Democracy, income and pollution

RESEARCH ARTICLE

Democracy, income and pollution

Clas Eriksson • Joakim Persson

Received: 3 November 2011 / Accepted: 4 February 2013 / Published online: 23 February 2013

� Springer Japan 2013

Abstract Empirical evidence suggests that increased democracy reduces pollu-

tion. 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 (&)

Malardalen University College,

P. O. Box 833, 721 23 Vasteras, Sweden

e-mail: [email protected]

J. Persson

Department of Economics, Linkoping University,

581 83 Linkoping, Sweden

e-mail: [email protected]

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Environ Econ Policy Stud (2013) 15:291–308

DOI 10.1007/s10018-013-0057-7

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 require-

ments 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.

292 Environ Econ Policy Stud (2013) 15:291–308

123

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.

Environ Econ Policy Stud (2013) 15:291–308 293

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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 environ-

mental 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 aif 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 repre-

sents 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:

x ¼Z1

0

aigðzÞdi ¼ gðzÞZ1

0

aidi:

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 compo-

nent, 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

aidi ¼ a

Z1

0

bidi � a:

The productivity distribution is unchanged in the analysis, which means that the

sumR 1

0bidi 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 yi=ðabiÞð Þ; and substituting this into (2), pollution is

related to income in the transformation function

x ¼ ag f�1 yi

abi

� �� ; ð3Þ

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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Differentiation of (3) with respect to yi shows that the slope of this transformation

curve is positive:

dx

dyi¼ dx

dz� dz

dyi¼ x0

ðyiÞ0[ 0:

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).

Fig. 1 The transformation curve


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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

f ¼ dðx0=ðyiÞ0Þdðx=yiÞ

x=yi

x0=ðyiÞ0¼

~bðzÞ � ~aðzÞbðzÞ � aðzÞ ; ð4Þ

where we have defined the elasticities8

aðzÞ ¼ f 0z

f[ 0; bðzÞ ¼ g0z

g[ 0; ~aðzÞ ¼ f 00z

f 0\0 and ~bðzÞ ¼ g00z

g0[ 0:

The final expression in (4) is the form in which the elasticity appears in the com-

putations below. To see that the final equality holds, note that

x

yi¼ gðzÞ

bif ðzÞ andx0

ðyiÞ0¼ g0ðzÞ

bif 0ðzÞ :

Therefore, (see ‘‘Computation of f’’ in Appendix)

dðx=yiÞdz

z

x=yi¼ bðzÞ � aðzÞ and

dðx0=ðyiÞ0Þdz

z

x0=ðyiÞ0¼ ~bðzÞ � ~aðzÞ:

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 z� z0ð 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 b � zz� z0ð Þ and ~bðzÞ ¼ ðb� 1Þ � z

z� z0ð Þ :

Hence,

f ¼ ðb� aÞz� ð1� aÞz0

ðb� aÞzþ az0

¼ 1� z0

ðb� aÞzþ az0

\1: 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

ViðzÞ ¼ u½abif ðzÞ� � v½agðzÞ�; ð6Þ

which the household maximizes with respect z, to determine its preferred policy. We

also define the elasticities

rðciÞ ¼ � u00ci

u0[ 0 and eðxÞ ¼ v00x

v0[ 0:

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

Vizi ¼ u0½abif ðziÞ�abif 0ðziÞ � v0½agðziÞ�ag0ðziÞ 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

Vizizi ¼ u00abif 0abif 0 þ u0abif 00 � v00ag0ag0 � v0ag00\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 Vizi 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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~zi ¼ ~ziða; biÞ; i 2 ½0; 1�: ð9Þ

Moreover, the single-peakedness implies that the further away a value of z is from

~ziða; biÞ, the worse it will be considered by individual i. There is, therefore, a

median voter (signified by m) with a preferred policy ~zmða; bmÞ, who will win a

vote against any other ~ziða; biÞ. 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~ziÞvaries 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 ~zmD. 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

Fig. 2 Voting profile


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to vote are found in the interval between iL and 1. The median voter is then

positioned at iNm, and her preferred policy is ~zm

N .12

Now consider the effect of increased democracy, which here means lowering iL,

possibly to 0. The result is that ~zmða; bmÞ 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 ~ziða; biÞ 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

oa

a

~zi¼ � 1

Di� rðciÞ þ eðxiÞ� �

\0; ð10Þ

where

Di ¼ rðciÞaðziÞ þ eðxiÞ � bðziÞ � ~aðziÞ þ ~bðziÞ[ 0:

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, ~zmða; bmÞ 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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u0½abif ð~ziÞ�bif 0ð~ziÞ ¼ v0½agð~ziÞ�g0ð~ziÞ: 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~zi

obi

bi

~zi¼ 1

Di1� rðciÞ� �

: 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 ten-

dency to satiation in consumption is more pronounced, and the individual seeks

higher utility by lowering pollution to a greater extent. The opposite case is illus-

trated 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 ~ziða; biÞ from Sect. 4 can be used

in (2) to write the preferred level of pollution, in the view of household i, as

~xi ¼ agð~ziða; biÞÞ: 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

oa¼ g � 1þ ag0

g

o~zi

oa

� �¼ g

Di� Di � b rðciÞ þ eðxiÞ

� �� ;

where we have used (10). By the definition of Di we then have

o~xi

oa

a

~xi¼ b� a

Di� fi � rðciÞ� �

; ð14Þ

where fi (defined in (4)) is evaluated at ~zi. Since b[ 1 and a\ 1, by the

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 counter-

acting 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

has this property is the CARA function, uðciÞ ¼ 1� e�wci

, 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 Lopez (1994). Note, however, that the interpretation of the first elasticity in the

parenthesis is different here. More importantly, however, Lopez (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 ~xi ¼ agð~ziða; biÞÞ with respect to bi and get

o~xi

obi¼ ag0

o~zi

obi¼ ag0

~zi

bi

1


;

where (12) has been used. After some rearrangement, we have

o~xi

obi

bi

~xi¼ b


: 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 Vzzi 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

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 � rðcmÞ. 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 � rðcmÞ 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.


123

Appendix

Derivative of the transformation function

The first-order derivative of (3) with respect to yi can be written as:

dx

dyi¼ ag0½�� f�1 yi

abi

� �� 0� 1

abi¼ g0

bif 0¼ x0

ðyiÞ0[ 0:

The second-order derivative of (3) is

d2x

dðyiÞ2¼ 1

big00 � ½f�1�0 1

abi½f�1�0 þ 1

big0 � ½f�1�00 1

abi

¼ 1

aðbiÞ2g00

1

f 0

� �2

� 1

aðbiÞ2g0

f 00

f 0ð Þ3[ 0:

This can be rewritten as

d2x

dðyiÞ2¼ g0

aðbiÞ21

f 0

� �2g00

g0� f 00

f 0

� �¼ ag0

ðabif 0Þ21

z

g00z

g0� f 00z

f 0

� �

¼ x0

ððyiÞ0Þ21

z~bðzÞ � ~aðzÞ�

[ 0:

Computation of f

To get the expression for f; we first compute

d

dz

x

yi

� �¼ d

dz

gðzÞbif ðzÞ

� �¼ g0ðzÞbif ðzÞ � gbif 0ðzÞ

ðbif ðzÞÞ2:

Multiplying by z/(x/yi):

dðx=yiÞdz

z

ðx=yiÞ ¼g0ðzÞbif ðzÞ � gbif 0ðzÞ

ðbif ðzÞÞ2� zbif ðzÞ

gðzÞ

dðx=yiÞdz

z

ðx=yiÞ ¼g0ðzÞf ðzÞz� gf 0ðzÞz

f ðzÞgðzÞ ¼ g0ðzÞzgðzÞ �

f 0ðzÞzf ðzÞ ¼ bðzÞ � aðzÞ:

We also have

d

dz

dx

dyi

� �¼ d

dz

g0ðzÞbif 0ðzÞ

� �¼ g00ðzÞbif 0ðzÞ � g0bif 00ðzÞ

ðbif 0ðzÞÞ2:

Multiplying by z/(dx/dyi):

dðdx=dyiÞdz

z

ðdx=dyiÞ ¼g00ðzÞbif 0ðzÞ � g0bif 00ðzÞ

ðbif 0ðzÞÞ2� zbif 0ðzÞ

g0ðzÞ


123

dðdx=dyiÞdz

z

ðdx=dyiÞ ¼g00ðzÞf 0ðzÞz� g0f 00ðzÞz

f 0ðzÞg0ðzÞ ¼ g00ðzÞzg0ðzÞ �

f 00ðzÞzf 0ðzÞ ¼

~bðzÞ � ~aðzÞ:

Vzzi

Equation (8) can be rewritten as

Vizz ¼ u00abif 0abif 0 � v00ag0ag0 þ u0abif 00 � v0ag00:

These terms can be expanded. For instance, the first term is multiplied by u0/u0, f/

f and z/z, and so on:

Vizz ¼ u00abif 0abif 0

u0

u0f

f

z

z� v00ag0ag0

v0

v0g

g

z

zþ u0abif 00

f 0

f 0z

z� v0ag00

g0

g0z

z:

Rearranging:

Vizz ¼

u00abif

u0� f0z

f� abif 0u0

z� v00ag

v0� g0z

g� v0ag0

zþ f 00z

f 0� u0abif 0

z� v0ag0

z� g00z

g0:

Since, by (7), u0abif0 = v0ag0:

Vizz ¼

abif 0u0

z

u00abif

u0� f0z

f� v00ag

v0� g0z

gþ f 00z

f 0� g00z

g0

� �:

Using the definitions of elasticities above:

Vizz ¼

abif 0u0

zi�rðciÞaðziÞ � eðxÞ � bðziÞ þ ~aðziÞ � ~bðziÞ�

Vizz ¼ �

abif 0ðziÞu0ðciÞzi

rðciÞaðziÞ þ eðxÞ � bðziÞ � ~aðziÞ þ ~bðziÞ�

:

Computing the derivatives

The effects of variations in the productivity parameters are obtained by implicit

differentiation of (7). We then get

o~zi

oa¼ �Vi

za

Vizz

ando~zi

obi¼ �

Vizbi

Vizz

; 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 ‘‘Vzzi ’’ in Appendix)

Vizz ¼ �

u0abif 0

z� Di; ð17Þ

where


123

Di ¼ rðciÞaðziÞ þ eðxiÞ � bðziÞ � ~aðziÞ þ ~bðziÞ[ 0:

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

Viza ¼ u00bifabif 0 � v00gag0 ¼ � u0abif 0

arðciÞ þ eðxiÞ� �

ð18Þ

and

Vizbi ¼ u00afabif 0 þ u0af 0 ¼ u0abif 0

bi1� rðciÞ� �

: 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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