Is there an Environmental Kuznets Curve?

Transcription

1 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 I = MD( p, β (p),z), Income: I = G( p,k,l,z). Three endogenous variables: τ, I, z.

2

3

4

5

6

7

8

9

10 3.3 Sources of Growth 2 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: z ˆ = ε xk K ˆ I ˆ = s r K ˆ + s τ z ˆ. s r > 0 and s τ > 0 shares of capital and emission charges in national income, ˆ z = dz / z, etc., ε xk > 0 is the elasticity of X with respect to K ˆ I = ˆ z = ( s r + s τ ε xk ) K ˆ. ε xk s r + s τ ε xk ( +) ˆ I

11 3 Alternatively, suppose growth occurs via accumulation of human capital: z ˆ = ε xl L ˆ I ˆ = s w L ˆ + s τ z ˆ = ( s w + s τ ε xl ) L ˆ, where s w > 0 is the share of human capital in national income. ˆ z = ε xl s w + s τ ε xl If growth occurs via accumulation of the factor used ( ) intensively in the clean industry, there is a negative monotonic relation between pollution and income. ˆ I Similar result can be obtained even with an endogenous policy response, provided that the income elasticity of marginal damage is not too high.

12 3.4 Income Effects 4 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( K x,l x ) ( ) y = λh K y,l y ( ) z = ϕ( θ)f K x,l x

13 5 Equilibrium: λg z (p,k,l,z) = MD( p, λg(p,k,l,z) β( p),z) ( ) dz τ 1 ε dλ = Δ MD,R, where Δ > 0 and ε MD,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.

14 6 Neutral factor accumulation: G( p,λk,λl,z) G z ( p,λk,λl,z) = MD(p,,z) β( p) ( ) dz dλ = τ s r + s w Δ s r + σ ZK s w ε σ MD,R ZL s i s i /(s r + s w ) is the share of factor i in income accruing to primary factors (excluding emission payments) σ ij G i G j /GG ij 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 σ ij 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 σ ij are small, and pollution is more likely to rise with factor accumulation.

15 7 Lopez (1994) considers the special case where σ ZK = σ ZL σ. ( ) dz dλ = τ s r + s w Δ 1 σ ε MD,R (0.1) Example. Suppose only one good X with specific technology above: G(p,K,L,z) = pz α F(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) = pz α F(λK,λL) 1 α = λ 1 α pz α F(K,L) 1 α Factor accumulation at rate λ is equivalent to neutral primary-factor-augmenting technical progress at rate λ 1-α.

16 8 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.

17 9 Example V(p,I,z) = c 1 c 2 e R/δ γz where R = I/β(p) is real income One-good model (no composition effects) I = pλz α F(K,L) 1 α, Inverse pollution demand, (value of the marginal product of emissions): τ D = αpλz α 1 F(K,L) 1 α = α z I. Pollution supply: τ S = MD = V z V I = γβ(p)δ c 2 e R/δ Supply = Demand implies: z = αc 2 γδ R e R/δ.

18 10 Slope of EKC: dz dr 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. ε MD,R = R δ. That is, ε MD,R < 1 for R < δ, and ε MD,R > 1 for R > δ. Because level and responsiveness of marginal damage differ across pollutants, expect very different EKC's for different pollutants.

19

20 11 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.

21

22 3.5 Threshold Effects 12 Jones and Manuelli (1995) John and Pecchenino (1994) Stokey (1998). The Abatement Threshold Model Again suppose only good X, so that income is for z F(K,L). I = pz α F(K,L) 1 α. Suppose V(p,I,z) = [ I /β(p)]1 η 1 η γz with η 1 Reduced form (at interior solution): z = α γ R1 η.

23

24

25 Pollution demand curve in the region where abatement does occur: 13 τ = G z = αp F(K,L) 1 α. (0.2) z 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: For τ S = V z V I = γβ(p) 1 η I η. I < I T there is no abatement: αp γβ(p) 1 η 1/η, (0.3) z = F(K,L) = I p = β( p) p R.

26 14 z = β( p) R p T if pf(k,l) < I α γ R1 η if pf(k,l) I T.

27 15 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 α γ R1 η if F(K,L) < F T if F(K,L) F T. 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.

28 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,x A ), where a defines the abatement function. Up to now, we have assume a is linearly homogeneous.

29 17 Now suppose that an individual firm's abatement A i is given by: A i = A δ a(f i,x i A ) where A denotes aggregate abatement in the economy, the function a has constant returns to scale, and 0 < δ < 1. Can show: e = z x = (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.