On pollution and R&D-based growth in a trade model between countries concerned and unconcerned about climate change

On pollution and R&D-based growth in a trade model between countries concerned and unconcerned about climate change Francisco Cabo 1 Guiomar Martín-Herrán 1 M.Pilar Martínez-García 2 1 IMUVa, Dpt. Economía Aplicada (Matemáticas) Universidad de Valladolid 2 Dpt. Métodos Cuantitativos para la Economía Universidad de Murcia 5-th Atlantic Workshop on Energy and Environmental Economics, 25-26 June 2012

Motivation Full cooperation difficult in a global environmental problem (Barret 2003 and Finus 2001). Kyoto protocol: Annex I vs. Non-annex I countries. Countries concerned and countries who disregard global warming Emissions from non-renewable fossil fuels Carbon leakage Research question Conditions to reverse/alleviate the carbon leakage hypothesis Emissions from final output production, using a renewable resource, forest products (timber), as an input Forest: provides a productive input + carbon sink

Bilateral trade model Motivation Small group of technological leading countries (Coe et al. (1997)) Annex I - concerned countries Developing countries are not investing in R&D. They are well endowed with natural resources timber Non-annex I - unconcerned countries Pattern of trade: Non-abating developing countries export timber in exchange for technology intensive goods from abating technologically leading countries Research question Sustainability of the economic growth in both regions

Outline Motivation 1 Introduction 2 The model 3 The business as usual (BAU) scenario. Countries disregard global warming 4 Commitment by technologically leading countries to acknowledge global warming 5 Comparison of emissions, concentration of pollutants and economic growth

The model Technologically leading region Technological progress: expansion in the number of varieties of intermediate inputs Grossman & Helpman (1997), Barro & Sala-i-Martin (2004) Output producers: Produce final output using a growing number of intermediate inputs, labor and timber. Perfectly competitive markets. Production dependent on the environmental quality. Innovators: Create new intermediate inputs and produce one monopolistically. Static maximization of profits from sales in the leading and the forest regions. Consumers: Decide between consumption and assets accumulation. Dynamic maximization of utility from consumption and environmental quality.

The model Technologically leading region Technological progress: expansion in the number of varieties of intermediate inputs Grossman & Helpman (1997), Barro & Sala-i-Martin (2004) Output producers: Y L = AZ φ L 1 α β L N XLjH α β L, j=1 Z concentration of pollutants, L L labor, N number of intermediate inputs, X Lj intermediate input j, H L timber. Innovators: Create new intermediate inputs and produce one monopolistically. Static maximization of profits from sales in the leading and the forest regions. Consumers: Decide between consumption and assets accumulation. Dynamic maximization of utility from consumption and environmental quality.

The model Technologically leading region Technological progress: expansion in the number of varieties of intermediate inputs Grossman & Helpman (1997), Barro & Sala-i-Martin (2004) Output producers: Y L = AZ φ L 1 α β L N XLjH α β L, j=1 Z concentration of pollutants, L L labor, N number of intermediate inputs, X Lj intermediate input j, H L timber. Innovators: π j = (p j 1) (X Lj + X F j ), p j price of the intermediate input j Consumers: Decide between consumption and assets accumulation. Dynamic maximization of utility from consumption and environmental quality.

The model Technologically leading region Technological progress: expansion in the number of varieties of intermediate inputs Grossman & Helpman (1997), Barro & Sala-i-Martin (2004) Output producers: Y L = AZ φ L 1 α β L N XLjH α β L, j=1 Z concentration of pollutants, L L labor, N number of intermediate inputs, X Lj intermediate input j, H L timber. Innovators: π j = (p j 1) (X Lj + X F j ), p j price of the intermediate input j Consumers: max [ c1 ε L c L 0 1 ε θ Z1+µ 1 + µ ] e ρt dt, ρ, ε, µ, θ > 0, s.t.: a L = ra L + w L c L, a L (0) = a L0. c L consumption, a L assets, w L wages, r rate of return.

Forest region The model Output producers: Produce final output using a growing number of intermediate inputs, labor and timber. Perfectly competitive markets. Production dependent on the environmental quality. Consumers/harvesters: Do not accumulate assets. Own the forest in equal shares. Decide the share of labor to harvest and to produce final output. Maximize utility from consumption and environmental quality.

Forest region The model Output producers: Y F = ÃZ φ (vl F ) 1 α β N XF α jh β F, j=1 v share of labor in the final output sector, Z concentration of pollutants, L F labor, X F j intermediate input j, H F timber. Consumers/harvesters: Do not accumulate assets. Own the forest in equal shares. Decide the share of labor to harvest and to produce final output. Maximize utility from consumption and environmental quality.

Forest region The model Output producers: Y F = ÃZ φ (vl F ) 1 α β N XF α jh β F, j=1 v share of labor in the final output sector, Z concentration of pollutants, L F labor, X F j intermediate input j, H F timber. Consumers/harvesters: c1 ε F { Z1+ µ max θ v 1 ε 1 + µ }, s.t.: c F = vw F + p h h, h = b(1 v) 1 ϕ, b > 0, ϕ (0, 1). c F consumption, w F wages, p h price of timber.

The model Forest and the accumulation of pollutants Forest: Dynamics of the forest in aggregate terms: Ṡ = G(S) H = gs (1 S/C) L F b(1 v) 1 ϕ, S(0) = S 0 G(S) logistic gross reproduction rate, H = L F h harvestings. Concentration of pollutants in the atmosphere Ż =E L +E F δ(s, Z)=E L +E F δ 1 Z δ 2 S, Z(0) = Z 0, δ 1, δ 2 > 0. E L, E F emissions from producers in L and F. Assumption: E i Y i = g i (N), g i(n) < 0, i {L, F }. Emissions if g i (N) is a hyperbolic function: E L Y L = τ N E L = τ Y L N, E F Y F = τ N E F = τ Y L N.

The model Forest and the accumulation of pollutants Forest: Dynamics of the forest in aggregate terms: Ṡ = G(S) H = gs (1 S/C) L F b(1 v) 1 ϕ, S(0) = S 0 G(S) logistic gross reproduction rate, H = L F h harvestings. Concentration of pollutants in the atmosphere Ż =E L +E F δ(s, Z)=E L +E F δ 1 Z δ 2 S, Z(0) = Z 0, δ 1, δ 2 > 0. E L, E F emissions from producers in L and F. Assumption: E i Y i = g i (N), g i(n) < 0, i {L, F }. Emissions if g i (N) is a hyperbolic function: E L Y L = τ N E L = τ Y L N, E F Y F = τ N E F = τ Y L N.

BAU vs Commitment BAU vs Commitment to acknowledge global warming BAU: Countries disregard global warming. Commitment: agreement in technologically leading countries to: 1 consider global warming in their decision making process, 2 settle the price of intermediate inputs in a centralized manner. Equivalent to a central planner in this region, who maximizes: Ṅ = max c L,H L,X L,p j 0 ( c1 ε L 1 ε θ Z1+µ 1 + µ ) e ρt dt, 1 η+ν [Y L+N(p j 1)X F (p j ) NX L p h H L c L L L ], N(0)=N 0 >0 Ż = τ Y L N + τ Y F N δ 1Z δ 2 S, Z(0) = Z 0 > 0, Ṡ = gs (1 S C ) (H L + H F ), S(0) = S 0 > 0,

BAU vs Commitment Emissions: BAU vs Commitment Emissions under BAU E L = (τλl L H β 1 α ) Z φ 1 α = Ē L Z φ 1 α, E F = ( τβ αp F ΛL L H β 1 α ) Z φ 1 α = Ē F Z φ 1 α. Λ = CST (parameters), p F the terms of trade Emissions under Commitment E L = ( 1 + τψ α α ) 1 α φ Z 1 α = ĒL C Z φ E F = ( αp F + τψ αp F ) 1 α, α 1 α Z φ 1 α = Ē C F Z φ 1 α. Ψ = λ Z c L L L, c L = C L /N, λ Z shadow price of Z, p F the terms of trade

BAU vs Commitment Steady-State equilibrium Steady-State equilibrium v, X L, X F, E L, E F, Z, H L, H F remain constant C L, C F, N, Y L, Y F, w L, w F, p h grow at the same constant rate Existence and uniqueness Under the assumption gc > 4H a saddle-path stable Steady-State equilibrium exists and is unique. Growth rate of consumption γ = (γ C ) = with Z, (Z C ) implicitly given. (1 α)(α + β) Ē L ε(η + ν) τ (Z ) φ ρ 1 α ε B C ĒL C (η + ν) τ ((ZC ) ) φ 1 α ρ

Comparison: BAU versus Commitment Comparison of emissions Emissions under the two scenarios: E L = ĒLZ φ 1 α, E C L = ĒC L Z φ 1 α, EF = ĒF Z φ 1 α, E C F = ĒC F Z φ 1 α, E = ĒZ φ 1 α, E C = ĒC Z φ 1 α. Autonomous variation in emissions (no change in Z) Ē C L ĒL Ē L > ĒC F ĒF Ē F Two possibilities for global emissions reductions: Condition Leader Forest World Economy α > 1 + τψ Ē C L < ĒL Ē C F << ĒF Ē C < Ē α < 1 + τψ < α α Ē C L > ĒL Ē C F < ĒF Ē C < Ē

Comparison: BAU versus Commitment Comparison of emissions Price of intermediate inputs charged to forest region producers p C j > p j Assumption: ĒL C + ĒC F ĒC < Ē ĒL + ĒF At the steady state it follows: 1 The concentration of pollutants decreases (Z C ) < Z 2 Global emissions decrease (E C ) ĒC ((Z C ) ) φ 1 α < Ē(Z ) φ 1 α E

Comparison: BAU versus Commitment Comparison of growth rates Growth rates under BAU and Coommitment: B C γ B = (η+ν)τ Ē L(Z ) φ 1 α ρ, (γ C ) = (η+ν)τ (ĒC L ) ((Z C ) ) φ with B < B C. Commitment does not necessarily reduces growth Ē C L < ĒL (Z C ) < Z (B C > B, ((Z C ) ) φ 1 α > (Z ) φ 1 α ) (γ C ) < γ 1 α ρ.

Comparison: BAU versus Commitment Numerical Results Parameters values: α = 0.5, β = 0.2, δ = 0.5, ρ = ρ = 0.01, η = 0.2, ν = 0.1, τ = τ = 0.3, δ 1 = δ 2 = 0.1, g = 4, A = Ã = b = L L = L F = θ = µ = C = 1. p j p F Ē L Ē F Ē Ẑ Ê L ÊF Ê γ φ = 0.5 α > 1 + τψ + + + φ = 0.3 α < 1 + τψ < α α + + + + X = XC X X

Comparison: BAU versus Commitment Conclusions Sustainable growth is feasible and saddle-path stable in a bilateral trade model. Technology developed in one region is traded in exchange for timber harvested in its counterpart. If technologically leading countries commit to acknowledge global warming and agree on a coordinated price for traded technology: Willingness to reduce emissions transferred from countries concerned to countries who disregard global warming. Mechanism: a higher price of the intermediate inputs. Forest countries reduce emissions stronger than the technologically leading countries. Concentration of pollutants decreases and still emissions are globally reduced. Growth does not necessarily shrink. Numerically it grows.