Environ Econ Policy Stud
DOI 10.1007/s10018-013-0057-7
RESEARCH ARTICLE
Democracy, income and pollution
Clas Eriksson • Joakim Persson
Received: 3 November 2011 / Accepted: 4 February 2013
Ó Springer Japan 2013
Abstract Empirical evidence suggests that increased democracy reduces pollution. Using a median-voter model (where a democratization reform typically
changes the income of the median voter), we analyze how the effect of a change of
the individual income differs from the effect of a change in the economy-wide
productivity in the determination of pollution. We find that a democratization
reform that brings poorer groups into the franchise leads to lower pollution only if
the elasticity of the marginal utility of consumption, r, is smaller than unity. At the
same time, the EKC literature suggests that a country tends to improve aspects of
the environment as its per capita income rises, at least when it is above some critical
level. For the model to be consistent with this observation, when r \ 1, the
transformation function between income and pollution must be generous, i.e. little
income has to be given up as pollution is reduced.
Keywords
Environmental policy Voting Democracy Pollution
JEL Classification
H23 H30
C. Eriksson (&)
Mälardalen University College,
P. O. Box 833, 721 23 Västerås, Sweden
e-mail: [email protected]
J. Persson
Department of Economics, Linköping University,
581 83 Linköping, Sweden
e-mail: [email protected]
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1 Introduction
The empirical literature on the Environmental Kuznets Curve (EKC)1 indicates
that democracy is good for the environment. For example, Harbaugh et al.
(2002) include an index of democracy among the regressors to explain the level
of pollution in a sample of countries. They report negative relationships between
democracy and the concentrations of sulphur dioxide, smoke and total suspended
particulates. This pattern is robust and arises in numerous specifications.2
This paper theoretically examines a mechanism that provides an explanation of
these results. We use a model where environmental policy is determined by the
median voter. The analysis focuses on two different effects. On the one hand, a
democratization process typically changes the income of the median voter and, thus,
his preferred environmental policy. On the other hand, income growth on the macro
level is also the main driver of the EKC curve itself. A central purpose is to single
out each of these two mechanisms.
Regarding the effect of democratization, the historical analysis in Aidt et al.
(2006) indicates that it is often poorer groups who enter the electorate when it is
expanded (see also Acemoglu and Robinson 2006). These results, thus, indicate that
when a country becomes more democratic the income of the median voter tends to
fall, ceteris paribus. Following the results in Harbaugh et al. (2002), this median
voter prefers a cleaner environment than the richer median voter in a less
democratic country, with the same average income. In other words, poorer
individuals prefer a cleaner environment.
At the same time, the EKC literature provides evidence that countries improve
aspects of the environment as their per capita incomes rise, at least when per capita
income has surpassed some critical level. It, thus, appears that there could be
notable differences between responses to changed incomes on the individual and
aggregate levels, respectively. We, therefore, examine what the common requirements are for the model to give the following two results: (1) pollution declines if
the country as a whole gets richer; (2) pollution declines if the median voter
becomes a person with a lower income.
A possible explanation for a negative empirical relation between democracy and
pollution could come from the assumption that poorer groups are more exposed to
emissions, e.g. because they live closer to polluting activities. We have provided an
analysis along such lines in Eriksson and Persson (2003). This paper explores an
alternative mechanism, which is based only on core micro fundamentals:
preferences and technology. This makes income (individual and national) the
1
According to this literature, environmental quality varies with, among other things, per capita income.
For some pollutants, evidence indicates that there is an inverse U-shaped relationship between pollution
and per capita income. For other pollutants, however, the relation between pollution and per capita
income is monotonously increasing or monotonously decreasing over most of the income range. The
results of this literature are debated, however. See Dasgupta et al. (2002), Stern (2004) and Carson
(2010). Grossman and Krueger (1995) is a seminal article.
2
Similar results are obtained by Farzin and Bond (2006). For a list of more references that report the
same result, see Fredriksson et al. (2005), footnote 5.
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Environ Econ Policy Stud
primary driver of the pollution time path.3 By reducing the importance of the
localization of voters, this paper focuses on emissions that are uniformly mixing,
reaching all inhabitants to the same extent. We, thus, foremost have mobile air
pollutants in mind.
In the analysis below, we extend the model of our earlier paper (Eriksson and
Persson 2003), by generalizing the elementary functions, which earlier were all
constant-elastic. We thereby obtain modifications of the results that are non-trivial.
In particular, we are able to make a distinction between the effects on pollution,
following an income change on the individual level and on the economy-wide level,
respectively. The production side of the economy has an exogenous production and
pollution capacity, which grows at the same rate as aggregate productivity. This
scale effect on pollution can be counteracted by a technique effect, through switches
to cleaner production methods, at the cost of a lower growth in income. The
technical standard is decided by the median voter, who faces a trade-off between
consumption and environmental quality.
The results of the paper depend largely on two elasticities, f and r. The former
is derived from the transformation function between pollution and income: f is the
elasticity of the slope of this function. A high f means that it costs much, in terms
of lost income, to reduce pollution. We define r as the elasticity of the marginal
utility of consumption. If r is large, the marginal utility of consumption declines
rapidly when consumption increases, which tends to make the consumer more
prone to seek higher utility from reduced pollution. To get the effect that more
democracy lowers pollution, it is required that r \ 1 for the median voter when a
democratization makes the median voter poorer. Thus, the utility function cannot
exhibit satiation in consumption, although this has been pointed out as important
for a reduction of pollution in other models (e.g. Stokey 1998). For the model to
generate the result that pollution is reduced as the entire economy gets richer, it is
required that f\r. Thus, for a decline of pollution in response to growth in
aggregate productivity level, a moderately high r must be compensated by a
‘generous’ curve of transformation (between income and pollution), i.e. by a low
f.
These results arise because individual productivity and aggregate productivity
have different effects on the individual households’ desired environmental policy. In
particular, only the economy-wide productivity will influence the marginal cost of
pollution. This absence of a perceivable individual influence on the marginal cost is
due to the public-bad nature of pollution.
There is an obvious formal similarity between this paper and the articles by
Romer (1975), Roberts (1977), Meltzer and Richard (1981) and others, which
endogenize the size of public spending in median voter models. Since we here
consider pollution (a public bad), however, there is no need to finance the supply of
it (as opposed to the public good in those papers). Moreover, the motives for
3
There is no proper dynamic optimization problem in this paper. We follow a simplified economy over
time, which exogenously receives an increased productivity (and pollution capacity) as time runs, without
having to make any investments to get it. Some of the analysis focuses on the development of pollution
over time, but a part of the analysis is ‘cross-sectional’ in the sense that it studies the effects of increased
democracy at a given productivity.
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Environ Econ Policy Stud
subsidizing the reduction of pollution are weak.4 There is, thus, no need to raise
public funds in this paper (and no need to explicitly model any governmental budget
constraint), since the environmental policy is implemented by a technical standard.
These modelling differences make this paper more specialized towards environmental policy, in contrast to the papers mentioned above which consider public
goods.
Although using a median voter model is a simplification,5 it serves as an initial
check on how individual preferences can be transformed into social policy, and it is
also a useful reference point to which one can compare the outcomes of more
elaborate political models. In particular, this model is suitable for an examination of
the interaction between various properties of fundamental microeconomic functions
in the determination of environmental policy. The median voter model has not been
frequently used in the literature on the endogenous formation of environmental
policy, but some examples are McAusland (2003), which analyzes the endogenous
formation of environmental policy in open economies, and Jones and Manuelli
(2001), which presents a dynamic analysis of environmental policy.6
The rest of this paper is organized as follows. The model is presented in Sect. 2.
In Sect. 3, the preferred environmental policy is derived, in particular, for the
median voter. In Sect. 4, we examine how the preferred policy varies in response to
changes in aggregate and individual productivity, respectively. We analyze the
consequences of these changes on pollution in Sect. 5, where we also compare the
results to the empirical observations mentioned above. Section 6 concludes the
paper.
2 The model
2.1 Income and pollution
There is a continuum of one-individual households/voters, the measure of which is
normalized to unity. We assume that there is only household production, and that
the income of household i is
yi ¼ ai f ðzÞ;
z 2 ½0; 1;
ð1Þ
where f(0) = 0, f0 [ 0, f00 \ 0 and ai is the productivity factor of household i.
Income is, thus, increasing in the political choice variable, z. This variable represents the regulated production technique, which is decided by voting.
4
It would lower the firms’ average costs, which may lead to excess entry. To counteract this, the subsidy
must be higher (too high). See, for instance, Goulder and Parry (2008).
5
Despite this simplification, the median voter theorem is widely applied to so-called general interest
issues (as opposed to special interest issues; see Persson 1998).
6
The recent literature on the political economics of environmental policy has paid attention to the role of
special interest groups. See, for example, Aidt (1998), Fredriksson (1997) and Yu (2005). In addition, in
two recent papers (List and Sturm 2006; Cremer et al. 2008), the politicians are not merely modeled as
motivated by staying in office, but they care about the policy per se as well.
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While a higher z increases income, it also makes production dirtier. Pollution
from household i is aig(z), where g(0) = 0, g0 [ 0 and g00 [ 0. The total quantity of
pollution is the sum of pollution from all households:
x¼
Z1
i
a gðzÞdi ¼ gðzÞ
0
Z1
ai di:
0
This means that output and polluting emissions arise solely from home production.7
The productivity variable consists of two factors: ai ¼ a bi : The first component, a, is a common productivity factor for all households. There is an upward
trend in a, which increases the productivity of the entire economy over time. The
second part, bi, determines the relative position of household i on the productivity
scale. It is assumed that bi increases with i. The sum of productivity levels is
Z1
0
i
a di ¼ a
Z1
bi di a:
0
The productivity distribution is unchanged in the analysis, which means that the
R1
sum 0 bi di is constant. Without loss of generality, it is equated to unity, to simplify
the notation.
Putting these pieces together, total pollution is a function of the two variables a
and z:
x ¼ agðzÞ:
ð2Þ
An economy with a high productivity level is potentially also a big polluter. This is
a scale effect, represented by an increasing a. Pollution can, however, be reduced by
lowering z, at the cost of a reduced (growth in) income. This is a technique effect.
The net change in pollution is determined by the relative magnitudes of these two
effects.
2.2 The transformation function
The transformation function between pollution and income, and, in particular, the
elasticity of its slope, is important for the results below. We, therefore, define it here.
Solving (1) for z ¼ f 1 ðyi =ðabi ÞÞ; and substituting this into (2), pollution is
related to income in the transformation function
i y
x ¼ ag f 1
;
ð3Þ
abi
which is illustrated in Fig. 1. Each individual will have his own transformation
curve, because of the variation in bi between households; a higher bi allows a higher
yi at given x.
7
A model with explicitly modelled markets would give the same results, but with more variables and
algebra.
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Fig. 1 The transformation curve
Differentiation of (3) with respect to yi shows that the slope of this transformation
curve is positive:
dx dx dz
x0
¼ i ¼ i 0 [ 0:
i
dy
dz dy
ðy Þ
A higher income can, thus, be obtained if more pollution is accepted. Moreover, this
slope rises when yi grows, i.e. if we raise z to go further along the curve at constant
productivities, a and bi (see ‘‘Derivative of the transformation function’’ in
Appendix). This means that an increase in income by one unit is more costly, in
terms of pollution, if pollution and income are high.
The subsequent analysis will show that the value of z that maximizes the
individual’s utility (given in (7) below) monotonically falls when a grows
exogenously over time. Thus, when we go in the other direction along the
transformation curve, the slope is declining. If it does so rapidly, a large amount of
income must be given up to get one extra unit of reduction in pollution. This high
cost will tend to result in less effort to reduce pollution (by lowering z).
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In the analysis below, the change in the slope of the transformation curve is
expressed in elasticity form. More precisely, the elasticity of the slope of the
transformation curve is
f¼
~ ~aðzÞ
bðzÞ
dðx0 =ðyi Þ0 Þ x=yi
;
0 ¼
i
0
i
bðzÞ aðzÞ
dðx=y Þ x =ðy Þ
ð4Þ
where we have defined the elasticities8
aðzÞ ¼
f 0z
[ 0;
f
bðzÞ ¼
g0 z
[ 0;
g
~
aðzÞ ¼
f 00 z
\0
f0
and
00
~ ¼ g z [ 0:
bðzÞ
g0
The final expression in (4) is the form in which the elasticity appears in the computations below. To see that the final equality holds, note that
x
gðzÞ
¼
yi bi f ðzÞ
and
x0
g0 ðzÞ
:
0 ¼ i 0
i
b f ðzÞ
ðy Þ
Therefore, (see ‘‘Computation of f’’ in Appendix)
dðx=yi Þ z
¼ bðzÞ aðzÞ
dz x=yi
and
dðx0 =ðyi Þ0 Þ z
~ ~aðzÞ:
¼ bðzÞ
dz
x0 =ðyi Þ0
The final equality in (4) is motivated by a combination of these expressions.
A high elasticity implies that a small increase in the ratio of pollution to income
leads to a large increase in the slope of the transformation function. Conversely, the
slope declines substantially as x/yi falls, if f is large. This means that it costs a lot, in
terms of lost income, to reduce pollution. Consequently, a large f will tend to keep
pollution high, while a small f will tend to keep pollution low.
For an illustrating example, assume that f(z) = za and gðzÞ ¼ ðz z0 Þb ; where
0 \ a \ 1, b [ 1 and g(z) = 0 for z 2 ½0; z0 : This means that productive activities
generate pollution only when z [ z0.9 Then, a(z) = a and ~aðzÞ ¼ a 1 are constant.
Furthermore,
bðzÞ ¼
bz
ðz z0 Þ
and
~ ¼ ðb 1Þ z :
bðzÞ
ðz z0 Þ
Hence,
f¼
ðb aÞz ð1 aÞz0
z0
¼1
\1:
ðb aÞz þ az0
ðb aÞz þ az0
ð5Þ
For the later discussion, we note that f gets smaller if z declines. Moreover, f ¼ 1 if
z0 = 0 which is the case that Stokey (1998) and Eriksson and Persson (2003) choose.
8
We have here written f as independent of i, because there is no bi in this expression. However, f will be
evaluated at the z preferred by individual i in the expressions below and, therefore, we will then write fi :
9
There are, thus, some (low-productive) techniques that do not pollute at all. Examples of this could be
some traditional agricultural methods, where all emissions are organic compounds which nature is
capable of breaking down at a pace corresponding to the emission flows (e.g. manure, wool-based textile
and wood constructions).
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2.3 Utility
Households derive utility from consumption, ci (which is equal to income), and
experience disutility from pollution. The utility function is Vi = u(yi) - v(x), where
u0 [ 0, u00 \ 0, v0 [ 0 and v00 [ 0.10 Thus, the marginal utility of consumption,
u0 (yi), is decreasing when consumption increases, whereas the marginal utility of
pollution, v0 (x), is increasing when pollution increases. Using Eqs. (1) and (2), we
have
V i ðzÞ ¼ u½abi f ðzÞ v½agðzÞ;
ð6Þ
which the household maximizes with respect z, to determine its preferred policy. We
also define the elasticities
rðci Þ ¼ u00 ci
[0
u0
and
eðxÞ ¼
v00 x
[ 0:
v0
In the analysis below, r(ci) is (together with f) found to be essential for the direction
in which pollution changes as productivity varies.
3 Preferred policy
The level of the production technique that maximizes the utility of household i in (6)
satisfies the condition
Vzii ¼ u0 ½abi f ðzi Þabi f 0 ðzi Þ v0 ½agðzi Þag0 ðzi Þ ¼ 0;
i 2 ½0; 1:
ð7Þ
The subscript zi signifies the partial derivative with respect to zi. Every household,
thus, finds it optimal to increase the dirtiness of production up to the point where its
own marginal benefit is equal to the marginal cost.11
Condition (7) yields a unique optimal zi (for each i) if Vi is strictly concave in zi.
The second-order derivative of Vi with respect to zi is
Vzii zi ¼ u00 abi f 0 abi f 0 þ u0 abi f 00 v00 ag0 ag0 v0 ag00 \0:
ð8Þ
This derivative is negative by the assumptions about the elementary functions.
Preferences are, therefore, single-peaked and (7) implicitly defines a unique optimal
environmental policy for household i,
10
The utility function is, thus, additively separable, which means that there is no cross effect between
consumption and pollution. In reality, there could be such an effect, but there does not seem to be any
consensus in the literature about the sign of it. For this reason, we choose this simplified utility function,
which gives an opportunity to display some central results in a more transparent way. (Hopefully, this
simplifying assumption will be relaxed in future research.)
11
There might be a corner solution, with zi = 1 and Vzii ð1Þ [ 0. However, this can only happen if a is
sufficiently low, as we will see in Sect. 4. To simplify the exposition, we focus on the range of
productivity which is high enough for an interior solution. A corner solution at zi = 0 is ruled out because
the second term of (7) would approach zero, by the assumptions about the basic functions, while the first
would go to infinity if zi ? 0. This would violate (7).
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Fig. 2 Voting profile
z~i ¼ ~
zi ða; bi Þ;
i 2 ½0; 1:
ð9Þ
Moreover, the single-peakedness implies that the further away a value of z is from
zi ða; bi Þ, the worse it will be considered by individual i. There is, therefore, a
~
median voter (signified by m) with a preferred policy ~zm ða; bm Þ, who will win a
vote against any other ~
zi ða; bi Þ. This follows from the fact that he/she can be
singled out by a simple separation argument (see Persson and Tabellini 2000). In
this sense, the voting equilibrium is well-defined: the Condorcet winner can
always be found.
Figure 2 depicts a possible voting profile, showing how the preferred policy ð~zi Þ
varies over the individuals in the population. Note that the voting profile in Fig. 2 is
just one possibility, but it is an interesting one that plays an important part in the
subsequent sections of the paper. Recalling that bi is growing in i, the positive slope
in Fig. 2 means that poorer households prefer (and vote for) a more stringent
environmental policy than richer households do.
In a perfect democracy, the median voter is found at i = 1/2, and she prefers the
policy ~
zm
D . If democracy is restricted, some households are excluded from voting,
which changes the identity of the median voter. As mentioned in the introduction,
historical evidence (see e.g. Aidt et al. 2006) suggests that it typically is poorer
people who are excluded from the political decision process in non-democracies.
Assuming that these people also are less productive, we can formalize a limitation
of democracy by excluding the lower part of the unit interval from the franchise, i.e.
those with low bi:s. In Fig. 2, this would be to say that the citizens that are allowed
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to vote are found in the interval between iL and 1. The median voter is then
12
positioned at im
zm
N , and her preferred policy is ~
N.
Now consider the effect of increased democracy, which here means lowering iL,
possibly to 0. The result is that ~
zm ða; bm Þ falls, because bm declines as the identity of
the median voter changes. Just like the empirical evidence mentioned in the
introduction suggests, democratization here leads to lower pollution. This result
arises because we have chosen to draw the voting profile with a positive slope.13
The next section examines formally what is required to have a positively sloping
voting profile. It also shows that the curve shifts down over time, as a grows. The
results are then used to analyze the effects of productivity changes on pollution in
Sect. 5.
4 Effects of productivity on policy
In this section, we show how ~
zi ða; bi Þ varies in response to changes in a and bi, by
differentiation of (7). The computations are found in ‘‘Computing the derivatives’’
in Appendix.
4.1 Varying a
The change in the policy preferred by household i, when the general productivity
grows, is given by:
o~
zi a
1 ¼ i rðci Þ þ eðxi Þ \0;
zi
D
oa ~
ð10Þ
where
~ i Þ [ 0:
Di ¼ rðci Þaðzi Þ þ eðxi Þ bðzi Þ ~
aðzi Þ þ bðz
Since the sign is unambiguously negative for every voter, including the median
voter, an economy on a higher level of development always chooses a cleaner
technique. As we will see in Sect. 5, however, this does not necessarily imply that
the desired level of pollution will fall, because of the scale effect.
It is helpful for the interpretation to rewrite Eq. (7) into an equality between
marginal benefit and marginal cost:
12
If the voting profile is non-monotonous, ~zm ða; bm Þ can be found by use of the horizontal line that cuts
the voting profile in half, i.e. the line that leaves equally much of the curve above it as below it.
13
The process of democratization is exogenous here, but it could be made endogenous, at the cost of a
much more complicated analysis. There is, for instance, the ‘modernization hypothesis’, which in some
versions says that more democracy almost automatically follows from a higher per capita income in the
economy (and possibly also more democracy promotes the speed of growth). An alternative theory (with
more microeconomic underpinnings) is provided by Acemoglu and Robinson (2000), where institutional
reforms towards more democracy result from strategic decisions by the political elite to prevent social
unrest and revolution.
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u0 ½abi f ð~
zi Þbi f 0 ð~
zi Þ ¼ v0 ½agð~zi Þg0 ð~zi Þ:
ð11Þ
The result in (10) is, thus, due to the diminishing marginal utility of consumption
and the increasing disutility of pollution that a rising a causes.
4.2 Varying bi
The effect of a change in the personal productivity level14 is described by the
following expression:
o~
z i bi
1
¼ i 1 rðci Þ :
i
i
D
ob ~
z
ð12Þ
The sign of (12) is ambiguous because a higher bi has two opposing effects in the
marginal benefit term of (11): it increases income but decreases marginal utility of
income. The latter effect is dominating if and only if r(ci) [ 1, which, thus, is
necessary and sufficient to make the richer household prefer a lower z. At a higher
r(ci), the marginal utility of consumption declines more rapidly. That is, the tendency to satiation in consumption is more pronounced, and the individual seeks
higher utility by lowering pollution to a greater extent. The opposite case is illustrated in Fig. 2, and it occurs when r(ci) \ 1. In this case, a poorer individual
prefers a lower z.
Comparing the effects of the two productivity factors, we note from (10) and (12)
that ~
zi always falls when a grows, but not necessarily when bi increases. The
explanation can be found from the fact that we have a once on each side of (11),
while bi just appears twice on the left hand side. Thus, a higher bi will not raise the
disutility of pollution, due to the public character of pollution. On the other hand,
only (12) includes a positive effect on marginal benefit from a higher (individual)
productivity, which gives the two counteracting effects.
5 Effects of productivity on pollution
The variable that consumers care about is x rather than z, because it is x that enters
the utility function. In this section, we make use of the information from the
previous section about how the preferred policy is influenced by the two
productivity factors to see how these factors affect the preferred level of pollution
of any household. Formally, the knowledge about ~zi ða; bi Þ from Sect. 4 can be used
in (2) to write the preferred level of pollution, in the view of household i, as
x~i ¼ agð~
zi ða; bi ÞÞ:
ð13Þ
Variations in the two types of productivities seem, at a first glance, to render quite
different changes in the preferred level of pollution, since a appears twice on the
14
Recall that the productivity distribution does not change during the analysis. The variation in bi means
that we follow the productivity distribution from one individual to another.
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right hand side, while bi (giving no scale effect) is only to be found in one place. We
now examine this closer.
5.1 Varying a
The downward trend in z, implied by (10), is a necessary but not a sufficient
condition for a monotonous decline in pollution, since the growth of a also directly
boosts pollution. To determine which effect is dominating, we use (13) to compute
the preferred change in pollution when aggregate productivity increases:
o~
xi
ag0 o~
zi
g ¼g 1þ
¼ i Di b rðci Þ þ eðxi Þ ;
D
oa
g oa
where we have used (10). By the definition of Di we then have
o~
xi a b a i
¼
f rðci Þ ;
i
i
D
oa x~
ð14Þ
zi . Since b [ 1 and a \ 1, by the
where fi (defined in (4)) is evaluated at ~
assumptions about f and g, the ratio is unambiguously positive. Whether household
i’s preferred level of pollution grows over time, thus depends on the two counteracting terms in the parenthesis of (14).15
Consider first the positive term. If fi is high, then pollution reduction (by
lowering z) costs a lot of foregone income. The forces working towards an
increasing pollution are then strong (z falls slowly). On the other hand, when fi is
low, the transformation curve is relatively flat, and the tendency to prefer a higher
level of pollution is weaker. In the limiting case when the transformation curve
approaches a straight line, fi approaches zero and the tendency to increase pollution
vanishes.
The opposing force is in (14) captured by r(ci). The more rapidly marginal utility
of consumption declines (when consumption increases), the larger is this expression.
A higher r(ci), therefore, makes it more likely that the individual wants pollution to
fall when the general productivity grows over time.
In the political equilibrium, where i = m, the actual change of pollution, as the
general productivity grows, depends on the sign of fm rm . Monotonous time paths
of pollution are obviously possible: if fm [ rm , pollution is steadily increasing,
while it would be declining if the inequality were reversed. Since the variables
change, however, so can the relative strengths of the two terms. For example, there
could be an EKC, along which pollution first grows and then declines. This would
happen if, for instance, fm were non-increasing over time (as zm falls) and
moderately large, while rm were growing with consumption. A utility function that
i
has this property is the CARA function, uðci Þ ¼ 1 ewc , for which r(ci) = w ci is
proportional to consumption (which is a normal good and, therefore, grows over
15
Confer Section 1.3 in López (1994). Note, however, that the interpretation of the first elasticity in the
parenthesis is different here. More importantly, however, López (1994) does not discuss household
heterogeneity and voting.
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time). The negative term would then eventually dominate in the parenthesis of (14),
and thereby bring the economy onto the downward sloping part of the EKC.
5.2 Varying bi
To see how the preferred amount of pollution varies with the individual productivity
factor, we differentiate x~i ¼ agð~
zi ða; bi ÞÞ with respect to bi and get
o~
xi
zi
zi 1 0 o~
0~
¼
ag
¼
ag
1 rðci Þ ;
i
i
i
i
ob
ob
b D
where (12) has been used. After some rearrangement, we have
o~
x i bi
b
¼ i 1 rðci Þ :
i
i
D
ob x~
ð15Þ
Since this change in pollution is entirely derived from the technique effect, the total
effect is simply proportional to the change in policy, due to a variation in individual
productivity, given by (12) (with the factor of proportion equal to b). Hence, the
magnitude of r determines whether a rich voter prefers less or more pollution than a
poor voter.
Comparing the effects on pollution, we find fi only in (14), while the number 1
takes its place in (15). To see why fi appears only in (14), note that it builds on
second-order derivatives of f and g, the functions that constitute the transformation
function. These are included only in Vizz and, in particular, in Di. This expression
occurs in the numerator only when there is both a scale effect and a technique effect,
which is only the case in (14).
In the special case where fi ¼ 1, the parentheses of (14) and (15) are identical.
The level of pollution preferred by household i will, therefore, always change in the
same direction for both productivity factors. This result is, thus, built in with the
assumptions of Eriksson and Persson (2003), where all basic functions were
constant-elastic. That model was, thus, unable to explain a phenomenon where the
responses to higher incomes on the individual and aggregate levels go in opposite
directions. Only by the more general approach that has been taken here, are we able
to make the model consistent with empirical evidence on the relation between
democracy and the level of pollution. We now turn to this.
5.3 Relation to empirical findings
As mentioned in the introduction, empirical research reports a negative relationship
between pollution and democracy. In the model of this paper, a democratization
reform that expands the franchise to poorer groups means that the median voter gets
poorer, i.e. bm falls. According to Eq. (15), this leads to lower pollution only if
r(ci) \ 1 over the interval of households that covers the median voters before and
after the reform (which requires that the voting profile is positively sloping, like in
Fig. 2).16
16
If the voting profile is non-monotonous, other possibilities could of course arise.
123
Environ Econ Policy Stud
An implication of this inequality is, however, that a possible downward trend in
pollution, due to the economy-wide productivity growth, cannot be explained by a very
high r(cm). Recall from Eq. (14) that the preferred direction of change in pollution, as a
grows, according to the median voter is determined by the sign of fm rðcm Þ. If a
downward trend in pollution cannot be caused by a rapidly declining marginal utility
of consumption, it has to be driven by good conditions on the technology side, i.e. by a
fm low enough to make fm rðcm Þ negative. This does not seem implausible. For
instance, the illustrative example of Section 2.2 shows that fm \1 can be found for a
choice of functions that is not unreasonable. Moreover, it was found that fðzÞ is falling
as z declines, which it does over time in this model.
In this context, one could mention that rich countries are typically classified as
‘complete’ democracies, implying that there is no variation in the degree of
democracy over time for these countries. The negative empirical relation between
democracy and pollution must, thus, arise due to the behavior over time of poorer
countries. Theoretically, poor countries can have an upward-sloping voting profile,
whereas it may be downward sloping for rich countries. A simple mechanism to
generate such a behavior could come from an assumption that r(cm) is increasing in
consumption (like in the CARA case mentioned above), possibly combined with a
declining fm . Thus, a high r(cm) can be a reason for the downward sloping part of
the EKC, provided that this applies for rich, democratic countries.
Finally, we cannot rule out the more pessimistic case, in which fi [ 1 (at least for
the median voter). If, in addition, r(cm) \ 1 then the growth in a leads to more
pollution. (This is the way some people interpret the empirical literature on the
Environmental Kuznets Curve: economic growth leads to more pollution; see
Carson (2010) for a discussion.) Meanwhile, democratization leading to a lower bm
will give less pollution, because the poor exchange conditions of the transformation
curve do not affect the pollution choice when the individual productivity varies.
6 Conclusions
Income varies across individuals and at the aggregate level over time. Do these two types
of changes have qualitatively similar or different impacts on pollution if environmental
policy is modelled as a result of voting? We analyze this question in a median voter
model. The answer depends much on the elasticity of transformation between pollution
and income. If it equals unity, both types of productivity change generate variation in
pollution in the same direction. If it differs from unity, this may no longer hold.
The groups in the electorate vary with respect to their preferred environmental
policy. The voting profile is determined by the elasticity of the marginal utility of
consumption. A positive slope requires that this elasticity is lower than unity. In this
case, a democratization reform that brings poorer households into the franchise results
in lower pollution. For a downward trend in pollution, due to the general productivity
growth over time, the transformation curve has to be ‘generous’, meaning that little
income is given up when pollution is reduced.
Acknowledgments We are grateful for comments from from Rob Hart, Mitesh Kataria, Yves Surry,
Ficre Zehaie and two anonymous reviewers.
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Environ Econ Policy Stud
Appendix
Derivative of the transformation function
The first-order derivative of (3) with respect to yi can be written as:
i 0
dx
y
1
g0
x0
0
1
¼
ag
½
f
¼
¼
[ 0:
dyi
abi bi f 0 ðyi Þ0
abi
The second-order derivative of (3) is
d2 x
dðyi Þ2
1 00 1 0 1 1 0 1 0 1 00 1
g ½f i ½f þ i g ½f bi
ab
b
abi
2
00
1
1
1
f
¼
g00 0 g0
[ 0:
2
2
i
i
f
aðb Þ
aðb Þ ðf 0 Þ3
¼
This can be rewritten as
2 00
1
g
f 00
ag0 1 g00 z f 00 z
¼
f0
g0 f 0
ðabi f 0 Þ2 z g0
dðyi Þ2 aðbi Þ2 f 0
0
x
1 ~
bðzÞ ~
aðzÞ [ 0:
¼
0 2z
i
ððy Þ Þ
d2 x
¼
g0
Computation of f
To get the expression for f; we first compute
d x
d gðzÞ
g0 ðzÞbi f ðzÞ gbi f 0 ðzÞ
:
¼
¼
i
i
dz y
dz b f ðzÞ
ðbi f ðzÞÞ2
Multiplying by z/(x/yi):
dðx=yi Þ z
g0 ðzÞbi f ðzÞ gbi f 0 ðzÞ zbi f ðzÞ
¼
i
dz ðx=y Þ
gðzÞ
ðbi f ðzÞÞ2
dðx=yi Þ z
g0 ðzÞf ðzÞz gf 0 ðzÞz g0 ðzÞz f 0 ðzÞz
¼
¼ bðzÞ aðzÞ:
¼
dz ðx=yi Þ
f ðzÞgðzÞ
gðzÞ
f ðzÞ
We also have
d dx
d g0 ðzÞ
g00 ðzÞbi f 0 ðzÞ g0 bi f 00 ðzÞ
:
¼
¼
i
i
0
dz dy
dz b f ðzÞ
ðbi f 0 ðzÞÞ2
Multiplying by z/(dx/dyi):
dðdx=dyi Þ
z
g00 ðzÞbi f 0 ðzÞ g0 bi f 00 ðzÞ zbi f 0 ðzÞ
¼
0
i
dz
ðdx=dy Þ
g ðzÞ
ðbi f 0 ðzÞÞ2
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Environ Econ Policy Stud
dðdx=dyi Þ
z
g00 ðzÞf 0 ðzÞz g0 f 00 ðzÞz g00 ðzÞz f 00 ðzÞz ~
¼
¼ 0
0
¼ bðzÞ ~aðzÞ:
dz
ðdx=dyi Þ
f 0 ðzÞg0 ðzÞ
g ðzÞ
f ðzÞ
Vizz
Equation (8) can be rewritten as
Vzzi ¼ u00 abi f 0 abi f 0 v00 ag0 ag0 þ u0 abi f 00 v0 ag00 :
These terms can be expanded. For instance, the first term is multiplied by u0 /u0 , f/
f and z/z, and so on:
u0 f z
v0 g z
f0 z
g0 z
Vzzi ¼ u00 abi f 0 abi f 0 0 v00 ag0 ag0 0 þ u0 abi f 00 0 v0 ag00 0 :
u fz
v gz
f z
g z
Rearranging:
Vzzi ¼
u00 abi f f 0 z abi f 0 u0 v00 ag g0 z v0 ag0 f 00 z u0 abi f 0 v0 ag0 g00 z
0 þ 0 0 :
u0
f
v
g
f
g
z
z
z
z
Since, by (7), u0 abif0 = v0 ag0 :
abi f 0 u0 u00 abi f f 0 z v00 ag g0 z f 00 z g00 z
i
þ 0 0 :
Vzz ¼
0 u0
f
v
g
f
g
z
Using the definitions of elasticities above:
abi f 0 u0 i
i
i
i
~ iÞ
~
Vzzi ¼
rðc
Þaðz
Þ
eðxÞ
bðz
Þ
þ
a
ðz
Þ
bðz
zi
i 0 i 0 i ab f ðz Þu ðc Þ
i
i
i
i
~ iÞ :
~
Vzzi ¼ rðc
Þaðz
Þ
þ
eðxÞ
bðz
Þ
a
ðz
Þ
þ
bðz
zi
Computing the derivatives
The effects of variations in the productivity parameters are obtained by implicit
differentiation of (7). We then get
Vi
o~
zi
¼ zai
oa
Vzz
and
i
Vzb
o~
zi
i
¼
;
obi
Vzzi
ð16Þ
respectively. We now need expressions for the second-order derivatives on the
right-hand sides.
It will prove useful to express these formulae in terms of the elasticities defined
above. For instance, (8) can be simplified to (see ‘‘Vizz’’ in Appendix)
Vzzi ¼ where
123
u0 abi f 0 i
D;
z
ð17Þ
Environ Econ Policy Stud
~ i Þ [ 0:
Di ¼ rðci Þaðzi Þ þ eðxi Þ bðzi Þ ~
aðzi Þ þ bðz
We have the index i on xi because the preferred z of individual i also implies a
preferred x. Note that Di is positive. Similarly, we have
i
Vza
¼ u00 bi fabi f 0 v00 gag0 ¼ u0 abi f 0 i
rðc Þ þ eðxi Þ
a
ð18Þ
and
i
00
i 0
0 0
Vzb
i ¼ u afab f þ u af ¼
u0 abi f 0 1 rðci Þ :
bi
ð19Þ
In (18) two terms cancel out, due to (7). Equation (10) in the main text is obtained
by using (17) and (18) in (16). Equation (12) is obtained by using (17) and (19) in
(16).
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