Environmental Policy in the Presence of Corruption:
An Alternative Perspective∗
Athanasios Lapatinas
Department of Economics, University of Ioannina
Anastasia Litina†
Faculty of Law, Economics and Finance
University of Luxembourg
Eftichios Sophocles Sartzetakis
Department of Economics, University of Macedonia
June 15, 2014
Abstract
This paper establishes an alternative channel through which corruption affects the
quality of the environment. In particular, it is argued that widespread corruption can
reduce the effectiveness of an environmental policy via the extortion of public funds
earmarked for the environment. Moreover, it suggests that policy makers may as well
direct more funds to environmental policies not as a means to improve environmental
quality but as a means to increase their extracted rents. The observed outcome is
that the effectiveness of the policy on environmental quality is inferior to the expected
outcome. A critical determinant of the ability to extract environmental funds is the
level of abatement technology thereby suggesting that more advanced technology may
not result in better environmental outcomes due to the fact that it may allow for a more
extensive rent seeking.
JEL Classification: Q5, D73
Keywords: Corruption, Environment, Technology
∗
We would like to thank Theodore Palivos for insightful comments.
Corresponding author: Faculty of Law, Economics and Finance, University of Luxembourg, 162a, avenue
de la Faiencerie, L - 1511 Luxembourg. E-mail: anastasia.litina@uni.lu Tel.+352-661-981692
†
1
1
Introduction
Corruption in its various forms is a long-lasting phenomenon prevalent in most contemporary
societies. There are abundant examples not only in developing countries and in transition
economies, but also in a number of developed economies as well.1 Its detrimental effects
have been extensively analyzed and cover a wide range of social and economic aspects. A
few economists have contributed to the study of corruption in the past but recently this field
attracts growing interest.2 A number of different analytic approaches to corruption have been
developed exploring among other issues, the degree of benevolence of the policy maker, the role
of institutions in determining the level of corruption and the effect of corruption on growth.
Recently the corruption literature has explored the detrimental effect of corruption on
the implementation of environmental policies. More analytically, it has been established both
theoretically and empirically, that the presence of lobbying groups that can affect governmental
policy via bribing or exerting pressure on government officials, has an adverse effect on the
stringency of environmental policy and ultimately on the quality of the environment.
This research establishes an alternative channel through which corruption can affect
the quality of the environment. In particular, we argue that even after the adoption of an
environmental policy, widespread corruption can reduce its effectiveness via the extortion of
public funds earmarked for the environment. More importantly, policy makers may as well
direct more funds to environmental policies not as a means to improve environmental quality
but as a means to increase their extracted rents. The observed outcome is that the effectiveness
of the policy on environmental quality is inferior to the expected outcome. A critical determinant of the ability to extract environmental funds is the level of abatement technology. More
advanced technology may not result in better environmental outcomes due to the fact that
it may allow for more extensive rent seeking activities. The suggested theoretical framework
captures therefore the interaction of corruption with the level of abatement technologies and
provides an explanation as to why more advanced technologies are not always associated with
better environmental outcomes.
The existing literature on corruption has explored the role of technology and the
ability to extract rents. The main argument is that for certain categories of public spending,
embezzlement of public funds is easier and/or better concealed relative to other types. Thus,
politicians and/or bureaucrats prefer to shift resources to areas in which a higher rate of
embezzlement is possible, such as high-technology goods produced in oligopolistic markets.
Studies have shown that corruption enhances the portion of military spending, public services
and order, fuel and energy, relative to more transparent activities such as education.3 Hessami
(2010) suggests that the perceived level of corruption increases the share of spending on
environmental protection.
1
Extensive documentation of instances of corruption can be found in the four volumes of "The Politics of
Corruption", edited by Robert Williams and associates.
2
For a recent survey of the economics literature on corruption see Aidt (2003).
3
See for example Gupta et al.(2000), Delavallade (2006) and Mauro (1998).
2
Our research addresses the above issues in a framework where taxpayers and politicians
interact in the economy, both gaining utility from the environment by providing a good
environmental quality to their offsprings. Nevertheless, they also want to maximize their
consumption which can be achieved by increasing their income via being engaged in corrupt
activities. More analytically, taxpayers have the option to evade part of their income, while
politicians have the option to embezzle part of the tax revenue.4 The extend of embezzlement
on the part of the politicians depends on the allocation of funds between activities. They
can allocate part of the total tax revenue on abatement activities and the remaining part on
another type of public good which for illustration purposes we will assume that it is public
education. Each activity is associated with different rent seeking opportunities. Which of
the two activities involves more rent seeking depends on a number of factors, i.e. on whether
each activity is human capital intensive, thereby involving transparent expenses, or technology
intensive, thereby involving less transparent expenditure.5 To give an example, if spending on
education is associated with teachers’ wages whereas environmental protection involves high
technology investment on renewable energy and/or abatement, then environmental protection
can be a more rent seeking activity. In the proposed framework it is assumed that the
associated rent seeking rates are fixed and exogenous, a simplification that will allow us
to analytically demonstrate the channel through which corruption can affect environmental
quality.
What we observe in our model is strategic interactions between the two groups of
agents. Whenever taxpayers observe that politicians direct disproportionately higher level of
public funds to the more rent seeking activity, they react by increasing their evasion rate.
On the contrary whenever they observe that the politicians are not corrupt, directing more
recources to the less rent seeking activity, they respond by increasing their compliance, a
reaction based on the notion of reciprocity between taxpayers and politicians, an argument
that has been reported in the relevant literature (Alm, Mc Clelandand, and Schulze, 1992; Alm,
Jackson and McKee, 1992). Critically, the type of interaction between the two groups as well
as the emerging equilibria depend primarily on the level of technology used in each sector and
the associated rent seeking rates. Therefore, the quality of the environment associated with
the realized equilibrium critically depends on the interaction between abatement technology
and rent seeking opportunities.
Whereas the model is developed in such a way that the emerging equilibria are selffulfilling, nevertheless initial conditions confer a role on the realized equilibria captured by
the parameters of the model. A more elaborate version of the model that introduces less
4
In this framework we will adopt the term corruption both for rent-seeking activities and for tax evasion.
While there is a broad consensus as to the fact that rent-seeking is indeed a corrupt activity, there is a debate
as to whether tax evasion can be classified as corruption according to the term employed by the World Bank
(-the abuse of public office for private gain). Nevertheless, evasion is certainly viewed as an illegal activity
that contributes to the enlargement of the shadow economy in a country. Therefore, as this debate is beyond
the scope of this research, we will adopt the term corruption for both activities just for brevity.
5
See Tanzi and Davoodi (1997) and (2000) and Hessami (2010).
3
restrictive assumptions is also employed that also allows to capture the stage of development.
The augmented version of the model is not fully tractable analytically, yet solving the model
numerically suggests that qualitatively similar results can be obtained.
Based upon the parameters of the model and the comparative statics, two main
inferences can be made with respect to environmental policy. The first policy lesson is that
commitment on better environmental outcomes on the part of politicians is critical for the
achievement of policy goals. The reason is that in the absence of transparency and proper
implementation of each policy, citizens interested in environmental quality will reciprocate by
contributing less to the public funds, therefore adding one additional source of deterioration
of the environment, namely a decrease in public revenues.
Second, in the presence of corruption, better technology and more funds allocated to
the environment are not always associated with better environmental outcomes. Therefore,
it is critical for governments to ensure the maximum possible transparency and exert control
over the funds allocated to abatement policies, in order to reduce the associated rent-seeking
opportunities and to ensure the best possible implementation of policies.
Our research contributes primarily to the strand of literature that explores the effect
of corruption on environmental quality. The dominant argument is this literature focuses
on the effect of bureaucracy and lobbying groups on the stringency of environmental policy.
Pashigian (1985) explained how locational competition among regions with different growth
rates affects the stringency of regulations in these regions. Cropper et al. (1992) and Helland
(1998) report the effect of environmental interests, of political and budget considerations on
US Environmental Protection Agency (US EPA) regulations. Lopez and Mitra (2000) examine
the effect of corruption and rent seeking on the relationship between pollution and growth
and on the shape of the environmental Kuznets curve, while Fredriksson and Millimet (2000)
and Fredriksson et al. (2003) examine the effect of corruption and rent seeking on US FDI,
on the pollution haven hypothesis and on environmental policy stringency.
We explore the same reduced form, namely the effect of corruption on environmental
quality. However, we focus on a different, critical in our opinion, channel through which
this effect may take place, i.e. via the rent-seeking opportunities associated with abatement,
which allows us to examine the effect of the interaction between technology and corruption on
environmental quality. Therefore, we emphasize that governments should bear both channels
in mind when planning environmental policy since the simultaneous presence of both channels
can have detrimental effect on environmental outcomes.
Second, we build upon the existing literature that explores interactions between different societal groups, including the government, to make the argument that in the presence
of environmentally aware individuals, government activities that reduce the effectiveness of
environmental policy may be reciprocated by individuals, thereby leading to reduced public
revenues and ultimately to lower environmental quality. Alm, Mc Clelandand, and Schulze
(1992) and Alm, Jackson and McKee (1992) report that the introduction of a public good in
exchange for the taxes paid, increases compliance rates. Furthermore, a number of studies
4
have shown that corruption seems to be contagious, or as Andvig and Moene (1990) put it
"corruption may corrupt". Tanzi and Davoodi (2000) investigated the relationship between
levels of corruption (measured by corruption perception indices) and GDP in a sample of 97
countries and found that higher corruption is consistent with lower revenues of all types of
taxes, especially from income taxes. Whenever taxpayers feel that politicians are corrupt or
that their burden is not fair compared to others they choose to become more corrupt as well.
Litina and Palivos (2013) associate the current Greek crisis with the interaction in corrupt
activities of different societal groups.
Section 2 of the paper provides some anecdotal evidence that motivates our analysis.
Section 3 introduces the benchmark model. We resort to a simple framework that allow
us to obtain analytical results and discus the intuition regarding the interaction between
taxpayers and politicians. More realistic assumptions are introduced in Section 4 which tests
the robustness of the model to a number of different assumption. As these assumptions
increase the complexity of the model we solve it numerically and show that it can yield
qualitatively similar predictions. Section 5 concludes the paper.
2
Anecdotal Evidence
One of the major problem associated with tracing corrupt activities is related to the fact that
they take place secretly and come to the surface only when revealed and investigated. Even
when revealed it is not always feasible to prove the presence of illegal activities.
In the case of environmental policy and illegal activities associated with it, very few
cases have been publicized. A second reason why this occurs is that environmental awareness
is a relatively recent phenomenon. Only in the last few decades strict environmental policies
have been adopted, providing incentives for the development and widespread adoption of
environmental technologies. It is sufficient to examine the agenda of political parties to realize
that environmental concerns have entered the public debate only in the last few decades in
the developed countries and only very recently in the developing countries.
Consequently, the public pressure for more transparent policies on environmental issues
is reduced not because of lack of interested but mostly due to the fact that it is not yet clear
how rent-seeking may operate with respect to abatement policies and the ways to mitigate it.
Yet, recent examples suggest that public awareness is needed in order to ensure the proper
environmental protection.
2.1
Lesotho Highlands Water Project
The Lesotho Highlands Water Project (LHWP) was initiated in 1986 by an agreement between
the governments of Lesotho and South Africa, and it was the most extensive international
water transfer in the world. Its aim was to provide extra water to Johannesburg via diverting
it from the Orange to the Vaal river. Moreover it was supposed to generate royalties from water
5
sales and to generate hydroelectric power for Lesotho. Finally it involved the development of
the rural areas of Lesotho, compensation for those who have been displaced and amendments
for those areas affected by the project.6
The implementation of the project required the development of a number of dams
and tunnels and the estimated cost of the project was more than $8 billion. As the project
expanded across a large area, the benefits associated with it came with the environmental costs
of nearby communities. A significant part of the project’s cost was related to the development
of a social fund aimed to mitigate the environmental consequences. During the first phase of
the project 4 dams were created and 110km of tunnels. Nevertheless, the project is largely
unfinished and environmental protection not only has not been implement, but in addition
environmental degradation occurred primarily due to a number of corruption scandals related
to the project. In 1999 the corruption scandal burst out that involved 12 of the companies and
the Chief executive of the Lesotho Highlands Development Agency. In particular they were
accused of offering huge bribes to win the contracts, that resulted in a inefficient management
of the project’s funds, inflating the financial cost and increasing the environmental burden.
After the CEO himself was found guilty, three major European firms were also found guilty
and charged, and one Canadian firm has been debarred at the World Bank.7 This situation
defamed the project, delaying its second phase which was initiated only very recently (March
2014) amidst concerns about the possibility of corruption in tender processes.
2.2
The SISTRI Project
In 2009 the Italian Ministry of Environment launched an information system, SISTRI, aimed
to unify the waste management services at the national level and to improve the urban waste
management at the Campania region. The implementation of the system would imply a
substantial improvement in the environment through a reduction of the cost and deterrence of
illegal dumping of waste. The estimated cost of the project was about 400 million euros and
it involved sufficiently sophisticated technology to ensure that the ambitious goals set would
be achieved. Nevertheless, a large part of the funds were collected by the companies via
non-transparent procedures without any advancement of the project. After a large scandal
revolving around bribes, embezzlement of the funds and a number of illegal activities, the
project was never fully implemented and improvements on environmental quality were much
inferior to the expectations and the cost of the project. A number of people have been
persecuted among them government officials and a member of the parliament.8 More recently
(March 2014), two former managers of Finmeccanica SpA, Italy’s state-controlled defense and
6
http://www.ipocafrica.org/index.php?option=com_content&id=71&Itemid=66
Further details are provided in the World Bank’s note on this particular corruption
http://star.worldbank.org/corruption-cases/node/18540
8
http://www.diplomattitle.com/waste-scandal-22-arrests-handcuffs-also-former-undersecretarymelancholy/
7
6
case:
industrial group, have also been arrested over allegations of international corruption connected
the SISTRI project.
2.3
Empirical Evidence
To further motivate the analysis and in order to quantify the hypothesis advanced in this paper
we show correlations on the interaction between environment improving policies, corruption
and the quality of the environment.
The analysis of this section is only illustrative and is not aspiring to provide an
empirical argument. Nevertheless is it quite useful in quantifying the ideas of the paper
and in illustrating the channel through which corruption is affecting the environment. Overall
the hypothesis advanced in the paper is that the effectiveness of environmental policies on
the quality of the environment depends on the extend of corruption and the rent-seeking
associated with environmental technologies. We employ a sample of 132 countries, drawing
data from the World Bank for the period 1996-2010 for which the data are available.
In Column (1), we use a per capita measure of CO2 emissions measured in metric tons
as proxy for environmental quality. As a proxy of environmental policy we use a measure of
electricity production from renewable resources as a fraction of the total electricity production
(both measured in kWh). In the absence of data on the actual cost of implementing this policy,
we make the implicit assumption that this measure proxies both the involved costs associated
with these technologies and the level of the technology employed. As a proxy for the level of
corruption in a country we employ a measure on the control of corruption from Transparency
International (CPI index-TI). This measure ranges from 0-10 with the latter referring to the
least corrupt country. It should be noted that we have rescaled the standard CPI measure, to
make the interpretation of our results more tractable. Therefore, higher values of our index,
indicate more corrupt countries.
Interestingly, the results support the hypothesis of this paper. First, our results —the
negative coefficient of investment in renewables— confirm that higher investment in renewables
is associated with lower per capita emissions. Most importantly though, the coefficient on
corruption is positive, thereby capturing the adverse effect of corruption on environmental
quality. The positive and statistically significant coefficient of the interactive term captures
the partial effect of investment in renewables holding the level of corruption constant, i.e.
investment in renewables is less efficient in more corrupt economies. The aim of the paper
is to capture precisely this interaction between environmental technology and the extend of
corruption in an economy.
Column (2) uses an alternative measure of electricity production, namely production
from natural gas resources as a percentage of total electricity. Natural gas resources, although
not as technologically advanced as renewables, are sufficiently technologically advanced as a
sector to capture the argument that we make about the level of corruption. The analysis
yields similar results.
7
Finally Column (3) repeats the analysis in Column (1) using an alternative measure
of corruption, namely a measure on the control of corruption from the World Governance
Indicators (WGI). This measure ranges from 0 to 5.5 with the latter referring to the most
corrupt country.9 The results are very similar, with the coefficient on corruption being positive,
thereby suggesting that indeed corruption confers a negative effect on environmental quality.
All three columns introduce time and country fixed effects therefore netting out many
sources of unobserved heterogeneity.
(1)
(2)
(3)
Per Cap. CO2 Emissions
Renewable Resources (RR)
-0.123***
(0.0235)
Natural Gas Resources (NR)
Corruption Perception Index-Rescaled (CPI)
0.112*
(0.0610)
-0.154***
(0.0356)
-0.0454***
(0.00663)
-0.0916
(0.0661)
Control of Corruption-Rescaled (CC)
Interaction
0.0159***
(0.00494)
0.00885***
(0.00111)
0.538***
(0.169)
0.0347**
(0.0146)
Time Fixed Effects
Yes
Yes
Yes
Country Fixed Effects
Yes
Yes
Yes
Observations
1670
1670
1460
Countries
132
132
134
Years
15
15
11
R-squared
0.0395
0.0604
0.0483
Summary:
This table illustrates that the reduction of CO2 emissions via
the use of alternative sources of electricity production is less effective in the
presence of corruption, while controlling for country and time fixed effects.
Notes: (i)Per capita CO2 Emissions measure is the per capita level of CO2 emissions
measured in metric tons; (ii) Nuclear Electricity Production is a measure of electricity
production from nuclear sources as a fraction of the total electricity production (both
measured in kWh); (iii) CPI is a measure of corruption provided by Transparency
International (TI). Countries are scaled from 0-10 with 10 being the least corrupt. In
this table the measure of corruption has been rescaled with 10 indicating the msot corrupt
country; (iv) Control of Corruption is a measure on the control of corruption from the World
Governance Indicators (WGI). This measure ranges from -2.5 to 2.5 with the latter referring
to the least corrupt country. Similarly, this measure has been rescaled with 2.5 indicating
the most corrupt country; (v) robust standard error estimates are reported in parentheses;
(vi) *** denotes statistical significance at the 1 percent level, ** at the 5 percent level, and
* at the 10 percent level, all for two-sided hypothesis tests.
9
Similarly to Column (1) the measure of corruption has been rescaled.
8
We view these results as simple correlations that nevertheless clarify the argument
advanced in the paper. A robust analytical work should employ more refined proxies for
environmental technology and employ IV analysis in order to establish a casual effect, since
in this framework reverse causality and omitted variables bias can be plausible concerns.
Overall the aim of this section is to bring to the surface anecdotal evidence that
illustrate the necessity to capture this alternative channel through which corruption can have
an adverse effect on the quality of the environment. The model developed in the following
section explores this channel more analytically.
3
The Benchmark Model
Consider a perfectly competitive overlapping generations economy where economic activity
extends over infinite discrete time and a single good is being produced in the private sector.
Individuals live for two periods i.e. childhood and adulthood. During the first period of their
lives individuals acquire human capital via public schooling whereas in the second period
of their lives they either enter the private market or they become politicians via a random
selection process. Their preferences are defined over their own consumption, as well as the
well being of their offsprings, which is reflected by the level of human capital they acquire and
the quality of the environment that they receive from their parents.
3.1
The Structure of the Economy
In each period  a generation of individuals of measure one is born. Each individual has a
single parent and lives through two periods: childhood and adulthood. In the first period of
their lives, individuals acquire human capital and for simplicity, it is assumed that they are
not economically active: their consumption is incorporated into their parents’ consumption.
During the second period of their lives, individuals are economically active and they decide
the allocation of their income between current consumption and their offsprings’ well being
which is assumed to depend on the level of human capital and the quality of environment.10
Formally, individuals born at  − 1, during their adulthood, that is, at period , maximize the
following utility function,
(1)
 =  (+1 + +1 ) 
where  denotes adults’ level of consumption, +1 their offspring’s human capital and +1 the
environmental quality handed over to their offsprings. The presence of the offspring’s human
capital level and environmental quality in the parental utility function captures the adult
agent’s vested interest in public education and public abatement. For analytical convenience
10
Environmental quality affects individuals’ well being either directly, affecting their health, as we assume
in this version of the model, or both directly and indirectly, affecting also production, as it is assumed in the
more elaborate version of the model, examined in the next section.
9
it is assumed that adults’ marginal utility derived from improving their offsprings’ human
capital and environmental quality are the same.11
Following the literature12 we assume that the learning technology is described by
(2)
 = −1 + −1 
where  denotes time,  the level of human capital acquired by an individual born at −1, −1
the average stock of human capital present in the economy at time  − 1 and −1 the public
spending on education in the same period. According to this human capital accumulation
process, a young agent born in period  − 1, can pick up a fraction  ∈ [0 1] of the existing
(average) level of human capital −1 without any cost, simply by observing what the previous
generation does.13 The enhancement of an agent’s human capital is possible only with the
allocation of public resources in education, −1 . The parameter   0 measures the efficiency
of the public education system. Therefore the overall level of human capital reflects both the
effect of societal knowledge and of formal education.
The evolution of environmental quality is described by,
 = 0 −1 − −1 + Π−1 
0   
(3)
where 0 −1 denotes the initial state of environmental quality 0  conditional on the level of
production −1 in period  − 1. The term −1 captures the environmental damage caused
by production, which is assumed to depend only on human capital, and  is a technological
parameter that can be interpreted as the rate of environmental degradation per unit of output.
The term Π−1 captures the beneficial effect of publicly funded abatement on environmental
quality, where  is a technological parameter.14
3.2
Citizens and politicians
Entering into aduldhood, individuals, via a random process, are either employed in the
private sector (hereafter called citizens) or they become politicians. Individual preferences are
independent of occupation. For analytical convenience it is assumed that there is a continuum
of agents within each group that is normalized to unity. The subscripts  and  are used to
denote variables that are related to citizens and politicians respectively.
Citizens produce a single good consumed by both groups. In this Section, as noted
previously, we assume that production depends only on human capital, while environmental
quality does not contribute to production.15 Thus, using the appropriate normalization of
11
The introduction of a parameter measuring the strength of the altruistic motive associated with each
activity would further complicate our analysis without providing additional intuition.
12
See for example De Gregorio and Kim (2000) and Ceroni (2001).
13
The term 1 −  can be taken to capture the depreciation rate of the stock of knowledge.
14
This particular formulation has been chosen because it allows for analytical results and captures the
coevolution of human activity with the quality of the environment (Galor, 2011). In the next Section
we introduce a more standard formulation of the evolution of environmental quality, with constant initial
environmental quality, 0 , independent of −1 , and a production function that depends on both  and 
and we illustrate, using numerical simulations, that our results hold.
15
The robustness to this assumption will be tested in the more elaborate version of the model.
10
units, individual’s output  , and income, is,16
 =  
(4)
It follows that the aggregate production function is linear to the aggregate level of human
capital.
The revenue for the provision of public education and abatement comes from taxing
citizens’ income. In particular, citizens are being taxed at the rate   which is assumed
to be exogenous and time invariant. Citizens have the option to evade a fraction of their
taxes and thus they can decide upon the fraction  of their income that is declared to the
tax authority. For the shake of brevity it is assumed that the citizen’s declaration is never
audited; consequently, tax evasion does not involve any risk.17 Although tax payments are
assumed a voluntary contribution, citizens’ free riding incentive is mitigated by their altruistic
concerns about their offsprings’ education and environmental quality and thus, they always
declare a positive fraction of their income, as will be later verified.
Politicians do not participate in the production process. Instead their role lies in
determining the allocation of public funds between abatement ( of the total tax revenue)
and education. The politician receives a fixed income, as a reimbursement for her service,
which for analytical convenience and without loss of generality we assume zero. Moreover,
she has the option to embezzle part of the total tax revenue as a means of supplementing
her income.18 More specifically, she can embezzle a rate (1 −  ) of public funds directed
to abatement, and a rate (1 −  ) to education. It is assumed that both   and   are
exogenously given, strictly positive and less than one. The magnitude of the s depends on
the economy’s institutional, political and social characteristics, while their relative magnitude,
i.e. whether  ≷   , depends on the public activity’s characteristics.
For instance one could argue that     , since education involves mainly transparent
transactions, such as wages and standard equipment, and thus, it is associated with low rates
of rent seeking,19 whereas abatement technology can be rather sophisticated and thus less
transparent. As suggested by Tanzi and Davoodi (1997), the more technology-intensive is an
activity, the less accessible to citizens’ scrutiny it is, i.e. less transparent, and thus the higher
the level of rent seeking associated with it. However, rent seeking rates on abatement can
vary significantly depending on the choice of abatement technology. For example, reforestation
involves much less sophisticated technology and is thus a much more transparent activity. In
16
Since all agents have the same level of human capital we omit the subscript  =   from the level of
human capital  
17
Adding the possibility of auditing and the subsequent fines would not qualitatively affect the main results.
18
Assuming a positive reimbursement for the politician (either a constant amount, or a fraction of the tax
revenue) reduces the incentive to embezzle public funds, but it does not qualitatively affect the results. As
long as there is an incentive to embezzle funds the results of the model remain unaffected. In order to focus
on the decision of allocating public funds between the two policies, we choose not to model the decision of
whether to embezzle or not.
19
The literature shows that the rate of rent-seeking in education is low but can vary across countries
(Reinikka and Svensson, 2005) depending on the overall level of corruption and the expenses involved.
11
order to be able to discuss the choice between any type of environmental policy and any
other public policy we allow the relative magnitude of ’s to vary. We assume though that
the politician is aware of the values of  and  before allocating the available public funds
between the two activities.
We further assume that the politician is never investigated and hence peculation does
not involve any risk. Since we have assumed that the politician has zero income, she will
always have an incentive to embezzle a fraction of the tax revenue. However, the politician’s
concern over her offspring’s well being ensures that she will always have an incentive to allocate
the public funds between both activities instead of the more rent-seeking one.20
Since only citizens are being taxed, total tax revenue  , collected in period , is the
fraction of income that is being declared and therefore taxed, i.e.  =    . In the absence of
embezzlement by the politician, a fraction (1 − )   of the tax revenue would be earmarked
to fund education and the remaining    abatement.
However, the politician peculates a fraction of this revenue. In particular, she peculates
a fraction 1 −   (1 −   ) of the tax revenue earmarked for education (abatement), and thus,
the actual amount spent on education  (abatement Π ) is,
 = (1 −  )    
Π =      
(5)
(6)
respectively. Overall, individuals’ decisions at time  regarding the level of evasion, embezzlement and the allocation of public funds, have an indirect effect on the aggregate level (quality)
of both public goods, i.e. education and abatement, which is enjoyed by the offsprings of both
types of individuals. Therefore, via the altruistic incentives of individuals associated with the
provision of the public good, the decisions of citizens are indirectly affected by the decision of
politicians and vice versa, suggesting the emergence of a strategic interaction in their decision
making process, which we analyze in the following sub-Section.
3.3
Optimization
Citizen
As discussed above, citizen’s preferences are defined over his own and his offspring’s
consumption in period ,  , and his offspring’s well being in the next period  + 1 as affected
by the level of human capital they acquire +1 , and the quality of the environment handed
over by the parents’ generation +1 . His gross income in period  is  , which is taxed at
the exogenous rate  . The citizen chooses the fraction  of his income to declare to the
tax authorities and pays income tax    , which implicitly determines consumption at  and
the level of public goods transferred to his offspring.21 We assume that citizens have full
20
An alternative way to model the incentives of the politician to allocate money to both public policies
would be to incorporate a re-election probability and allow for a political economy structure of the model.
21
Consumption at  equals citizen’s disposable income (1 −  )  + (1 −  ) = (1 −   ) .
12
information regarding politicians’ option to embezzle part of the total tax revenue. That is,
they know the values of  and   and they observe the politicians’ decision of allocating public
funds between the two activities.22 Therefore, each citizen solves the following optimization
problem,
max (+1  ++1 ) 
 
(7)
subject to  = (1 −   ) 
 ≥ 0 1 ≥  ≥ 0 
where , ,  and Π are determined by equations (2), (3), (5) and (6), taking  , 0 and 
as given.
Maximization of the above yields the citizen’s choice of  as function of the model’s
parameters and the politician’s choice of . Thus, we get citizen’s best response function to
the politician’s choice of ,
 = ( ) =
(  −  Ω ) − Ψ

2 (  −  Ω )
(8)
where Ω =   −  and Ψ = 0 −  + . Second order condition, ensuring concavity,
require that   −  Ω  0, which always holds since  ≤ 1.
Furthermore, an interior solution (1    0) exists iff (1 − 2 )(  −  Ω ) 
Ψ   −  Ω . On the contrary, a corner solution will emerge if Ψ ≥ ( −  Ω )
( = 0) or Ψ ≤ (1 − 2 )(  −  Ω ) ( = 1). These conditions suggest that a corner
solution may emerge when the rate of human capital transferred freely to the next generation,
, is sufficiently high (low), the initial state of the environment, 0 , high (low) and the
rate of degradation of environmental quality, , sufficiently low (high). Capturing a large
(small) percentage of the existing human capital freely implies that parents have a weak
(strong) incentive to invest in education and thus declare none (all) of their income to the tax
authorities. Starting off with a high (low) environmental quality implies that parents have
a weak (strong) incentive to invest n abatement and thus declare none (all) of their income
to the tax authorities. Finally, when environmental damage from production, , is limited
(extensive) then parents choose to evade all (none) of their income for abatement.
Whenever an interior solution emerges, the tax evasion rate (1 −  ) is reduced, the
more efficient is the use of tax revenues, (i.e. the higher are the  and  parameters) and the
lower are the rent seeking and tax rates. For sufficiently high rate of taxation (  12 ) citizens
will always choose to evade some fraction of their income, since   1.23
Politician
22
Introducing partial information would unnecessarily complicate the analysis, without changing the main
results.
23
From (8),   1 =⇒ (1 − 2 ) (  − Ω )  Ψ, for which a sufficient condition is   12 , given that
both Ψ and (  − Ω ) are positive. Since this is a sufficient but not a necessary condition, citizens might
choose to evade taxes even at lower tax rates.
13
Since we have assumed that individual preferences are independent of occupation,
politician’s preferences are given by (1). Assuming zero income from other sources, the
politician derives income only through the embezzlement of public funds. Taking as given the
rent-seeking rate associated with education 1 −    and abatement 1 −   , she determines the
allocation of public revenues between the two activities in order to maximize her utility. Her
income equals the sum of the funds embezzled from the education and abatement activities,
i.e.  (1 −  )   + (1 −  )(1 −  )   . The politician solves the following optimization
problem with respect to the fraction of revenue that will be allocated in each activity  ,
max  (+1  ++1 ) 
 
(9)
subject to  = [ (1 −   ) + (1 −  )(1 −  )]   
 ≥ 0 1 ≥  ≥ 0
where , ,  and Π are determined by equations (2), (3), (5) and (6), taking  , 0 and 
as given.
The first order condition of (9) yields the politician’s best response function to citizen’s
choice of  ,
ΨΩ −   (1 −   )Ω
(1 −   )
Ψ
 = ( ) =

(10)
=−
+
2  Ω Ω
2Ω
2  Ω
where Ω =   −  and Ω , Ψ were defined above. Second order conditions require that
Ω Ω  0. Furthermore, an interior solution (0    1) emerges iff   (1 −   ) ΩΩ  Ψ 
  [2 (1 −   ) − (1 −   )] ΩΩ . A corner solution will emerge if Ψ ≥   [2 (1 −   ) − (1 −   )] ΩΩ
( = 1) or Ψ ≤   (1 −   ) ΩΩ ( = 0). The politician will allocate the total revenue to
abatement ( = 1) if the rate of rent seeking on abatement is too high relative to that on

 2.
education, that is, if 1−
1−
Not surprisingly,  , is increasing in  and decreasing in . The effect of  on the
allocation of public revenue depends on the sign of Ω . If Ω  0 =⇒      , that is,
education is the more effective public activity, then the politician allocates less revenue to
abatement as the tax rate increases. She does so in order to maximize the effectiveness of
pubic spending24 and to maximize her own income by minimizing citizens’ tax evasion.25 The
opposite holds when Ω  0 =⇒      which suggests that she allocates more revenue
to abatement as the tax rate increases.
Overall, the politicians’ decision process has many analogies to that of citizens. In
allocating the public funds between the two activities, she balances her own consumption and
her offsprings’ well being while taking into account citizens’ reaction to her choice.
Strategic Interactions
As suggested by the the two groups’ reaction functions, given in equations (8) and (10),
each group’s expectations regarding the other group’s choice are an important determinant of
24
Similar to the citizens, the politician behaves in an altruistic fashion and therefore cares about her
offspring’s well being.
25
Citizens are willing to pay higher taxes when they observe the politician to direct a higher share of the
tax revenue to the most productive activity.
14
their own decision making process. Therefore strategic interaction emerges, operating through
the common interest for the level and the quality of the public goods. In particular, taking
the derivative of each group’s reaction function, equations (8) and (10), with respect to the
other group’s decision variable, yields,
−ΨΩ
 2 
−ΨΩ2

=
≷
0
=
 0

 ( − Ω )3
2 (  − Ω )2
( )2

−Ψ
 2 
Ψ
=
≷
0
≷ 0
2 =
2

2  Ω
 3 Ω
( )
(11)
(12)
The sign of both reaction functions’ slope depends critically on the sign of the term Ω . In
particular, we can dinstighuish between the following two cases:
A) Ω  0 =⇒      =⇒
B) Ω  0 =⇒     =⇒




 0
 0




 0
 0
(13)
Case (A) refers to a situation in which public spending on education is less effective
relative to abatement, due to relatively higher rates of rent seeking and/or to less efficient
technology. In this case, the reaction functions of the two types of individuals are increasing
at a decreasing rate. Citizens declare a higher fraction  of their income to tax authorities
as they observe politicians directing a higher share of public funds to the improvement of
environmental quality  , which is the more productive activity.26 That is, citizens "reward"
politicians’ "honest" attitude by evading less. Furthermore, politicians choose to direct more
public funds to abatement, the higher is the fraction of income that citizens declare to tax
authorities. Each group reciprocates to the cheating behavior of the other group and thus,
defining both groups’ strategic choices as cheat - not cheat, they are mutually reinforcing,
i.e. they are strategic complements (higher  leads to higher  and vise versa). Figure 1a
illustrates citizens’ ( ) and politicians’ ( ) reaction functions when Ω  0.
Case (B) depicts a situation in which public spending on abatement is less effective
relative to education and both reaction functions are negatively sloped. However, citizens’
reaction function decreases in a decreasing rate while that of politicians in an increasing rate.
Figure 1b illustrates both groups’ reaction functions when Ω  0. If politicians choose to
invest a higher share of public funds on abatement (higher  ), which is the less productive
activity,27 thereby signalling a more corrupt behavior, citizens "punish" them by evading a
higher fraction of their income. Similarly, politicians choose to direct more public funds to the
more effective public activity as they observe lower levels of tax evasion. Keeping in mind the
definition of strategic choices as cheat - not cheat, the strategic decisions of the two groups are
again mutually reinforcing, that is they are strategic complements (higher  leads to higher
1 −  and vise versa). This is so despite the fact that both reaction functions are decreasing in
26
Second order condition of the politician’s maximization problem requires that when Ω  0, then Ω  0,
i.e.      .
27
Again, the second order condition of (9) require that when Ω  0, then Ω  0, i.e.      .
15
the [ ,  ] space, which could lead one to think of strategic substitutes. When Ω  0, second
order conditions of the politician’s maximization problem require that Ω  0, i.e.     and
thus the meaning of  is exactly the opposite from case (A): an increase in  now indicates
cheating, while in case (A) indicated not cheating.28
(a) Ω  0
(b) Ω  0
Figure 1. Citizen’s ( ) and politician’s ( ) reaction function
3.4
Environmental policy
Based on the above discussion regarding the strategic interaction between the two groups of
individuals, we can now examine the effect of environmental policy on individuals’ utility
and environmental quality. The effect of an increase in  on utility is expected to be
ambiguous and depend on the relative effectiveness of the two public policies, since the
marginal utility of human capital and environmental quality are assumed equal. Shifting
public revenue towards abatement improves utility if abatement is more effective relative to
education. However, the effect of an increase in  on environmental quality is not obvious. The
layman’s presumption, resulting from direct observation of equations (3) and (6), is that an
increase in the share of public funds directed towards abatement activities has always a positive
effect on environmental quality. However, this is not always true, since the effectiveness of
publicly funded abatement depends on the the level of corruption and technological efficiency.
The above discussion can be formalized in the main proposition of the paper:
Proposition 1 Increasing the share of public revenue on abatement activities,
(i) increases (decreases) utility if abatement is more (less) effective relative to education,
(ii) does not necessarily improves environmental quality. The effectiveness of public spending
28
In order to keep the graphical illustration aligned with the mathematical modelling, we choose to illustrate
reaction functions in the [ ,  ] space instead of the [cheat, not cheat] space.
16
on environmental quality depends on the technological efficiency and the corruption level of
abatement relative to education.
Proof. (i) Using (5), (6), (2) and (3) we can express utility,
h given in (1), as function of
i


(  +   ) + (  −  ) .
 and  . Differentiating with respect to  yields,  =    


From (13) and the second order condition of the politician’s maximization problem we get

 0 if
that: 


 0 if Ω  0.
Ω  0 and 

³
´



(ii) From equations (3) and (6) we get, 
=

1
+
 0 and
    . For Ω  0, 




 0. However, for Ω  0,
thus, 

(11), yields the following condition,



 0 and thus,




 0 if 1 + 
 0, which, utilizing

 
Ψ − 2 (1 −  ) [(1 −  )   + 2   ]

1.

Ψ + 2 2 
(14)
The right hand side of the inequality takes the following extreme values: Ψ+2Ψ for  = 1
and Ψ−2Ψ for  = 1. Therefore, if public spending on abatement is substantial less
effective relative to education, shifting public funds towards abatement could actually reduce
environmental quality. This result is more likely, the lower is the tax rate.
Proposition 1 formally proves that increasing the share of the less effective segment
of the public sector in total public expenditure is not only detrimental for social welfare29
but it could even decrease the quality of this segment’s services. This result holds for
economies with relatively loose enforcement mechanisms, in which reciprocity of corrupt
behavior between citizens and politicians is a key determinant of public revenue raising and
distribution. However, even these, more corrupt economies are under international pressure
and consider increasing investments in environmental protection, involving high technology,
such as solar and wind energy production equipment. Shifting public revenues towards such
activities, despite of the great potential they present, it might prove not only ineffective but
also detrimental if Ω  0 and condition (14) holds.
Although it is more than obvious that a decrease in the rate of corruption is always
beneficial, an intervention that decreases the rate of embezzlement in the environmental
segment of the public sector is crucial in situations characterised by Ω  0 resulting from
   and     . In economies that are highly susceptible to corruption, successful
anti-corruption campaigns could play a crucial role in defining the effectiveness of introducing
technologically advanced environmental policies. Given the importance of addressing local,
but most importantly global environmental problems, such as global warming, which require
highly avanced technological solutions and the participation of all countries, the results of our
paper emphasize the importance of the fight against corruption.
29
Since environmental quality is incorporated into utility and there are no production costs, social welfare
is represented by utility.
17
3.5
Equilibrium
For the above proposition to be meaningful one needs to establish that an equilibrium indeed
exists. Adopting the results of the corruption literature that suggest reciprocity in corrupt
activities of individuals (Alm, Mc Clelandand, and Schulze, 1992; Alm, Jackson and McKee,
1992), we will focus hereafter to the more plausible case of strategic complementarity in
order to establish the necessary conditions for the existence of an equilibrium. Note that the
assumption of strategic complementarity implies    , that is, abatement is a more
effective relative to education activity.
Before presenting the formal notion of equilibrium under the assumption of strategic
complementarity, it is important to depict the potential equilibria with a best response
diagram. Figure 1 illustrates citizens’ ( ) and politicians’ ( ) reaction functions in the case
that both possible intersections occur within (0 1).30 Three equilibria may occur denoted
by points    and   Using best reply dynamics we observe that  and  are stable
equilibria whereas  is an unstable equilibrium.  denotes the high corruption equilibrium

} and  = 0 implies high tax evasion and that the total tax
(since  = min{0 21 − 2Ψ

revenue is directed to the less effective, and thus, more profitable in terms of rent seeking,
activity) whereas  denotes the low corruption equilibrium where citizens declare part of
their income (  0) and a positive part of the tax revenue is directed to the more effective
activity (  0).
Formal proof
The interaction between the two types of individuals can be described as a coordination
game in which strategic complementarity exists.31 Games of strategic complementarity are
those in which the best response of any player is increasing in the actions of the rival, as is
the case for  and  . Strategic complementarity is a necessary condition for the existence of
multiple equilibria in symmetric coordination games.32 The resulting equilibria are not driven
by fundamentals. Instead, they are self-fulfilling and critically depend on the expectation of
one group concerning the behavior of the other.33 Nevertheless, the game that we analyze here
30
In order to obtain Figure 1 the following steps should be followed. In the presence of strategic
complementarity, both types of individuals’ reaction functions are increasing in a decreasing rate, that is,

 2 
  −Ψ

 2 
  0, ( )2  0 and   0, ( )2  0. From (8) we have that | =0 =  ( = 0) = 2   , which is



Ψ
.
the citizen reaction function’s vertical intercept. For this to be less than unity requires that   12 − 2

Note that the politician tends to direct all revenues to public education (in this case the more rent-seeking
activity), as citizens declare a small part of their income, that is, from (10) we have   = −∞. From (10)
 →0
ΨΩ
ΨΩ
we also derive that  = 0 =⇒  =  (1−
. For this to be less than unity requires that   (1−
.
 )Ω
 )Ω
31
See, for example, Cooper and John (1988) and Vives (2005).
32
Notice however that also in games with strategic substitutability multiple equilibria may occur as well
(Randon, 2009).
33
As already noted in the introduction though, the various parameters of the models, such as the level of
technological sophistication of public schooling and abatement or the rates of rent-seeking could be an indicator
of different stages of development across countries and therefore even in a such a model with self-fulfilling
equilibria the initial conditions can be accounted for. Moreover, a model that will account explicitly for initial
condition and will lead to path-dependent equilibria as well, further reinforced by individual expectations
18
is not symmetric. Moreover the choice space is bounded and this necessitates the consideration
of corner solutions. In fact, as we show below, this game does not share many of the
properties of games with strategic complementarities. Consider first the following definition
of equilibrium:
∞
Definition 2 A Nash equilibrium in this economy consists of sequences { }∞
=0  { }=0 
∞
∞
∞
∞
∞
∞
{ }∞
=0  { }=0  { }=0  { }=0  { }=0  { }=0  {Π }=0   =  , such that, given an
initial average stock of human capital −1  0 and an average level of environmental quality
−1  0 in every period 
1. Private citizens choose  to maximize their utility, taking  as given.
2. Politicians choose  to maximize their utility, taking  as given.
∞
∞
∞
∞
∞
3. The sequences { }∞
=0  { }=0  { }=0  { }=0  {Π }=0 and { }=0  are determined
according to (2), (4), (3), (5), (6), (7), and (??).
4.  = 
Each group’s individual optimization problem is well defined since its utility function is
strictly concave and the budget constraint linear with respect to the relevant decision variable,
 or   In Proposition 1 below, we prove the existence of a pair (   ) that satisfies Definition
1 in every period. Given the existence of the equilibrium pair (   ) we can easily establish
the equilibrium values of the remaining variables, following Definition 1.
Proposition 3 An equilibrium pair (   ) exists for every .
Proof. We must establish the existence of a pair (   ) that satisfies equations (8)
and (10) simultaneously. For an arbitrary time period , let  = ( ) denote the solution
to the citizen’s problem, as described by equation (8); for each value of the allocation rate
 there exists a unique value of the tax evasion rate   Similarly, let  = ( ) denote the
solution to each politician’s problem, as described by equation (10). Note that both of these
functions are continuous (see equations (8) and (10)). Thus, the composite function  ◦  from
[0 1] to [0 1] is continuous and, by Brower’s fixed point theorem, has a fixed point.
Solving for the equilibrium values of individuals’ choice variables, yields,

2∗ =
3∗ =
√
√
Ξ− Ξ−8Ω
Ω
√
4 Ξ
√
√
Ξ+ Ξ−8Ω
Ω
√
4 Ξ
∗2 =
∗3 =
√
4  Ω+Ξ− (Ξ−8ΩΨ)Ξ
4Ω√
Ω
4  Ω+Ξ+ (Ξ−8ΩΨ)Ξ
4Ω Ω
where, Ξ =     ( − ) − Ω . For the non-zero equilibrium values of  to be real
(1− ) 
. That is, for the citizen
number in (0 1), we need Ξ ≥ 0, which implies that   (1−
 ) 
would be feasible but much less tractable. In addition this model illustrates in a neat way the interactions
between the two groups of agents.
19
to declare any positive amount of his income to the tax authority, the ratio of technological
efficiency of abatement to education should exceed the ratio of the rates of embezzlement.
Depending on the parameter values, sufficient conditions for the existence of a unique or
multiple equilibria can be established. We call an equilibrium interior (corner) if it lies in the
interior (on the boundary) of the unit square. Figure 1 presents an example in which there
are three equilibria: the corner one  (1∗  ∗1 ) and two interior, from which we identify, using
best reply dynamics,  (2∗  ∗2 ) as not stable while the  (3∗  ∗3 ) as stable.
Overall, the presence of multiple equilibria with different levels of corruption, driven
by expectations as well as by parameters involving the level of abatement technologies and the
associated rent-seeking rates, further reinforces the result that the effectiveness of abatement
spending on environmental quality can be mitigated by the presence of corruption.
Policy implications
Although we have treated as exogenous the tax rate,  , and the rates of embezzlement
  and  , these parameters could actually change. For example, there could be a public
authority at a higher level of decision making, which we could call regulator, which influences
—through institutional changes—  ,   and  , while the politician (at a lower level of the
decision making process) chooses only . Given the importance of these parameters, it is
worth dscussing some comperative static results.
Straightforward manipulations of (8) indicate that in order to preclude  = 0, i.e. the
full corruption corner solution  (1∗  ∗1 ) in Figure 1, a policy maker must either mitigate rent
seeking on education spending,34 or mitigate rent seeking on abatement activities.35 Such a
policy would not only increase the available tax revenue, but more importantly it would give
an end to the vicious circle of reciprocal activities.
As far as tax policy is concerned, the condition   12 is necessary for a nil-evasion
( = 1) equilibrium to be feasible. Can the policy maker ensure that the no corruption
equilibrium is always chosen? Sufficiently low tax rates and high     cannot ensure  = 1
since other variables, i.e. , , and Ψ, play an important role as well. Therefore, the main

}
concern of the regulator should be to eliminate the corner solution  = min{0 21 − 2Ψ

Assuming strategic complementarity, i.e. Ω  0, equation (10) implies that the
regulator should try to preclude that  = 0, i.e. that the total tax revenue is directed to the
less effective activity, that is, education spending (since Ω  0 ⇒    Ω ). Therefore
even if eliminating rent-seeking opportunities is not feasible, a first course of action for the
regulator would be to undertake the appropriate institutional changes that will decrease the
value of   relative to  .36
34
Setting  = 0 yields that a necessary condition for   0 implies    Ψ.
Setting  = 1 yields that a necessary condition for   0 implies    Ψ.
36
Note from eq. (10) that for   0 (for  = 0) we must assume that       Even for  = 1 the
condition      is not necessary but sufficient for   0
35
20
4
A natural resources model: A numerical illustration
Analytical results of the benchmark model suggest two things: First that there is a reciprocity
in corrupt activities between the two groups of agents and second and more importantly that
the effect of abatement on environmental quality may be decreasing in the degree of corruption
in a country depending on the level of abatement technology. The reason is that when more
sophisticated abatement technology is involved this can allow for higher rent seeking and thus
the effect on environmental quality is lower than expected. Moreover this effect is magnified
by the fact that citizens also react to higher rent-seeking by evading more and thus the overall
amount of money spend of abatement is further reduced.
In order to obtain clear analytical results in the previous section some restricting
assumption have been employe. To further reinforce these results, a more elaborate version
of the model is developed in this section, which however can be numerically approached. The
aim of the section is to show, using numerical simulations, that the main properties of the
benchmark model hold in this more elaborate setting.
The main assumption that differentiates the two models, is that the environment
contributes to production. It could be perceived either as environmental quality that is
indirectly affecting citizens’ productive capacity, and/or as natural resources directly employe
in the production process. While this assumption along with other more plausible assumptions
add realism to the model, nevertheless they significantly complicate the analysis. Therefore
analytical results will be provided until the derivation reaction function while the remainder
of the model will be numerically illustrated.
4.1
The Structure of the Economy
The basic structure of the model is identical to the benchmark model, i.e. individuals live for
two periods i.e. childhood and adulthood. During the first period of their lives individuals
acquire human capital via public schooling whereas in the second period of their lives they
either enter the private market or they become politicians via a random selection process.
Their preferences are defined over their own consumption as well as the well being of their
offsprings, which is reflected by the level of human capital they acquire as well as by the
quality of environment their receive from their parents.
Accumulation of Human Capital
The learning technology in the public education system is quite similar as in the
benchmark model and given by,
(15)
 =  + −1 
where  denotes time,  the level of human capital acquired by an individual born
at  − 1, −1 the public spending on education in the same period whereas the parameter
  0 measures the efficiency of the public education system. According to this human
capital accumulation process, a young agent born in period  − 1, can acquire, without effort,
21
a minimum level of human capital  ∈ [0 1] of the previous period’s accumulated human
capital.37 As in the benchmark model the revenue for financing public schooling comes from
taxing the economic activity of agents.
Production
Production uses both human capital and the environment/natural resources as in38
puts. That is, we assume that citizens’ output  is,39
 =   
(16)
where  is the production technology. Evidently at the aggregate level there are increasing
returns to scale. This is a simplifying assumption that allow to make the model slightly more
tractable.
Environmental Quality
The evolution of environmental quality is described by
 = −1 − −1 −1 + Π−1
(17)
where −1 denotes the state of the environment in the previous period and  the
extent of environmental damage, or the rate of the natural resource depletion, caused by
aggregate economic activity −1 −1 40 The term Π−1 captures the beneficial effect of
public spending on abatement on environmental quality, where  is a technological parameter
associated with the abatement process. The revenue for financing abatement come from taxing
the economic activity of agents as will be analyzed in a following section. We assume that
1 − −1  0, that is, production cannot deplete the environment / natural resource.
This formulation is rather common in the literature and more plausible than our previous
specification.41
Tax Revenue
Both types of individuals make the same choices by maximizing their utility function as
described by equation (1) in the basic model. The citizen chooses the fraction  of his income
to declare to the tax authority and the politician the fraction  of the total tax revenue to
allocate to abatement / preservation of natural resources.
The total tax revenue collected within a period  is  =     . As in the previous
model a fraction (1 − )    of the total tax revenue is earmarked for public education.
Since the politician peculates a fraction 1 −  of (1 − ) , the actual amount spent on
37
This alternative assumption has also been employed in the literature. The reason why we resort to this is
to show that our results are robust to this specification as well.
38
We enrich the production function in order to extend our results to the natural resource strand of the
literature and to highlight the robustness of our results to a more elaborate production structure.
39
Since all agents have the same level of human capital and the natural resource is commonly owned, we
omit the subscript  =   from both variables.
40
This is an additional robustness control to the equation of motion for the environment, in which case in
the absence of any economic activity the initial environmental quality 0 would be positive.
41
See for example, John and Pecchenino (1994).
22
education  is
 = (1 −  )     
(18)
The remaining fraction     of the collected revenue is earmarked for public
abatement. The politician peculates a fraction 1 −  of this sum, leaving Π to be spent on
abatement
Π =       
(19)
Individual optimization decisions regarding  and  affect the sum and the allocation
of public spending between education and abatement and consequently the human capital and
the state of the environment / natural resources enjoyed by the next generation.
4.2
Individual optimization
Citizen
Citizens declare a fraction  of their income  to the tax authority and an amount
   is paid as income tax. Hence, citizens’ disposable income is (1 −  ) 2  + (1 −
 )2  = (1 −   )2   The individual optimization problem solved by each citizen born
in period  − 1 is,
(20)
max  [+1  ++1 ]
  
subject to
 = (1 −   )  
(21)
 ≥ 0 1 ≥  ≥ 0 
where , ,  and Π are determined by equations equations (15), (17) (18) and (19), taking
 ,  and  as given.
Maximization with respect to the fraction of income declare to the tax authorities
yields the citizens’ best response function,
 = ( ) =
  ( −  Ω ) − Ψ

2   (  −  Ω )
(22)
where Ψ =  +  −   . Concavity holds since   −  Ω  0.
Citizens’ reaction function in (22) has similar characteristics as the one in the benchmark model (equation (8)).42
An additional element with respect to the benchmark model, that explores the robustness of the model to the assumption of path dependency is that in (22) the strategy of the
42
The slope of the citizen’s reaction function is,   = −Ψ Ω 2 2  (  − Ω )2 , with
   ( )2 = −Ψ Ω2 2 2  (  − Ω )3  0 since   − Ω  0. Therefore, as in the benchmark
model, the sign of citizen reaction function’s slope depends on the sigh of the term Ω . The intercept of
citizen’s reaction function is, | =0 =  ( = 0) = (2    − Ψ )2 2    . For this to be less than
unity requires that   12 − Ψ 4    .
2
23
citizen,  , depends not only the strategy of the politician,  , but on the realized values of
 and  . The interesting aspect of this approach is that the values of these terms evolve
over time until the economy approaches a steady state (in case it exists) and therefore the
optimal strategy differs among generations, nevertheless the role of self-fulfilling expectations
is still present in this setup. Importantly though at time  the values of  and  have been
already determined by the previous generation and therefore each generation treats them as
exogenous.
Inspection of equation (22) reveals that an interior solution (0    1) exists
iff (2 − 1)  ( −  Ω )  Ψ    (  −  Ω ). A corner solution  =
    −Ψ
} ( = 1) will emerge if the rate of human capital transferred freely to the
min{0 
2    
next generation, , is sufficiently high (low), the rate of degradation of environmental quality,
 sufficiently low (high) and the rent reeking rates, (1 −  ) and (1 −   ) sufficiently high
(low). As in the benchmark model, for sufficiently high  (  12 ), the tax evasion rate is
never zero, since   1.
Whenever an interior solution emerges, the tax evasion rate (1 −  ) is negatively
affected by the efficiency of the education system () and the abatement technology (), and
positively affected by the rates of rent seeking (1 −   ) and (1 −   ) and the tax rate  .
Politician
The politician’s income is derived solely from peculation of tax revenue and is [ (1 −
  ) + (1 −  )(1 −   )]    . The politician’s optimization problem is,
max  [+1  ++1 ]
(23)
 = [ (1 −   ) + (1 −  )(1 −  )]    
(24)
 
subject to
 ≥ 0 1 ≥  ≥ 0 
where , ,  and Π are determined by equations equations (15), (17) (18) and (19), taking
 ,  and  as given.
Maximization of the politician’s best response function yields,
 = ( ) =
Ψ
ΩΨ −    

+
=−

2  Ω Ω 
2Ω Ω 2  Ω  
(25)
where  = (1 −   ) Ω −  Ω.43
For interior solutions (0    1) it is required that     Ω  Ψ      (2Ω Ω+
)Ω. On the other hand, corner solutions of directing revenue to a unique policy ( = 0 and
 = 1 respectively) emerge depending on the values of     . Moreover,  is decreasing in
 and increasing in  Similarly to the benchmark case the effect of tax rate on the allocation
43
Similar to the benchmark model, for concavity to hold we must have Ω Ω  0. The slope of the
2
politician’s reaction function is,   = −Ψ2 2 2  Ω , with  2   ( ) = Ψ4 3 2  Ω . The
sign of reaction functions’ slope depends on the sign of the term Ω .
24
of revenue depends on the sign of   −   and the same goes for the effects of 0   and
. Specifically




≶ 0  ≶ 0
≷ 0  ≷ 0


0

Overall we observe that despite the fact that our setting is more complex and realistic,
the predictions of the model are quite similar with respect to the reaction functions. As was
the case with the citizen reaction function, the politician’s reaction function also depends on
the realized values of  and  which are predetermined by the previous generation and
therefore each generation of politicians treats them as exogenous.
Strategic Interactions
Strategic interactions in this setting are similar to the benchmark case. As we show
above, the sign of both reaction functions’ slope depends on the sign of the term Ω . Analytically
 −  ≷ 0 =⇒
i) Ω  0 =⇒      =⇒
ii) Ω  0 =⇒      =⇒




 0
 0




 0 i.e. Strategic Complements
 0 i.e. Strategic Substitutes
yielding similar predictions to the benchmark model, namely in the case of strategic
complement citizens will choose to "punish" politicians in case they perceive their attitude as
corrupt, whereas in the case of strategic substitute they will prefer to substitute for the loss
in public revenue by behaving more honestly.
Following the literature and the strategy of the benchmark model we will focus on the
case of strategic complementarity.
4.3
Equilibrium
The definition of equilibrium remains the same in both models. However, the existence of
equilibrium is more complicated in this model. Each group’s individual optimization problem
is well defined since its utility function is strictly concave and the budget constraint linear
with respect to the relevant decision variable,  or   In Proposition 2 below, we prove the
existence of a pair (   ) that satisfies Definition 1 in every period, for given values of  and
 . Given the existence of the equilibrium pair (   ) we can easily establish the equilibrium
values of  and  and subsequently of the remaining variables, following Definition 1.
Proposition 4 An equilibrium pair (   ) exists for given values of  and  
Proof. We must establish the existence of a pair (   ) that satisfies equations
(22) and (25) simultaneously. For an arbitrary time period , let  = (     ) denote
the solution to each citizen’s problem, as described by equation (22); for each value of the
allocation rate  there exists a unique value of the evasion rate   Similarly, let  =
25
(     ) denote the solution to each politician’s problem, as described by equation (25).
Note that both of these functions are continuous (see equations (22) and (25)). Thus, the
composite function  ◦ from [0 1] to [0 1] is continuous and, by Brower’s fixed point theorem,
has a fixed point.
Solving for the equilibrium values of the model we obtain,44
    −Ψ
1∗ = min{0 
}
∗1 = 0
2   
∗2 = 2 (   )
2∗ =  2 (   )
∗3 = 3 (   )
3∗ =  3 (   )
(26)
Therefore in terms of strategies there always exists an equilibrium for given values of 
and   Since however there is a law of motion describing how these two variables evolve, there
will be different equilibrium values in each period for  and  unless the system approaches
a steady state. The dynamics of the model are analyzed in the following subsection.
4.4
Dynamic behavior of the system of difference equations
As noted above the stable solutions of the model (if all three are valid) are (1∗  ∗1 ) and
(3∗  ∗3 ) using best reply dynamics. Since the set (1∗  ∗1 ) represents a trivial equilibrium
of full corruption we will focus on the low-corruption equilibrium (3∗  ∗3 ). Replacing the
equilibrium values for (3∗  ∗3 ) from equation (26) into equations. (15), (17) we obtain the
following system of two autonomous non-linear first order difference equations
+1 =  (   ) 
+1 = (   ) 
where  and 0 denote the initial values for  and  and are exogenously given. The
dynamics of the system are too complex to be analytically studied. Still though we can
describe analytically and numerically the kind of solution that is desirable in order for our
model to be meaningful.
In order to approximate the dynamics of our benchmark model, i.e. a set of equilibrium
values for (   ) that remain unchanged in every period, our system of difference equations
must reach a steady state. Therefore we first assume that the dynamic system has steady-state
equilibrium (̄ ̄). Namely, ∈ (̄ ̄) such that
̄ =  (̄ ̄) 
̄ = (̄ ̄) 
44
We omit analytical expression due to their complexity.
26
A Taylor expansion of the system around the steady state values (̄ ̄), yields:
(27)
+1 =  (   )
=  (̄) +  (̄ ̄)( − ̄) +  (̄ ̄)( − ̄) + 1 + 2 
(28)
+1 = (   )
= (̄) +  (̄ ̄)( − ̄) +  (̄ ̄)( − ̄) + 1 + 2 
where  (̄ ̄) and  (̄ ̄) are the partial derivatives of the functions  (   ) and (   )
evaluated at (̄ ̄) and 1 and 2 are the error terms which are very small in the neighborhood
of (̄ ̄) and have little influence on the behavior of the system. Thus, the non-linear system
is been approximated, locally (around the steady-state equilibrium) by the linear system:
¸ ∙
¸∙
¸
¸ ∙
∙
 (̄ ̄)  (̄ ̄)  − ̄
 (̄)
+1
+

=
(̄)
 (̄ ̄)  (̄ ̄)  − ̄
+1
where,
¸
 (̄ ̄)  (̄ ̄)

(̄ ̄) =
 (̄ ̄)  (̄ ̄)
∙
(29)
is the Jacobian matrix evaluated at the steady-state equilibrium.
If all eigenvalues of (̄ ̄) have moduli strictly less than 1, (̄ ̄) is asymptotically
stable (a sink). If at least one eigenvalue of (̄ ̄) has modulus greater than 1, then (̄ ̄)
is unstable (a source). If the eigenvalues of (̄ ̄) are all inside the unit circle, but at least
one is on the boundary (has modulus 1), then (̄ ̄) may be stable, asymptotically stable or
unstable. Therefore we take the following steps:
i) Test whether our system approaches the steady state (̄ ̄)
ii) For this steady state to be a feasible solution, the dynamics of the system must
satisfy the limitations of the model, namely concavity and the implied values ̄ ≤ 1 ̄ ≤ 1
Second the dynamics of the system must be characterized by stability, i.e. the eigenvalues
must be inside the unit circle.
If the above restrictions hold, then we are fully able to describe the behavior of the
equilibrium values of ( ∗  ∗ ) in every period of the model up to the steady state. Why is it
important to have a stable steady state? Because if the system is unstable, then  and 
∗
∗
grow without limits and taking into account that 
 0 
 0 this implies that as  and


 grow without bound the same will hold for  which will eventually become equal to unity.
5
Numerical approximations
The model in Section 4 closely follows the benchmark model up to the point were we obtain
the reaction functions. However due to occurring system of non-linear difference equations
it quickly becomes rather complicated. Therefore we will make some numerical calculations
27
illustrating our results. The same illustrative method is applied to the benchmark model as
well to highlight the similarities between the two models. In what follows we will shortly
describe the procedure followed to obtain our equilibrium values in the natural resources
model.
In our model there is a wide range of parameters that can vary, namely   ,  ,  
    and  As became evident from the above analysis of the model the most significant
term that drives most of our results was the equation   −   which defines the kind of
strategic interactions between the two groups of agents. Therefore we assume a wide range
of parameters for the variables   ,     and we also let  vary in order to derive some
comparative statics results with respect to policy implications.
Evidently the model is a rough approximation of reality therefore it is hard to clarify
what values of the parameters can be considered as "realistic". Still though with respect
to tax evasion there is some evidence that in the Western developed countries the rates of
tax evasion are estimated around 5%-25% of potential tax revenue (Feige, 1989, Pyle, 1989,
Thomas, 1992) while for developing countries higher rates may appear (Tanzi and Shome,
1994). For the year 1988 in the US, the TCMP has estimated that only a 53% has paid its
taxes correctly. Of course non compliance does not apply for all these cases, since a 7% has
overpaid its taxes while a part of the remaining 40% has underpaid due to errors that result
from the complicated procedure involved. According to Fanzoni (1998) the federal income tax
gap of the US had been estimated for 1998 at 17%.
Concerning the values of  and  there is much evidence that different allocations
of public budget are associated with different rent-seeking rates. Mauro (1998) finds evidence
that public expenditure on high-technology goods is associated with higher rent-seeking due
to low detectability and the same goes for military expenditure. On the other hand education
and health sectors involve more transparent expenditure and are thus associated with lower
rent-seeking rates. The literature on rent-seeking estimates the social waste in each sector
as imposed by bribery and suggests that increases in perceived corruption by one unit (in
the BI Index) reduce spending on certain allocations by 0.1-0.5% (0.4% for health, 0.05 for
environmental protection according to Hessami, 2010; 0.6% for education spending according
to Mauro, 1998). Even though this is a different measure, attempting to counterpart these
rates with   and    would imply a rate of 0.5%-0.25% depending on how corrupt a country
is according to the BI Index. Tax rates vary between 0.25-0.55.
As far as the parameters    are concerned it is hard to pin down which range of
values would be plausible and we will therefore focus on their between ratio as implied by our
model, namely   0   0 and      for strategic complementarity which is the case
we analyze. For the value of  there is also no evidence, still though it is easy to assume that
it will take rather small values, well below unity (e.g. Ceroni (2001) takes values of  as low
as  = 02).
Having pinned down the range of parameter values we also imposed the restrictions
mentioned earlier, namely concavity, strategic complementarity and an asymptotically stable
28
steady state. A number of feasible steady states occur implying different kinds of equilibria.
Below in Figure 3 we illustrate a numerical example of the natural resources economy:
Figure 3: Numerical Reaction Functions-The parameter values are  = 3  = 8   = 07
 = 085  = 035  = 0025  = −5  = 2
Figure 3: Numerical Reaction Functions-The parameter values are  = 3  = 8   = 07
 = 085  = 035  = 0025  = −5 0 = 185  = 2
Figure 2 closely resembles Figure 1, illustrating the similarities between the two models.
Interestingly the stable equilibrium denoted 1 is given by ( ∗  ∗ ) = (082 025) It is hard
to comment on the value of ∗ due to the duality of the model with respect to the allocation
of budget, still though we observe that  ∗ can take quite realistic values.
Plotting the benchmark economy when using the same parameter values in Figure 3
we observe that we obtain quite similar results. The stable equilibrium denoted 1 is given
by ( ∗  ∗ ) = (086 029) therefore indicating that the two models are very close even with
respect to the occurring equilibria.
Overall the findings of this section reinforce the robustness of the analytical results
obtained in the first part of the model and highlight the channels through which corruption
and rent-seeking on the one hand as well as individual’s expectations on the other hand are
determining the effectiveness of abatement on the quality of the environment.
6
Conclusions
This paper has theoretically established an alternative channel through which corruption may
have a detrimental effect on environmental policy. In particular it has suggested that in the
presence of corruption, the adoption of environmental policies may facilitate the extraction of
rents, particularly when the involved abatement technologies reduce transparency and thus
societal control. Moreover, in a world where individuals gain utility from a better environment,
corrupt activities on the part of governments that deteriorate the environmental quality may
be reciprocated by citizens, thereby further reducing the available funds for abatement.
In the light of recent scandals that suggest that public abatement can be a rather
"profitable" domain for rent-seeking activities, and the recent awareness of the need for a better
environmental quality, this research highlights that anti-corruption policies should target to
the reduction of rent seeking profits, to greater transparency and to the commitment to the
proper implementation of environmental policies.
29
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