Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland ›...

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1 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 = G z ( p,K ,L ,z ) . Pollution supply: τ S = MD ( p, I β ( p ) , z) , Income: I = G( p,K ,L ,z ) . Three endogenous variables: τ, I, z.

Transcript of Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland ›...

Page 1: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz

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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.

Page 2: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz
Page 3: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz
Page 4: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz
Page 5: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz
Page 6: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz
Page 7: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz
Page 8: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz
Page 9: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz
Page 10: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz

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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

(+)

Page 11: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz

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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.

Page 12: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz

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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( )

Page 13: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz

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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.

Page 15: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz

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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.

Page 16: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz

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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 .

Page 18: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz

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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.

Page 19: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz
Page 20: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz

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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.

Page 21: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz
Page 22: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz

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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.

Page 23: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz
Page 24: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz
Page 25: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz

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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 .

Page 26: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz

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z =

β( p)p

R if pF(K ,L) < I T

αγR1−η if pF(K,L) ≥ IT

⎨ ⎪ ⎪

⎩ ⎪ ⎪

.

Page 27: Is there an Environmental Kuznets Curve?faculty.arts.ubc.ca › bcopeland › 573-ch3-slides-2007.pdf6 Neutral factor accumulation: Gz(p,λK,λL,z)= MD(p, G(p,λK,λL,z) β(p),z) dz

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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.