Automatic Change versus Induced Policy Response in the Environmental
Kuznets Curve: The Case of U.S. Water Pollution
Irene Lai
C.C. Yang*
Institute of Economics, Academia Sinica, Nankang, Taipei 115, Taiwan
Department of Public Finance, National Chengchi University, Wenshan, Taipei 116, Taiwan
October 2006
[Abstract] This paper considers a model in which the link between income and pollution is
through two channels: (i) “automatic change,” which includes the scale effect in abatement
technology as emphasized by Andreoni and Levinson (2001), and (ii) “induced policy
response,” which is driven by citizen demands for a cleaner environmental policy when
income grows as emphasized by Grossman and Krueger (1995). We apply our model to the
case of U.S. water pollution, evaluating quantitatively the relative importance of the automatic
change versus the induced policy response in shaping the environmental Kuznets curve
(EKC). Our main findings include: (i) while it is the induced policy response that is
responsible for turning the EKC from a positive to a negative slope, the fraction of pollution
reduction attributed to the automatic change will overtake that attributed to the induced policy
response once per capita GDP has exceeded $30,000, (ii) the scale effect contributes to the
earlier occurrence of the turning point of the EKC by mitigating automatic pollution and
enhancing induced policy response and, in particular, the turning point income for U.S. water
pollution would be at much and much higher if there were no scale effect.
Key words: Environmental Kuznets curve; Abatement technology; Scale effect
JEL classification: H41; O40; Q20
*Corresponding author, C.C. Yang. Mailing address: Institute of Economics, Academia Sinica,
Nankang, Taipei 115, Taiwan. E-mail: [email protected]
1. Introduction
Kuznets (1955) studied the relation between income inequality and economic growth,
showing that income inequality against income per capita exhibits an inverted-U shape:
increased incomes are associated with a deterioration in income inequality when incomes are
low, but with an improvement when incomes become high. This relation is known as the
“Kuznets curve.” Starting from the seminal work of Grossman and Krueger (1993), many
studies found that pollution against income per capita for various pollutants also exhibits an
inverted-U shape and so the relation is dubbed the “environmental Kuznets curve” (EKC).1
The existence of the EKC implies that economic growth may be a remedy to
environmental problems since it will level off pollution and bring about environmental
improvement eventually. Andreoni and Levinson (2001) provided a case for this possibility.
They argued for increasing returns in pollution abatement technology (doubling the
environmental efforts more than doubles the abatement of pollution) and showed that the scale
effect alone is sufficient to generate the EKC. By contrast, Grossman and Krueger (1995)
emphasized that the eventual decline in pollution as income rises is not automatic or
inevitable; instead, they suggested: “the strongest link between income and pollution in fact is
via an induced policy response” (p. 372).
In this paper we incorporate the two contrary views above into a model and allow the
link between income and pollution to be through two channels: (i) “automatic change,” which
includes the scale effect in abatement technology as emphasized by Andreoni and Levinson
(2001), and (ii) “induced policy response,” which, following the suggestion of Grossman and
Krueger (1995), is via a collective-decision process by which citizen demands for a cleaner
environment drive environmental policy. Our main purpose is twofold. First, we make an
attempt to discern quantitatively the relative importance of the automatic change versus the
induced policy response in shaping the EKC. Second, papers including Panayotou (1997), De
1
For recent reviews on the EKC hypothesis, see Dasgupta et al. (2002), Copeland and Taylor (2004), Dinda
(2004), Stern (2004) and Yandle et al (2004).
1
Bruyn (1997), Hettige et al. (2000), Bruvoll and Medin (2003) and Bhattarai and Hammig
(2004) have searched for the possible importance of environmental policy in the context of the
EKC hypothesis. We go a step further: disentangling the role of individual preferences,
abatement technology, and distributional conflict behind environmental policy, and examining
quantitatively the relative importance between these factors in shaping the induced policy
response. The U.S. water pollution will be our case study.
Besides the two main purposes stated above, we also address several related issues.
Kristrom and Riera (1996) reviewed contingent valuation studies and evaluated the
evidence on the income elasticity of people’s willingness-to-pay for environmental
improvement. They concluded that the value of this parameter is positive but consistently
found to be less than one. Later studies including Aldy et al. (1999), Ready et al. (2002) and
Hokby and Soderqvist (2003) also confirmed this conclusion. However, Pearce and Palmer
(2001) documented the OECD public expenditures on pollution abatement and control, and
found that the income elasticity of these expenditures is near 1.2. One may wonder if there is
an inconsistency between Pearce and Palmer’s “luxury good” finding and Kristrom and
Riera’s “normal good” finding. Indeed, Kristrom and Riera (1996, p. 45) remarked at the
beginning of their paper: “most economists would argue intuitively that environmental quality
is a luxury good, [but] our results do not support this intuition.” On the other hand, Pearce and
Palmer (2001, p. 426) commented on Kristrom and Riera’s finding: “If they are right, then
‘environment’ is a normal good but not a luxury good, contradicting the usual intuition about
the demand for environmental quality.” In this paper we reconcile these two seemingly
contradictory findings.
The importance of preferences in shaping the EKC has been emphasized in several
papers.2 By contrast, Andreoni and Levinson (2001) argued for increasing returns in pollution
abatement and showed that the scale effect alone is sufficient to generate the EKC. Andreoni
2
See Dinda (2004) for a brief review
2
and Levinson did not address the implications of increasing returns for environmental policy.
We do that in this paper. In particular, we sort out how preferences and technology may drive
public environmental expenditures differently as an economy grows.
The more recent evidence has shown that the inverted U-shaped relation between
pollution and income per capita is less robust than previously thought (see Stern 2004 for a
critical review). Some papers such as Stern and Common (2001) and Hill and Magnani
(2002) attacked the EKC issue from the viewpoint of the omitted-variable problem. The latter
paper found empirically that income inequality is an important omitted variable.
Boyce (1994) is perhaps the first to point out the possible link between distributional
conflict and environmental degradation. He hypothesized that the inequality of power and
wealth will contribute to environmental degradation. In a subsequence paper, Torras and
Boyce (1998) empirically tested the Boyce hypothesis. In the case where the Gini coefficient
is employed as a proxy for the inequality, their findings were mixed (of those that show
statistically significant, there are three cases in which greater income inequality is associated
with more pollution, but there are four cases in which the opposite is found). Scruggs (1998)
questioned the Boyce hypothesis on both theoretical and empirical grounds. Later empirical
studies including Ravallion et al. (2000), Heerink et al. (2001) and Hill and Magnani (2002)
actually detected that an increase in income inequality reduces rather than increases pollution.
Ravallion et al. (2000) and Heerink et al. (2001) provided two theoretic channels for this
result. The former paper is based on the observation that “the marginal impacts of economic
growth on carbon emissions decline as average income increases” (p.651), while the latter
paper is built on the bias from aggregating over households. Both are not via “an induced
policy response.” In this paper we provide a policy-response channel through which income
inequality will be negatively rather than positively related to environmental degradation.
In the context of the EKC hypothesis, Magnani (2000) and Eriksson and Persson (2003)
offered two political-economy models to examine the effect of income inequality on pollution.
However, the derived results of both papers are built on the implausible assumption that the
3
income elasticity of people’s willingness-to-pay for environmental improvement exceeds
unity.3 McAusland (2003) also studied the effect of income inequality on pollution through a
political-economy model, but his focus is not on the EKC hypothesis. Unlike these three
papers, we put together individual preferences, abatement technology and income inequality in
a parsimonious political-economy model and sort out their respective impact on pollution via
the induced policy response in the context of the EKC hypothesis.
The rest of the paper is organized as follows. Section 2 introduces our model. Section 3
provides some preliminary analysis of the model. Section 4 derives the environmental policy
resulting from the model. Section 5 explores theoretically the link between income and
pollution as an economy grows. Section 6 evaluates quantitatively: (i) the relative importance
of the automatic effect versus the induced policy response in shaping the EKC, and (ii) the
relative importance of individual preferences, abatement technology, and distributional
conflict in shaping the environmental policy. Section 7 concludes.
2. Model
Our model is built on Andreoni and Levinson (2001, hereafter A&L), but with two main
modifications. First, instead of being a constant, we allow a person’s willingness-to-pay for
environmental improvement (wtp) to positively depend on her own income. As noted in the
Introduction, the extant evidence shows that wtp is an increasing function of income. This
dependence will play an important role in our analysis. Second, environmental effort to clean
up pollution is assumed to be a private action in A&L. We replace the private action with the
collective action. This replacement will facilitate us to study the link between income and
pollution via an induced policy response. Pearce and Palmer (2001) documented the OECD
data on pollution abatement and control expenditures. A large part of environmental effort is
3
Eriksson and Persson (2003) also explored the effect of democratization on pollution.
4
channeled through collective action (as public expenditures directly or private expenditures
indirectly via regulation).
Both preferences and technology are assumed to take specific functional forms. This
will enable us to derive a closed-form solution and pave way for the simulation study later.
Consider an economy in which the size of the population is normalized to unity so that
the aggregate income of the economy is equal to its mean income. Each individual in the
economy is characterized by an income. Individual i’s income is denoted by mi  (0, ) and
her preferences are represented by the utility function:
U i  ci   i P
(1)
where ci is consumption (a private good), P is pollution (a public bad), and  i  0 is the
marginal disutility of pollution with  i  (mi ) , where  (.) is a common function. Note that
 i represents individual i’s willingness-to-pay for environmental improvement (wtp) since
(dci / dP) ui u   i .
Assumption 1. 0   i  1 for all i’s, where  i  (d / dmi )(mi / ) .
 i denotes the income elasticity of wtp. Kristrom and Riera (1996) reviewed and
evaluated the evidence on the income elasticity of people’s willingness-to-pay for
environmental improvement. They concluded that the value of this parameter is positive but
consistently found to be less than one. Recent papers by Aldy et al. (1999), Ready et al.
(2002) and Hokby and Soderqvist (2003) also confirmed this conclusion. As long as the
median-voter theorem is applicable (see later), Assumption 1 can be relaxed and need not hold
for all individuals.
As in A&L, pollution is a byproduct of consumption but it can be abated through
environmental effort. The pollution-abatement technology is represented by:
P  C  C G
(2)
where C is the aggregate or mean consumption of the economy and G  sM (M is the
aggregate or mean income of the economy and s is the share of income devoted to pollution
5
abatement and control). If there were no environmental effort ( G  0 ), P  C would hold
according to (2). A main difference between our model and A&L’s is that while s is privately
chosen in A&L, it is collectively determined (say, by taxation or regulation) in our setting.
The variable s represents the environmental policy of the economy.
Assumption 2. 0  ,   1 and     1 .
The case where   0 is obviously uninteresting, and the case where   0 leaves out
the plausible possibility that the abatement productivity of G has to do with the existing level
of pollution. Most of our results hold under the weaker assumption that ,   1 . However,
the assumption ,   1 will enable us to rule out the “corner” policy s  0 or 1. A&L
argued for increasing returns to abatement and provided some supportive evidence in the case
of air pollutants. Papers including Fraas and Munley (1984), McConnell and Schwartz
(1992), James and Murty (1996), Pandey (1998), Zhand and Folmer (2001), Goldar et al.
(2001), Yiannaka et al. (2001) and Managi (2006) also find evidence in support of increasing
returns to abatement in other pollutants. In our analysis we take constant returns (i.e.
    1 ) as the benchmark, but allow for the impact of increasing returns (i.e.     1 ).
3. Preliminary analysis
Utilizing the constraint ci  (1  s)mi and (1)-(2), one can derive individual i’s policy
preferences over s:
Vi ( s)  (1  s)( mi   i M )   i (1  s)  s  M  
(3)
The preferred environmental policy of individual i is implicitly defined by the following
equation:
Vi ci
P

 i
0
s
s
s
(4)
with
ci
 mi
s
(4-1)
6
P
  M  M   (1  s )  1 s 1 [  (  ) s ]
s
(4-2)
From (4-2), note that lim (P / s )   and lim (P / s )   under Assumption 2. Thus the
s 0
s 1
preferred environmental policy of individual i, denoted by s i , must satisfy 0  si  1 .
Using (4-2) yields:
2P
  M   (1  s)  2 s 2 [(  1) s 2  (  1)(1  s) 2  2s(1  s)]
2
s
(5)
The sign of (5) is positive under Assumption 2, which implies that P(.) is strictly convex with
respect to s and reaches its minimum at P / s  0 . Putting this result together with that
ci / s is a negative constant (see Eq. (4-1)), we see from (4) that s i will be located in the
Finally,  2 P / s 2  0 implies
regime where P / s  0 and that this s i is unique.
 2Vi / s 2  0 and, therefore, the unique s i that satisfies (4) is the preferred environmental
policy of individual i.
Let f (s)  (1  s) 1 s 1[  (  )s] (see Eq. (4-2)). The function f (s ) has several
properties: (i) df / ds  0 because  2 P / s 2  0 , (ii) lim f ( s )   and lim f ( s )  
s 0
s 1
under Assumption 2, and (iii) f ( s )  0 (  0 ) if s   /(   ) ( s   /(   ) ), and
f ( s )  0 if and only if s   /(   ) . From (4), we obtain:
1 m
si  f 1[(  i  1) M 1( ) ]
i M
where f
1
(6)
(.) is the inverse function of f (.) .
Utilizing (6) gives:
si
1  i

 
mi  i M (df / ds)
(7)
whose sign is negative since  i  1 under Assumption 1 and df / ds  0 . Thus, given M, the
preferred share of income devoted to pollution abatement and control is strictly decreasing
with respect to individual income: the higher the mi , the lower the s i .
7
Two opposing forces govern the sign of si / mi . A higher mi implies a higher  i .
This indirect effect (via the term 1 /  i in (6)) leads to a higher s i . However, given M, a
higher mi also means that the person bears a higher share of “tax burden” than others, even
though she does not enjoy a higher quality of the environment. This direct effect (via the term
mi / M in (6)) results in a lower s i . As long as Assumption 1 holds, the direct effect will
dominate the indirect effect.
Let the status quo policy s0 correspond to the preferred policy of the middle-income
class. Since si / mi  0 , the low-income class will have si  s 0 while high-income class
will have si  s0 . Assume that the economy grows so that the middle-income class put forth
a proposal with an increased share of income devoted to environmental effort ( s  s0 ). While
both the low- and middle-income classes will vote for the proposal, the high-income will vote
against it according to our model. This theoretic prediction is consistent with the empirical
findings by Kahn and Matsusaka (1997) and Kahn (2002). The former paper studied voting
behavior on pro-environment initiatives in California between 1970 and 1994. The unit of
observation is a county. It is found that the derivative of percentage vote in favor with respect
to a change in income is positive if evaluated at the mean level of income, but it becomes
negative if evaluated at the maximum level of income. 4 The later paper, among others,
studied the California votes on environmental initiatives between 1994 and 1998. It is found
that richer people exhibit less support for environmental regulation.5
Kahn (2002) emphasized that a distinction must be made between “being proenvironment” and “being pro-environmental regulation.” In terms of our model, a higher mi
implies a higher  i but it does not automatically mean a higher s i . Environmental regulation
likely involves a form of redistribution such that an individual with a higher mi prefers a
lower to a higher s i at any given point in time.
4
There are 14 ballot propositions. An exception occurred at the mean income while two exceptions occurred at
the maximum income.
5
There are 6 ballot propositions. An exception is that the rich oppose repealing smoking ban.
8
4. Environmental policy
4.1. Equilibrium policy
Now suppose that the individuals in the economy vote over the environmental policy
under simple majority rule.
Since policy preferences of the individuals are single peaked
(  2Vi / s 2  0 ) and since their preferred share of income devoted to pollution abatement is
strictly decreasing with respect to income ( si / mi  0 ), one can invoke the median-voter
theorem. From (6), the economy’s environmental policy in voting equilibrium is given by
1 m
s m  f 1 [(

 1) M 1(  ) ]
(8)
m M
where m is the median income of the economy and  m  (m).
According to (8), three factors drive the economy’s share of income devoted to pollution
abatement and control (remember that df / ds  0 ):
(i)
Individual preferences (  m ). Given m / M , an increase in the aggregate or
mean income of the economy will raise the median-income voter’s wtp and
hence a higher s m .
(ii)
Abatement technology (    ). From the property of f (s ) , the effect induced
by preferences in (i) will be strengthened by increasing returns to abatement
(     1 ) if m / M  m , but it will be weakened if m / M  m .
(iii)
Income inequality ( m / M ). The income distributions of almost all economies
are found skewed to the right and hence M  m . The ratio m / M can be
regarded as a metaphor of income inequality in the economy: the lower the ratio,
the higher the income inequality. Eq. (8) tells us that the higher the income
inequality in the economy, all else equal, the higher the share of the economy’s
income will be devoted to pollution abatement.
Let us consider what would happen to s m if M   . When     1 , f ( s m )  1 if
M   according to (8). This implies by (4-2) that P / s  0 and hence that s m  s as
9
M   , where (P / s)( s )  0 . Note that  /(   )  s  1 . On the other hand, when
    1 , f ( s m )  0 if M   according to (8). This implies that s m   /(   ) as
M  .
4.2. Comparative statics
To examine more precisely the impact of M on s m , we let m be a function of M. From
(8), we then have:
ds m
1
1 m
dm
m

{ [  (1   m )
] (
 1)[(  )  1]}M ( )
dM df / ds  m M
dM
mM
(9)
where  m is the median-income voter’s income elasticity of wtp. Eq. (9) allows for the
impact of individual preferences, abatement technology, and income inequality
simultaneously. It is the most general result.
If the abatement technology exhibits constant returns to scale so that     1 , (9) will
be reduced to
ds m
1
m
dm

[  (1   m )
]
dM  m M (df / ds) M
dM
(9-1)
On the other hand, if m and M grow at the same rate so that dm / dM  m / M or,
equivalently, the ratio m / M remains the same (i.e. the income inequality of the economy
remains unchanged), (9) will be reduced to
ds m
1
m
m

{
m  (
 1)[(   )  1]}M ()
dM df / ds  m M
mM
(9-2)
Finally, if both     1 and dm / dM  m / M hold at the same time, (9) will be
further reduced to
ds m
m

m
dM  m M 2 (df / ds)
(9-3)
whose sign will always be positive. Eq. (9-3) sorts out the single impact of individual
preferences for environmental quality (wtp) on the evolution of public expenditures on
pollution abatement and control. It is clear from (9-3) that ds m / dM  0 if and only if
 m  0 . That is, the share of income devoted to pollution abatement and control will rise as
10
an economy grows (the so-called “luxury good”) as long as the income elasticity of wtp is
positive. Thus there is no need for the income elasticity of wtp to exceed one as thought by
Kristrom and Riera (1996), Pearce and Palmer (2001) and others.
In our simulation study later, the preferences-driven policy response captured by (9-3)
will be treated as the benchmark. We examine whether income inequality (the difference
between (9-1) and (9-3)) or scale effect in abatement technology (the difference between (9-2)
and (9-3)) will contribute to the induced policy response significantly.
5. Income and pollution
This section turns to explore the link between income and pollution. We only bring up
questions and leave our answer to the next section.
Grossman and Krueger (1996) emphasized that the inverted-U EKC is a reduced form
relationship and hence its existence tells us nothing about the mechanisms by which the
growth affects the environment. They suggested three possible mechanisms that could explain
the decline in pollution after certain income levels: (i) a change in the composition of output
that contributes less to environmental degradation, (ii) the use of more “modern” technologies
that results in a cleaner environment, and (iii) greater public demands for a clean environment
that are associated with an increase in income, and governments respond to these demands.
Our focus is on the last mechanism and, in particular, on the relative importance of the
induced policy response as emphasized by Grossman and Krueger (1995) versus the automatic
effect as emphasized by Andreoni and Levinson (2001).
Using (2) yields:
dP
P P ds



dM M s dM
(10)
with
P
 (1  s )  (  )(1  s )  s  M  1
M
(10-1)
11
where P / s and ds / dM are given by (4-2) and (9), respectively. According to (10), the
effect of income on pollution can be decomposed into two components: the autonomous
change represented by the first RHS term of (10) and the induced policy response captured by
the second RHS term of (10). We consider them in turn.
5.1. Autonomous change
It is interesting to know what would happen if there were no induced policy response, i.e.
ds / dM  0 in (10). Consider the benchmark technology with     1 . Then (10-1) is
reduced to
P
 (1  s )  (1  s )  s 
M
(10-2)
which implies that P is a linear, increasing function of M. This is obviously inconsistent with
the EKC hypothesis. Grossman and Krueger’s (1995) suggestion appears correct in this case,
in the sense that there is no automatic decline in pollution as income rises.
However, with     1 , it can be seen from (10-1) that P / M  0 will hold once
income M is large enough. If doubling the environmental efforts can more than double the
abatement of pollution, pollution will decline eventually as an economy grows. Thus the
shape of the pollution-income relationship follows the EKC hypothesis even if there were no
induced policy response. This is basically the result discovered by A&L, though we derive it
in the context of collective rather than private environmental effort. Grossman and Krueger’s
(1995) suggestion appears incorrect in this case, in the sense that, as argued by A&L,
increasing returns to abatement alone is sufficient to level off pollution.
To be sure, the autonomous change presents only a partial picture. In order to see the
whole picture, one needs to know induced policy responses as well as autonomous changes.
Grossman and Krueger (1995) suggested the important role of induced policy responses in the
generation of the EKC. This leads us to study the link between income and pollution via the
induced environmental policy response.
12
5.2. Induced policy response
Again, let us consider     1 and     1 separately.
Constant returns to abatement
If     1 , (2) becomes:
P  [(1  s)  (1  s)  s1 ]M
(11)
It is clear from (11) that the economy’s pollution would increase proportionally to its income
if there were no induced policy response (i.e. no change in s). We are interested in knowing in
this case if the EKC hypothesis will hold once the induced policy response is taken into
account.
Increasing returns to abatement
If     1 , (2) becomes:
P  (1  s) M  (1  s)  s  M 
(12)
We have shown that, even in the absence of induced policy response, increasing returns to
abatement alone is sufficient to level off pollution so that the pollution-income relationship
will obey the EKC hypothesis. We are interested in knowing in this case the relative
importance of the automatic effect versus the induced policy response in shaping the EKC.
6. Quantitative evaluation of automatic change versus induced policy response
In this section we apply our model to the case of U.S. water pollution, evaluating
quantitatively the relative importance of the automatic effect as emphasized by Andreoni and
Levinson (2001) versus the induced policy response as emphasized by Grossman and Krueger
(1995) in shaping the EKC. Our evaluation is on the basis of Eq. (10), in which the first RHS
term represents the automatic change while the second RHS term represents the induced
policy response. As is clear from Eq. (10), we need to specify or estimate several key
parameters for this evaluation. Our methodology has five steps:
13
Step 1. Specifying a value for  m (the median-income voter’s income elasticity of wtp).
To estimate m in (8), we let  m   (m)  a  m  m . Note that  m  (d / dm)(m /  ) by
this specification. The U.S. public’s income elasticity of willingness to pay for quality water
is between 0.1 to 0.16 according to Jordan and Elnagheeb (1993), between 0.2 to 0.3
according to Carson et al. (1993), but it equals 0.959 according to Carson and Mitchell (1993).
The last work studied the case of Exxon Valdez oil spill. Its estimation 0.959 seems to an
outliner compared to the other two studies. Nevertheless, in our study we use it as the upper
bound and pick four alternative values for  m : 0.1, 0.2, 0.3 and 0.959. The parameter a that
appears in m will be estimated from real-world data.
Step 2. Choosing a value for    (abatement technology).
Hayes (1987) studied the scale economy of the U.S. water factories and found supportive
evidence for increasing returns to scale, which are estimated to be between 1.0116 and 1.3157.
We choose a value for    within this range. The choice criterion will be spelt out in Step
5. Note that, to evaluate (10) quantitatively, we need to know the value of  as well as that of
   . After the choice of    , the parameter  will be estimated from real-world data.
Step 3. Estimating a and  .
By the definition of the function f (s ) , we obtain from (8):
1 m
(1  s m )  1 ( s m )  1 [   (   ) s m ]  ( 
 1) M 1(   )
m M
Substituting m  a  m  m in the above equation, specifying a value for  m and choosing a
value for    , we utilize the real-world data on M , m / M and s m to estimate a and  .
Specifically, we pick a and  that minimize the following loss function:
2000
 [(1  s
t 1972
m
(t ))  1 ( s m (t ))  1[   (   ) s m (t )]  (
1
m
 (t )  1)( M (t ))1(   ) ]2
m (t ) M
Both M (per capita GDP in constant 1985 dollars) and m / M (the ratio of median to mean
income) are readily available from the U.S. Census Bureau. However, there are two different
14
data sources on s m . We explain our choice of the data on s m in the Appendix. Table 1 lists
the data we use in our estimation.
[Insert Table 1 about here]
Step 4. Simulating the evolution of s m and dP / dM .
For any combination of  m and    from Steps 1-2, and the corresponding estimated a
and  from Step 3, we can simulate the evolution of s m from (8) and that of dP / dM from
(10). Unless stated otherwise, we let m / M  0.75 in our simulation for simplicity. We
examine the sensitivity of varying values for m / M later on.
Step 5. Picking the right value for    .
Our methodology starts from specifying four different values for  m : 0.1, 0.2, 0.3 and
0.959. After the choice of    from Step 2, we then estimate a and  from Step 3.
However, for each value of  m , there are infinite many of    that could be chosen from
Step 2 since we only require them to be between 1.0116 and 1.3157. How to differentiate
between them? Grossman and Krueger (1995) studied the EKC hypothesis for the U.S. river
pollution, finding that the turning point incomes for various water quality indicators are around
per capita GDP $7600 to $7900. We use this as a criterion to differentiate between various
   ’s. That is, for each value of  m , we will pick a corresponding value for    such
that the resulting turning point income (i.e. the income that satisfies dP / dM  0 in (10)) is
simulated to be around per capita GDP $7600 to $7900 from our Step 4.6 The way of our
picking the right value for    is through trials and errors. For example, if     1.1
leads to a turning point income higher than $8000 while     1.3 leads to a turning point
lower than $7000, then we will try     1.2 .
6
There are other estimates for the turning point of water quality indicators. (.) found a higher turning point at per
capita GDP? However, using this turning point income as an alternative criterion will not alter our findings in
quality.
15
Employing the methodology described above, we detect four scenarios that meet the
criterion that the turning point income is around per capita GDP $7600 to $7900:7
Scenario 1:  m  0.1 ,     1.3155 , a  0.003589 ,   0.625047 , turning point
income=$7781, s m  0.003567 at the turning point;
Scenario 2:  m  0.2 ,     1.305 , a  0.001383 ,   0.595763 , turning point
income=$7792, s m  0.003054 at the turning point;
Scenario 3:  m  0.3 ,     1.294 , a  0.000538 ,   0.566745 , turning point
income=$7764, s m  0.002654 at the turning point;
Scenario 4:  m  0.959 ,     1.205 , a  0.000001374 ,   0.383214 , turning
point income=$7771, s m  0.001489 at the turning point.
Several features of these scenarios are worth noting. First, the resulting values for   
are all compatible with the extant empirical evidence reported by Hayes (1987), though the
values are near the upper rather than the lower bound. Secondly, the estimated s m ’s
corresponding to the turning points are all smaller than the actual s m (0.0034) at year 1972.
This is reasonable since the per capita GDP at 1972 is $13632, while the per capita GDP at the
tuning point is $7750. Thirdly, there exists some substitution between  m and    : as the
value of  m increases, the corresponding value of    decreases. However, note that a
substantial increase in  m (from 0.1 to 0.959) only brings about a small reduction in   
(from 1.3155 to 1.205).
To save space, in what follows we only report our simulated findings for scenarios 2 and
4. The results from scenarios 1 and 3 are close to that from scenario 2.
Share of income devoted to pollution abatement and control
Figure 1-1 plots our simulated s m ’s against the actual and projected s m ’s reported by the
EPA for the income range between $13,000 and $25,000, while Figure 1-2 plots the same
7
Of course, other scenarios that deviate a bit from these four scenarios may still satisfy the turning-point criterion.
However, the qualitative results of these “near” scenarios remain the same as our four scenarios.
16
thing but for the income range between $5,000 and $40,000. Our simulated s m ’s include two
scenarios:  m  0.2 (represented by the solid curve) and  m  0.959 (represented by the
dotted curve). The actual and projected s m ’s reported by the EPA are represented by the
diamond-shaped points in the figures. Note that the s m ’s projected by the EPA decline all the
way from 0.008871 at year 1995 to 0.008317 at year 2000 (see Table 1). This causes some
deviation between our simulated s m and the projected s m reported by the EPA after year
1995.
The share of income devoted to water pollution abatement and control is shown to be
rising in the income range in the figures and it will exceed 2% (reach 3%) at income $40,000
if  m  0.2 (  m  0.959 ) according to our simulation.
[Insert Figure 1 about here]
Automatic change versus induced policy response
Figures 2-1 and 2-2 simulate the total marginal effect as captured by Eq. (10) on the basis
of the scenarios 2 and 4, respectively. In our simulation, we normalize the pollution level at
income $5,000 to zero, and let the s in Eq. (10) be always evaluated at the corresponding
equilibrium s m at each point of time. We divide the total marginal effect into the automatic
change (the first RHS term of (10), represented by the dotted line in the figures) and the
induced policy response (the second RHS term of (10), represented by the solid line in the
figures).
[Insert Figure 2 about here]
When the total marginal effect is zero (i.e. dP / dM  0 in Eq. (10) or, equivalently,
P / M  (P / s)( ds / dM ) ), it corresponds to the turning point of the EKC. As can be
seen, the turning points occur around $7,750 in both Figures 2-1 and 2-2. Note that the
induced policy response contributes to the reduction of pollution right from the beginning in
the figures. This implies that it is the automatic change that is responsible for the rising
portion of the U.S. EKC for water pollution in the income range we consider.
17
The level off and the eventual decline of pollution can be due to the scale effect of the
automatic change according to Andreoni and Levinson (2001), but it can also be due to the
induced policy response according to Grossman and Krueger (1995). Which view is more
correct? From both Figures 2-1 and 2-2, we see that the automatic change will reduce
pollution only if per capita income has been beyond $10,000. However, the turning point of
the EKC occurs at income levels lower than $10,000. This observation tells us that it is the
induced policy response rather than the automatic change that is responsible for turning the
EKC from a positive to a negative slope in the case of U.S. water pollution. Grossman and
Krueger’s (1995) emphasis that “the strongest link between income and pollution in fact is via
an induced policy response” is correct in explaining the level off and the eventual decline of
U.S. water pollution.
From both Figures 2-1 and 2-2, we also see that the fraction of pollution reduction
attributed to the automatic change will become higher and higher relative to that attributed to
the induced policy response as income grows. Indeed, pollution reduction that comes from the
automatic change will exceed that comes from the induced policy response once per capita
GDP is around $25,000 ($30,000) in the case  m  0.2 (  m  0.959 ). Although the scale
effect emphasized by Andreoni and Levinson (2001) cannot explain the eventual decline of
U.S. water pollution, its potential importance in accelerating the water cleanup is clearly
demonstrated via our simulation.
Let us consider the criterion that the turning point occurs at per capita GDP $. The
following summarizes the scenarios that meet this alternative criterion:
Sensitivity to distributional conflict
In our simulation, we let m / M  0.75 for simplicity. We now examine the sensitivity
of varying values for m / M . From Table 1, we see that m / M  0.88 at year 1972, but it
declines all the way to m / M  0.73 at year 2000. We pick three different values for m / M
18
(0.72, 0.75 and 0.9) to check the sensitivity of our previous evaluation. We still employ the
same criterion as before to choose    . Table 2 reports our findings, which show that: (i)
when  m  0.2 , increasing m / M from 0.72 to 0.9 will enhance the value of    from
1.301 to 1.323, and (ii) when  m  0.959 , increasing m / M from 0.72 to 0.9 will enhance the
value of    from 1.205 to 1.2055. The sensitivity is somewhat higher when the value of
 m is smaller. However, the values of    remain around 1.3 when  m  0.2 while they
remain around 1.2 when  m  0.959 . Overall, our results seem not sensitive to the realistic
change in m / M .
[Insert Table 2 about here]
What if     1 ?
Following our methodology, we find that the resulting    is always greater than 1.
This result is consistent with most of the extant evidence. Here we conduct an alternative
exercise. What would happen if     1 rather than     1 ? This exercise will allow
us to see the role played by the scale effect in shaping the EKC.
Table 3 reports our finding. We pick four different values for  m (0.1, 0.2, 0.3 and
0.959) and three different values for m / M (0.72, 0.75 and 0.9). Given  m and     1 ,
the first row of the table shows the resulting estimated values for a and  . As can be seen
from the table, if     1 were to hold, both the turning point income and the corresponding
share of income devoted to pollution abatement would be much and much higher than our
previous findings. For example, consider the case where  m  0.2 and m / M  0.75 . The
associated turning point income and s m would become respectively $1,197, 473 and 0.301537
if     1 rather than $7,792 and 0.003054 in our scenario 3. This result suggests to us that
the scale effect of the abatement technology would contribute to the earlier occurrence of the
turning point of the EKC through mitigating pollution (i.e. making the term P / M in (10)
smaller even though P / M  0 ).
Figure 3 confirms our conjecture.
19
This result is
anticipated. If     1 , P / M  (1  s)  (1  s) s  , which is a constant independent of
income M if s remains unchanged.
[Insert Table 3 and Figure 3 about here]
Compared Figure 3 to Figure 2, we also see that not only the graph for the automatic
change but also the graph for the induced policy response has been changed substantially.
This may not be surprising. From (8), the scale effect (     1 ) will strengthen the demand
for a higher s m induced by individual preferences if m / M  m . To examine the role of the
scale effect in the determination of the induced policy response, we consider a scenario which
has the same parameters as those in Scenario 2, except that we choose a smaller value for 
such that     1 rather than     1.305 .8 Figure 4 presents our finding, which shows
that if there were no scale effect, s m would be near zero and the induced policy response
would be almost none. This finding demonstrates the important role of the scale effect even in
the induced policy response.
[Insert Figure 4 about here]
Other turning point incomes
Since P / s  0 , we see from (10) that the induced policy response will contribute to
the reduction of pollution if and only if ds / dM  0 . However, note that ds / dM  0 as
M   . This result is intuitive and unsurprising: there is an upper limit for s. Of course, the
result does not rule out that the induced policy response could be important in shaping the
environment of an economy in the short, medium, or even long run.9
7. Conclusion
8
An alternative way is to choose a smaller value for
 such that     1 . The results remain qualitatively
the same.
9
Can the planet support unlimited economic growth so that M   ? Grossman and Krueger’s (1996, p. 121)
response: “We do not know the answer to this question, nor do we think the answer is knowable.”
20
This paper incorporates the two contrary views suggested respectively by Grossman and
Krueger (1995) and Andreoni and Levinson (2001) into a model in the context of the EKC
hypothesis. We evaluate quantitatively their relative importance in the case of U.S. water
pollution. We find that: (i) while it is the induced policy response that is responsible for
turning the EKC from a positive to a negative slope, the fraction of pollution reduction
attributed to the automatic change will overtake that attributed to the induced policy response
once per capita GDP has exceeded $30,000, and (ii) the scale effect contributes to the
occurrence of the turning point of the EKC indirectly by significantly mitigating the addition
to pollution and, in particular, the turning point income for U.S. water pollution would be
beyond $1,197,473 if there were no scale effect according to our simulation.
Overall, the
automatic change via the scale effect as emphasized by Andreoni and Levinson is as important
as, if not more important than, the induced policy response as emphasized by Grossman and
Krueger in shaping the EKC in the case of U.S. water pollution.
21
Appendix
Following the standard practice in empirical studies, we assume that the actual share of
income devoted to pollution abatement and control reflects the equilibrium share s m . There
are two different data sources for the U.S. pollution abatement and control expenditures
(including both public expenditures directly and private expenditures indirectly via
regulation).
The U.S. Environmental Protection Agency (EPA, 1990) covers actual
expenditures from 1972 to 1986 and projects future expenditures from year 1987 to 2000. The
U.S. Census Bureau (CB, 1995) covers actual expenditures from year 1972 to 1994.10 While
the CB data only report current capital expenditures, the EPA data report both current and
annual capital expenditures after the 20-year appropriation. Also, while the CB data leave out
private expenditures in the household sector, the EPA data include private expenditures in
both the household and business sectors. An obvious disadvantage of the EPA data is that
expenditures from 1987 to 2000 are projected rather than actual. However, because the
questionnaire used by the Census Bureau to collect data asks corporate or government officials
how capital expenditures compared to what they would have been in the absence of
environmental regulation, there are some potential problems involved; see Jaffe et al (1995)
for the detail. In the Appendix, we compare these two different data, showing that the patterns
of changes in s m from these two data are roughly the same, even though s m on the basis of
the EPA data is always higher than that on the basis of the CB data. This difference does not
seem surprising, in view of the fact that the CB data leave out expenditures in the household
sector, while the EPA data include expenditures in both the household and business sectors.
We will use the EPA data (with the 20-year appropriation for capital expenditures) to calculate
s m in this study.
10
The U.S. Census Bureau renewed her data collection in 1999. However, there are some changes in the way of
data collection.
22
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26
Table 1. Data on per capita GDP (M), ratio of median to mean income (m/M), and share of income devoted to
pollution abatement and control ( s m )
year
1972
1973
1974
1975
1976
1977
1978
1979
1980
M
m/M
sm
13632.47
14280.12
14079.12
13916.18
14514.58
15032.84
15703.21
16021.27
15800.65
0.88074
0.003389
0.884651
0.003713
0.877034
0.004366
0.882482
0.004924
0.886646
0.005384
0.887689
0.005729
0.877994
0.005899
0.877708
0.006232
0.876914
0.006728
year
1981
1982
1983
1984
1985
1986
1987
1988
1989
M
m/M
sm
16038.27
15578.34
16134.9
17144.11
17695
18142.01
18588.29
19181.34
19673.45
0.86842
0.007035
0.855494
0.007608
0.856159
0.007702
0.851264
0.007553
0.841881
0.007683
0.843469
0.007924
0.839646
0.008135
0.833795
0.008012
0.826676
0.008094
year
1990
1991
1992
1993
1994
1995
1996
1997
1998
M
m/M
19818.52
19524.33
19907.16
20175.37
20733.4
21002.61
21527.75
22228.9
22888.4
0.800551
0.008306
0.79442
0.008717
0.788774
0.008768
0.754104
0.008843
0.748012
0.008791
0.758289
0.008871
0.753178
0.00882
0.744687
0.008684
0.749879
0.008576
sm
year
1999
2000
M
m/M
sm
23635.38
24231.54
0.743482
0.008427
0.734926
0.008317
Source:
Table 2. Sensitivity of varying values for m/M
m/M=0.72
m/M=0.75
m/M=0.9
 m =0.2
 m =0.959
   =1.301
   =1.205
a=0.001447
 =0.597688
a=0.000001374
 =0.383213773
M * =7779
s m =0.003317
M * =7762.201714
s m =0.001490148
   =1.305
   =1.205
a=0.001383
 =0.595763
a=0.000001374
 =0.383213773
M * =7792
s m =0.003054
M * =7771
s m =0.001489257
   =1.323
   =1.2055
a=0.00113
 =0.587052
a=0.000001366
 =0.383005228
M * =7766
sm
=0.002103
M * =7760
sm
=0.001467547
*
Note: M denotes the turning point income
Table 3. What if     1 ?
1
 m =0.1
 m =0.2
 m =0.3
 m =0.959
a=0.123683
 =0.222674
a= 0.12398
 =0.374175
a=0.00985694
 =0.6475628
a=0.0000101363
 =0.429036532
m/M
=0.72
M * =37,124,080
s m =0.39270291
M * =1,017,069
s m =0.30153712
M * =31,8936
s m =0.242031
M * =73,053
s m =0.11838588
m/M
=0.75
M * =53,606,148
s m =0.39270291
M * =1,197,473
s m =0.30153712
M * =350809
s m =0.242031
M * =73,180
s m =0.11838588
m/M =0.9
M * =276,595,954
s m =0.39270291
M * =2,483,081
s m =0.30153712
M * =536819
s m =0.242031
M * =73,753
s m =0.11838588
*
Note: M denotes the turning point income
2
0.03
environmental expenditure ratio
0.025
0.02
0.015
0.01
0.005
0
13000
15000
17000
19000
21000
23000
25000
per capita income
Figure 1-1 estimated against actual sm
0.03
0.025
0.02
0.015
0.01
0.005
0
5000
10000
15000
20000
25000
Figure 1-2 estimated against actual sm
30000
35000
40000
1
0.5
0
marignal effect
5000
10000
15000
20000
25000
30000
35000
40000
35000
40000
-0.5
-1
-1.5
-2
-2.5
per capita income
Figure 2-1 Automatic change versus induced policy response
when
 m  0.2 and     1.305
1
0.5
0
marginal effect
5000
10000
15000
20000
25000
30000
-0.5
-1
-1.5
-2
-2.5
per capita income
Figure 2-2 Automatic change versus induced policy response when
 m  0.959 and     1.205
1
Fig 12 scattor of environmental expenditure ratio and per capita income for under CRTS
0.0025
environmental expenditure ratio
0.0020
0.0015
0.0010
0.0005
0.0000
5000
10000
15000
20000
25000
30000
35000
40000
per capita income
scenario 1A(0.75)
scenario 1A(0.9)
scenario 1B(0.75)
scenario 1B(0.9)
Fig 13 scattor of environmental expenditure ratio and per capita income for different sceanrios
0.0025
environmental expenditure ratio
0.0020
0.0015
0.0010
0.0005
0.0000
5000
10000
15000
20000
25000
30000
35000
per capita income
"scenario 3A(0.75)"
2
scenario 3A(0.9)
scenario 3B(0.75)
scenario 3B(0.9)
40000
Fig 12 policy-induced effect for different scenarios
0.000
5000
10000
15000
20000
25000
30000
35000
40000
-0.010
marginal effect
-0.020
-0.030
-0.040
-0.050
-0.060
-0.070
-0.080
per capita income
scenario 1A(0.75)
scenario 1A(0.9)
scenario 1B(0.75)
scenario 1B(0.9)
Fig 15 policy-induced effect for different scenarios
0.00
5000
10000
15000
20000
25000
30000
-0.01
maiginal effect
-0.02
-0.03
-0.04
-0.05
-0.06
-0.07
-0.08
per capita income
scenario 3A(0.75)
scenario 3A(0.9)
3
scenario 3B(0.75)
scenario 3B(0.9)
35000
40000