Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland ›...
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Is there an Environmental Kuznets Curve?
• small open economy - fixed world price
• normalize population so that N = 1.
• growth treated as once-and-for-all changes in
endowments or technology.
Pollution Demand:
�
τ D = Gz( p,K ,L ,z).
Pollution supply:
�
τ S = MD( p, Iβ (p)
,z),
Income:
�
I =G( p,K ,L ,z).
Three endogenous variables: τ, I, z.
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3.3 Sources of Growth
Assume pollution tax fixed:
�
τ = τ .Implies emission intensity is fixed.
� �
z = e x(p,τ ,K,L)
�
I =G( p,K ,L ,z)
Consider growth via capital accumulation alone:
�
ˆ z = ε xKˆ K
�
ˆ I = srˆ K + sτ ˆ z .
sr > 0 and sτ > 0 shares of capital and emission charges in
national income,
�
ˆ z = dz / z, etc.,
εxK > 0 is the elasticity of X with respect to K
�
ˆ I = sr + sτε xK( ) ˆ K .
�
ˆ z =ε xK
sr + sτε xK
ˆ I
(+)
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Alternatively, suppose growth occurs via accumulation of
human capital:
�
ˆ z = ε xLˆ L
�
ˆ I = swˆ L + sτ ˆ z = sw + sτε xL( ) ˆ L ,
where sw > 0 is the share of human capital in national
income.
�
ˆ z =ε xL
sw + sτε xL
ˆ I
(−)
If growth occurs via accumulation of the factor used
intensively in the clean industry, there is a negative
monotonic relation between pollution and income.
Similar result can be obtained even with an endogenous
policy response, provided that the income elasticity of
marginal damage is not too high.
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3.4 Income Effects
Three assumptions:
• Neutral growth
• Firms at an interior solution for abatement purposes.
• Income elasticity of marginal damage rising in income
levels.
Neutral technical progress:
Given (K,L z,) feasible outputs of X and Y are both
shifted up by a factor λ
National income: λG(p,K,L,z)
For our more specific technology:
�
x = λ 1−θ( )F Kx ,Lx( )y = λH Ky ,Ly( )z = ϕ θ( )F Kx ,Lx( )
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Equilibrium:
�
λGz (p,K,L,z) = MD( p,λG(p,K ,L,z)β(p)
,z)
�
dzdλ
=τ 1− ε
MD ,R( )Δ
,
where Δ > 0 and
�
εMD ,R is the elasticity of marginal damage
with respect to real income.
• Demand for pollution shifts out because the marginal
product of pollution rises.
• Supply shifts inward because real income has grown.
Result does not rely on the separability or Cobb-Douglas
assumptions of our more specific technology.
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Neutral factor accumulation:
�
Gz( p,λK ,λL, z) = MD(p,G(p,λK ,λL,z)β(p)
,z)
�
dzdλ
=τ sr + sw( )
Δ˜ s r
σ ZK+
˜ s wσ ZL
− εMD ,R⎡ ⎣ ⎢
⎤ ⎦ ⎥
�
˜ s i ≡ si / (sr + sw ) is the share of factor i in income accruing
to primary factors (excluding emission payments)
�
σ ij ≡GiG j /GGij is the Hicks-Allen elasticity of
substitution between inputs i and j in generating aggregate
national income.
If it is easy to substitute either input for emissions then the
σij are large, and it is more likely for pollution to fall as the
supply of primary factors rises.
If it is difficult to substitute primary factors for emissions,
then the σij are small, and pollution is more likely to rise
with factor accumulation.
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Lopez (1994) considers the special case where
�
σ ZK = σ ZL ≡ σ .
�
dzdλ
=τ sr + sw( )
Δ1σ−εMD,R
⎡ ⎣ ⎢
⎤ ⎦ ⎥ (0.1)
Example. Suppose only one good X with specific
technology above:
�
G(p,K,L,z) = pzαF(K,L)1−α ,
Then
�
σ ZK = σ ZL =1. Factor accumulation will raise emissions if the income
elasticity of marginal damage is less than 1, and lower
emissions otherwise.
�
G(p,λK ,λL,z ) = pzαF(λK,λL)1−α = λ1−α pzαF(K,L)1−α
Factor accumulation at rate λ is equivalent to neutral
primary-factor-augmenting technical progress at
rate λ1-α.
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Implications of neutral growth for the EKC
Because the EKC has both an increasing and decreasing
segment, a pure income-driven explanation requires either
a variable elasticity of marginal damage, or factor
accumulation combined with variable elasticities of
substitution.
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Example
�
V (p,I,z) = c1 – c2e−R /δ −γz
where R = I/β(p) is real income
One-good model (no composition effects)
�
I = pλzαF(K,L)1−α ,
Inverse pollution demand, (value of the marginal product
of emissions):
�
τ D = αpλzα−1F(K,L)1−α =αzI .
Pollution supply:
�
τ S = MD = −Vz
VI=γβ(p)δc2
eR /δ
Supply = Demand implies:
�
z =αc2
γδR e−R /δ .
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Slope of EKC:
�
dzdR
=z(δ − R)Rδ
.
For low income (R < δ), the curve slopes upward;
For high income (R > δ), it slopes down.
Peak at R = δ.
�
εMD ,R =Rδ
.
That is,
�
εMD ,R < 1 for R < δ, and
�
εMD ,R > 1 for R > δ.
Because level and responsiveness of marginal damage
differ across pollutants, expect very different EKC's for
different pollutants.
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Income Effects Theory: Discussion
Any theory of the EKC requires some force to eventually
more than fully offset the scale effect of growth.
In the "sources of growth" explanation, a very strong
composition effect (created by clean factor growth)
outweighed the scale effect.
In the income effect explanation, it is primarily a technique
effect that does this.
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3.5 Threshold Effects
Jones and Manuelli (1995)
John and Pecchenino (1994)
Stokey (1998).
The Abatement Threshold Model
Again suppose only good X, so that income is
�
I = pzαF(K,L)1−α .
for z ≤ F(K,L).
Suppose
�
V (p,I,z) =I /β(p)[ ]1−η1−η
−γz withη ≠1
Reduced form (at interior solution):
�
z =αγR1−η.
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Pollution demand curve in the region where abatement
does occur:
�
τ = Gz = αp F(K,L)z
⎛ ⎝
⎞ ⎠
1−α
. (0.2)
Valid only for z ≤ F, since emissions cannot exceed
potential output.
At τ = αp, we have z = F,
Pollution demand curve is vertical for τ < τ*.
Pollution supply:
�
τ S = −VzVI
= γβ(p)1−η Iη .
For
�
I < IT ≡ αpγβ(p)1−η⎡ ⎣ ⎢
⎤ ⎦ ⎥
1/η
, (0.3)
there is no abatement:
�
z = F(K ,L) =Ip
=β( p)p
R .
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�
z =
β( p)p
R if pF(K ,L) < I T
αγR1−η if pF(K,L) ≥ IT
⎧
⎨ ⎪ ⎪
⎩ ⎪ ⎪
.
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The Policy Threshold Model
Assume a fixed cost of regulating.
Either incur a fixed cost and regulate pollution, or allow
pollution to be fully demand determined.
Choose option that leads to the highest utility for the
representative consumer.
�
z =R if F(K ,L) < FT
αγR1−η if F(K ,L) ≥ FT
⎧ ⎨ ⎪
⎩ ⎪ .
When the threshold is reached, environmental regulations
are introduced and pollution drops discretely.
Threshold theories rely on a strong policy response after
the threshold is breached.
Policy threshold model generalizes to the case of multiple
goods; abatement threshold model does not.
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3.6 Increasing Returns to Abatement
Andreoni and Levinson (2001): one good, endowment
model with a central planner.
We adopt a formulation with industry-wide external
economies of scale in abatement.
Fix the pollution tax to distinguish this explanation from
the income-effect explanation.
In our earlier model, actual pollution emitted can be
written as:
�
z = F − a(F,xA ),
where a defines the abatement function.
Up to now, we have assume a is linearly homogeneous.
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Now suppose that an individual firm's abatement Ai is
given by:
�
Ai = Aδa(Fi ,xiA )
where A denotes aggregate abatement in the economy, the
function a has constant returns to scale, and 0 < δ < 1.
Can show:
�
e =zx
= (αp /τ )A−δ
Emissions per unit of output can fall a aggregate abatement
rises even with τ fixed.
As in all theories of the EKC, the model needs some force
to offset the increase in pollution driven by the scale effect
of growth. In the increasing returns model, the increase in
scale creates its own technique effect as a larger market
leads to increased productivity in abatement.