Directory UMM :Data Elmu:jurnal:E:Ecological Economics:Vol34.Issue3.Sept2000:

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ANALYSIS

The Environmental Kuznets Curve, environmental

protection policy and income distribution

Elisabetta Magnani *

School of Economics,The Uni6ersity of New South Wales,Sydney NSW2052,Australia Received 30 October 1998; received in revised form 9 August 1999; accepted 20 August 1999

Abstract

The effect of economic growth on pollution emissions differs substantially among high-income countries. I address this issue by analyzing public environmental policy decisions. Individual heterogeneity, relative income effect and the political framework in which policy decisions are taken determine the emergence of the downward sloping segment of the Environmental Kuznets Curve (EKC). Income inequality produces a gap between the country’s ability to pay for environmental protection and a country’s willingness to pay. I test this result by using OECD data on public R&D expenditure for environmental protection. The conclusion is that contrary to the EK hypothesis, moments of the income distribution function other than the mean may be important for the emergence of a virtuous path of sustainable growth in high-income countries. © 2000 Elsevier Science Ltd. All rights reserved.

Keywords: Environmental policy; Environmental curve; Voting models; Development path; Income inequality; Median voter theorem

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1. Introduction

The hypothesis of an inverted U-shaped rela-tionship between growth in per capita income and environmental degradation, as illustrated by the Environmental Kuznets Curve (EKC), has re-cently been the subject of much empirical investi-gation. The argument according to which economic growth is ultimately beneficial for the

environment is controversial since it prompts the idea of a development path, a stage-based link between environmental quality and economic growth.

Studies of the link between levels of per capita income and environmental pressure, particularly pollution emissions, have revealed clear patterns. Pollution emissions usually decline for higher lev-els of per capita income. However, the explana-tory power of a polynomial in per capita GDP in regressions for environmental quality drops sig-nificantly when we move from poor countries to

* Tel.: +61-2-93853370; fax:+61-2-93136337. E-mail address:[email protected] (E. Magnani)

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high income countries (Roberts and Grimes, 1997; Magnani, 1999). Furthermore, in this latter group the effect of economic growth on emissions differs substantially among countries (De Bruyn et al., 1998). By suggesting that there may be other variables, besides the level of economic activity, that explain the evolution of pollution emissions in high income countries, the empirical results invite an examination of socio-economic factors that can directly affect the quality of the environment.

In recent times, scholars in the field have re-turned to the role of policy as a determining factor for the emergence of a downward sloping segment in the EKC (Baldwin, 1995; Grossman and Krueger, 1995). The environmental literature argues that the link between economic growth and environmental amenities in high income countries hinges upon the evolution of supply and demand for environmental care (Antle and Heidebrink, 1995). In particular, if the income elasticity of demand for environmental amenities is large, the demand for pollution abatement policies is likely to rise with GDP per capita. If the income elastic-ity condition (IEC) holds, an economy is more likely to experience declining levels of pollution emissions as per capita income increases.

This article focuses on the theoretical and em-pirical foundations of the EKC hypothesis by examining the determinants of public expenditure for environmental care in high income countries. Section two contrasts the foundations of the IEC of the traditional environmental literature with the hypothesis that withcountry income in-equality may damage the environment by reduc-ing the demand for pollution abatement (DPA). By combining a political economy approach to policy determination (Alesina and Rodrik, 1994) with the literature on the relative income effect on consumption decisions in rich countries (Ng and Wang, 1993), section three of this study goes on to provide the IEC with further specification. It establishes that when a relative income effect is in place, voters’ preferences over consumption of private goods and public goods, such as environ-mental amenities, depend on their relative posi-tion in the income distribuposi-tion funcposi-tion. In particular, I show that in countries where a

ma-joritarian voting system applies, income distribu-tion parameters and the exposure to environmental risk determine the level of pollu-tion emissions by impacting upon the willingness of the median voter to pay for environmental protection. The level of environmental protection depends on two effects, an absolute income effect and a relative-income effect. While growth in per capita income may increase the capacity to pay for environmental amenities (the absolute income effect), income inequality may drastically reduce a country’s willingness to pay (the relative income effect) by shifting the median voter’s preferences away from consumption of the public good ‘envi-ronmental amenities’. This result sheds light on the important question as to whether economic growth is sufficient for improvements in environ-mental care in economically advanced societies. A high income elasticity of demand for DPA is not a sufficient condition to lead to declining levels of pollution as per capita income grows.

The analysis of a model of environmental pol-icy determination leads to interesting testable re-sults. If there is a relative income effect and the IEC holds in this new environment, income in-equality has a negative effect on pro-environment public expenditure. Furthermore, the positive im-pact of economic growth (growth in per capita income) on environmental policy is reduced by income inequality. To test these hypotheses, sec-tion four uses OECD data on R&D expenditure for pollution abatement from 1980 to 1991. The empirical results point to a positive absolute in-come effect and a negative impact of inin-come inequality on environmental protection. This sec-ond finding implicitly evidences the importance of the relative income effect in individual consump-tion decisions and the need for a reformulated IEC. The concluding section argues for the ex-planatory power of a model where income distri-bution parameters affect preferences and the political process of decision making. Such a model accounts for the fact that countries who have similarly high rates of economic growth show very different responses of pollution emis-sion to GDP and GDP growth.

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2. Economic growth and environmental quality

A large set of studies has recently shed light on the empirical relationship between economic growth and environmental quality, the purported Environmental Kuznets curve. While the notion of environmental quality is broadly conceived and multidimensional (Antle and Heidebrink, 1995)1_,

broad measures of environmental quality such as human health and life expectancy are often only partially linked to the actual state of the natural environment (Braden and Kolstad, 1991). Fur-thermore, the aggregation of various measures of environmental pressure into a single index of envi-ronmental quality is problematic whenever the single components present, as it has been shown, very different trends and responses to crucial ex-planatory variables (Shafik, 1994; Grossman and Krueger, 1995). Policy evaluations often need analyses of single environmental quality indica-tors to address their relationship with economic growth and with policy parameters. For these reasons the concept of environmental quality is not immediately suitable for empirical investiga-tion, where the many dimensions of environmen-tal damage (air pollution, soil and water degradation, deforestation, depletion of non-re-newable resources, big-diversity loss) are often analyzed separately.

Even with this limitation, studies of the link between levels of per capita income and indicators of environmental pressure, such as emissions of those pollutants that immediately impact upon human health and activities (e.g. sulfur dioxide, nitrous oxide, suspended particular matters, car-bon dioxide), have revealed clear patterns. The focus of the empirical analyses has been on the relationship between per capita emissions (flows) of pollutant mit in country i at time t, real per

capita well-being, as measured by per capita

GDP, Yit and a time trendt:

mit=a0+bf(Yit)+b2t+uit (1)

To date, the literature on the EKC has stressed the issue of the choice of the functional form f (.) in Eq. (1). While such a choice is bound to affect the type and number of turning points in the empirical EKC, estimates of the range of per capita income in which pollution emissions are expected to descend are often significantly differ-ent (Grossman and Krueger, 1994; Selden and Song, 1994; Grossman, 1995; Stern et al., 1996).

Furthermore, the EKC only describes a rela-tionship between economic growth and specific pollutants, such as suspended particular matters and sulfur dioxide (Shafik, 1994; Grossman and Krueger, 1995). For these pollutants the estimated relationship between per capita income and pollu-tion emissions is highly sensitive not only to the choice of functional form but also to the data, that is, the sample of countries used and the sampling duration (Grossman and Krueger, 1994; Shafik, 1994; Stern et al., 1996; Roberts and Grimes, 1997). For instance, the explanatory power of a polynomial in GDP per capita ac-counts for a much smaller fraction of per capita pollution emission in high income countries than in low and middle income countries (Roberts and Grimes, 1997; Magnani, 1999). For high income countries the best functional form is not quadratic in GDP per capita but cubic. This implies that for very high levels of GDP environmental degrada-tion starts to increase again (Grossman and Krueger, 1995; Torras and Boyce, 1998).

Finally, the role of factors that evolve in time, e.g. technology, is quite uncertain. Analyses of the evolution in time of the EKCs for poor countries and for rich countries suggest that it is only in high-income countries that pollution emissions have declined over time (Roberts and Grimes, 1997; Magnani, 1999). However, even in high-in-come countries the effects of time and economic growth have not been uniform since the early 1970s (De Bruyn et al., 1998).

The instability of the empirical results, both across time and across countries, shows clearly an omitted variable problem. To solve the mispecifi-cation issue of the EKC, the literature has 1_{For instance, in the early 1960s the American Public}

Health Association suggested four levels of concerns in assess-ing environmental quality: (a) ensurassess-ing survival; (b) prevention of diseases and accidents; (c) maintenance of an environment suited to human activities; (d) preservation of comfort and the enjoyment of living. The American National Wildlife Federa-tion index of environmental quality, firstly published in 1969, is an example of such aggregate measures.

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searched for factors that can play a particularly important role in determining the environmental impact per unit of economic activity. Such factors include industrial composition of output (Gross-man and Krueger, 1995), population density (Cropper and Griffiths, 1994; Selden and Song, 1994), openness to trade (Hettige et al., 1992; Grossman and Krueger, 1994 Suri and Chapman, 1998), environmental regulation and control (Shafik, 1994; Baldwin, 1995). Notwithstanding, a definitive solution remains elusive. In Selden and Song (1994) the coefficient for population density is not statistically significant, although it has the expected negative sign. Likewise, the empirical evidence about the role of international trade and population density on the EKC is rather inconclu-sive (Stern et al., 1996). Since the effect of the scale of production is likely to overwhelm the composition effect of changes in its industrial composition (Grossman and Krueger, 1995), spe-cial consideration needs to be devoted to environ-mental regulation and control.

2.1. Pollution abatement and the EKC

The literature on the EKC has sparked a num-ber of critical positions. As Baldwin (1995) points out, a better understanding of the relationship between environmental quality and development may come from the decomposition of actual pol-lution into two quantities: incipient polpol-lution and abatement. Incipient pollutionIitis defined as the

level of pollution a country would produce at its current level and composition of output if envi-ronmental costs were zero. Abatement Eit is the

policy-induced difference between incipient pollu-tion and actual pollupollu-tion. Using the symbols in-troduced in Eq. (1) for pollution emission in country i at time t, mit=Iit−Eit.

The relationship between environmental quality and per capita income (the EKC) depends on how growth changes both components. The EKC hy-pothesis assumes that growth impacts upon both components, orIit=I(Yit) and Eit=E(Yit) where

Yitis a measure of economic well-being in country

i at time t. Economic growth positively impacts on incipient pollution Iit=I(Yit), I%(.)\0 as the

scale effect of output overwhelms the beneficial

effect on the natural environment induced by the shift from industrial to post-industrial and service activities characteristic of mature economies (the composition effect) (Baldwin, 1995; Grossman and Krueger, 1995). The virtuous development path from high to low pollution emissions passes through an increase in pollution abatement as per capita income grows E(Yit), E%(.)\0. The

envi-ronmental literature explains the sign of this derivative, there being an increase in the demand for environmental qualityDitas per capita income

increases. In particular, if the income elasticity of demand for environmental amenities is large, the demand for pollution abatement policies is likely to rise with GDP per capita (Antle and Heide-brink, 1995). If the income elasticity condition (IEC) holds, an economy is more likely to experi-ence declining levels of pollution emissions as per capita income increases. By differentiating actual pollution with respect to per capita income we obtain ((_m_it₎_/₍(_Y_it₎₌₍(_I_it₎_/₍(_Y_it₎₋₍(_E_it_/(_D_it₎ ((_D_it_/(_Y_it_{). Focusing on the role of the demand} for environmental qualityDitand with evidence of

no loss of generality, we assume that ((_E_it₎_/ ((_D_it₎₌_{1 or, in other words, environmental} pol-icy is totally accommodating to people’s preferences and the supply side of the economy does not constitute a constraint to the satisfaction of such a demand (Baldwin, 1995). Thus ((_m

it)/

((_Y

it)B0 if e\((I/(Yit) (Yit/Dit) where e

((_D

it/(Yit)(Yit/Dit) is the income elasticity of the

demand for environmental quality. If the income elasticity of demand for environmental amenities is high, the combination of changes in the indus-trial composition of output and high demand for environmental quality induced by economic growth guarantees that at advanced stages of development economic growth will be accompa-nied by a sensible decrease in environmental dam-age. The IEC thus provides theoretical foundations for the purported inverted U-shaped curve that describes the link between per capita GDP and environmental quality. Since central to the EKC hypothesis is the role played by pollu-tion abatement, it is legitimate to ask whether a specification such as Eit=E(Yit), which relates

environmental expenditure to the mean of the income distribution function, is general enough to

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encompass cases of economies that differ for a wide range of economic, social and political fac-tors while having the same level of per capita income.

3. Environmental protection policy, redistribution and growth

There is little doubt that non-economic vari-ables such as the features of the political system or some cultural values play an important role in the implementation of environmental-friendly policies (Ng and Wang, 1993; Antle and Heide-brink, 1995; Baldwin, 1995; Hettige et al., 1996). For instance, diffused property rights, a demo-cratic voting system and respect of basic human rights, may facilitate the implementation of regu-lation that protects the environment. In fact, there is wide consensus now that an understanding of the nature of the interactions between the eco-nomic sphere and political sphere may shed light on the actual determinants of policy decisions (Alesina and Rodrik, 1994; Verdier, 1994). The purpose of the analysis that follows is to model a situation in which moments of the income distri-bution function other than its mean affect the level of pollution abatement expenditure. Let us assume an additively separable utility function for individual l:

Ul=cl+glQ (2)

where cl is the level of consumption of a private

good, environmental quality Q is a pure public good and gl expresses the preference for

environ-mental quality. The public good nature of envi-ronmental amenitiesQimplies that environmental policy E is necessary to solve market failures, or specifically Q=Q(E), where Eis public expendi-ture for environmental care, and Q%_(.)\0.

Envi-ronmental care is financed through taxation, or

E=Y(t−t2

/2), wheretis the environmental tax rate,t(0, 1), and _Y is average income. Thus to

finance public policy for environmental care a fractiontylof personal incomeylis paid in taxes.

The functional form for public environmental protection E is quite general [see, for example, Bolton and Roland (1996)]. The quadratic term in

the tax rate multiplied by per capita income de-notes the cost of public funds.

Individuals are heterogeneous. They differ by personal income levels. In this economy income is distributed according to a unimodal function

h(yl), where yl[0,yH] and yH is the maximum

level of personal income. Income inequality im-plies that the majority of the population has income below the average so that we can assume (ym/Y)B1, where ymis the median income of the

distribution h(yl). Furthermore, individuals have

different preferences over conflicting goals, say consumption of the private good cand consump-tion of the public good environmental amenities. Central to the analysis that follows is the as-sumption that preferences for the public good Q

are positively correlated with the individual rela-tive income as expressed by the ratio Rl=(yl/Y)

between personal income and average income. In other words, the preference parameterglin Eq. (2)

is a function of the ‘distance’ between individual

l’s income and average income, gl=g(Rl), with

l(.)\0. In this way, the marginal rate of

substi-tution between consumption goods and environ-mental quality depends on the individual’s relative income. This ‘relative income effect’ states that one’s subjective feeling of well-being is based more on relative income than on absolute income. Ng and Wang (1993) have surveyed both the theoretical and empirical literature and show that the evidence in support of this hypothesis is vast, particularly in high-income countries. Glazer and Konrad (1996) further explore the relative income effect using a wealth-signalling model. The impli-cation of this assumption is that poor people (those whose income is below the average) care less for the environment than those relatively close to the average Yof the income distribution (Antle and Heidebrink, 1995; Broad, 1997). The relative income effect, as it pertains to environ-mental policy decisions, is the fundaenviron-mental hy-pothesis to be tested in the empirical investigation of the next section.

In a static framework consumers and govern-ment will satisfy their budget constraint as equali-ties. The indirect utility function for the individual

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Vl=(1−t)yl+gl[Y(t−t

/2)] (3)

Note that by Eq. (3) preferences are single-peaked in the environmental tax ratet, as each individual has only one most preferred tax ratetl*.

Differen-tiation of Eq. (3) with respect to the choice vari-able t leads to tl*=1−(1/gl)Rl. Furthermore,

there exist, a monotonic relationship between ideal policies and voters’ relative income. In fact, ((_t

*)/

((_R_l₎₌₍₋_g_l₊_g%_l_R_l₎_/_(g_l2_{) . Note that the optimal}

taxation rate for individuallis a monotonic func-tion of relative income. In particular, ((_t_*_l₎_/ ((_R_l₎\0 , if the income elasticity o_l of the

preference gl for environmental care is \1, or

ol(gl(Rl(Rl/gl)\1. Conversely forolB1, the

op-timal environmental tax is a decreasing function of relative income.

With a majority voting system the political arena will set the environmental tax at the level that captures the majority’s support to its eco-nomic plan. The median voter theorem can be applied to this case because voting takes place over a single issue (t), preferences are single-peaked with respect to the tax rate t and there exists a monotonic relationship between ideal poli-cies and voters’ relative income (Gans and Smart, 1996). Thus the politician maximizes the indirect utility function of the median voter as expressed by Eq. (3) withl=m, wheremis the index for the median voter. The equilibrium tax rate t* is the most preferred tax rate of the median voter: t*=1−1

R (4)

whereR=(ym/Y) is the ratio between the median

income and the average incomeY. By Eq. (4) the equilibrium level of environmental abatement ex-penditure is an explicit function of the parameters of the income distribution function:

E*=E*(Y,ym

Y)=Y(t*−

(t*)2

2 ) (5)

The optimal taxation rate responds to changes in income inequality. In fact:

(_t_* (_R=

−gm+g%mR

2 (6)

whereg%

m(.)(dgm/dR) is by assumption positive.

From Eq. (5) I derive the following:

Proposition 1. Define R as the ratio between median and average income of the domestic in-come distribution function,R=(ym/Y).

Pro-envi-ronment public expenditure is an increasing function of income equalityR, or ((_E*₎_/₍(_R₎\0 ,

if the income elasticity o of the median voter’s preferencegm for environmental quality is greater

than one, or o((g_m/(R)(R/g_m)\1 . Proof. See

Appendix A.

In part the result illustrated with proposition 1 reproduces the characterization of the aggregate demand and supply of environmental quality as often used to support the view that economic growth (poverty reduction) and environmental quality go hand in hand (Ruttan, 1971). As Antle and Heidebrink (1995) explain, ‘if the income elasticity of demand for environmental quality or amenities is high, then the increased prosperity engendered by economic growth could lead to significantly higher demand for environmental quality.’ However, an important caveat here ap-plies. The ‘relative income effect’ introduced in Eq. (2) by means of the parameter g requires us to specify this elasticity condition in terms of a rela-tive income, such as (ym/Y), as opposed to an

absolute one. The relative income effect shows how economic development can impact upon envi-ronmental quality through quite distinct processes.

3.1. En6_{ironmental protection policy and income}

inequality

Economic growth has an effect on environmen-tal care through two channels. Firstly, it involves growth of the average incomeY, which positively impacts upon abatement expenditureE. Secondly, it affects the optimal environmental tax rate through its effect on income inequality as ex-pressed by the ratio between median income and average income R. The model in the previous section has shown that whenever political power is evenly distributed in the national community and a democratic voting system is in place the prefer-ences of the median voter will be pivotal to deci-sions involving environmental policies. If there

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is a ‘relative income effect’ on individual consump-tion decisions as in Hirsch (1976) or more recently in Ng and Wang (1993) and Glazer and Konrad (1996), the median’ voter preferences will depend on her relative income, an indicator of her relative social position. In other words we can think of the private good as a ‘positional good’ in Hirsch (1976) terminology insofar as individual satisfaction does not depend on its absolute level of consumption, but on the relative social status generated by it. If the income elasticity condition holds, proposition 1 has shown that the optimal taxation rate (Eq. (4)) is a monotonic function of the median voter’s relative income. The larger income inequality, the lower the relative income of the median voter, and the more he will be willing to spend in consumption of the private good rather than financing public environ-mental expenditure for enjoyment of the pure public good ‘environmental amenities’. Owing to the con-cern about relative standing, people tend to over-in-vest in private goods c(Frank, 1989).

Using Eq. (5): dE*(Y,R)

dY =

(_E* (_Y+

(_E* (_t

(_t_* (_R

(_R

(_Y (7)

Expression Eq. (7) introduces a disaggregation of the demand for environmental policy into a compo-nent that depends on the economy’s capacity to pay ((_E*_/(_Y_{) and another that depends on its} willing-ness to pay ((_E*_/(_t)((_t_*_/(_R₎₍(_R_/(_Y_{). Note that in} principle there is no guarantee that the demand for pollution abatement will increase during the process of development since the second term in Eq. (7) may be negative and large in size. Thus:

Proposition 2. Assume that proposition 1 is satisfied. Sufficient condition for pollution abate-mentE*(Y,R) to positively respond to growth in per capita income is that economic inequality decreases when average income rises. Proof. See Appendix A.

If we now decompose actual pollutionm (drop-ping for convenience subscripts i and t) into its incipient componentI(Y) and pollution abatement

E(Y,t),m=I(Y)−E(Y,t), the effect of economic growth (an increase in per capita income Y) on pollution emission is:

(_m (_Y=

dY−

(_E* (_Y−

(_E* (_t

(_t_* (_R

(_R

(_Y (8)

Eq. (8) introduces an interesting specification to the claim that economic growth leads to improvement in environmental quality. In fact the following remark holds:

Proposition 3. Assume that the ‘income’ elasticity of the preferences for environmental amenities is greater than one (as in proposition 1). If [((_I_/(_Y₎₋ ((_E*_/(_Y_)]\0 , then, economic growth will lead to

a reduction in pollution emission if and only if economic growth leads to a sensible reduction in income inequality or ((_R_/(_Y)\[((I/(Y)−((E*/ (_Y_)][((_E*_/(_t)((_t_*_/(_R_)]−1_\_{0 . Under the same}

assumption, if [((_I_/(_Y₎₋₍(_E*_/(_Y_)]B0 , economic

growth will lead to a reduction in pollution emission if and only if the effect of economic growth on income inequality is not too large, or (_R_/(_YB

[((_I_/(_Y₎₋₍(_E*_/(_Y_)][((_E*_/(_t)((_t_*_/(_R_)]−1_.

Proof. See Appendix A.

If relative income effects are relevant for individ-uals’ preferences, whether economic growth eventu-ally decreases pollution emissions also depends on whether economic growth is accompanied by a reduction in income inequality. A large income elasticity of the demand for environmental quality is not necessary nor sufficient to guarantee a decline in environmental damage as an economy grows. If (_R_/(_Y _{is negative and large in size, economic} growth may depress the demand for environmental care even if it is relative-income elastic. While growth in per capita income may increase the capacity to pay for environmental amenities, in-come inequality may drastically reduce voters’ willingness to pay. The net effect of economic growth on pollution abatement is unspecified, intro-ducing an important element of uncertainty on the effect of economic growth on pollution emissions.2

2_{Interestingly, expression 8 establishes a link between the} Environmental Kuznets Curve and the traditional Kuznets Curve (Kuznets, 1955) that goes beyond a purely formal analogy of the two inverted U-shaped relationships. See Tor-ras and Boyce (1998) for an interesting empirical analysis of the environmental impact of income (and power) inequality.

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Eq. (5) is a reduced form specification for pub-lic environmental expenditure suitable for testing the hypothesis that other moments of the income distribution function besides its mean may be relevant to explain the relationship between public environmental care and economic growth in high income countries. In the next section I explore this hypothesis empirically by investigating the impact of income inequality upon environmental expenditure in economically advanced societies.

4. Environmental protection policy and income distribution: An empirical investigation

Empirical analyses involving income inequality as a dependent variable or as an explanatory variable have usually encountered the problems of missing time series, non-comparability and low-quality of data (Ruttan, 1971; Shafik, 1994; Antle and Heidebrink, 1995; Deininger and Squire, 1996; Torras and Boyce, 1998). My empirical analysis of the determinant of the public policy for environmental protection uses a new data set on inequality put together by Deininger and Squire (1996). Deininger and Squire report the Gini index and the income shares by quintile for a wide group of countries. The Gini index (GINI) and the ratio of the income shares of the first and the fourth quintile of the income distribution (RATIO), allow me to assess the impact of in-come inequality on environmental policy. The first index (GINI) offers the advantage of being widely reported in official sources that are based on primary data. It has a disadvantage, however, in common with any aggregate measure of in-equality, that it may change of the same amount and in the same direction following very different changes in income distribution. The second index (RATIO) better uncovers possible movements in the income received by individual groups that could be obscured by the use of an aggregate index such as the Gini coefficient.

Data on environmental policy are rare (Shafik, 1994). The OECD Environmental Program pro-vides information on environmental protection that satisfy the criteria of reliability and interna-tional comparability. Information on public R&D

expenditure intended to protect the physical envi-ronment from degradation is collected for OECD countries in all years between 1980 and 1991. The countries included in the sample are: Canada; USA; Japan; Australia; New Zealand; Belgium; Denmark; Finland; France; Germany; Greece; Ireland; Italy; Netherlands; Norway; Portugal; Spain; Sweden; United Kingdom. Environmental protection includes all research relating to pollu-tion: study of origins and causes, diffusion and transformation and the effects on human beings and the environment, but excludes research on changes in the production process that result in the generation of less pollution. Environmental charges and taxes have multiplied over the last decades in OECD countries. To the extent that environmental policy requires knowledge of its impact, expenditure for environmental R&D is here used as proxy for the intensity of public engagement in environmental problems.

The regression equation is:

eit=a+b0xit+b1(xit)

+b2rit+b3(x*rit it)+b4t

+uit (9)

where the error term uit=oit+mi is decomposed

into a country effect mi, which captures

unobserv-able country-specific characteristics, and a white noise component oit. In Eq. (9) the dependent

variable eit is the logarithm of per capita R&D

expenditure for environmental protection. Ex-planatory variables are per capita income (GDP)

xit, converted at purchasing power parity into real

1985 US dollars, an income inequality index rit

(GINI or RATIO), and a time trend t. The Gini index is a measure of inequality, while the vari-able RATIO measures income equality. By propo-sition 1, the effect of income inequality on environmental expenditure depends on the level of per capita income. I allow for such a non-linear effect by including the interaction (xit*rit) among

the explanatory variables. Furthermore, the anal-ysis carried out in the previous section predicts that the overall effect of income inequality on public environmental protection expenditure is negative, i.e.b2+b3xitB0, if the income elasticity

of the preference for environmental quality is ‘large’ (proposition 1). Finally, if the income elas-ticity condition is satisfied, the net effect of per

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Table 1

Public R&D expenditure for environmental protection in OECD countries: Summary statistics

S.D. Min. Max

Variable Number of obs. Mean

361.2

Public abatement expenda ₇₈ _69.5 _89.08 _0.6

18 339 4382

GDP per capitab ₁₇₁ _{10 526} ₃₀₀₄

41.8

Gini coefficient 79 33.0 3.93 24.9

0.29

Ratioc ₇₄ _0.18 _0.05 _0.1

a_{Data refer to government research and development (R&D) budget appropriation (OECD, 1993). Public expenditure for} environmental protection is measured in million PPP US$ at 1985 price levels.

b_{Gross domestic product at purchasing power parities 1985 US dollars.}

c_{The ratio between the percentage of the income share held by the first quintile of the population and the income share of the} fourth quintile of the population. The raw income inequality data are from Deininger and Squire (1996).

capita income on environmental policy, i.e. (b0+

2b1xit+b3rit), is greater than zero provided

in-come inequality decreases with economic growth (proposition 2). Table 1 contains some summary statistics.

4.1. The empirical results

anal-ysis of residuals and leverage I performed have revealed the existence of particularly anomalous observations that incisively affect the nature of the relationships uncovered. The Ramsey (1969) test for omitted variables and the Cook – Weisberg (1983) test for heteroscedasticity do not provide evidence of mispecification problems. The statis-tics for these tests are reported in the tables.

In Table 2 the index of inequality is the Gini coefficient. In all regressions the coefficients for per capita income and for income inequality have the expected signs. The correlation between per capita GDP and expenditure in environmental protection, computed at the average income level, b0+2b1*(10 526), is positive, while income

in-equality is negatively correlated with per capita expenditure in environmental protection. These results are not affected by the inclusion or exclu-sion of a time trend, which improves slightly the goodness of fit of some specifications. When I control for a possible serial correlation in the error term by using pooled cross section observa-tions [specificaobserva-tions (V) and (VI)], I obtain results comparable to the random effect estimates.

Table 3 illustrates the empirical results obtained with the index of income equality RATIO. The inclusion of a time trend only marginally im-proves the goodness of fit of all specifications. It also decreases the size of the regression coefficient for RATIO in both specifications (II) and (VI) compared to the corresponding specifications without the time trend. Two empirical results deserve some attention. Firstly, in all specifica-tions the net average effect of per capita income on the dependent variable, computed as b0+

2b1(xit)+b3(rit) at the average levels $10 526 and

0.18 for per capita GDP and RATIO, respec-tively, is positive. The non-linearity in per capita income implies that the correlation with the de-pendent variable, computed at the RATIO aver-age 0.18, turns negative at relatively high levels of per capita GDP (above $14 000 in the RE specifi-3_{This is not to say that countries’ experiences in terms of}

pollution emissions and control do not differ widely. See, for example, De Bruyn et al. (1998).

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Table 2

Public R&D expenditure for environmental protectiona _and income inequality

Explanatory REb _FE _PCSc

var.

I III

0.002*** 0.001*** Per capita 0.0009***

GDP (0.0002) (0.0004) (0.0002) −2.9e−08***

(Per capita −5.1e−08*** −3.5e−08 GDP)2 _(9.1e−09) _(1.5e−08) _(7.4e−09)

−0.03 −0.06

−0.035 GINI coeff.

(0.05)

(0.031) (0.025)

– – –

Time trend

−11.9*** −15.6***

Constant −11.3***

(3.21)

(1.90) (1.52)

Hausman x2_(3)=5.2 testd

0.60 0.58 0.63

N=17 N=51 N=17

Number of

obs. t(avg.)=2.1 t(avg.)=3.1 r=0.03 IV

II VI

Explanatory var.

−0.0013**

Per capita 0.001*** 0.001***

GDP (0.0002) (0.0005) (0.0002) −4.7e−08*** −4e −3.6e−08***

(Per capita GDP)2

−08*** (7.3e−09) (9.9e−09) (1.6e−08)

GINI coeff. −0.032 −0.047 −0.025 (0.025) (0.055)

(0.034)

Time trend 0.053** 0.035 0.062** (0.028) (0.045)

(0.022)

−16.77***

−16.2*** −18.1***

Constant

(3.54) (3.03) (2.81)

x2_(4)=0.8 Hausman

test

R2 _0.64 _0.63 _0.62

Number of N=17 N=17 N=52

obs.

r=0.06 t(avg.)=2.1 t(avg.)=3.0

a_{The dependent variable is the natural logarithm of per} capita public expenditure for environmental protection (1980– 1991) in selected OECD countries.

b_{Estimation procedure: maximum likelihood estimator.} c_{Pooled cross section estimation corrected for serially} corre-lated residuals.

d_{Other specification tests include the Ramsey test for} omit-ted variables, which produce aF(3,44)=0.63, and the Cook– Weisberg test for heteroschedasticity,x2_{(1)=4.71, which does} not allow rejecting the hypothesis of constant variance.

*** , ** , * Indicate statistical significance at the 1, 5 and 10% levels, respectively. Standard errors are in parentheses.

cations). Interestingly, the only country whose GDP per capita is consistently above this level is the United States, in which income inequality sharply increased in the 1980s.

per capita)] is positive in all specifications. Given the signs of the estimated coefficients b2 and b3

(negative and positive, respectively, in both ran-dom effect and pooled cross section regressions of Table 3), there is a critical level of per capita income (reported in the table) at which income equality starts having a positive impact upon pub-lic environmental expenditure. The level of GDP per capita at which the correlation between public environmental expenditure and income equality becomes positive is given by xmin= −b2/b3.

Us-ing the estimated coefficient of Table 3, such critical levels of per capita income are xRE

min(I)=

$9250 and xRE

min; (II)=$11 400 in the random

ef-fect estimations (I) and (II), respectively. The interpretation of these results is that for countries with per capita GDP greater than these critical values of per capita income, a reduction in the gap between the income shares of the first and the fourth quintile of the population (an increase in RATIO) unambiguously increases the expenditure in research for environmental protection.

5. Conclusions

In recent years empirical studies have ques-tioned the Environmental Kuznets hypothesis, the idea of a ‘development path’ that automatically links growth in GDP per capita with improve-ments in environmental quality. The present study contributes to this literature by questioning the theoretical foundations of the EKC. Traditionally the emergence of an EKC hinges on the properties of the aggregate demand and supply of environ-mental quality (Antle and Heidebrink, 1995). This paper argues that the income-elasticity condition (IEC) (a high income elasticity of the demand for environmental quality) may not be a robust

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foun-Table 3

Public R&D expenditure for environmental protectiona_{and income inequality}

Explanatory var. REb _FE _PCSc

III V

I 0.0007***

Per capita GDP 0.002*** 0.0007***

(0.0006)

(0.0002) (0.0002)

−3e−08***

(Per capita GDP)2 _{−6.4e−08***} _−3.2e−08

(8.0e−09) (1.9e−08) (7.5e−09)

16.06

−11.1* −12.6**

RATIO coeff.

(14.56) (5.42)

(6.69)

−0.001

0.0012* 0.0013**

RATIO*(GDP per capita)

(0.0006) (0.001) (0.0005)

–

Time trend – –

−22.02*** (5.01)

−10.67*** (1.71) −10.65*** (1.59)

Constant

US$ 9250

Critical level of per capita GDPd _– _{US$ 9690}

x2_(4)=6.21

Hausman teste _– _–

0.54

0.68 0.66

N=16

Number of obs. N=16 N=49

t(avg.) 2.3 t(avg.)=3.1 r=0.006

IV VI

Per capita GDP 0.0009*** 0.002*** 0.0008***

(0.0006)

(0.0002) (0.0002)

−3.7e−08***

(Per capita GDP)2 _{−5.7e−08**} _−3.7e−08

(1.9e−08) (7.8e−09)

(8.2e−09)

12.64

−9.12 −11.6**

RATIO coeff.

(6.64) (15.55) (5.28)

0.0008

RATIO*(GDP per capita) −0.001 0.001**

(0.001)

(0.0006) (0.0005)

0.052**

Time trend 0.032 0.062**

(0.02) (0.048) (0.029)

−21.79***

−15.88*** −16.48***

Constant

(5.07)

(2.78) (3.11)

–

US$ 11 400 US$ 11 600

Critical level of per capita GDP

x2_(5)=2.56

Hausman test – –

0.59

R-squared 0.68 0.68

N=16

N=16 N=49

Number of obs.

t(avg.)2.3 t(avg.)=3.1 r=0.009

a_{The dependent variable is the natural logarithm of per capita public expenditure for environmental protection (1980–1991) in} selected OECD countries.

b_{Estimation procedure: maximum likelihood estimator.}

c_{Pooled cross section estimation corrected for serially correlated residuals.}

d_{The critical levels of GDP; at which the correlation between public environmental expenditure and income equality becomes} positive, are given byxmin= −b2/b3, withb2andb3defined in the text.

e_{Other specification tests include the Ramsey test for omitted variables, which produce a}_{F(3,41)=1.97, and the Cook–Weisberg} test for heteroschedasticityx2₍₁₎_{=0.64, which does not allow rejecting the hypothesis of constant variance.}

*** , ** , * Indicate statistical significance at the 1, 5 and 10% levels, respectively. Standard errors are in parentheses.

dation for the EKC in models of fiscal policy decisions with heterogeneous individuals. In high-income countries agents’ relative high-incomes affect preferences over private goods and public goods

such as environmental amenities (Hirsch, 1976; Frank, 1989; Ng and Wang, 1993). I show that the emergence of a high demand for pollution abatement depends on an absolute income effect

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and a relative income effect, which impact respec-tively upon the ability to pay and the willingness to pay for environmental care.

The results of the empirical investigation of public environmental expenditure in selected OECD countries between 1980 and 1991 provide support to the hypothesis developed in this paper according to which relative income and thus in-come inequality affect environmental public pol-icy decisions. For this OECD sample, income inequality shows the expected negative correlation with environmental care as predicted by the theo-retical discussion. Furthermore, as both proposi-tion 1 and proposiproposi-tion 2 hold, provided the necessary income elasticity condition is satisfied, the finding of empirical results consistent with such propositions validates the hypothesis dear to the environmental literature that public concern for the environment grows with per capita in-come. Lastly, as stated in proposition 2, countries where growth in per capita income is accompa-nied by rise in income inequality (e.g. the US in the 1980s) are the ones that may witness a nega-tive impact of economic growth on public envi-ronmental expenditure. A caveat accompanies these results. This analysis has explicitly restricted the focus to high-income countries. It is particu-larly important to bear this in mind when inter-preting Table 3. The association between decreasing income equality and increasing envi-ronmental protection for values of per capita GDP below the reported critical level cannot be generalized to low-income countries. Whether or not the suggested relationship applies to these countries remains to be answered. This caution applies a fortiori because the assumptions used in the present analysis are known not to apply for the majority of low-income countries.

The main implication of the analysis carried out in this study is that the downward sloping seg-ment of the EKC emerges in high-income coun-tries if and only if economic growth does not lead to a ‘large’ increase in income inequality. The rising spread in earnings distribution functions recently observed in advanced economies warns us that such a condition is not necessarily sa-tisfied. These empirical results help to reconcile the EK hypothesis with the evidence of a low

explanatory power of polynomials in per capita GDP in regressions for pollution emissions in high income countries.

This study shows that economic growth is po-tentially able to increase environmental quality provided the negative effect of production of goods and services on incipient pollution is more than counterbalanced by the positive effect of growth on the demand for pollution abatement policy. A reduction of pollution emissions in high income countries is more likely to be observed if economic growth accompanies improvements in other social indicators, particularly income in-equality, that shift social preferences away from consumption of private goods toward consump-tion of public goods such as environmental amenities.

Acknowledgements

I thank seminar participants at the University of Melbourne, Monash University and Murdoch University, and to Catherine De Fontenay, Dhammika Dharmapala, Lata Gangadharan, Brett Neilson, Megan Neilson and two anony-mous referees for helpful comments to previous versions of this paper. All errors are mine.

Appendix A. Proofs

Proof of proposition 1. From Eq. (5) by differ-entiating with respect to the index of income inequality R, ((_E*_/(_R₎₌_Y₍(_t_*_/(_R_{) (1}₋_t_*_{) ,} with t* (0, 1) . The sign of ((E*/(R) only

de-pends on the sign of ((_t_*_/(_R_{) By Eq. (6) (}(_t_*_/ (_R₎\0 provided o((g_m/(R)(R/g_m)\1 , where

o if the relative income elasticity of the ‘demand for environmental care’ as expressed by gm.

Proof of proposition 2. If proposition 1 is sa-tisfied, ((_E*_/(t)((_t_*_/(_R)\0 . From inspection of

Eq. (7) (dE*(Y,R))/(dY)\0 is guaranteed if ((_R_/ (_Y₎\0. Since _R measures the gap between

me-dian and mean income, an increase in R

corresponds to a decrease in income inequality. Proof of proposition 3. If the relative income elasticity of the demand for environmental

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ameni-ties is greater than one, by proposition 1 the term ((_E*_/(_t)((_t_*_/(_R_{) in Eq. (8) is positive. From Eq.} (8), the assumption that [((_I_/(_Y₎₋₍(_E*_/(_Y_)]\

0 , implies [((_I_/(_Y₎₋₍(_E*_/(_Y_)][((_E*_/(_t)((_t_*_/ (_R_)]−1_\_{0 . Necessary and sufficient condition}

for economic growth to decrease pollution emis-sion abatement is a positive and ‘large’ effect of economic growth on income equality as expressed by the condition (_R_/(_Y\[((I/(Y)−((E*/ (_Y_)][((_E*_/(_t)((_t_*_/(_R_)]−1_\_0.

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4. Environmental protection policy and income distribution: An empirical investigation

The regression equation is: eit=a+b0xit+b1(xit)

+b2rit+b3(x*rit it)+b4t

+uit (9)

where the error term uit=oit+mi is decomposed

into a country effect mi, which captures

unobserv-able country-specific characteristics, and a white noise component oit. In Eq. (9) the dependent

variable eit is the logarithm of per capita R&D

expenditure for environmental protection. Ex-planatory variables are per capita income (GDP) xit, converted at purchasing power parity into real

1985 US dollars, an income inequality index rit

of the preference for environmental quality is ‘large’ (proposition 1). Finally, if the income elas-ticity condition is satisfied, the net effect of per

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Table 1

Public R&D expenditure for environmental protection in OECD countries: Summary statistics

S.D. Min. Max

Variable Number of obs. Mean

361.2

Public abatement expenda ₇₈ _69.5 _89.08 _0.6

18 339 4382

GDP per capitab ₁₇₁ _{10 526} ₃₀₀₄

41.8

Gini coefficient 79 33.0 3.93 24.9

0.29

Ratioc ₇₄ _0.18 _0.05 _0.1

a_{Data refer to government research and development (R&D) budget appropriation (OECD, 1993). Public expenditure for}

environmental protection is measured in million PPP US$ at 1985 price levels.

b_{Gross domestic product at purchasing power parities 1985 US dollars.}

c_{The ratio between the percentage of the income share held by the first quintile of the population and the income share of the}

fourth quintile of the population. The raw income inequality data are from Deininger and Squire (1996). capita income on environmental policy, i.e. (b0+

2b1xit+b3rit), is greater than zero provided

in-come inequality decreases with economic growth (proposition 2). Table 1 contains some summary statistics.

4.1. The empirical results

Tables 2 and 3 illustrate random effect (RE), fixed effect (FE) and pooled cross section (PCS) observation results obtained with the inequality indexes GINI and RATIO, respectively. Specifica-tions (I), (III) and (V) do not contain a time trend, while specifications (II), (IV) and (VI) do. The functional form for per capita GDP is quadratic, although the results are robust to a linear specification in per capita income. The hy-pothesis of no systematic difference between ran-dom effect and fixed effect results is tested and not rejected by the Hausman test in all specifica-tions.3_{None of the sensitivity tests involving} anal-ysis of residuals and leverage I performed have revealed the existence of particularly anomalous observations that incisively affect the nature of the relationships uncovered. The Ramsey (1969) test for omitted variables and the Cook – Weisberg (1983) test for heteroscedasticity do not provide evidence of mispecification problems. The statis-tics for these tests are reported in the tables.

b0+2b1*(10 526), is positive, while income in-equality is negatively correlated with per capita expenditure in environmental protection. These results are not affected by the inclusion or exclu-sion of a time trend, which improves slightly the goodness of fit of some specifications. When I control for a possible serial correlation in the error term by using pooled cross section observa-tions [specificaobserva-tions (V) and (VI)], I obtain results comparable to the random effect estimates.

specifi-3_{This is not to say that countries’ experiences in terms of}

pollution emissions and control do not differ widely. See, for example, De Bruyn et al. (1998).

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Table 2

Public R&D expenditure for environmental protectiona _and

income inequality

Explanatory REb _FE _PCSc

var.

I III

0.002*** 0.001*** Per capita 0.0009***

GDP (0.0002) (0.0004) (0.0002)

−2.9e−08***

(Per capita −5.1e−08*** −3.5e−08 GDP)2 _(9.1e₋₀₉₎ _(1.5e₋₀₈₎ _(7.4e₋₀₉₎

−0.03

−0.06

−0.035 GINI coeff.

(0.05)

(0.031) (0.025)

– – –

Time trend

−11.9***

−15.6*** Constant −11.3***

(3.21)

(1.90) (1.52)

Hausman x2₍₃₎₌_5.2

testd

0.60 0.58 0.63

N=17 N=51

N=17 Number of

obs. t(avg.)=2.1 t(avg.)=3.1 r=0.03 IV

II VI

Explanatory var.

−0.0013**

Per capita 0.001*** 0.001***

GDP (0.0002) (0.0005) (0.0002)

−4.7e−08*** −4e

−3.6e−08*** (Per capita

GDP)2

−08*** (7.3e−09) (9.9e−09) (1.6e−08)

GINI coeff. −0.032 −0.047 −0.025

(0.025) (0.055)

(0.034)

Time trend 0.053** 0.035 0.062**

(0.028) (0.045)

(0.022)

−16.77***

−16.2*** −18.1***

Constant

(3.54) (3.03) (2.81)

x2₍₄₎₌_0.8

Hausman test

R2 _0.64 _0.63 _0.62

Number of N=17 N=17 N=52

obs.

r=0.06

t(avg.)=2.1 t(avg.)=3.0

a_{The dependent variable is the natural logarithm of per}

capita public expenditure for environmental protection (1980– 1991) in selected OECD countries.

b_{Estimation procedure: maximum likelihood estimator.} c_{Pooled cross section estimation corrected for serially}

corre-lated residuals.

d_{Other specification tests include the Ramsey test for}

omit-ted variables, which produce aF(3,44)=0.63, and the Cook– Weisberg test for heteroschedasticity,x2₍₁₎₌_{4.71, which does}

not allow rejecting the hypothesis of constant variance. *** , ** , * Indicate statistical significance at the 1, 5 and 10% levels, respectively. Standard errors are in parentheses.

cations). Interestingly, the only country whose GDP per capita is consistently above this level is the United States, in which income inequality sharply increased in the 1980s.

Secondly, consistent with the hypothesis that a relative income effect impacts upon countries’ preferences for environmental protection, I find that the net (average) effect of income equality on environmental expenditure [b2+b3*(average GDP per capita)] is positive in all specifications. Given the signs of the estimated coefficients b2 and b3 (negative and positive, respectively, in both ran-dom effect and pooled cross section regressions of Table 3), there is a critical level of per capita income (reported in the table) at which income equality starts having a positive impact upon pub-lic environmental expenditure. The level of GDP per capita at which the correlation between public environmental expenditure and income equality becomes positive is given by xmin= −b2/b3. Us-ing the estimated coefficient of Table 3, such critical levels of per capita income are xRE

min(I)= $9250 and xRE

min; (II)=$11 400 in the random

5. Conclusions

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foun-Table 3

Public R&D expenditure for environmental protectiona_{and income inequality}

Explanatory var. REb _FE _PCSc

III V

I 0.0007***

Per capita GDP 0.002*** 0.0007***

(0.0006)

(0.0002) (0.0002)

−3e−08***

(Per capita GDP)2 ₋_6.4e₋_08*** ₋_3.2e₋₀₈

(8.0e−09) (1.9e−08) (7.5e−09)

16.06

−11.1* −12.6**

RATIO coeff.

(14.56) (5.42)

(6.69)

−0.001

0.0012* 0.0013**

RATIO*(GDP per capita)

(0.0006) (0.001) (0.0005)

–

Time trend – –

−22.02*** (5.01)

−10.67*** (1.71) −10.65*** (1.59)

Constant

US$ 9250

Critical level of per capita GDPd _– _{US$ 9690}

x2₍₄₎₌_6.21

Hausman teste _– _–

0.54

0.68 0.66

N=16

Number of obs. N=16 N=49

t(avg.) 2.3 t(avg.)=3.1 r=0.006

IV VI

Per capita GDP 0.0009*** 0.002*** 0.0008***

(0.0006)

(0.0002) (0.0002)

−3.7e−08***

(Per capita GDP)2 ₋_5.7e₋_08** ₋_3.7e₋₀₈

(1.9e−08) (7.8e−09)

(8.2e−09)

12.64

−9.12 −11.6**

RATIO coeff.

(6.64) (15.55) (5.28)

0.0008

RATIO*(GDP per capita) −0.001 0.001**

(0.001)

(0.0006) (0.0005)

0.052**

Time trend 0.032 0.062**

(0.02) (0.048) (0.029)

−21.79***

−15.88*** −16.48***

Constant

(5.07)

(2.78) (3.11)

–

US$ 11 400 US$ 11 600

Critical level of per capita GDP

x2₍₅₎₌_2.56

Hausman test – –

0.59

R-squared 0.68 0.68

N=16

N=16 N=49

Number of obs.

t(avg.)2.3 t(avg.)=3.1 r=0.009

a_{The dependent variable is the natural logarithm of per capita public expenditure for environmental protection (1980–1991) in}

selected OECD countries.

b_{Estimation procedure: maximum likelihood estimator.}

c_{Pooled cross section estimation corrected for serially correlated residuals.}

d_{The critical levels of GDP; at which the correlation between public environmental expenditure and income equality becomes}

positive, are given byxmin= −b2/b3, withb2andb3defined in the text.

e_{Other specification tests include the Ramsey test for omitted variables, which produce a}_F_(3,41)₌_{1.97, and the Cook–Weisberg}

test for heteroschedasticityx2₍₁₎₌_{0.64, which does not allow rejecting the hypothesis of constant variance.}

*** , ** , * Indicate statistical significance at the 1, 5 and 10% levels, respectively. Standard errors are in parentheses.

dation for the EKC in models of fiscal policy decisions with heterogeneous individuals. In high-income countries agents’ relative high-incomes affect preferences over private goods and public goods

such as environmental amenities (Hirsch, 1976; Frank, 1989; Ng and Wang, 1993). I show that the emergence of a high demand for pollution abatement depends on an absolute income effect

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and a relative income effect, which impact respec-tively upon the ability to pay and the willingness to pay for environmental care.

inter-preting Table 3. The association between

decreasing income equality and increasing envi-ronmental protection for values of per capita GDP below the reported critical level cannot be generalized to low-income countries. Whether or not the suggested relationship applies to these countries remains to be answered. This caution applies a fortiori because the assumptions used in the present analysis are known not to apply for the majority of low-income countries.

explanatory power of polynomials in per capita GDP in regressions for pollution emissions in high income countries.

Acknowledgements

I thank seminar participants at the University of Melbourne, Monash University and Murdoch University, and to Catherine De Fontenay,

Dhammika Dharmapala, Lata Gangadharan,

Brett Neilson, Megan Neilson and two anony-mous referees for helpful comments to previous versions of this paper. All errors are mine.

Appendix A. Proofs

Proof of proposition 1. From Eq. (5) by differ-entiating with respect to the index of income inequality R, ((_E*_/(_R₎₌_Y₍(_t_*_/(_R_{) (1}₋_t_*_{) ,}

with t* (0, 1) . The sign of ((E*/(R) only de-pends on the sign of ((_t_*_/(_R_{) By Eq. (6) (}(_t_*_/ (_R₎\0 provided o((g_m/(R)(R/g_m)\1 , where

o if the relative income elasticity of the ‘demand for environmental care’ as expressed by gm.

Proof of proposition 2. If proposition 1 is sa-tisfied, ((_E*_/(_t)((_t_*_/(_R)\0 . From inspection of Eq. (7) (dE*(Y,R))/(dY)\0 is guaranteed if ((_R_/ (_Y₎\0. Since _R measures the gap between

me-dian and mean income, an increase in R

corresponds to a decrease in income inequality. Proof of proposition 3. If the relative income elasticity of the demand for environmental

(6)

ameni-ties is greater than one, by proposition 1 the term ((_E*_/(_t₎₍(_t_*_/(_R_{) in Eq. (8) is positive. From Eq.}

(8), the assumption that [((_I_/(_Y₎₋₍(_E*_/(_Y_)]\ 0 , implies [((_I_/(_Y₎₋₍(_E*_/(_Y_)][((_E*_/(_t₎₍(_t_*_/ (_R_)]−1_\_{0 . Necessary and sufficient condition} for economic growth to decrease pollution emis-sion abatement is a positive and ‘large’ effect of economic growth on income equality as expressed by the condition (_R_/(_Y\[((I/(Y)−((E*/ (_Y_)][((_E*_/(_t₎₍(_t_*_/(_R_)]−1_\_0.