOWLEDGMENTS

Throughout all the hours of work my wife provided an almost unbelievable
amount of emotional, spiritual and philosophical support. It was her who listened to all
the crazy ideas, emotional speeches and broken-hearted monologues that came along my
doctorate with unbounded love, sincere interest and inevitable patience. Thank you
AnneLyse for all the efforts you made, they were not for granted.

I am forever indebted with Gerhard Glomm and Rowena Pecchenino, who taught
me economics and guided me through the completion of this dissertation. I am also
thankful to Paul Strassmann for his numerous advices and for all the housing
conversations that he granted me. I am honored to call myself their student and their
friend.

In a similar way, I want to give special thanks to Jeffrey Wooldridge and
Pierfederico Asdrubali for their comments and dedication. I also want to thank Facundo
Sepulveda with whom I shared long hours of work and to Daiji Kawaguchi, Tom Davis,
Stephan Krause, Francisco Alpizar, Frederic Derusseau, Paul Corrigan, Douglas Harris,
Alina Luca, Iva Pestova and other fellow students who also helped with their comments.

Finally, I must recognize the important contribution in all facets of life that I
received from my friends here in East Lansing. Sin Juan Carlos “papito”, los “settlers”
con el Matias, Christian y el “Bena”, los asados donde los Queijo, las vivencias de Luis,
el basket con Miguel y Sergio, los serbios, todos los ticos de Michigan, los regalitos de

Johnny, y los aportes de tantos personajes inolvidables, nada hubiese sido lo mismo...

TABLE OF CONTENTS

LIST OF TABLES viii
LIST OF FIGURES ix
CHAPTER 1
CORRUPTION AND GROWTH: THEORY AND EVIDENCE 1
1. Introduction 1
2. Theory 6
2.1 Micro-foundations 6
2.2 A Growth Model with Corruption 12
3. Evidence 14
3.1 Description of the Data 14
3.2 Empirical Analysis 17
3.3 The Endogeneity of Corruption 20
4. Conclusions and Future Research 23
Appendix 1: Mathematical Appendix 35
Appendix 2: Variable Definitions 37
Appendix 3: Average Indexes of Corruption, Freedom and
Growth ( 1 984- 1992) 38
References 40
CHAPTER 2
REGUALTIONS, CORRUPTION AND INCOME DISTRIBUTION 43

1. Introduction 43

vi

3.

4.

The Basic Model
2.1 Solution of the Basic Model
The Model with Endogenous Bribes

Conclusions and Future Research

References

CHAPTER 3
PRIVATIZATION, DEREGULATION AND CAPITAL ACCUMULATION

l.

2.

4.

5.

Introduction

The Model

2.1 The Case of Public Monopoly Intermediate Sector
2.2 The Case of Private Monopoly Intermediate Sector
2.3 The Case of Perfect Competitive Intermediate Sector
Solution of the Model: The Cobb-Douglas Case

The General CES Technology Case

Conclusions and Future Research

References

vii

48

54

59

62

73

77

77

80

83

85

86

86

91

95

109

LIST OF TABLES

CHAPTER]
CORRUPTION AND GROWTH: THEORY AND EVIDENCE

Table 1. Dependent Variable: Per Capita GDP Growth (1984-1992 average) 25
Table 2. Dependent Variable: Per Capita GDP Growth (1984-1992 average) 26
Table 3. Dependent Variable: Per Capita GDP Growth (1984-1992 average) 27
Table 4. Dependent Variable: Per Capita GDP Growth (1984-1992 average) 28
Table 5. Dependent Variable: Change in Per Capita GDP Growth 29
Table 6. Dependent Variable: Per Capita GDP Growth (1989-1993 average).

All independent variables refer to the respective 1989-1993 values
except for the values of corruption that correspond to the 1984-1988

period 30
Table 7. Dependent Variable: Change in Per Capita GDP Growth 31
CHAPTER 3

PRIVATIZATION, DEREGULATION AND CAPITAL ACCUMULATION
Table 1. Steady State Closed Form Solutions for the Cobb-Douglas Technology 97

Table 2. Parameter Values 98

viii

LIST OF FIGURES

CHAPTER]
CORRUPTION AND GROWTH: THEORY AND EVIDENCE

Figure 1.

Figure 2.

Bribe Functions (CL = 0.15, 5 = 0.97)

The Investment/accumulation Ratio

CHAPTER 2
REGULATIONS, CORRUPTION AND INCOME DISTRIBUTION

Figure 1.
Figure 2.
Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

The Level of Corruption vs. the Cost of Government Regulations
Phase Diagram for Capital Accumulation
Steady State Income Level per Unit of Effective Labor

Steady State Coefficient of Variation for Total Consumption
Expenditures

Steady State Income Level per Unit of Effective Labor. The Case
of endogenous 6

Steady State Coefficient of Variation for Total Consumption
Expenditures. The case of endogenous 6

The Level of Corruption as a Function of the Costs of Bureaucratic
Rules

Steady State Level of Income for Different Values of the
Redistribution Parameter 7

CHAPTER 3
PRIVATIZATION, DEREGULATION AND CAPITAL ACCUMULATION

Figure 1.

Steady State Level of Income for Different Intermediate Market
Structures and Different Levels of Public Investment. ((p = 0.04)

ix

32

33

65

66

67

68

69

7O

71

99

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Steady State Level of Income for Different Intermediate Market
Structures and Different Levels of Public Investment (cp = 0.1)

Steady State Level of Income for Different Intermediate Market
Structures and Different Levels of Public Investment ((9 = 0.2)

Steady State Level of Income for Different Intermediate Market
Structures and Different Levels of Public Investment ((p = 0.3)

Steady State Price of the Intermediate Good for Different
Intermediate Market Structures and Different Levels of Public
Investment ((p = 0.04)

Steady State Wage Rates for Different Intermediate Market
Structures and Different Levels of Public Investment (tp = 0.04)

Steady State Levels of Income for Different Values of p when
\V = 0.05

Steady State Levels of Income for Different Values of p when
w = 0.025

Steady State Levels of Income for Different Values of p when
w=001

100

101

102

103

104

105

106

107

CHAPTER 1

CORRUPTION AND GROWTH: THEORY AND EVIDENCE
1. Introduction

Over the last few years, economists have begun to study how the institutional
framework of societies affects economic growth'. Within this literature, the issue of
corruption has captured a great deal of attention. The 1997 World Bank’s World
Development Report, for example, stated that without an honest state “sustainable
development, both economic and social, is impossible”. Similarly, Gray and Kaufrnann
(1998) reported a recent survey in which high-ranking officials from more than 60
developing countries classified corruption as “the most severe impediment to
development and growth”.

The theoretical literature on this matter has generated a rich debate for the last
thirty years. On one hand, people like Krueger (1974), Myrda] (1989), Shleifer and
Vishny (1993), Tanzi (1997), and Mauro (1995,1998) have argued that corruption is
detrimental to economic growth. They point out that corruption modifies the goals of the
government and creates a diversion of resources from public purposes to private ones,
therefore, resulting in a deadweight loss to societyz. Furthermore, governmental
corruption may also discourage private investment by raising the cost of public

administration (since it is likely to take the form of a bribe for a public service) or by

 

I See for example North ( 1993), Keefer and Knack (1997), Sachs and Warner(l997)
2 In a related argument Krueger (1974) explains how unproductive, “rent-seeking” activities can be
expected to arise in a corrupt environment.

generating social discontent and political unrest, which in turn, may slow down economic
growth (Alesina (1992)).

At the same time, authors like Leff (1964), Huntington (1968), Friedrich (1972)
and Nye (1989) have suggested that it is also possible for corruption to be beneficial for
economic growth. They argue that, if the government has produced a package of
pervasive and inefficient regulations, then, corruption may help circumvent these
regulations at a low cost. Under this scenario, it is plausible that corruption may improve
the efficiency of the system and actually help economic growth3.

In many developing countries, cumbersome government regulation is pervasive.
In Mexico, for example, the problem became so evident that in 1988 the president
appointed a “deregulation czar”. Under this system the “czar” would have to amend any
regulation that had been questioned by private agents in less than 45 days after the initial
complaint; otherwise, the regulation would be automatically eliminated“.

Another argument in favor of corruption has viewed bribery as “speed money”;
that is, as payments that speed up the bureaucratic process, or payments that are intended
to “mediate” between political parties that would not reach an agreement otherwise.
Then, as long as the time consumed by administrative procedures is reduced by the bribe,
the bribers could be made better off. Lui (1985), for example, presents a model in which
the costs of “standing in line” are minimized by the use of bribes. Kaufmann and Wey

(1998), however, contest the empirical validity of this hypothesis.

 

3 In a famous passage Huntington (p.69) states it simply: “In terms of economic growth, the only thing
worse than a society with a rigid, over centralized, dishonest bureaucracy is one with a rigid, over
centralized, honest bureaucracy”.

4 See the World Bank’s World Development Report (1997) for more detail.

In contrast, the empirical literature in the field has consistently reported a negative
correlation between economic growth and the level of corruption, and the evidence for
beneficial effects has been scarce at bests. Using a cross section of countries, Mauro
(1995) demonstrated that after controlling for a number of economic and sociopolitical
factors, the relationship between corruption and economic growth is negative. Keefer and
Knack (1997) also reported a negative correlation between corruption and GDP growth.
Others like Hall and Jones (1999) and Sachs and Warner (1997) obtained similar results.

Thus, most of the empirical evidence seems to be consistent with the theories that
hold corruption as purely detrimental. However, all these empirical studies assume that
corruption has only a monotonic impact upon growth, and therefore, provide an
incomplete test of the hypothesis that have treated this impact as a differentiated
phenomenon depending on the size of corruption. Neither the theoretical model nor the
empirical work presented in this paper use such assumptions and allow the effects of
corruption to vary as the size of corruption changes.

Our modeling strategy is motivated by the results of a 1997 World Bank survey
“Obstacles for Doing Business” (see Brunnetti, Kisunko and Weder (1998)). The Survey
was conducted in 72 countries and asked firm managers to rate the relative importance of
different obstacles for the normal operation of their projects. The results of the survey
reveal corruption and tax regulations as the worst obstacles for doing businesses. The
level of these regulations is considered to be a higher obstacle than their unpredictability
in 65 of the 72 countries, and more problematic than policy instability and crime in at

least 57 of the 72 countries. Moreover, there is a high positive correlation between the

 

5 A good review of all cases can be found in Klitgaard (1988)

importance attached to corruption and that attached to tax and other regulations. This
motivates the inclusion of government regulations as an important part of the story.

The survey also points to the fact that, in the process of dealing with a corrupt
government official, the investor has the option of having his case reexamined by a
different agent. Specifically, 60% of the sample indicated that once they faced a corrupt
official, they were able to “go to another official or to his superior” in order to obtain
proper treatment at least “sometimes” (question 18). This suggests that the actual process
of dealing with public officials can be modeled as a search process.

Finally, anecdotal evidence indicates that corrupt officials are only seldom
penalized. We interpret this as evidence that bribing corrupt officials, instead of
denouncing them, is in the best private interest of both parties (corrupt officials and
private individuals). We therefore model the determination of the bribe level as a
bargaining process.

While most of the theoretical literature has taken a microeconomic approach (see
for example Shleifer and Vishny (1994), Cadot (1987)), we present in Section 2 a
dynamic general equilibrium model of the impact of corruption on growth. In this model,
bribery allows investors to avoid regulations imposed by the government. Given that
these regulations decrease the returns to investment, the model predicts that corruption is
not necessarily detrimental to economic growth. Specifically, corruption is shown to
have two separate effects: on one hand, it fosters economic growth by allowing the
private agents to circumvent existing regulations; on the other hand, corruption represents
a drain on investment. The relative size of these effects determines the total impact of

corruption on income growth.

The results obtained in our theoretical model are then corroborated by the
empirical work presented in Section 3. Unlike previous studies, we allow for a non-
monotonic relationship between corruption and growth by adding a quadratic term to the
econometric specification. Moreover, we believe we cannot say anything about the
behavior of economic agents in non-free countries like North Korea, where individuals
face important restrictions on their choices and their liberties. Thus, we separate our
sample of countries into two groups: those countries that are classified as free according
to the Freedom House International Index, and those that are not. Then, by isolating those
countries considered to be free, the growth maximizing level of corruption is found to be
significantly greater than zero.

The specification that yields this outcome is found to be robust to the inclusion of
several other variables and is preferred to a simple linear specification after comparing
the goodness of fit and the robustness of the models. Furthermore, the paper addresses
the issue of endogeneity differently than has been done before by conducting a regression
in first differences and a Granger causality test. The empirical evidence also shows that
the distinction made between free and not free countries is indeed important. Without
freedom, the effects that corruption imposes upon economic growth may not work in the
same fashion described by the arguments presented before. Finally, the conclusions and

possible directions for future research are presented in Section 4.

2. Theory
2.1 Micro-foundations

The economy is populated by a large number of consumers who live forever;
some of them also act as government officials. Officials have the responsibility to enforce
a set of public regulations on investment that have a cost of 0t per unit of (gross)
investment. Examples of such regulations are safety standards, zoning regulations, and
licenses.

Officials are of two types. A proportion p of them is corrupt, and allows investors
to ignore the regulations in exchange of a bribe b, which is a fraction of the value of the
investment project. The remaining officials are honest, and they exercise no choice other
than enforcing the regulations.

Whenever an agent decides to invest 1' units of capital, he has to be granted
permission by government officials. Thus, besides making inter-temporal decisions on
consumption and capital accumulation, agents must decide every period whether to pay
bribes or abide by the regulations.

In addition, we will assume that all investment projects are identical so that their
size can be normalized to one. Investors maximize their profits, but since investment
projects are homogeneous and face the same risk-less rate of return, their problem
amounts to maximizing their investment net of searching costs and bribes/regulation
costs.

The investors first draw a ticket from a lottery and get an official who asks for a
share 0t (when honest) or b (when corrupt) of the initial investment project, in order to

grant the permission. Then, investors can either accept the official’s offer or draw

another ticket, in which case their payoff is discounted by a factor 5 6 (0,1), which
captures searching costs.

If an investor gets a corrupt official, his value function (per unit of investment) is,

VC= Max {l-b, 8(p VC +(l-p) VH)}. (l.a)

If he gets an honest official, his value function is,

VH = Max { l-(X, 8(1) VC +( l -p)VH) } . (Lb)

Once the investor is faced with a corrupt official, a Nash bargaining process
determines the resulting bribe charged. Formally, the equilibrium bribe function b*(p) is

defined as:

b*=arg max(b—,uc)(l—b—#,) (2)
{b}

where |J.c and u] are the corresponding payoffs for the corrupt official and the investor in
the non-cooperative case. For this particular model, the payoffs in the case of no
cooperation are tic = 0 and u] = 5(p VC + (1-p)VH).
An equilibrium for this model consists of a bribe function b*(p) that is defined by
(2), and decision rules for investors that are consistent with the Bellman equations (La)
and (lb).
Solving for the investors decision rules conditional on the bribe level, and given
that the solution to problem (2) is single valued, we find a unique equilibrium which can

be of two types depending on the parameter values. The first type corresponds to the case

where the investor always pays a bribe when faced with a corrupt official and always
abides by the regulations when faced with an honest official. Solving for both Bellman
equations we find that these equilibrium arises whenever the bribe b*(p) lies in the
interval:
b*e [bmi”(p,a),b'"“x(p,a)]

where bmax is the bribe level such that for any bribe greater than bmax it is always optimal
for the investor to search for an honest official, and bmin is the level of bribe such that for
any bribe below bmin it is always optimal for the investor to search for a corrupt official.
This interval is obtained by substituting Vc = l- b and VH = l-a into the equations (1 .a)

and (lb), and obtaining the following inequalities:

 

1-b > 8(1) (l-b) +(1-p)(1-a)) (A)

1-a > 5(p(l-b) +(1-p) (l-a» (B)
Simplifying both inequalities one obtains b < 1—6(1_1p);—a) -=- bmax and
b>l_(l—a)—5(l—a)(l—p) E bmin, respectively. Furthermore, as shown in the

 

p5
appendix, the value bum is greater than bmin for all values of p.
The second type of equilibrium corresponds to the case for which investors will
always prefer to keep searching if faced with an honest official, and will always choose to
pay the bribe when faced with corrupt officials. Again, by solving the Bellman equations

we find that this equilibrium can only arise for b< bmin and for a level of corruption p

min(0t), 1]”, which ensures that b'"‘">0 at the interior of the interval.

lying in an interval [p
Therefore, a bribe compatible with this equilibrium must then lie in the interval

be [0,bmi"(p,0t)]

Again, in order to obtain this interval, we substitute Vc = l- b and

(WI-b)

H = l_6(1__) (since in this equilibrium VH = 25(ch + (l-p)VH)) into equations (1.a)
‘ - P

and ( l .b), and obtaining the following inequalities:

5;)(1—b)
l-b l-b 1- —— 3.
>5{p( )+( p)l-5(l—p)} ( 21)
@(i—b)
l- - - I
0t<5{p(1 b)+(1 p) ————1_5(1_p) } (3b)

Grouping all factors into the left hand side of inequality (3.a) and factoring out (l—b), one

obtains the condition b<1; which is not binding at any time. From inequality (3.b) one

(1-a)(1—6+ap)
6p

 

obtains b<l — , which after adding and subtracting the term

(1+ (1-0t)/5p) becomes b<1 — 1 " a + (1" “X5 _ ‘5") = bmm.
p5 p5

 

Finally, if b* > bm‘“, investors will find it always optimal to keep searching until
they get an honest official. In this case, a corrupt official would be better off by setting
b*= b”, so b > b'“‘”‘ would not arise as an equilibrium bribe level. In what follows, we
choose to concentrate on the first type of equilibrium in which investment is conducted

through both kinds of officials.

 

6 See Appendix 1.

In order to solve for the equilibrium level of bribes, we need to determine the non-
cooperative payoffs no and m. In the case of no cooperation, the corrupt agent obtains a
payoff of zero and the investor is forced to search for another official. Therefore, NC = 0
and It] = 5(ch + (l-p)VH). Using the symmetric nature of the problem, we obtain

= 50— mo -a)

V
c l-5p

= l-bmax and V”: l-(x.

 

Then, the Nash Bargaining problem can be specified as

max (I) '(b "m — b)) (4)
{b}

The solution to (4) is given by b*(p) = bmax/2. Once this equilibrium level of the bribe is
determined, and given that the conditions for an interior solution are met7, we can study
the set of prices faced by the consumer in his inter-temporal allocation problem. To do
this, we begin by defining the expected fraction of spending on investment that will
accrue to the productive capital stock of the investor as 9:

9 = p (1-b*) +(1-p)(1-a).

Since it is not the purpose of this paper to deal with uncertainty issues, we assume
that each household diversifies its portfolio into many projects and interviews as many
officials as projects he has. This is done so that, in the spirit of the law of large numbers, _
0 can be seen as the actual rate at which an agent can transform investment spending into
new capital goods at every period of time.

To characterize 0 note that its first two derivatives with respect to p are:

3]) aP 0p2 8p 3p2

 

10

Although the first derivative of 0 with respect to p cannot be signed, it can be shown to

depend specifically on the size of or. As demonstrated in the appendix, 0 reaches a unique

maximum at a level p* of corruption, when the following sufficient conditions are met

 

 

p*=0 ifor<1_5

2—5
O<p*<l ifa> — andor<%
p*=l if0t>l

2

Thus, the effect of corruption upon the variable 0 depends on the size of or; and
one cannot rule out any theoretical possibility. For reasonable parameter values, however,
the first two possibilities seem more realisticg. Figures 1 and 2 illustrate the solution for
the values (F 0.15, 5 = 0.97 and show how the level of corruption that maximizes 0 lies
between zero and one.

The following section embeds the results obtained here into a growth model and
analyses the impact of corruption on the rate of growth. In order to do this we begin by
using 0 to derive the constraints faced by the representative household in his inter-

temporal allocation problem.

 

7 A sufficient condition is 5 S 2 - J5 +

 

(l-afiXJE—l)
l—a '

8 Empirical evidence on the costs of government regulations indicates that the value of a ranges between
7% and 19% of GDP for OECD countries (see Guasch and Hahn (1999)). No empirical estimates of 8
were available.

11

2.2 A Growth Model with Corruption

We now proceed to study the effects of corruption on the growth rate of output.
To do so, we first build on the results of the last section to derive a household budget
constraint, and state the general form of the household problem. Then, we derive the
growth rate of output and examine its properties using a simple Ak production function.
Let ip be productive investment, if d is the depreciation rate, we have:

k,,,=(1-d)k,+ i"t . (5)
Let i be spending in investment projects from a household point of view, then:

i"l = 6 x it , (6)

h=fi+n+h . 0)
Where r, denotes the cost of regulations and b represents the bribes at time t.
The national account identity says:

y, = el + i"t + rt . (8)
As resources can be used for consumption, additions to the capital stock or can be lost in
the form of regulation costs. Furthermore, if bribes are returned as lump-sum transfers,
we have:

t,+y,=c,+ip,+r,+b,. (9)
Where t. represent the transfers at time t.

Note that the lump sum return of bribes can be seen as an accounting device:
bribes imply a redistribution of wealth from investors to officials who, given that they
cannot profitably deviate from b=b*, see them as lump-sum transfers. The way the
distribution of bribes is modeled then has no effects on the growth rates, and for the

purpose of this paper we could just assume they are destroyed.

12

The same applies for the cost of regulations r. The way we think about these
resources is as goods that may enter into the utility function but do not add to the
productive capital stock. In line with this idea, we chose to model r as pure losses to
society, which can be motivated as agents having no (collective) choice on the level of
regulations.

Using equations (6) and (7), equation (9) is equivalent to:

tt+y,=c,+ip,/0 . (10)
The above budget constraint shows that the growth effects of corruption are, in this
model, similar in nature to those of a tax on investment.

The general form of the growth model can then be summarized by the following

household problem:
Max ZB‘u(c,)
s.t. i) tt + y[ = el + ip,/6
ii) km = (1-d)k, + ipt

In defining a candidate growth model, we choose to pick the simplest form for the
technology that allows for policy to have growth implications. It can be seen however
that the same results obtain where a model of the type of Rebelo (1991) or Jones and
Manuelli (1990) is used instead.

Using iso-elastic utility and Ak technology (y: Ak), the common growth rate for

all real variables is:

g=[3(1—d+0A)°

l3

Thus, the growth rate inherits all the relevant features of 0. In particular, the level of
corruption that maximizes the rate of growth can take any value between zero and one

depending on the size of the government regulations.

3. Evidence
The main contribution of the empirical analysis presented here is to show that, in
order to derive robust results, additional structure has to be imposed on the data by
differentiation among “free” countries and “not-free” countries. Once this is done, we are
able to derive the following set of results:
i) The growth rate is a hump-shaped function of the corruption level.
ii) A quadratic specification is preferred, in terms of goodness of fit, to the
traditional linear specification.
iii) The growth maximizing level of corruption increases with the level of
government expenditures under some specifications.
iv) For not-free countries, there is no statistical correlation between the level

of corruption and the growth rate.

3.1 Description of the Data
The index of corruption used comes from Political Risk Services Inc., a private
firm that annually publishes the International Country Risk Guide (ICRG). The ICRG
contains a corruption index that covers the period 1982-1995: this index is an assessment
of the degree of corruption prevailing in a certain country and is based on a survey made

of foreign investors.

l4

The ICRG as presented here ranges from 1 (most corrupt) to 10 (least corrupt). A
lower number indicates that “high government officials are likely to demand special
payments” and “illegal payments are generally expected throughout lower levels of
government” in the forms of “bribes connected with import and export licenses, exchange
controls, tax assessment, police protection, or loans” (Tanzi (1997)). In contrast with
other indices, the ICRG looks directly into the frequency of corrupt acts among
government officials.

We use the index of freedom from Freedom House International. Since 1970 they
have conducted surveys that rank the rights and freedoms of individuals in several
countries; these surveys are intended to fill out a checklist of elements that are considered
essential for freedom.

This index is divided into political rights and the civil liberties. Each sub-index
ranges from 1 to 7, where a lower number indicates a higher degree of freedom. To give
and idea of what those numbers represent, their report9 states that “ as one moves down
the scale below the category of 2, the level of oppression increases, especially in the areas
of censorship, political terror and prevention of free association”‘0.

Freedom House classifies countries as “free” if the sub-indices do not add more
than five, as “partly free” (a gray area in their classification) if they add up between five
and ten, and as “not free” if they add up to 11 or more. For the purposes of this study,

countries will be categorized as free if the total index is less than six; however, the results

remain unaltered if a value of 4, 5, 6, 7 or even 8 is chosen to separate the categories.

 

9 Freedom in the World: 1996-1997
'0 After reading their report, it is clear that “moving down the scale below the category of 2" is intended to
represent a movement in the index from 2 to 3 and higher.

15

The political rights sub-index was used to create a variable intended to
approximate the degree of political instability within a country; this variable was
constructed by taking the standard deviation of the political rights index for the period in
question. Although this might not be a perfect measure of political instability, one would
certainly expect that the countries that have a more volatile score in political rights are
the ones who are less stable.

Other studies have used the probability of the opposition taking over, or the
number of changes in power over a certain period in time, as a measure of political
instability. However, these measures are evidently flawed, since a perfectly stable
democracy is also likely to have frequent changes in power. Thus, the alternative
proposed here is considered an improvement over other measures used before.

The average growth of GDP per-capita for the period 1984-1992 was obtained
from the World Bank National Account Statistics as reported by Bruno and Easterly
(1996). Although the same analysis can be conducted using the Barro—Lee data set
without any change in the results; the World Bank statistics allowed us to work with a
bigger sample.

Values of population growth, income per capita, and the total shares of investment
and government expenditures in GDP were obtained from Summers and Heston (1991).
All other variables like the secondary and primary school enrollment ratios where taken

from the United Nations Educational, Scientific and Cultural Organization (UNESCO).

16

3.2 Empirical Analysis

The majority of the empirical work on growth accounting and corruption
conducted in the past has followed the work of Mankiw (1992) and Barro (1994,1992).
In these studies the rate of economic growth depends on the level of corruption and
several other variables that include human and physical capital, initial level of income,
etc. This type of framework (to which we will refer as “traditional” from now on) can be
summarized in the following equation:

Growth = a + ,6 Corruption + y (other variables) +8

It is immediately apparent, however, that this traditional setting does not allow for
the growth-maximizing level of corruption to differ from zero or infinity; and therefore,
that it does not provide an ideal test for the broad body of theory introduced in the
preceding sections. Thus, in order to overcome this limitation, an alternative

specification is considered:

Growth = 03+ ,5, Corruption + ,6; ( Corruption )2 + y (other variables) +8

By studying both formulations, the analysis will reveal that the distinction made
between free and not-free countries is in fact pertinent. Furthermore, the non-traditional
specification will show very robust results that confirm the existence of a positive growth
maximizing level of corruption in those countries labeled as free.

Table 1 presents the results obtained for the traditional model. Each column
shows the result of a different regression and the only difference between regressions is
the number of explanatory variables. Under the simplest specification (column 1) the

coefficient on corruption is found to be significantly different from zero (with a value of

17

 

 

 

0.00}

C063

st:

“1

0.0034), however, as other relevant variables are included, the significance of this
coefficient disappears.

The results reported here coincide with the ones obtained in other empirical
studies. Mauro (1995) for example, using very similar models to the ones in columns (1)
and (2), finds significant coefficientsH for corruption of 0.002 and 0.003 respectively”.
In his study, after controlling for other important determinants of growth, the coefficient
on corruption becomes insignificant. In their study of growth and convergence, Keefer
and Knack (1997) also reported that the coefficient on corruption becomes insignificant
after other variables were included in their regressions.

Table 2 also uses the traditional model but separates the sample between free and
not-free countries. For the free countries, the results are similar to those obtained for the
entire sample, except now, the coefficients on corruption remain significant for column
(2) also and the goodness of fit is improved in almost all regressions. For the not-free
countries, in contrast, the results obtained differ completely form the ones shown in Table
l and, even in the simplest regression, there seems to be no effect of corruption on
growth.

The alternative specification is presented in Tables 3 and 4. When the complete
sample is used (Table 3), the coefficients on corruption and corruption squared are never
significantly different than zero. Thus, comparing the performance of the two models
over the whole sample (outcomes of tables 1 and 3), it is not surprising that the traditional

specification had been preferred in the past.

 

” Mauro’s sample is 58 countries. The sample used here is as large as 94 and as small as 67 depending on
the data available for different regressions.

18

However, once the two sub-samples are considered separately (Table 4), the
situation is reversed. For the case of free countries, the alternative specification yields a
much bigger explanatory power (78%) than the traditional one (31%) and obtains
coefficient estimates that are robust to the inclusion of many other independent variables.

These coefficients are significant at the 1% level for all regressions and their sign,
as expected, suggests the existence of a positive growth maximizing level of corruption.
Specifically, corruption was found to become detrimental to economic growth for ICRG
values lower than 7.7, 7.12 and 7.12 in columns (1), (2) and (3) respectively13 (it is
important to remember that a lower ICRG number denotes a higher incidence of
corruption).

As shown in the appendix countries like Botswana, Malaysia, Singapore, Spain
and Costa Rica (which have rates of growth well above the average) have indexes of
corruption that are remarkably close to the estimated optimal level of corruption.

The coefficient of the interaction term between corruption and the share of
Government expenditure is particularly interesting, since its negative sign implies that the
growth-maximizing level of corruption is bigger for those countries in which the
government takes a bigger share of the economic activity. Such phenomena could be
explained if corruption was harder to control in bigger governments (as suggested in
Klitgaard’s model) or if the bigger and more complicated bureaucracies gave way to

corruption (as Friedrich (1972), McMullan (1961) and others had pointed out).

 

'2 Although not reported in the table, the results are almost identical when ZSLS procedures are used
instead of OLS. Following Mauro’s work, the index of ethnolinguistic fractionalization was used as an
instrument

'3 In order to calculate those, the average size of the government was used.

19

For the not-free countries, as was the case with the traditional framework, the
alternative formulation does not find a significant link between the incidence of
corruption and the rate of growth. Thus, the distinction made of free and not free appears

to be relevant for the study of corruption and its consequences.

3.3 The Endogeneity of Corruption

The results presented in Table 4 are susceptible to two major criticisms. First, it is
possible that corruption and growth respond simultaneously to an omitted factor. Such
factor could be a cultural disposition towards leisure or morality, the legal framework, the
historical evolution of the nation in question, the date of independence, etc. Second, one
may think that the incidence of corruption is directly affected by the rate of economic
growth; as for example, it could be the case that rich, fast-growing countries have more
resources to combat and control corruption.

In either case, corruption would be correlated with the error term in the OLS
regression and the estimates would be biased. Thus, in order to overcome this difficulty,
several authors in the past included an instrumental variable and conducted a two stage
least squares regression. In theory, this is a perfectly valid procedure, in practice;
however, it is very difficult to find a valid instrument.

Even logical candidates such as the Index of Ethnolinguistic Fractionalization
(ELF)l4 used by Mauro (1995) and others were inadequate for this study. In the specific
case of the ELF, although it is correlated with corruption in the whole sample, when

considering free countries only, this correlation disappears.

20

Thus, in order to address the first criticism, the sample was separated in two
periods (1984-1988 and 1989-1992), and an OLS regression was conducted using the
first differences of each variable. This procedure is equivalent to allowing for fixed
effects and would diminish considerably the effects of potentially omitted variables like
the ones described above.

Table 5 presents the results obtained in this regression. As shown, the main result
remains unchanged, as the coefficients of both corruption and corruption squared
preserved the expected sign and stay significant at the 1% level. As for the second
criticism, let us assume that economic growth today determines the present and future
level of corruption but that the rate of growth today has no direct effect upon the level of
corruption in the past. Thus, consider the following equation, where the subscript t

stands for time:

Growth ,= 61+ ,6 Corruption ,-, + ,8; (Corruption ”)2 + y (Other Variables ,) + E

This specification does not suffer from the shortcomings exposed above;
however, the coefficient B could still be picking up the correlation between growth at
time t and growth at time t-l (if those were correlated). Therefore, in order to complete

the estimation, the equation must be modified as follows:

Growth ,= a + ,6 Corruption H + ,6; (Corruption ,.,)Z + y (Other Variables ,) + ¢( Growth ,.,) + E

 

'4 Although not free of criticisms, the ELF is the most used instrument in a very short list.

21

Table 6 reports the estimations obtained using these specifications. As before, the
estimated coefficients remained significant at the 1% level.

Finally, in Table 7 we modify the first differences specification used in Table 5
so, instead of dividing the sample into two different groups, the complete sample was
used and the coefficient of corruption was allowed to differ from free to not free
countries by using dummy variable interactions. As can be seen in the table, our results
remain unchanged.

Summarizing the analysis, the empirical evidence suggests the existence of a
quadratic relationship between corruption and income growth for the case of free
countries. This is to say, that controlling for all other characteristics, the level of
corruption that maximizes the rate of growth is greater than zero.

This result can be interpreted in the light of the model of Section H. When the
level of corruption is low, paying bribes is cheaper than abiding by the regulations, so
that increasing the level of corruption will only make it more likely that an investor gets
the chance of bypassing the regulations and therefore face a higher

investment/accumulation ratio 0.

As the proportion of corrupt officials increase, the level of bribes rises over the
cost of abiding by the regulations, and further increments in the corruption level only
increase the likelihood that an investor will have to pay a high “corruption tax”, therefore
decreasing the net return to his investment and at the same time the growth rate of the

economy.

22

4. Conclusions and Future Research

In this paper we demonstrate how, in the presence of government regulations, the
growth maximizing level of corruption is not necessarily equal to zero. In addition, we
present new empirical evidence that suggests the existence of a hump-shaped relationship
between corruption and the economic growth of free countries. This finding remains
unchanged under several specifications even after conducting a first difference regression
and controlling for endogeneity.

The empirical literature that noticed a linear relationship between corruption and
growth failed to differentiate between free and not free countries. Once this
differentiation is made the alternative specification proposed in this study is preferred to
the traditional one in terms of robustness and goodness of fit. Thus, the incorporation of
the Freedom Index proves to be a key element in the analysis and may be an important
avenue of future research.

The main result obtained here: that the growth maximizing level of corruption is
not necessarily equal to zero, confirms the predictions of the theory of political
economics developed in the last three decades. The specific model borrows from the
game theoretic approach to corruption, pioneered among others by Cadot, and goes a step
further by showing how the results can be embedded into a modern endogenous growth
model. In doing so, we offer a general equilibrium explanation for the relationship
between corruption and growth.

In constructing the model, a number of issues have deliberately been left aside. In
particular, important topics like the effects of corruption upon social welfare, income

distribution, investment uncertainty, and allocation of public expenditures were not

23

discussed here. Similarly, the lack of relevant data did not allow us to identify the
specific reasons why corruption has a different impact at different levels. We leave these

issues for further research.

24

Table 1
Dependent Variable: Per Capita GDP Growth (1984-1992 average)

Independent
Variab'“ (1) (2) (3) (4)
Corruption 0.0034 0.0022 0.0005 0.0001
(3.908) (1.75) (0.344) (1.09)
I/GDP 0.00134 0.001
(3.249) (2.29)
G/GDP 0.00017 0.0003
(0.571) (1.07)
Political -0.0017 -0.002
Instability (-0.245) (-0.33)
Primary 0.0064 0.006
education (0.452) (0.41)
Secondary 0.0008 -0.0267 -0.32
education (0.069) (-1 .63) (- l .95)
depc84 0.0000 0.0000
(0.739 (0.78)
POP -0.2337 -0. 1485 -0.12
(0944) (-0.618) (-0.53)
Lat.Amer -0.004
(07)
Africa -0.015
(-1.93)
Constant 0.98 0.99 0.98 .99
(183.22) (104.8) (61.3) (59)
Number of 94 77 74 74
Observations
R2 .14 .1 15 .261 .3

 

 

All results obtained with OLS regressions. T-statistics are in parentheses.

25

Table 2

Dependent Variable: Per Capita GDP Growth (1984-1992 average)

Independent
Variables

Corruption

I/GDP

G/GDP

Political
Instability

Primary
Education

Secondary
Education

depc84

POP

Lat.Amer

Africa

Constant

Number of
Observations

R2

 

Free Countries

(1) (2)
0.00207 0.0038
(2.308) (2.334)
-0.014
(-090)
-.0000
(045)
-0.138
(-051)
1.00 1.003
(148.6) (78.2)
37 31
.13 .24

(3)

0.0007
(0.44)

0.0007
(1.34)

0.001
(2.19)

0.0018
(0.22)

0.083
(1.97)

-0.021
(-1.39)

0.0000
(0.84)

-0.57
(-2. 14)

0.0054
(0.72)

0.018
(1.59)

.93
(25.9)

30

.60

 

Not-Free Countries

(1)

0.0030
(1.787)

.98
(1 16.4)

57

0.054

(2)

-0.0003
(-0.18)

-0.017
(-0.87)

0.000
(2.34)

-0.307
(-0.90)

1
(76.1)

46

.15

(3)

-0.0004
(-0.l6)

0.0013
(1.94)

-0.0005
(-O. 10)

0.0026
(0.22)

0.0015
(0.07)

-0.029
(-1 . 15)

.00000
(0.362)

0.038
(0.107)

—0.005
(-0.52)

-0.0071
(-0.62)

.99
(39.4)

44

.23

 

All results obtained with OLS regressions. T-statistics are in parentheses.
Countries catalogued as free if the total index of freedom was no more than 6

26

Independent
Variables

Corruption

Corruption
squared

Corrup * G
I/GDP

G/GDP

Political
Instability

Primary
Education

Secondary
Education

depc84
POP
Lat.Amer.
Africa

Constant

Number of
Observations

R2

 

(1)

0.0042
(1.12)

-0.00007
(-0.22)

0.984
(93.6)

94

.142

Table 3

(2)

0.0025
(0.557)

-0.00014
(-0.339)

0.0168
(1.17)

-0.021
(-1.282)

0.0000
(1.76)

-0.232
(-0.941)

0.99
(60.6)

77

.166

(3)

0.002
(0.35)

-0.00008
(-0.209)

-0.00003
(-0.203)

0.0013
(3.20)

0.00032
(0.427)

-0.0018
(-0.25)

0.0065
(0.443)

-0.026
(-1 .58)

0.0000
(0.673)

-0.137
(-0.535)

0.98
(36)

74

.26

Dependent Variable: Per Capita GDP Growth (1984-1992 average)

(4)

0.003
(0.59)

-0.00016
(-0.37)

-0.00002
(-0.189)

0.001 1
(2.58)

0.0004
(0.61)

-0.0035
(-0.47)

0.0065
(0.43)

-0.03
(-l .8)

0.0000
(0.314)

-0.147
(-0.575)

0.0024
(0.363)

-0.01 l
(-1 .47)

0.98
(35.3)

74

.289

 

All results obtained with OLS regression. T-statistics are in

parentheses.

27

Independent

Variable

Corruption

Corruption
squared

Corrup * G
I/GDP

G/GDP

Political
Instability

Primary
Education

Secondary
Education

depc84
POP
Lat.Amer.
Africa

Constant

Number of

Observations

R2

 

Table 4
Dependent Variable: Per Capita GDP Growth (1984-1992 average)

Free Countries

(1)

0.0185
(3.22)

-0.0012
(-2.89)

0.95
(52.2)

37

.30

(2)

0.022
(3.92)

-0.0010
(-3.07)

-0.0004
(-2.68)

0.0003
(0.831)

0.004
(3.62)

-0.004
(-0.63)

0.1 19
(3.43)

-0.012
(-1 .0)

0.000
(0.746)

-0.26
(-1.25)

0.78
(15.12)

30

.75

(3)

0.0219
(4.1)

-0.0010
(-3.04)

-0.0001
(-3-25)

0.0005
(1.27)

0.0049
(4.08)

-0.0025
(-0.39)

0.129
(3.68)

-0.0034
(-0.27)

0.000
(1.31)

-0.422
(~2.05)

0.011
(1.88)

0.013
(1.58)

0.75
(14.9)

30

.8

 

Not-Free Countries

(1)

-0.0012
(-0.20)

0.0004
(0.733)

0.99
(70.1)

57

.02

(2)

0.009
(0.84)

-0.0003
(-0.45)

—0.0003
(- l .2)

0.0015
(2.34)

0.001 1
(0.98)

0.005
(0.49)

0.0015
(0.08)

-0.03
(-1.2)

0.000
(0.02)

0.253
(0.62)

0.95
(21.8)

44

.25

(3)

0.009
(0.76)

-0.0003
(-0.43)

-0.0002
(-1 -00)

0.0014
(2.03)

0.001
(0.87)

0.0037
(0.31)

0.002
(0.13)

-0.031
(-1 . 19)

-0.000
(-0.08)

0.221
(0.51)

-0.002
(-0. l 8)

-0.004
(—0.35)

0.95
(19.5)

44

.25

 

All results obtained with OLS. T-statistics are in parentheses.

28

Table 5

Independent
Variables

ACorruption

ACorruption
squared

A(Corrup *G)

A(I/GDP)

A(G/GDP)

APolitical
Instability

APrimary
Education

ASecondary
Education

Adepc
APOP

Constant

Number of
Observations

R2

 

Dependent Variable: Change in Per Capita GDP Growth

0.067
(4.28)

-0.0033
(-3.26)

-0.0005
(- l .08)

0.0006
(0.55)

-0.0032
(-0.79)

0.008
(1 .00)

0.286
(1.54)

0.108
(1.08)

0.000
(0.757)

-0.861
(-1.84)

-0.021
(-4.8)

25

.76

T-statistics in parentheses.

29

Table 6

Dependent Variable: Per Capita GDP Growth (1989-1993 average)

All independent variables refer to the respective 1989-1993 values except for the

values of corruption that correspond the 1984-1988 period.

Independent
Variables

Corruption

Corruption
squared

Corrup *G
I/GDP

G/GDP

Political
Instability

Primary
Education

Secondary
Education

depc 1 989
POP
Growth 84-88

Constant

Number of
Observations

R2

T-statistics in Parentheses

 

(1)

0.014
(2.13)

-0.0011
(-2.29)

-0.0001
(-0.78)

0.0001 1
(0.018)

0.0014
(1.18)

-0.013
(-1.06)

-0.053
(-0.37)

0.013
(0.74)

—0.000
(-0.053)

-0.16
(-0.48)

1.01
(7.11)

26

.35

30

(2)

0.022
(2.47)

-0.0015
(-2.66)

-0.0002
(- l .28)

0.0003
(0.53)

0.0025
(1.72)

-0.015
(-1 .24)

0009
(-0.064)

0.014
(0.764)

-0.000
(-0. 17)

-0.21
(-0.64)

-0.399
(-1 .26)

1.33
(4.6)

26

.42

Table 7

Independent
Variables

ACorruption

ACorruption
squared

A(Comrp *G)

ACorruption*
Dummy

ACorpn. sqrd. *
Dummy

A(Corpn *G)*
Dummy

A(I/GDP)

A(G/GDP)

APolitical
Instability

APrimary
Education

ASecondary
Education

Adepc
APOP
Dummy

Constant

Number of
Observations

R2

 

Dependent Variable: Change in Per Capita GDP Growth

0.03616
(2.72)

-0.0029
(-3.15)

-0.0001 1
(~0.32)

-0.087
(—3.00)

0.0055
(2.28)

0.001
(2.19)

0.003
(2.86)

-0.005
(-2.39)

-0.008
(-1 .7)

0.059
(1 .167)

-0. 124
(-1.93)

-0.000
(-1 .83)

-l .452
(-2.54)

0.025
(2.933)

-0.01 16
(-2.36)

61

.57

T-statistics in parentheses

31

0.8

0.6

0.4;

0.2

 

4 f

bmax

M

bmx/Z

 

 

0.2 0.4 ,m 0.6 0.8

Figure 1. Bribe Functions (0t=0.15, 8:0.97)

32

That:

07‘

QBj

041

01‘

 

 

 

01

Figure 2. The Investment/accumulation Ratio

33

4

APPENDICES

34

Appendix 1: Mathematical Appendix

One needs to show that bum > bmm for all values of p. In order to do this, let’s first

write down the expression bmax > bmm:

 

l_1—a+(l-p)(l—a) <1_5<1—p)(1—oc)
{)5 p 1-5p

 

Simplify this expression and obtain

 

(H41 _(l-p)]>(1—p)(l—a')6=>_l_>5(l-p)+5(1-p)
p5 p l-él P5 5P 1‘8)

Finally, add the terms in the right hand side and multiply both sides by p8 to obtain

5(1-p)
l-ri)

l>

 

. Given that both p and 8 are numbers between zero and one, it is clear after

the above simplifications that the inequality bmm<bmax will always hold. Q.E.D.

The Behavior of 0

Consider the following derivatives under the assumptions made before:

 

 

 

 

 

86 8b 826 ab 82b
—=a—b— ._ =—2——p <0
0p p 8p 8P2 8P 8P2
azb*_6(1—6)(1-a) azb*_62(l-b‘)(l-a)
3P2 20-402 3102 (1-5p)3

35

:1:
Given that both, b* and 8b

3p

 

, are increasing functions of p, one can state

sufficient conditions for the growth maximizing value of p to be zero, one or any value

*

 

between zero and one. Particularly, if 0t< (b*- p ) lp=o then 0 is a decreasing function

31‘
of p for all values of p and is maximized at p=0. If 0t> b*lpzl + ddbb 0 is an
P

=1
increasing function of p for all values of p and is maximized at p=l. Finally, if 01> b*lp=0

db *
db

 

and OK b*lp=1 +

 

, 0 initially increases with p but eventually decreases and
[1:1

attains its maximum at a value p between zero and one.

max

The Nash bargaining equilibrium bribe b* =

 

can be used as an specific case.

The values provided in the text follow.

36

  

  

 

 

 

 

 

It‘.

Appendix 2: Variable Definitions

Corruption: Average ICRG index for the period 1984-92

Corruption squared: Corresponds to the square of corruption

I/GDP: Average total investment share of GDP

G/GDP: Average total government expenditures share of GDP

Political instability: Degree of political instability approximated by the standard
deviation of the political rights index provided by Freedom House International

Primary education: primary school enrollment among total population

depc84: Gross domestic product per-capita in 1984

depc89: Gross domestic product per-capita in 1989

POP: Average population growth

Corrup *G : Interaction term between Corruption and the government expenditures share
Lat.Amer: Dummy variable taking the value of l for Latin American countries and 0
otherwise

Euro: Dummy variable taking the value of 1 for European countries and 0 otherwise
Africa: Dummy variable taking the value of l for African countries and 0 otherwise
Dummy: Dummy variable taking the value of 1 for countries with a freedom index of 10

or more, and 0 otherwise.

37

Appendix 3: Average Indexes of Corruption, Freedom and Growth (1984-1992)

Country ICRG Freedom Growth Country ICRG Freedom Growth
Zaire 0.00 6.38 0.96 Iran, ls 5.35 5.79 0.98
Bangladesh 1.18 3.96 1.02 Zimbabwe 5.49 4.96 1.00
Haiti 1.60 5.83 0.97 Jordan 5.56 4.54 0.99
Paraguay 1.74 4.17 1.00 Cote d'lvore 5.62 5.42 0.96
Guyana 2.01 3.96 1.00 Bahrain 5.69 5.42 0.98
Indonesia 2.22 5.67 1 .04 Malta 5.76 1 .58 1.05
Sierra Leon. 2.65 5.58 0.99 Guinea 5.83 5.88 1.00
Gabon 2.71 5.04 0.98 Niger 5.83 5.46 0.97
Mali 2.78 4.92 1.01 Algeria 6.04 5.71 0.99
Bolivia 2.99 2.54 0.99 Malawi 6.04 5.75 0.99
Pakistan 3.19 4.21 1.03 Burkina F. 6.06 5.58 1.01
Nigeria 3.26 5.63 1.01 Argentina 6.18 2.00 1.00
Sudan 3.26 6.21 0.97 Italy 6.25 1 .21 1 .02
Guatemala 3.33 3.92 1 .00 Brazil 6.32 2.58 1.00
Guinea B 3.33 5.54 1.01 Botswana 6.46 2.13 1.06
Honduras 3.33 2.63 1.00 Madagascar 6.67 4.29 0.98
Togo 3.33 5.83 0.99 Malaysia 7.01 4.33 1 .04
Philippines 3.40 3.04 0.99 Spain 7.01 1 .33 1 .03
Jamaica 3.61 2.25 1 .01 Poland 7.36 3.46 1.00
El Salvador 3.75 3.29 1.01 Hungary 7.50 3.21 0.99
Sad. Arabia 3.96 6.67 0.98 Greece 7.64 1.79 1.02
Zambia 4.17 4.33 0.97 Portugal 7.78 1 .29 1 .03
Cameroon 4.17 5.96 0.96 Singapore 7.92 4.50 1.05
Uganda 4.17 5.00 1.00 Austria 8.33 1.00 1.02
Egypt 4.24 4.92 1.01 Costa Rica 8.33 1.13 1.02
Surinam 4.32 4.08 0.96 Israel 8.33 2.00 1.02
Ethiopia 4.32 6.17 0.97 Japan 8.33 1.29 1.04
Morocco 4.44 4.67 1.01 United S 8.40 1.00 1.02
Trinidad 4.44 1.21 0.98 Belgium 8.61 1.00 1.02
India 4.51 3.04 1.03 South Africa 8.82 4.58 0.99
Ghana 4.58 5.58 1 .02 France 8.89 1 .50 1.02
Kenya 4.86 5.75 1.00 United K 8.96 1.25 1.02
Romania 4.93 5.63 0.96 Canada 10.00 1.00 1.02
Peru 4.93 3.54 0.98 Denmark 10.00 1.00 1.02
Tunisia 4.93 5.13 1.02 Finland 10.00 1.33 1.01
Venezuela 4.93 2.13 1.01 Iceland 10.00 1.00 1.01
Colombia 5.00 3.00 1.02 Luxemburg 10.00 1.00 1.04
Congo 5.00 5.33 0.98 Netherlands 10.00 1.00 1.02
Dom. Flep. 5.00 2.46 1.00 Norway 10.00 1.00 1.02
Ecuador 5.00 2.33 1.01 Sweden 10.00 1.00 1.01
Gambia 5.00 3.25 1.00 Switzerland 10.00 1.00 1.01

Mexico 5.00 3.83 1 .00
Senegal 5.00 3.75 0.99
Sri Lanka 5.00 4.08 1.03
Thailand 5.00 3.42 1 .07
Uruguay 5.00 2.04 1 .03
Chile 5.07 3.63 1 .05
Turkey 5.21 3.63 1.03

38

REFERENCES

39

References

Alesina, Alberto, Nouriel Roubini, Sule Ozler and Phillip Swagel. “Political Instability
and Economic Growth”, NBER WP #4173, September 1992.

Brunetti, Aymo, Gregory Kisunko and Beatrice Weder. “How Businesses See
Government”, IFC discussion paper, 33, 1998.

Bruno, Michael and William Easterly. “Inflation Crisis and Long Run Growth”, World
Bank Policy Research Department, June 1996, manuscript.

Cadot, Olivier. “Corruption as a Gamble”, Journal of Public Economics, vol. 33, pp.
223-244, 1987.

Freedom in the World: 1996-1997.

Friedrich, C]. “The Pathology of Politics, Violence, Betrayal, Corruption, Secrecy and
Propaganda”, Harper and Row, New York, 1972.

Gray, Cheryl W. and Daniel Kaufmann. “Corruption and Development”, Finance &
Development, pp. 7-10, March 1998.

Guasch, J. Luis and Robert W. Hahn. “The Costs and Benefits of Regulation:
Implications for Developing Countries”, The World Bank Research Observer, vol.
14, no.1, pp. 137-158, February 1999.

Hall, Robert E. and Charles Jones. “Why do Some Countries Produce so Much More
Output Per Worker than Others?”, Quarterly Journal of Economics, pp.83-l 16,
February 1999.

Huntington, Samuel P. “Political Order in Changing Societies”, New Heaven: Yale

University Press, 1968.

40

Jones, Larry E. and Rodolfo E. Manuelli. “A Convex Model of Equilibrium Growth:
Theory and Implications”, Journal of Political Economy, pp. 1008-1038, October
1990.

Kaufmann, Daniel and Shan-J in Wey. “Does ‘Grease Money’ Speed Up the Wheels of
Commerce '2”, Paper presented at the American Economic Association Meeting,
Chicago, 1998.

Keefer, Philip and Stephen Knack. “Why Don’t Poor Countries Catch Up ? A Cross-
National Test Of An Institutional Explanation”, Economic Inquiry, vol.35, No.3,
pp.590-602, July 1997.

Klitgaard, Robert. “Controlling Corruption”, University of California Press, 1988.

Krueger, Anne 0. “The Political Economy of the Rent-Seeking Society”, American
Economic Review, vol. 64, pp. 291-303, June 1974.

Leff, Nathaniel H. “Economic Development Through Bureaucracy Corruption”, The
American Behavioral Economist, vol. 8, no. 2, pp. 8-14, November 1964.

Lui, Francis T. “An Equilibrium Queuing Model of Bribery”, Journal of Political
Economy, vol. 93, no. 4, pp. 760-81, August 1985.

Mauro, Paolo. “Corruption and Growth”, The Quarterly Journal of Economics, pp.681-
712, August 1995.

Mauro, Paolo. “Corruption and the composition of Government Expenditure”, Journal of
Public Economics, 69, pp.263-79, 1998.

McMullan, M. “A Theory of Corruption”, Sociological Review, vol. 9, 1961.

Myrdal, Gunnar. “Corruption: Its Causes and Effects”, Political Corruption A Handbook,

Transaction Publishers, pp. 953-962, 1989.

41

North, Douglass C. “Institutions and Economic Performance”, Rationality, Institutions
and Economic Methodology, edited by Maki, Gustafson and Knudsen (1993)

Nye, Joseph S. “Corruption and Political Development: A Cost-Benefit Analysis”,
Political Corruption A Handbook, Transaction Publishers, pp.963-984, 1989.

Rebelo, Sergio. “Long Run Policy Analysis and Long Run Growth”, Journal of Political
Economy, pp. 500-521, June 1991.

Sachs, Jeffrey D. and Andrew M. Warner. “Sources of Slow Growth in African
Economics”, Journal of African Economies, vol. 6, no.3, pp.335-76, 1997.
Shleifer, Andrei and Robert W. Vishny. “Corruption”, Quarterly Journal of Economics,

vol. 108, n. 3, pp. 599-617, Aug.l993.
Tanzi, Vito and Hamid Davoodi. “Corruption, Public Investment and Growth”, IMF
Working Paper, WP/97/139, October 1997.

World Development Report 1997. “The State in a Changing World”, World Bank (1997)

42

CHAPTER 2

REGULATIONS, CORRUPTION AND INCOME INEQUALITY

1. Introduction

Recently, there has been increased interest among economists in studying the
macroeconomic implications of a country’s political institutions. Specifically, it has been
argued that different elements like the access to political power, the rule of law,
corruption, economic freedom, bureaucratic efficiency, etc., have important influences on
the behavior of societies and affect both the creation and the distribution of wealth (see
for example Johnston (1989), Atkinson (1997), Keefer and Knack (1997), Guasch and
Hahn (1999), Hillman and Swank (2000)). All over Latin America and in most of the
developing world two of these elements stand above the rest: cumbersome government
regulations and corruption.

On the one hand, the amount of government regulation and the excessive paper
work associated with it have become obstructive for economic agents who wish to invest.
De Soto (1989), for example, describes this clearly for the Peruvian economy, where to
legally set up a (fictitious) clothing factory took 289 days and $1231 in related expenses
(an amount equivalent to 32 minimum monthly wages at the time) including necessary
bribes”. De Soto also reports similar problems for the housing and transportation
industries, where the majority of construction sites and transport vehicles operate without

official permits.

 

‘5 “Even to get a license to open a street kiosk or sell from a pushcart. . .” takes “forty three days of
commuting between bureaucrats and $590.56”.

43

Similar evidence of obstructive government regulations is often encountered
throughout the developing world. In 1997, for example, the World Bank conducted a
survey in 72 countries and asked firm managers to rate the relative importance of
different obstacles for the normal operation of their projects (see Brunnetti, Kisunko and
Weder (1998)). The results of the survey exposed tax regulations, along with other types
of government regulations and corruption, as the worst obstacles for doing businesses.
The level of these regulations was considered by the businessmen to be a higher obstacle
than their unpredictability in 65 of the 72 countries, and more problematic than policy
instability and crime in at least 57 of the 72 countries”.

On the other hand, in most of these economies it is understood that certain public
officials can grant investors the right to ignore these regulations (or at least eliminate the
costs associated with them) in exchange for a bribe or a “gift”. Corruption is such a
pervasive phenomenon that citizens “have accepted it as a social rule” (Marjit et al.
(2000)) and the extent of corruption is determined by the costs associated with
bureaucratic delays and regulations. Gray and Kaufmann (1998), for example, reported a
“positive relationship between the extent of bribery and the amount of time that
enterprise managers spend with public officials”. Similarly, as shown in Figure 1, the
data collected by the survey “Obstacles for Doing Business” (1997) can be used to
illustrate a positive correlation between the level of corruption and the burden imposed

by government regulations as perceived by the businessmen surveyed”.

 

'6 Further evidence for specific countries can be found on the World Bank’s World Development Report
(1997).

'7 The variables used to create this average were: Regulations for starting a new business/new operation,
Regulations of foreign trade and Tax regulations.

In the aggregate, the combination of bribery and excessive red tape not only
represents a drain on investment but can also affect the distribution of income. Given the
presence of cumbersome bureaucratic rules. corruption frequently takes the form of cash
bribes to junior officials, who control the paperwork associated with such rules and,
therefore, are able to reduce the legal, administrative and time costs for the investors. As
observed by Lowder (1989), this sort of corruption often acts as a “service charge” or fee
charged by the official in exchange for his services without regard of who is paying the
bribe. Thus, the burden imposed by this practice is disproportionately severe for the
poorest.

A similar conclusion was obtained by the European Bank for Reconstruction and
Development in their Transition Report for 1999 (EBRD (1999)). Their study shows that
the burden of bribes necessary for investment is higher for smaller investors; in fact, the
EBRD figures show that on average, the bribes paid by small Eastern European firms as a
percentage of annual revenues was twice that paid by large firms. Furthermore, the study
attributes the increased level of corruption during the latest years to the increased
willingness of businessman to pay bribes in order to keep “the state from wasting
management time”.

In addition, the distributional consequences of this type of corruption can also
arise from the way in which bribe revenues are allocated among the population. On this
matter, the anecdotal evidence suggests that richer individuals are likely to receive a
much bigger share of corruption revenues than poorer ones. In almost every Latin
American country, for example, high-ranking officials have been accused of “bending the

rules” in order to favor sympathetic businesses and personal friends with bureaucratic

45

promotions, government loans or privatization contracts (Serbin (1993), Manzetti and
Blake (1996), Klitgaard (1988)).

In her study of Cuenca (Ecuador), Lowder (1989) concludes “there is little doubt
that particular groups have benefited disproportionately from the central govemment’s
development policies and that the distribution of resources was orchestrated by an elite”.
Furthermore, she explains how Cuenca’s select few owe their position to their “inherited
status” and “blood ties”, and not to a democratic selection. Similar descriptions have also
been made for countries like China, Italy, Nigeria, Kenya, Russia, India, Uruguay, etc.
(Rowley (2000), Levin (2000), Tanzi (1995), Klitgaard(1988)).

Thus, even when in principle there exists competition for votes to determine who
controls the seat of political power, it is other factors like wealth, blood, family history,
social status or education level that determine ultimately who is to benefit from these
privileged positions and the rents generated by corruption (see for example Lowder
(1989), Rowley (2000), Rauch and Evans (2000)). In the words of Vargas Llosa when
referring to Latin America, “the names of the favored individuals or consortia change
with each government, but the system is always the same: not only does it concentrate the
nation’s wealth in a small minority but it also concedes to that minority the right to that
wealth” (De Soto (1989)).

Although central to the economic reality of several developing regions, the related
literature on these topics remains sparse, especially with respect to the distributional
aspects of institutionalized corruption and red tape. In a theoretical study, Norris (1998)
showed that an economy in which access to political positions implies the acquisition of

economic rents as well, it is the richer individuals who have a stronger incentive to join

46

political life. Norris does not explore the macroeconomic implications of her
conclusions, nor does she analyze the role of investment regulations. On the empirical
side, Sarel (1998) reported a positive correlation between the Gini coefficient and the
level of corruption using a cross-section of countries. The empirical work on
distributional issues, however, is severely constrained by the lack of adequate data sets on
income inequality, corruption, and the costs of regulations.

With respect to the effects of corruption and bureaucratic efficiency on the
creation of wealth the literature is more generous. Authors like Mauro (1995), Keefer
and Knack (1997) and Hall and Jones (1999), for example, have found empirical
evidence showing that increases in measures of corruption, bureaucratic delay and
institutional inefficiency across countries are negatively correlated with the average
growth rate. Others like Me’ndez and Sepulveda (2000) analyzed this matter from a
theoretical perspective and concluded that high levels of corruption have a detrimental
effect on growth even in the presence of costly government regulations.

This paper studies the effects of widespread corruption on both the aggregate
level of income and the inequality of the income distribution. It presents a general
equilibrium model in which individuals face a set of bureaucratic regulations, which they
can comply with or they can circumvent by paying a bribe to a government official. The
model assumes a heterogeneous population and acknowledges the existence of corruption
revenues that can be distributed among the individuals in a variety of ways. In order to
do this, a variant of the Diamond (1965) overlapping generations model is developed in
which the rents of corruption are allocated according to an exogenous parameter that

determines how unequal the distribution of these rents is. Then, by solving the model

47

one is able to study the distributional consequences of corruption and its impact on the
steady state level of income from a theoretical point of view.

The next section of the paper presents the basic theoretical model, the equations
that characterize the steady state equilibrium and the comparative statics resulting from
its numerical solution. Section 3 expands this basic model by endogenizing the bribes
charged by the corrupt officials and conducts numerical exercises similar to those in
Section 2. Finally, Section 4 provides some conclusions and possible areas of future

research.

2. The Basic Model

The economy is populated by a large number of consumers who live two periods,
youth and old age. Each individual i is endowed with 1, units of effective labor, where l, is
distributed exogenously along the interval (0,00) according to the probability density
function f (1). When young, the individual supplies his effective labor inelastically in
exchange for the wage rate per unit of effective labor w. He then allocates his total
income between consumption and investment and gives birth to exactly one other person.
At old age, the individual receives income from savings, consumes it all and disappears
from the economy.

The preferences of all individuals of generation t are represented by the same
utility function U (c,, cm), where ct is consumption at time t and cm is consumption at

time t+1. In this model, U (ct, cm) takes the form
U (Co 61.1) =1nct+131nceo (l)

where B represents a time discount factor.

48

The economy’s aggregate production function exhibits constant returns to scale
and is expressed as
Y, = A K,“ L,” (2)
where Yt is total output at time t, K1 is the aggregate stock of capital at time t and I4 is

aggregate effective labor supplied at time t, which is defined as
L, = j 1. f(1)dl. (3)
0

Thus, in what follows, the density function f(l) is restricted so that the value Lt exists and
is finite at all times. In addition, the productive sector is assumed to be competitive so
that the marginal products of capital and labor determine both the price of capital and the
wage rate, respectively.

The government in this economy is composed of a number of public officials
whose single function is to impose a set of regulations on investment. For simplicity, it is
assumed that the only cost associated with these regulations is the opportunity cost of all
these resources spent by investors in relation to bureaucratic paper work; this cost is
taken as exogenous by the agents and represents a deadweight loss to society. Instead,
one could think of these regulations as taxes that are used by the government to provide
public goods. This alternative assumption, however, would not alter the results obtained
in the model as long as part of the costs paid by the investors represent a loss to society.

Given the regulations, the individuals can invest their resources in two different
ways: they can follow the established government procedures and pay the costs
associated with them, or they can pay a bribe 0 to a corrupt government official who, in

exchange, allows them to invest without any other requirement or delay. Thus, it is

49

assumed here that the individuals are always able to find a corrupt official that is willing
to engage in these activities without any real costs and that the amount of the bribe
demanded is known by all agents.

The total amount of bribes collected at time t, R., is then redistributed among the
consumers in a lump sum fashion, such that the rents from corruption received by

individual i at time t, rm, are given by

 

= . 7’
’13: "R: 11' ’ (4)
1 . .
where n = 00 and y are posrtrve constants.
[17 - f(l)dl
0

This specific form guarantees that I rt (l) f (l)dl =Rt at all times and for all
0

values of 7 such that the y‘h moment of the distribution exists and is finite. Furthermore,
it allows one to study the economy when the rents of corruption are distributed in a
variety of ways, for a higher value of 7 implies that a higher share of these rents go to the
richer sectors of the population. A value of y = 0, for example, implies that the rents of
corruption are distributed equally among all individuals while a value of y = 1 implies
that these rents are distributed as a linear function of the individual’s effective labor. As
mentioned in the introduction, however, anecdotal evidence suggests a value of y > 0.

In this way, corruption can affect the distribution of income both because it alters
the incentives for investment and because it acts as a redistributive tax from the general

public to the well connected. The assumption made about the allocation of the resulting

50

bribery rents allows one to distinguish between these two effects and study them
separately.

Define VH as the maximum utility attainable by an individual i who does not pay
the bribe, then

) (5)

V”: max U(ct,c

{Ct’c } t+l

t +1
st. 1, wt + rm = ct + s, + b st
81(1 +it+l)= C1+la
[1.1 = 11 R1 117
given wt, it“, 11., Rt, 11 and b.
Here b represents the share of the investment project that is lost because of the costs
associated with the paper work required. These costs are assumed to increase with the
size of the investment, reflecting the fact that bigger businesses may have a bigger cost of
capital, are subject to more regulations as the scope of their actions becomes broader and
are likely to incur in higher administrative costs before the permit is granted.
Similarly, define VC as the maximum utility attainable by an individual i who

pays the bribe 0, then

) (6)

Vc = max U(ct,c

{Ct’c } t+1

t+l
s.t. 1,wt +r,.,= c,+s,+0
31(1 +it+l)=ct+la
ri,t=nRt 117

given Wt, iv”, 1i, RI? n and e.

51

Here im represents the net real interest rate at time 1+1 and the bribe 0 is assumed to be
the same for all investors. Moreover, since the individuals invest only when young, the
bribe is paid only when young also, and it takes the form of a once and for all fixed
payment.

Thus, the bribe 0 acts as a “service charge” demanded by the official in exchange
for his services, reflecting the empirical observations about the form of these bribes
(Lowder (1989)) and the heavier burden of bribery for smaller investors (EBRD 1999).
Throughout this section the value of 0 is taken as exogenous, while in Section 3 this
assumption is eliminated. A comparable way of modeling such fees has also been used
by Norris (1998) and Ahlin (2000).

Thus, given the individual’s endowment, he decides to pay the bribe as long as

Q a (VB — Vc) < 0. (7)
The aggregate savings at time t by the agents of generation t, St, can then be expressed as
the sum of the individual savings of both types of investors: those who follow
government rules (H), and those who pay the fee and may overlook the regulations (C).

That is,

S, = lSzUW + lStUW' (8)

H
Finally, the specific form for the density function f(l) is obtained from the Dagum
Type I cumulative density function defined as
F(x)=(1+2x"5)‘0. (9)
This specific function has been shown to fit actual income distributions remarkably well

(see Dagum (1977)), and at the same time it provides closed form probability density and

52

distribution functions”. As explained by Dagum and Lemmi (1989) and Dancelli (1986),
the parameter A is a parameter of scale, while the other two parameters (8, o) are
inequality parameters. Specifically, Dancelli (1986) showed that the degree of inequality
associated with this distribution is a strictly decreasing function of both 8 and 0'9.

In addition, for the Dagum Type I density function, it can be demonstrated that all
moments of order r about the origin exist for all values of r such that r < 8 (see Dagum
and Lemmi (1989)). Thus, in order for the values 11 and I4 to be finite it. is necessary for
the value of 8 to be greater than one in the case of I4, and greater than 7 in the case of n.
The empirical estimates available suggest a value of 8 that is close to 4 and a value of 7
below 1 (see Dagum and Lemmi (1989)).

A competitive equilibrium for this economy consists of a sequence of values {Yb
K, 1.4, 1‘, wt} for te(0,oo), and set of individual’s decision {ch cm, 8,} for {i, t}e(0,oo);
such that for these values the following conditions hold:

a. Given the values for 0 and R, the individual decision rules solve
maximization problems (5) and (6),

b. the competitive firms maximize profits,

c. all markets clear.

Specifically, since the capital market must clear in equilibrium, for all periods it
must be true that

Km = S, (10)

where S represents aggregate savings by the young generation at time t as defined before.

 

l8The exponential density function was also used without altering the main results.
'9 Dancelli (1986) demonstrated this fact for the Gini coefficient associated with the Dagum Type 1
distribution.

53

2.1 Solution of the Basic Model

By solving the individual maximization problems (5) and (6), substituting the

solution into (7), and simplifying the expressions one obtains the following:

lw, +R,l.7n ,6(1+i,+,)(l.w, +R,l,.7n)
V :1 I I l
” n[ 1+,B )+flln[ (1+b)(1+,6) ] (1”

7 _ ' 7 _
Vc =1“ liw, +R,l,. n 6 +,Bln fl(1+r,+l)(l,w, +R,l,. n (9) , (12)
1+fl (1+3)

 

 

 

 

£2 = (1 + fl)ln[l,.w, + R,l,7n] — (1 + fl)ln(l,w, + R,t,7n —19)— flln(1+b). (13)
The properties of the function 9 are important to the analysis since they determine the

individual decision on whether to pay the fee or not.

Proposition 1: Given positive values for 0, R! and w, at any time t there is a unique
positive value of 11 = 1: such that any individual with l, > 1: chooses to pay the bribe and
any individual with l, < l: chooses to pay the costs of investment associated with the

regulations.

Proof: Using equation (13), at any time t one can find a value 1; = l: for which it is true

that Q = 0, where this value of l: is given by the following equation:

[3
6(1+b)/+fl
)6
(1+b)/+'B—l

 

=1: :1:
. 7 =
It Wt + Rt (It ) n (14)

54

From equation (14) it follows that l: > 0 for any 0 >0. Furthermore, differentiating

equation (13) with respect to I, one obtains:

7—1 y—l
aQ:(1+fl)(wt+7Rtli n)_(l+,6)(wt+thli n)
3’,- l.w +R17n l.w +R17n—6

1 t t1 1 t tt

<0 (15)

 

 

for all values of 0 > 0.

Given the consumers’ decision rules and the value of 1:, the total rents collected

at time t can be expressed as
R.=9<1-F<1.*))=011-<1+4<I,*)‘5)“’1. (16)

Substituting equation (16) into (14), one can find a solution for is conditional on the

value of w(. Finally, with this solution one can obtain the level of aggregate savings S as

,B(wl+R17n) °°,B(wl+Rlyn—6)
’ ’ -f(l)dl+ ’ ’

(1+b)(l+.5) 1* (1+3)
t

- f(l)dl. (17)

 

St:

 

Using the fact that product markets are competitive and the wage rate takes the
value of w. = A (l-Ot) K5114“, equations (10), (14), (16) and (17) provide a differential
equation for the value of K.. The corresponding phase diagram for this equation is
illustrated in Figure 2 and suggests the existence of a unique positive steady state
equilibrium20 for the model. The nonlinear nature of these equations, however, makes it

very difficult to obtain an analytical solution for the steady state of the economy and thus,

 

2° The diagram in Figure 2 corresponds to the solution of the model with parameters y = l, or = 0.4, [3
=0.95, 2» =1, 8 = 4, o = 0.6 and b=0.l.

55

a numerical solution of the model that allows one to study the relevant comparative
statics was found.

In order to perform the numerical analysis required, values for the exogenous
parameters 01, [3, 3., A, o, 8, and b must be chosen. Throughout all of the exercises
presented here, the values of or and B were set equal to 0.4 and 0.95 respectively. The
first one of these values is set to match the capital share of income in several countries as
reported by Durlauf and Johnson (1995), while the second one is simply reflecting the
consumer’s preference for one unit of utility in the present relative to one unit of utility in
the future. As for the values of I. and A, since they are scale parameters, they could be
set to any number without altering the main results. Here, the value of A was set equal to
1 and, for simplicity, the value of the total factor productivity constant A was set equal to
the value of the constant L“ in a way such that the expression for the wage rate can be
simplified even further to wt = (l-or) K.“.

The income distribution parameters 8 and d were set equal to 4 and 0.6
respectively. The choices made for these parameters were based on several estimations
described by Dagum and Lemmi (1989); as they pointed out, the estimates for the
parameter 8 “often take values in the neighborhood of four”, while the estimates for the
parameter d were reported to be less than one in almost all of their regressions.
Furthermore, the distribution can be shown to be unimodal for values of o, 8 such that the
product (0 8) >1. Here the value of a was set equal to 0.6. A higher value of 0 would
yield a higher variance for the distribution, but would not alter the qualitative analysis

presented below.

56

Finally, the value of b is set in line with the empirical estimations of the total
costs of government regulations. Guasch and Hahn (1999), for example, reviewed the
existent empirical estimates and reported the costs of governmental red tape and
regulations to fall in the range of 7% to 19% of GDP for countries like Australia, Canada
and the USA. Similarly, the average firm in the World Bank survey (1998) reported that
between 25% and 50% of the senior’s management time was dedicated to tasks related
with the interpretation of government laws and regulations.

Although these numbers provide one with some idea about the value of b, their
estimation is faced with many limitations and, therefore, it is important to consider
several values for the parameter b. Throughout this section, the value of b is chosen to be
0.1; in Section 3, however, the analysis concentrates on the role of the costs imposed by
the legal investment procedures, and the value of b is allowed to vary within a wider
range.

Figures 3 and 4 describe two results obtained for the basic model. Here the
parameter 0 is allowed to vary within a range such that the resulting probability of an
individual choosing to pay the bribe is close to zero for the highest value of 0 and close to
one for the lowest value. Within this range, the size of 0 relative to the average income
level of an individual stayed below 10%.

Figure 3 illustrates the changes in the steady state level of income per unit of
effective labor as the exogenous level of bribe 0 changes leaving all other parameters
unchanged. When the bribe 0 increases, more people decide not to pay the bribe and as a
result, more resources are lost due to the costs incurred by honest investors. In addition,

those individuals who keep paying the bribe see the share of their income available for

57

investment diminished by the more expensive bribes. Thus, as shown in Figure 3, the
corresponding level of income decreases as corruption (measured by the size of the bribe)
increases.

Figure 4 illustrates the relationship between the bribe level and the income
distribution measured by the coefficient of variation of the present value of total
consumption expenditures. As the bribe becomes more expensive, two opposing effects
take place and generate the non-monotonic relationship shown in this figure. On the one
hand, the variance of the distribution decreases since only the richer individuals pay the
new bribe while the poorer ones are directly unaffected by the change. On the other
hand, the income level for the average individual is also decreasing relative to both the
poorest and the richest persons and therefore, causes the coefficient of variation to
increase.

Once 0 has reached a certain level, the number of corrupt investors relative to
honest ones becomes very small, and the loss of resources due to more agents having to
incur in the time costs of regulations are minimal. Then, as shown in figure 4, the impact
on the coefficient of variation caused by the decrease in the variance of the distribution
dominates the effect of the lower average income level.

Changes in the value of the bribe 0 that are independent of the costs of complying
with bureaucratic procedures, like the ones studied so far, can be interpreted as the effect
of other institutional variables like the administration of justice, general attitude of
society towards corruption, etc. However, the anecdotal evidence suggests that the bribes

charged by the officials depend importantly on the costs incurred by the investors were

58

they not to pay the bribe. Thus, in order to incorporate this element, the next section

treats the bribe 0 as an endogenous variable and a function of b.

3. The Model with Endogenous Bribes

This section expands the basic framework presented before by considering the
bribe as an endogenous variable in the model, while leaving all other aspects of the model
unchanged. Specifically, corrupt officials are assumed to collude and act as one single
official who chooses the level of bribe so as to maximize the total amount of rents
produced by corruption R. This sort of collusive behavior has been observed in several
instances (see for example Loaiza (2000)) and it reflects the fact that government
officials in charge of implementing the regulations often work together in a single
department for which each official’s function is a complement to others.

As before, after solving the individual’s maximization problem, the amount of

total rents R. (0) can be expressed as:
R. = 0 (1.1205(0)) )= e 11 -<1+ 2.0:" (9»- 5 )“01. (18)

where the value of 13(0), now expressed as a function of 0, is given by equations (14) and
(18) just as it was in the case of exogenous bribes. Thus, the corrupt officials’ problem is
reduced to choosing the value of 0 so as to maximize the total rents collected; that is, he

solves the following static problem:

max0 [1 -(1+t(1*(6))‘5)‘0], (19)
161 ’

given 71., o, 8 and 15(0) .

59

Differentiating equation (19) with respect to 0, one obtains the following first order

condition for the corrupt official:

 

 

:1:
* d1 (19)
1—(1 + 2(1:(6))‘ 5)‘ 0 — 6082(1+ 71(1’ (9))‘ ‘5 )"0r '1(1:(19))‘ 5 ‘ 1 —:119— = 0, (20)
where
dl:(9) c-n<1,*(6»711—<1+2(1,*(6))"5)‘“1
d‘9 w, +6-n10113607“11—0when-‘5)‘01—0611:<6))7‘5"<1+A<zf(6))‘5)“"“1

is found by substituting equation (18) into (14) and totally differentiating the resulting
expression. Here c is a constant that takes the value

.5
(1+b)/+fl

c: . (21)

.5
(mm/+34)

Then, at any time t the equilibrium values {0,1 l‘*(0(')} are given by the value of

 

0t that satisfy equations (l4), (l8) and (20) simultaneously. Given these values one can
obtain the level of aggregate savings St conditional of the wage rate w, and the steady
state level of income exactly as it was done in the previous section.

The results of the corresponding numerical exercises for this model are illustrated
in Figures 5 through 8. Figure 5 presents the resulting steady state income levels for
different costs of regulations b and different values for the parameter y. As expected, the
steady state income level is affected negatively by the amount of regulations. A

reduction in the cost of regulations from 20% of gross investment to 10%, for example,

60

leads to an increase in steady state income of approximately 0.9%. As before, the size of
these changes is not altered importantly by the value of y.

In Figure 5, when the cost b increases, the corrupt officials also increase the bribe
0 in order to maximize total revenues from corruption. As a result, the level of aggregate
income is affected negatively both because more resources are lost in the form of paper
work costs and because investment becomes more expensive for those who pay the bribe.
Here, in contrast with the exogenous bribe case presented in Section 2, the proportion of
investors who pay the bribe remains roughly constant.

Figure 6 illustrates how an increase in the costs b causes an increase in the
inequality of the income distribution measured by the coefficient of variation of total
consumption expenditures. When b increases, the average income level of the economy
decreases and causes the coefficient of variation to become greater than before.
Simultaneously, since the rents of corruption are redistributed back to the consumers in
an unequal fashion, as the public officials adjust the bribe 0 upwards and the number of
bribe payers remains constant, the variance of the distribution also increases. In this
figure, an increase in the costs of regulations from 10% of gross investment to 20% leads
to an increase in the coefficient of variation of about 10% for the case of y = 2 and less
for the other cases.

In fact, in both sections 2 and 3 the redistribution parameter 7 has a notable
impact on the aggregate income distribution independently of the extent of the costs b.
By keeping the cost b constant at 0.2 and increasing the parameter 7 from 1 to 2, for
example, the coefficient of variation grows from 0.451 to 0.526, a change of almost 17%.

Such result cannot be overlooked, since it suggests that a large part of the distributional

61

consequences of corruption is due to the lack of adequate and equitable access to political
power alone.

Figure 7 illustrates how the level of corruption measured by the size of the bribe
increases when the cost of regulations b increases. As explained before, higher
regulations motivate the officials to charge a higher 0 since the number of investors
willing to avoid the regulations becomes higher. This result matches the positive
correlation between the level of corruption and the time costs of government regulations
that was reported by Gray and Kaufmann (1998) and that was also illustrated by the
survey data presented in Figure 1.

Finally, Figure 8 shows the relation between the steady state level of income and
the redistribution parameter y while leaving all other parameters unchanged. As the
parameter 7 increases, the resulting rents from corruption concentrate even more in the
hands of a reduced group. As a result, two opposite effects on the level of income take
place: On the one hand, less people are willing to pay the bribe and more resources are
lost in bureaucratic procedures, thus affecting the steady state level of income negatively.
On the other hand, bigger values for y affect the steady state level of income positively as
richer individuals, who have higher incentives to invest, capture most of the corruption
rents. As shown in the figure, the second effect dominates the first one for big enough

values of y.

4. Conclusions and Future Research

The corruption phenomena can take many forms and each one of these can have

separate and distinguished effects on the aggregated variables of the economy. The kind

62

of corruption addressed here refers mainly to the bribes paid by economic agents in order
to avoid the costs generated by bureaucratic regulations and procedures. This kind of
corruption has been reported frequently in several regions of the world and has become
part of every day life for many.

By imposing numerical values for the model’s parameters and simulating the
comparative statics, this paper provides important intuition about the aggregate economy
that cannot be obtained empirically given the significant constraints imposed by the
limited data available on income inequality, bureaucratic inefficiency, and corruption.
The results obtained throughout the previous sections suggest that the combination of
cumbersome regulations and widespread bribery can alter both the creation and the
distribution of wealth in an important manner. Moreover, the results revealed the
distribution of corruption rents as one of the key elements on the problem.

In the future, the creation of adequate data sets that allow one to distinguish
between the different sources as well as the different kinds of corruption will be, without
a doubt, an important task of research. On the theoretical side, other ways of modeling
corruption need to be explored; specifically, the kind of corruption involving theft of a

public asset, which seems to be quite common in many countries.

63

5.1940

2.2633

 

 

“ O
O
O O
O O
O O
A O
O O O
O O O
O
Q) 0
o 0 00O 0
0% O O O O O
009 000 O o
o @(0080 0 (0(9 0
_ OO 0
8’ 0
0 0
8 0
O
O O
— O
l l l l l
1.74 5.44

Comption

Figure 1: The Level of Corruption vs. the Cost of Government
Regulations

 

 

K1+1
/

0.8-

’ Km
0.6~

//
0.4- /
0.2?
0.2 0.4 0.6 0.8 1 K‘

Figure 2: Phase Diagram for Capital Accumulation.

65

 

 

Income Level

;— Gamma=0 —- Gamma=1 Gammazz

 

 

0.42

 

0.415 7

0.41 i

0.405 ~

0.4

0.395 -

 

 

 

0.39 . T r . .
0 0.005 0.01 0.015 0.02 0.025

Theta

 

Figure 3: Steady State Income Level per Unit of Effective Labor.

66

 

 

 

Coefficient of Variation

 

l
l

— Gamma=0 — Gamma=1 =

 

0.446

 

0.444 ~

0.442 -

0.44 -

0.438 -

0.436 a

0.434 "

0.432 -

 

 

 

0.43 . r r .
0 0.005 0.01 0.015 0.02 0.025

Theta

 

Figure 4: Steady State Coefficient of Variation for Total Consumption
Expenditures.

67

 

 

Income Level

 

2+ Gamma=0 ——e— Gamma=1 ------ Gamma=2 f

 

0.414
0.413 .
0.412 .
0.411
0.41 ..
0.409 7
0.408 4
0.407 -
0.406 a
0.405 .
0.404 -
0.403 . .

 

 

 

 

 

 

 

Figure 5: Steady State Income Level per Unit of Effective Labor. The Case of
Endogenous 0.

68

 

 

Coefficient of Variations

 

._—L Gamma=0 + Gamma=1 —)I(—- Gamma=2 j

 

0.7

 

0.65 -*
0.6 --
0.55 ~
0.5 —

0.45 - K/o/A

0.4 . .

 

 

 

 

 

 

Figure 6: Steady State Coefficient of Variation for Total Consumption
Expenditures. The Case of Endogenous 0.

69

 

 

 

 

 

 

 

Corruption
i;x—Gamma=0 — +- Gamma=1 —e—Gamma=2§
0.025 1 -—~ —-—-—
1 i
0.02 i ‘
l :
i
0.015 j l
1 l
1 i
0.01-] l
1 i
0.005
l .'
0 4:. . . .
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
b

 

 

 

Figure 7: The Level of Corruption as a Function of the Costs of Bureaucratic Rules.

70

l .

 

Income level

0.41109

 

0.41108 ~
0.41107 -
0.41106 -
0.41105 1
0.41104 --
0.41103

0.41102 -

0.41101 -

 

 

0.411 1 4 T
0 0.5 1 1.5 2 2.5 3

Gamma

 

 

 

 

Figure 8: Steady State Level of Income for Different Values of the Redistribution
Parameter y.

71

REFERENCES

72

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76

CHAPTER 3

PRIVATIZATION, DEREGULATION AND CAPITAL ACCUMULATION

1. Introduction

Since the early 1980’s, many countries have privatized and deregulated
intermediate goods industries like gas, electricity or telecommunications that had
traditionally been run by the government. These policy reforms are described by
Newberry (1997), Parker (1998), and Kikery, Nellis and Shirley (1994). The European
Union, for example, has adopted aggressive policies towards the elimination of all
monopolies in the telecommunication market and has conducted a general privatization
program whose sales receipts amounted to more than 3% of total GDP between 1985 and
1995 (Constantinou and Lagoudakis (1996), Parker (1998)). In other regions of the
world, countries like Australia, Chile, Brazil, Argentina and the United States have
implemented similar policies (Winston (1993), Van der Vlies (1996), Vickers and
Yarrow (1991)).

Evidence from specific industries shows that these state-to-market transitions are
usually followed by increased production levels and productive efficiency. In Australia,
for instance, one year after the dissolution of the government monopoly over the
provision of telecommunications services and the introduction of competition, the
cellular mobile market alone had grown by 200% in total sales, while the total
telecommunications sector grew by 9% during the same period (Van der Vlies (1996))”.
In the case of England, total factor productivity of the electricity and telecommunications

industries increased approximately 60% relative to the whole manufacturing sector after

77

the government privatized these public utilities and allowed the entry of competitors
(Bishop and Thompson (1992), Price and Weyman-J ones (1996), Newberry (1997)).

The increased production levels experienced after such reforms have been
attributed to two main factors: first, increased competition provided by free market entry
is expected to improve allocative efficiency of resources, to decrease prices and to
improve monitoring possibilities (Vickers and Yarrow (1991)). Second, the change from
public to private ownership might make investment decisions more flexible and may also
improve the incentives for productive efficiency (Kay and Thompson (1986), Plane
(1992), (1997)).

The empirical evidence on the relationship between privatization and productivity
is mixed and, so far, there are no definite conclusions on whether privatization alone
(without free market entry) has an impact on productivity (see for example Kay and
Thompson (1986), Cook and Kirkpatrick (1988), and Domberger and Pigott (1994)). In
contrast, most empirical studies agree that the presence or absence of competition may be
an important determinant of a firrn’s economic performance even when such firms are
government owned (Domberger and Pigott (1994), Wallsten (1999)). Yet, as pointed out
by Kay and Thompson (1986), it is difficult to distinguish empirically whether any
changes in productive efficiency are caused by privatization or by increased competition.
Part of the difficulty, at least, arises because both privatization and market liberalization
usually occur together within a short time period.

To the extent that energy or telecommunications are complementary to either
physical or human capital, it is expected that any changes in their aggregate level of

output, or in their productive efficiency, would also have an impact on the rate of growth

 

2' Stoetzer and Tewes (1996) report a similar experience for the German cellular telephony market.

78

of the economy. Stern (1993), for example, shows that energy use and quality can be a
limiting aspect for economic growth, and that any factors that cut energy use would also
reduce aggregate income levels. At the business cycle frequencies Hamilton (1983,1996)
show that oil shocks have a substantial impact on aggregate output. Thus, understanding
the different aspects of such state-to-market transitions is of most importance for all those
countries that experience them.

This paper presents a model of capital accumulation under three alternative
scenarios: one where the intermediate sector is composed of a public monopoly under
government control, one where the intermediate sector is dominated by a private
monopoly, and one with a competitive intermediate sector. Here, a regime change from a
public monopoly system to a private monopoly one will be referred to as privatization,
whereas a regime change that introduces competition into a previously monopolistic
market will be referred to as a deregulation of that market.

We use this model to analyze some of the general equilibrium implications of
state-to-market transitions and examine separately the consequences of both, privatization
of public enterprises and deregulation of intermediate markets. In doing this, we abstract
completely from any changes due to productivity differences between public and private
firms. That is, we assume that all firms have access to the same production technology.

The following section describes the theoretical models and defines the
equilibrium for the economies. Sections 3 and 4 present the solutions to the model and
analyze the results. Finally, Section 5 contains the conclusions and the directions for

future research.

79

2. The Model
The economy is populated by a large number of individuals, which we set equal
to one. The individual lives forever and is endowed with k0 units of capital at time zero
and with one unit of labor in each period. At each point in time, he supplies labor
inelastically in exchange for the before-tax wage rate w and supplies as many units of
capital as he has in exchange for the before-tax rental price of capital q. The individual’s

lifetime utility function takes the form

 

where B is the discount factor, ct represents consumption of final goods at time t and Us
is the elasticity of inter-temporal substitution. Every period the individual divides his
total income between consumption at period t, c, and investment at period t, i,. In
addition, it is assumed that every period all units of capital depreciate at the rate 8
regardless of the specific use to which they are put.

Two goods are produced in this economy: a final good Y, that is used for
consumption and an intermediate good E, that is used completely in the production of
final goods. In this sense, the role of E, is similar to the role of many intermediate goods
like electricity, gas, coal, or general energy that are used in almost all production
processes. For simplicity, we assume that this intermediate good is not consumed directly
by the individuals.

The final good is produced competitively by a large number of firms that use the

same constant returns to scale technology, which is given by

80

p p A 1—a
- —
Y,— A<6KF,I+(1 6)Et ) NF,t . (1)

Here Kp, . and NR, represent the amount of capital and labor used in the production of
final goods at time t respectively, A is a constant measuring total factor productivity and
p and or are constants that measure the degree of substitutability and the marginal
products of the factors in the production function. Since the technology exhibits constant
returns to scale, we can assume that there is one firm and that Y. is aggregate output.

At the same time, the intermediate good E is produced using the constant returns

to scale technology

_ 7’ 1‘7
E'_KI,tNI,t ’ (2)

where K1,, and N 1.1 represent the total units of capital and labor used in the production of
intermediate goods at time t respectively, and y is a positive constant. As explained
before, this intermediate good is assumed to be produced under three alternative regimes:
public monopoly, private monopoly and perfect competition. Notice that since the
production function in equation (2) exhibits constant returns to scale we abstract from
any natural monopoly issues. In this model there are thus no efficiency reasons at all for
a public or a private monopoly.

In the public monopoly case, we assume the government captures any positive
profits 7rg generated by the intermediate industry and uses them in the same way as any
other type of revenue. In the case of a private monopoly, we assume that any positive
profits obtained by the firm, up, are distributed equally among the individuals. Finally,

when the intermediate industry behaves competitively there are no profits.

81

The government in these economies taxes labor and capital income at the
common rate 1:. This tax rate is exogenous and assumed to be constant over time. In the
perfect competition and private monopoly cases, we assume that total taxes collected are
redistributed back to the consumers in the form of a lump-sum transfer T. In the case of
the public monopoly, total taxes collected together with public monopoly profits 7rg are
used in order to finance the public capital investment. Specifically, we assume that a
fraction ‘V of total government revenues is used to finance investments in capital for the
public firm and the rest is redistributed back to the consumers in the same fashion as
before. In addition, we assume that the government budget is balanced in each period.

The representative final goods finn’s problem can be expressed as

{K mile/ix E}F(KF,I’Et’NF,t)_ C11 KF,1 - I’1 Er — Wt NF,1 (3)
, F,

a
_ p _ P /P 1—a
s.t. F(KF,I’EI’NF,I)_ A(6KFJ+(1 6)Et ) NF,r .

given q,, rt and w,,
where r. represents the price per unit of intermediate good E at time t, and the firm takes
all prices as given. Similarly, the individual’s utility maximization problem can be
expressed as
0,, C] -a

max 2 13’ t_. (4)

. 00 1—0'
(Ct’lt)t=0t=0
st 212. 111-001. k.+w.)+T.+n,,.1= 2p, 1c.+i.1 and
t=0 t=0

kt+l=(l'8) k1 + it a

82

given Tl, rtpj, wt, q,, p,, I and k0.
Here p, represents the price of a unit of consumption at time t relative to a unit of
consumption at time t +1, and 7:,” equals zero except in the private monopoly case. Since
population size is normalized to unity, individual capital stocks and individual
consumption are equal to aggregate levels. From now on, we will use upper case letters
to denote both.
Finally, in equilibrium the capital and labor markets must clear, that is to say, at

all times it must be true that

Kt = KF.1 '1' K1. 1, (5)

1 = NE: + Nu - (6)
Then, the model is solved under the three alternative specifications for the market
structure of the intermediate sector. Subsections 2.1, 2.2 and 2.3 describe the economy
under these alternative scenarios and provide the definition of equilibrium for each case

respectively.

2.1 The Case of Public Monopoly Intermediate Sector
We chose to model the public monopoly case as a monopolist who maximizes
profits, given an exogenous amount of capital that is determined by the government’s
investment 15. While the objective function of public sector enterprises is by no means
uncontroversial, we assume that the public firm’s objective is to maximize profits. This
provides a convenient comparison to the case of a private monopoly and to the case of
competitive markets, where profit maximization is more natural. Specifically, we assume

that

83

K11: (1‘8) K1.1-1 +1G.1- (7)
As mentioned before, government investment in public capital IQ, is modeled as a fixed
fraction V of total government revenues at time t, which are given by the sum of total tax

revenues and total monopoly profits at time t. That is,
10.1 = ‘1’ lug: + T (Qt Kt + W1)]- (8)
The remaining fraction (l-tll) of the government revenues is redistributed back to the
consumers as the lump sum transfer T.
Given these assumptions, the public monopolist’s problem can be expressed as
max r(Et)-Et _WtNI (9)

{Np

_ 7 1-7
S't'Et_Kl,er ,

given r(Et)9 Kl,“ wt, Q1-
Here, the inverse demand function for the intermediate good r(E,) corresponds to the
representative final good firm’s input demand function resulting from its maximization

problem as stated by (3).

The corresponding equilibrium for this economy is defined as a sequence
(ClaKpEtax,q,9nawt97:97rg.,):0 , SUCh that

i. the individuals solve their utility maximization problem as given by (4),

ii. the final good firms solve their profit maximization problem as given by (3),
iii. the monopolist solves his maximization problem as given by (9),
iv. the government budget is balanced in all periods, and

v. all markets clear.

84

lm:

2.2 The Case of Private Monopoly Intermediate Sector
This alternative scenario presents two important variations with respect to the one
presented in section 2.1. First, the intermediate sector production is now conducted by a
private monopoly. Second, the amount of capital used by the intermediate firm is no
longer determined by public investment but by the firm itself. Thus, the monopolist’s
problem can be written as

max r(Et)-E—th (10)

— K
1 qt
{N,.K,)

I

_ 7’ 1‘7
stiff—KIN] .

given r031). wt. C11;
where the inverse demand function r(E,) is identical to the one used in the public
monopoly case.

The corresponding equilibrium for this economy is defined as a sequence
(CHKHEHXaqt’nawt97:97:,”>20, SUCh that:

i. the individuals solve their utility maximization problem as given by (4),

ii. the final good firms solve their profit maximization problem as given by (3),
iii. the monopolist solves his maximization problem as given by (10),
iv. the government budget is balanced in all periods, and

v. all markets clear.

85

2.3 The Case of Perfect Competitive Intermediate Sector
Since the intermediate good technology exhibits constant returns to scale, there is
no natural monopoly case. We thus can allow this sector to be competitive. When the
intermediate good is produced by a number of competitive firms, the representative
intermediate good firm’s problem can be written as
max r -Et—-wN]—thI (11)

l
{N,.K,1

__ 71’?
s.t.Et.—KINI ,

given r,, w,, q,.
Then, an equilibrium for this economy can be defined as a sequence
(C,,K,,E,, ,,q,,r,,W,,T,):.0, such that:
i. the individuals solve their utility maximization problem as given by (4),
ii. the final good firms solve their profit maximization problem as given by (3),
iii. the intermediate good firms solve their maximization problem as given by (l 1),

iv. the government budget is balanced in all periods, and

v. all markets clear.

3. Solution of the Model: The Cobb-Douglas Case
For a value of p arbitrarily close to zero, the production function described by

equation (1) can be approximated by the simpler Cobb-Douglas technology

_ a (P l-a-(P
Yt—AKF,1E1 NF”! . (12)

86

This special case is useful to start with, since it allows us to obtain closed form solutions
for the model and it provides us with important intuition that can also be used to
understand the more general cases.

Solving the consumer’s dynamic utility maximization problem and the final good
finn’s profit maximization problem we obtain the Euler equation for the consumer and
the first order conditions for the firm. These equilibrium conditions are stated in

equations (1 3)-(16) respectively.

[5:1] =fl(q...(1-r)+(l-6)) (13)
q. = 04K fS'ElNlii'i’ (14)
W. =(1-a-¢)AK?,.EI”NEi-‘” (15)
r. = (04K ?..E.’”"NF§W. (16)

Throughout the rest of the paper, we will focus on steady states and drop time subscripts
whenever possible without the risk of confusion.

Furthermore, after solving the intermediate firm’s profit maximization problem
for the three alternative scenarios in question we obtain additional first order conditions
in each case. Equations (17)-(21) describe these first order conditions for the cases of
public monopoly, private monopoly and competition respectively. In the case of public
monopoly, we obtained only one first order condition for the amount of labor used in the
production process since capital investment is financed out of tax revenue and capital is

made available to the firm free of charge.

w = A(1— 7)092K,‘§N,‘;““"K,"”N,‘"7""“. (17)

87

For the case of private monopoly, an additional condition is obtained regarding the

amount of capital used, thus yielding
w:A(1—7)(p2Kf.’N,';”“”K,7"’N,”"7"”", (18)

q = A 710 zKiN'p”“"“’K1”"Ni"”“’ (19)

Similarly, for the perfect competition scenario the first order conditions are:
w=r(1—7)K,7N,’7, (20)
q = rrKl‘Nl". (21)

The system composed of equations (2), (12), (13)-(16), (20) and (21) can be
solved in order to obtain the steady state equilibrium for the economy with a competitive
intermediate sector; similarly, solving equations (2), (12), (13)-(l6), (18) and (19)
simultaneously, the steady state equilibrium for the economy with a private monopoly
intermediate sector is found. Finally, the corresponding steady state equilibrium for the
public monopoly case is obtained by solving equations (2), (7), (8), and (l2)-(17). Table
1 provides the closed form solutions of these systems of equations for the most relevant
variables in the model.

The analytical comparison of the model’s outcome under the alternative market
structures does not allow us to reach definitive conclusions about the performance of the
public monopoly relative to the other regimes. Thus, a numerical exercise was conducted
where the exogenous parameters of the model are identical in all cases and the fraction \V
of government revenues destined towards public investment is allowed to vary.

The specific amount of public investment on intermediate industries differs

significantly within a short period of time and across countries. Yet, the empirical

88

observations suggest a value of 01 that is very close to zero and even negative. The net
financial flow from the central government to all state-owned enterprises as reported for
several economies by the World Bank indicators, for example, averaged —0.97 % of
GDP between 1990 and 1997 and 0.08 % of GDP for the period 1985-1990 22.

Table 1 lists the parameter values chosen throughout all the computational
experiments in this section. For the parameter y, the share of capital in the value of the
intermediate input, a value of 0.4 was chosen; this value is in line with the empirical
observations about the role of capital in the production of several intermediate goods. In
the case of Britain, for example, Bishop and Thompson (1992) reported capital to
constitute 40.2% of total inputs used in the production of electricity, 44.4% in the
production of gas, and 46.7% for the telecommunication industry. Other values for this
parameter were also considered without altering the qualitative properties of the results.

Because specific data for the parameter (p, which measures the income share of
the intermediate good E, is difficult to obtain”, we performed the calculations under
different values for this parameter. Since before the 1990’s it was common for the
government to control the production of intermediate goods like public utilities and
telecommunications, a logical upper bound for (p is the total economic activity of all
state-owned enterprises as a percentage of GDP during this same period.

The average estimate of this ratio, as reported in the World Bank’s World

Development Indicators, was 0.099 during the period 1985-1990 and 0.11 during 1990-

 

22 The sample consists of 23 countries for the 1985-1990 period and only of 8 countries for the 1990-1997
period. Countries were included based on the availability of the relevant information. The countries in the
first period are: India, Indonesia, Kenya, Republic of Korea, Malawi, Mauritus, Mexico, Morocco,
Namibia, Panama, Paraguay, Peru, Rwanda, Senegal, Sierra Leone, Sri Lanka, Thailand, Togo, Trinidad
and Tobago, Tunisia, Turkey, Uruguay and Venezuela. The countries in the second period are: Indonesia,
Mexico, Panama, Paraguay, Peru, Sri Lanka, Thailand and Turkey.

89

199724. For our purposes, the parameter (p was allowed to range between 0.05 and 0.3.
The choice of values for the parameters 01, 8, and B is perhaps uncontroversial. Setting A
= l is simply a normalization, while a value of t = 0.2, corresponds to government’s
share of GDP in relatively poor countries.

Figures 1- 4 use these different values of (p and compare the resulting steady state
income levels for the three market structures as the value of 11! increases. As shown in all

of these figures, for most values of u! a public monopoly results in levels of income
superior to that ones of a private monopoly but inferior to that ones of perfect
competition. Only when the share of public revenues going to public investment (1}!) was
set very close to zero (from 0.05 in Figure 4 to 0.0017 in Figure 1) did the private
monopoly case produce a higher income level than the public monopoly one.

The differences in the steady state income levels among the three regimes are
substantial. In Figure l, for a value of \l’ = 0.05, for example, the steady state income
level resulting from a public monopoly is approximately 6.8% lower than the one
resulting from the perfect competition case and 10% higher than that from the private
monopoly case.

Similar exercises are conducted in Figures 5 and 6 for the price of intermediate
goods and the wage rate respectively. As shown there, the wage rate in a public
monopoly regime is in most cases higher than the one resulting from a private monopoly
and always lower than the one from competition; similarly, the price of the intermediate

good is lowest in the case of competition and highest in the case of private monopoly for

 

23 See Plane (1992) for a more detailed explanation of the limited available sources of data.

90

big enough values of values of 11!. Figures 5 and 6 were constructed using a value of 0.05
for the parameter (0; however, similar results were obtained when using other values.
These results imply that countries involved in state-to-market transitions are likely
to benefit from the introduction of competition under most circumstances, but will gain
from privatization alone only if the fraction of tax revenues destined towards public
investment was close enough to zero before the change. Even when public investment is
close to zero, the income gains from privatizing a public monopoly without allowing for

competition are small compared to those obtained when competition is introduced.

4. The General CES Technology Case

Although working with a Cobb-Douglas technology in Section 3 simplified the
analysis and provided a useful benchmark for other specifications, it may not be the case
that the elasticity of substitution between physical capital and the intermediate good
approaches one. In fact, it is possible that these factors of production act as complements
instead of substitutes. In this section, in order to overcome such limitations, we solve the
model for the more general CES technology as specified by (1).

In this case, the first order conditions coming out of the final good firm’s

maximization problem are

01-10
q = AaBKf“N‘;"[6K,€ +(1-9)Ep] /p, (22)

 

2‘ Their estimation is based on the value added of state-owned enterprises that generated most of their
revenue by selling goods and it excluded public services like education and health services that are
financed from the government’s revenue

91

w = A(1—a)N;“[6K;3 + (1—6)E”]%’ , (23)

r=Aa(1—o)E/*'N';“[arg +(1—6)EP]”'%, (24)
Similar to the Cobb-Douglas case, in order to solve the profit maximization problem for
the intermediate firm under the three alternative scenarios, we use equation (24) as the
conditional demand function for the intermediate good E. The resulting first order
conditions from the respective problems are given below. As before, only one condition

is obtained in the public monopoly case:

w: [Aa(1—6)(1— y)pN;-“N;"7’P—'Kf7(ar; +(1—6)K,"’N,”“‘7’ )‘Hflx

 

_ _ pr pU-r)
[1+ (1 6X“ mK’ N’ ]. (25)

p(6K;’ + (1—6)K,"7N,"”’7’)

For the private monopoly, in contrast, two first order conditions were obtained:

q=[Aa(l—6)}11V}.‘“Nf"7’pKf7“ (9K; +(1—t9)Kf7N,”“’7’ )a_%]x

 

_ _ P7 PU-Y)
[1+ (1 6X“ p)Kl N] J (26)

max: + (1 — 6)K,”7Nf“‘7’)

w: [Aa(l-6)(l— 7)pN,',’“N}“7’p"Kf7(6K£ +(1—6)Kf7Nf’“’7’ )a_%:|><

 

_ _ P7 I’ll-7)
[1+ (1 9X0! p)K, N, ] (27)

max}: + (1 — 9)K;”N;’“"’)
Finally, for the perfectly competitive firms the corresponding maximizing conditions are

w: r(1—}’)K,7N,’7 (28)

92

q = rrKl’Wi". (29)

The respective profit maximizing conditions of the firms together with the
consumer’s utility maximizing condition, the balanced budget condition and the market
clearing conditions, provide a system of equations that can be solved to find the steady
state equilibrium of the economy for each regime. Those systems, however, cannot be
solved analytically, and a numerical solution was necessary in order to be able to
compare the different steady states. Thus, as in the previous section, parameter values
need to be chosen in order to conduct the exercise.

We start by discussing the range of values chosen for p. The empirical estimates
for this parameter, which governs the elasticity of substitution between capital and
energy, go from —32 t012. Prywes (1986), for example, estimated the elasticity of
substitution between aggregate capital and total energy use for several US industries and
found values that ranged from 0.04 (p = -24) to -0.09 (p = 12). In Prywes (1986)
estimations the value of p takes on values above unity for 6 out of 19 industries, a
theoretical impossibility”. Others like Bemdt and Wood (1975), and Magnus (1979),
however, also obtained similar results.

In a more recent study, Kemfert (1998) conducted a study for Germany both at
the aggregate level and at the industry level. For the aggregate level, Kemfert estimates
the elasticity of substitution between capital and energy to be 0.65 (p = -0.5) while at the
industry level the estimated values varied from 0.93 (p = -0.07) to 0.34 (p = -l.9) for
most industries. Chang (1994), using a measure of energy that included coal, oil

products, natural gas and electricity, obtained a similar estimate for the aggregate

93

Taiwanese economy. His estimated elasticity of substitution is 0.87; thus implying a
value of p = -0.14. In contrast, authors like Burnside et al. (1995) have reported estimates
of p that are below —2.3.

In this paper we use a set of values for the parameter p between 0.5 and -1. This
range of values allows us to solve the model and observe how the results change as we
move away from the Cobb-Douglas case. For each value of p, however, there is a value

of 0 associated with it that determines the income shares of both K and E as well as the

ratio of total energy and total capital used. Here we have chosen to fit the value of 0 such
that the total income share of the intermediate good E in the perfect competition case is
approximately equal to 4%.

The specific value of 4% is in line with the empirical evidence presented in the
previous section about the income shares of such intermediate industries. Furthermore,
when 0 is chosen in such way, the resulting E/K ratio approaches 0.2 as p approaches
zero; a result that is not at odds with the empirical evidence available for countries like
the USA (see Kim and Loungani (1992) for references on the actual energy/capital ratio
for the US during the period 1949-198726 and for a similar way to choose this parameter).
Similar to the Cobb-Douglas case for the value of (0, however, a variation in the value of
0 is not likely to alter our results. Furthermore, the values for the parameters A, 01,1, y, 8,

and B are identical to the ones used in the previous section.

 

25 According to Prywes (1986), “most of these elasticity estimates are close to zero and the true statistics
may be zero”.
26 Energy use is measured as total consumption of fossil fuels

94

Figures 7-9 use these parameter values and show the steady state income levels
for the three regimes when the value of ‘1’ that equals 0.01, 0.025 and 0.05 respectively”.
Two important results can be highlighted from these figures. First, in terms of income
levels the benefits of competition relative to public monopoly become greater for smaller
values of p. Second, as the parameter p becomes more negative, the difference between
the income levels resulting from the private and the public monopoly cases becomes very
small. Intuitively, as the intermediate good becomes more necessary for the production
of final goods, the monopolist faces a more inelastic demand, and thus, their production
choice becomes smaller relative to the competitive regime.

Thus, the model predicts that the impact of state-to-market transitions on the
aggregate level of income depends crucially on whether markets are deregulated at the
same time they are privatized. The size of this impact varies according to the degree to
which capital and the intermediate good being deregulated act as complements or
substitutes; that is, on whether the production technology depends importantly on the

intermediate good or not.

5. Conclusions and Future Research
The last twenty years have seen a worldwide tendency toward the privatization
and the deregulation of intermediate markets that were previously kept under government
control. This transition has brought a heated debate and even national confrontations
about costs and benefits of privatization/deregulation, especially in countries where, in

the past, the government has played a large role in the provision of goods and services.

 

27 For ease of presentation, the scale on the horizontal axes of Figures 7-9 was reversed.

95

The contribution to this debate made by cross-country econometric comparisons
is limited because privatization and deregulation usually occur together within a short
time period and because those studies are unable to account for some relevant country
specific elements. Thus, at least some of the questions asked in this debate must be
answered using a theoretical framework like the one presented here.

The results obtained in this paper suggest that the benefits of state-to-market
transitions are mostly due to increased competition on the deregulated market, and that
the privatization of state enterprises by itself is not likely to generate significant changes
in the economy. In fact, the model predicts that for high enough levels of public
investment, a public monOpoly would be preferred to a private monopoly in terms of the
resulting aggregate income level. Furthermore, the model points out that the gains from
deregulation vary according to the production technology parameters chosen and thus,
that they are also likely to vary from one country to another as the availability of natural
and human resources vary.

In this paper, however, several important elements were not included. First, the
presence or absence of a monopolistic market might generate different incentives for
adopting new technologies. Second, the goals of a public enterprise might not be
maximizing profits. Third, the presence of strong bureaucracies and unions might act
against the productive efficiency of public firms. We believe that this and other issues

could be studied in the future within a similar theoretical framework.

96

Table 1: Steady State Closed Form Solutions for the Cobb-Douglas Technology

 

 

 

 

 

 

 

 

 

 

 

Perfect Competition Private Monopoly Public Monopoly
N zfl ¢2(1—}’) N __ rpz(l-y)
l - _.
l-a-W ’ 1-a-(p(l—(p+(oy) ' l—a-(p(1—(p+goy)
N ztflfl _ (l-a-w) _ (I-a-to)
F l-a—(oy F l-a—(p(1—(o+rpy) F l—a-(p(l-(o+(py)
. - 2 _'__
K: =59: Kfiw K =[EK'lI—W
((2)/+0: (pr-rat ’ 5 F
K' Kia .
KF: la KP- 2. KrzKF
(py+a (0 7+“

 

 

 

(flit)...

l
—l+a+}¢

 

 

 

L

Aa“(1 - r)((p(l - 7))“""” (1 - a- w)““"" (79))”

 

.1

 

 

 

 

 

 

 

 

 

 

 

1 l-a- 2 -1+ + 1-“me
70-6) l—a-(pu-wm) ”(79) +00 “W
K:=
“ Aa“(1-r)(to’(l-r))“"’“’(1-a-¢)““'°’(7v2)”
_ l l . q—l+oi'+yro
r)
K._ [3
F _ l 2 - (I-rw _ _ I-a-(P
L l-a-Ml-(pwr) l-a-toO-rpwr) _

 

 

 

c : A¢N;-a-¢Nl(l—r)¢ _ A¢N;:-a-¢Nl(l—y)(p—l(1 _ 7)(0 +
AN ;“'°’N,‘"”“’r(1 — a — (p) + A raN,‘"”"’N,',‘“"”

 

97

 

Table 2: Parameter Values

 

 

 

 

 

 

 

 

 

 

Parameter Value
A 1
01 0.36
8 0. 1
t 0.2
B 0.95
y 0.4
(p a

g 0.05, 0.1, 0.2, 0.3

 

98

 

 

Level of Income

 

 

 

 

 

 

 

 

Competition -.— — Priv. Monop. -- + --Pub. Monopfi
1.2 ,
1.15
. -+
.4"
1.1
l.+‘
0*‘.
1.05
.+.
1 . 7
2*
i
0.95 -
0.9 .
0 0.05 0.1 0.15 0.2

Share of Public Revenues Allocated to Investment.

 

 

 

Figure l: Steady State Level of Income for Different Intermediate Market
Structures and Different Levels of Public Investment. ((0 =0.04)

99

 

Level of Income

 

 

Competition — - — Priv. Monop. - - + - - Pub. Mogaj

 

 

1.1

 

0.9

0.8 1

0.7 4 .'

0.6 ~11

 

 

0.5 m r . ,
0 0.05 0.1 0.15 0.2

Share of Public Revenues Allocated to Investment

 

 

 

 

Figure 2: Steady State Level of Income for Different Intermediate Market
Structures and Different Levels of Public Investment ((0 =0.1)

100

 

 

Level of Income

 

 

Competition - - - Priv. Monop. - - + - - Pub. Monop. l

 

0.9

 

0.85 -

 

0.8
0.75 ~

0.7 .
0.65 -*
0.6 _ ,f

0.55 ~

 

 

0.5

 

0 0.05 0.1 0.15 0.2
Share of Public Revenues Allocated to Investment

 

Figure 3: Steady State Level of Income for Different Intermediate Market
Structures and Different Levels of Public Investment (0) =0.2)

101

 

 

 

Level of Income

 

 

 

 

 

 

 

 

g___ Competition — — — Priv. Mon—op. --+ - - Pub_ Monob’f’,
0.9
0.8 -
0.7 ..-"'+
0.6
.‘1‘.
0.5 ._ _______________________________
Gk'
0.4 '.
"f

0.3 I . g

0 0.05 0.1 0.15 0.2

Share of Public Revenues Allocated to Investment

 

Figure 4: Steady State Level of Income for Different Intermediate Market
Structures and Different Levels of Public Investment ((0 =0.3)

102

 

 

 

 

 

 

 

 

 

 

Price of Intermediate Good
_-: ----- Compet. :— — Priv.Monop. —-¢—Pub.Monopj
20 -
15 e
l
l
l
10 l"
5
l L-
-0.05 0.05 0.15 0.25 0.35 0.45
Share of Public Revenues Allocated to Investment

 

 

 

Figure 5: Steady State Price of the Intermediate Good for Different Intermediate
Market Structures and Different Levels of Public Investment ((p =0.04)

103

 

 

 

 

 

 

 

 

 

 

Wage Rate
,- _M_Compet. -:— Priv.Mon. :5- 9116-1166
0.75
0.7 ...---"’*
065 , .xaro.
f
.5
0.6 -4
t— ____________________________
(I-
0.55 -
0.5 . .
0 0.1 0.2 0.3 0.4
Share of Public Revenues Allocated to Investment

 

 

 

Figure 6: Steady State Wage Rates for Different Intermediate Market Structures
and Different Levels of Public Investment ((p =0.04)

104

 

Level of Income

_._ __

Comp. - --1- - - Priv.Mon. —e— Pub.Mon }

 

 

 

 

 

 

 

 

I‘O

 

 

 

Figure 7: Steady State Levels of Income for Different Values of p When u; = 0.05

105

 

Level of Income

 

 

 

_ Comp. - - + - - Priv.Monop —e— Pub.Monop ,

 

 

 

 

 

 

 

I'O

 

 

 

Figure 8: Steady State Levels of Income for Different Values of p When \p = 0.025

106

 

Level of Income

 

 

 

 

 

 

 

 

 

I’O

 

 

 

Figure 9: Steady State Levels of Income for Different Values of p When ‘1’ = 0.01

107

 

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108

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