Climate Change Around the World Per Krusell Institute for International Economic Studies, NBER, CEPR Anthony A. Smith, Jr. Yale University, NBER The Macro and Micro Economics of Climate Change Laboratory for Aggregate Economics and Finance University of California, Santa Barbara May 22 and 23, 217
The project Construct global model of economy-climate interactions featuring a high degree of geographic resolution (1 1 regions). Use the model as a laboratory to quantify the distributional effects of climate change and climate policy. If a set of regions imposes a carbon tax (or a quantity restriction on emissions), how does the path of global emissions respond? Which regions gain and which lose, and by how much? Related to small new literature on spatial equilibrium models of climate change: Desmet and Rossi-Hansberg; Krusell and Hassler; Brock, Engström, Grass, and Xepapadeas; Brock, Cai, and Xepapadeas.
The data Unit of analysis: 1 1 cells containing land. The model contains 19, regions (or cell-countries). Matsuura and Willmott: gridded (.5.5 ) monthly terrestrial temperature data for 19 28. Nordhaus s G-Econ database: gross domestic product (GDP) and population for all such cells in 199.
8 6 4 2 Average temperature (191-192) 3.8 26 23.8 2.4-2 14.7 8.7-4 -6-8 -18-12 -6 6 12 18 2.9-2.2-8.9-64.7
Global average land temperature (by year) 1.3 1 9.6 9.2 8.8 191 192 194 196 198 28 Year
8 6 4 2 Log of GDP in 199 6.6.9 -.1-1.1-2 -2-2.9-4 -6-8 -18-12 -6 6 12 18-3.7-4.6-6 -9.2
Natural-science background I: the climate Energy balance (inflow from the Sun equals outflow from the Earth) determines the Earth s temperature. Forcing, F, from CO 2 in the atmosphere (relative to pre-industrial) is: F = η ln(s/ S) ln(2), where S = 84GtC and S = 6GtC are current and pre-industrial stocks. Equilibrium temperature, T (relative to pre-industrial), is: T = κf = λ ln(s/ S) ln(2), where κ depends on various feedback effects. λ 3 ± 1.5 is climate sensitivity.
Natural-science background II: the carbon cycle Carbon cycle: how emissions of CO 2 enter/exit atmosphere. Key: emissions spread globally very quickly ( global externality ). Depreciation structure of atmospheric CO 2 : smooth, but very slow; some stays forever in atmosphere nonlinear but linear approximation okay. Emissions: 1GtC/year; S t 4.5GtC/year. Estimated remaining carbon: oil + gas = 3GtC, coal much bigger (> 3,GtC?). So coal is key! To summarize: emissions carbon in atmosphere forcing temperature. Bad if higher T causes damages : the mother of all externalities (Stern).
Integrated assessment models Pioneered by Nordhaus (DICE, RICE). Quantitative theory, computational. Key components: climate system (as above) carbon cycle (as above) economic model of emissions AND damages Economic model: needs to be dynamic, forward-looking, possibly allowing stochastics (temperature variations, disasters). Here: climate system more elaborate (regional variation) economic model and damages new the one-region version of the model is close to the representative-agent DSGE climate-economy model in Golosov, Hassler, Krusell, and Tsyvinski (214)
Overview for remainder of talk 1. our climate modeling 2. our damage specification 3. economic model 4. calibration, computation 5. results 6. conclusions, future
Our climate modeling How will region l s climate respond to global warming? Answer given by complex global and regional climate models. But not feasible (yet) to combine these with economic model. Therefore, use pattern scaling (aka statistical downscaling ): statistical description of temperature in a given region as a function of a single state variable average global temperature. Capture sensitivity of temperature in region l to global temperature T in a coefficient (linear structure; standard). With help of climate scientists, use runs of (highly) complex climate models into the future to estimate sensitivities.
8 6 4 2 Sensitivity to changes in global temperature 5.2 2.2 1.7 1.4-2 1.3 1.2-4 -6-8 -18-12 -6 6 12 18 1.1 1.8.4
Our damage specification What are the damages in region l as a result of global warming? Damage measurements: overall the weakest part of quantitative climate-economy models, especially for regional damages. Two common approaches: bottom up (Nordhaus, IPCC) and top down (Dell et al). Our approach: formulate a damage function D of local temperature that is: common across all regions; like Nordhaus s, a drag on total factor productivity (TFP); consistent with Nordhaus s worldwide damage function when aggregated across all regions. Desmet and Rossi-Hansberg (214) also use a common U-shape in a spatial application.
Nordhaus s damage function (percentage of GDP) 7 6 5 Percentage 4 3 2 1 1 2 3 4 5 Temperature
Damage function: productivity vs. temperature 1.75 Fraction of optimum.5.25.2 32 2 1 11.6 2 32 Temperature (degrees centigrade)
Share of world GDP vs. temperature 4.53732 Share of GDP 32 2 1 11.6 2 32 Temperature (degrees centigrade)
Share of world population vs. temperature 5.67524 Share of population 32 2 1 11.6 2 32 Temperature (degrees centigrade)
Share of world GDP vs. productivity (as a fraction of optimum) 21.8995 Share of GDP.176.25.5.75.9.995 Productivity
Share of world population vs. productivity (as a fraction of optimum) 1.6286 Share of population.5168.25.5.75.9.995 Productivity
8 6 4 2 Damage coefficient x 1 (at temperature in 191-192) 1 96.5 87.6 76-2 65.5 57.2-4 -6-8 -18-12 -6 6 12 18 5.6 4.9 16.5 2
The economic model Forward-looking consumers and firms in each region determine their consumption, saving, and energy use. No migration. Neoclassical production technologies, different TFPs both exogenously and due to climate. Energy as an input: coal, produced locally, at constant marginal cost (no profits). Coal slowly, exogenously replaced by (same-cost) green energy. Market structure: two cases. Autarky (regions only linked via emission externality). Unrestricted borrowing/lending (world interest rate clears market). Summary: like Aiyagari (1994) and our previous work, though no shocks in this version. Adaptation: consumption smoothing and, in case with international markets, capital mobility ( leakage ).
Regional problem In a recursive equilibrium, region l solves v t (ω, A, k, S; l) = max k,b [U(c) + β v t+1(ω, A, k, S ; l)], s.t. c = ω k q t ( k, S)b ω = max e [F (k, (1 D(T l (S )))A, e ) pe )] + (1 δ)k + b A = (1 + g)a k = H t ( k, S) S = Φ t ( k, S ). Can be interpreted as a decentralized equilibrium. Set up to deal with shocks, aggregate and/or local.
Calibration Annual time step, log utility, discount factor β =.985. Production function in region l: CES in kl α((1 D l)a l L) 1 α and energy e l, with: share parameter θ; elasticity = (1 ρ) 1 (set ρ = for now); α =.36; Al grows at rate g = 1%. Capital depreciates at rate δ = 6%. Initial distribution of region-specific capital, k l, and level of productivity, A l, chosen to: (1) match regional GDP per capita in 199 and; (2) equalize MPKs across regions. Price of coal and θ chosen to match: (1) total carbon emissions in 199; and (2) energy share of 6% along a balanced growth path. Green energy replaces coal slowly (logistic).
Fraction of carbon emissions abated 1.75 Fraction.5.25 199 29 219 229 Year
Carbon cycle The total stock of atmospheric carbon, S t, is the sum of a permanent stock, S 1t, and a (slowly) depreciating stock, S 2t : S t = S 1t + S 2t. S 1t =.25E t + S 1,t 1, where E t is total carbon emissions. S 2t =.36(1.25)E t +.998S 2,t 1. Half-life of a freshly-emitted unit of carbon is 3 years; half-life of the depreciating stock (given no new emissions) is 3 years.
Computation Richard Feynman: Imagine how much harder physics would be if electrons had feelings! Transition + heterogeneity = nontrivial fixed-point problem: guess on a temperature path, solve backwards for decisions, run globe forwards to confirm guessed path. Use mostly well-known methods but heterogeneity vast: exogenous TFP wealth/capital l captures entire path of future regional TFP endogenous to climate (this feature NOT one-dimensional); we don t actually solve 19,235 DP problems but so much heterogeneity that we need to solve 7 DPs and then nonlinearly interpolate decision rules between 7 types. Fortran 9 + OpenMP with 2 cores: less than five minutes.
Experiments Laissez-faire. Main policy experiment: all regions impose common path for carbon taxes, financed locally (no interregional transfers). Throughout: focus on relative effects, not aggregates.
Main findings Climate change affects regions very differently. Stakes big at regional level. Though a tax on carbon would affect welfare positively in some average sense, there is a large disparity of views across regions (56% of regions gain, while 44% lose). Findings are very close for two extreme market structures (autarky and international capital markets).
behavior of aggregates over time
Global emissions of atmospheric carbon (in gigatons) (no taxes; free capital movement) 13.7765 Gigatons of carbon 199 29 219 229 239 Year
Optimal carbon tax (dollars per ton of carbon) 1158.2 Dollars 49.3421 199 2288 Year
Global emissions of atmospheric carbon (in gigatons) (taxes vs. no taxes; free capital movement) 13.7765 Gigatons of carbon 199 29 219 229 239 Year
Gigatons of atmospheric carbon (no taxes; free capital movement) 167.5 Gigatons of carbon 768.754 199 29 219 229 239 Year
Gigatons of atmospheric carbon (taxes vs. no taxes; free capital movement) 167.5 Gigatons of carbon 768.115 199 29 219 229 239 Year
Temperature (degrees centrigrade above pre indudstrial) (no taxes; free capital movement) 4.4464 Degrees centigrade 1.21195 199 29 219 229 239 Year
Temperature (degrees centrigrade above pre indudstrial) (taxes vs. no taxes; free capital movement) 4.4464 Degrees centigrade 1.2835 199 29 219 229 239 Year
World GDP (trillions of dollars; detrended) (no taxes; free capital movement) 3.556 Trillions of dollars 28.2934 199 29 219 229 239 Year
World GDP (trillions of dollars; detrended) (taxes vs. no taxes; free capital movement) 3.556 Trillions of dollars 28.2934 199 29 219 229 239 Year
World consumption (trillions of dollars; detrended) (no taxes; free capital movement) 21.7 Trillions of dollars 19.9 199 29 219 229 239 Year
World consumption (trillions of dollars; detrended) (taxes vs. no taxes; free capital movement) 21.7 Trillions of dollars 19.9 199 29 219 229 239 Year
movie: temperature, laissez-faire animation: www.econ.yale.edu/smith/temperature1.mp4
8 6 4 2 Temperature in 2 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
8 6 4 2 Temperature in 21 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
8 6 4 2 Temperature in 22 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
8 6 4 2 Temperature in 23 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
8 6 4 2 Temperature in 24 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
8 6 4 2 Temperature in 25 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
8 6 4 2 Temperature in 26 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
8 6 4 2 Temperature in 27 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
8 6 4 2 Temperature in 28 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
8 6 4 2 Temperature in 29 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
8 6 4 2 Temperature in 21 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
8 6 4 2 Temperature in 211 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
8 6 4 2 Temperature in 212 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
8 6 4 2 Temperature in 213 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
8 6 4 2 Temperature in 214 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
8 6 4 2 Temperature in 215 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
8 6 4 2 Temperature in 216 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
8 6 4 2 Temperature in 217 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
8 6 4 2 Temperature in 218 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
8 6 4 2 Temperature in 219 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
8 6 4 2 Temperature in 22 35.7 3.3 28.1 24.8-2 19.2 13.6-4 -6-8 -18-12 -6 6 12 18 9.1 5.2 -.2-29.5
movie: change in temperature, laissez-faire animation: www.econ.yale.edu/smith/deltatemperature1.mp4
movie: 1 minus damage coefficient, laissez-faire animation: www.econ.yale.edu/smith/damage1.mp4
8 6 4 2 Damage coefficient (x 1) in 2 1 98.1 92.6 83.2-2 7.2 56.2-4 -6-8 -18-12 -6 6 12 18 45.9 38.1 32.2 2
8 6 4 2 Damage coefficient (x 1) in 21 1 98.1 92.6 83.2-2 7.2 56.2-4 -6-8 -18-12 -6 6 12 18 45.9 38.1 32.2 2
8 6 4 2 Damage coefficient (x 1) in 22 1 98.1 92.6 83.2-2 7.2 56.2-4 -6-8 -18-12 -6 6 12 18 45.9 38.1 32.2 2
8 6 4 2 Damage coefficient (x 1) in 23 1 98.1 92.6 83.2-2 7.2 56.2-4 -6-8 -18-12 -6 6 12 18 45.9 38.1 32.2 2
8 6 4 2 Damage coefficient (x 1) in 24 1 98.1 92.6 83.2-2 7.2 56.2-4 -6-8 -18-12 -6 6 12 18 45.9 38.1 32.2 2
8 6 4 2 Damage coefficient (x 1) in 25 1 98.1 92.6 83.2-2 7.2 56.2-4 -6-8 -18-12 -6 6 12 18 45.9 38.1 32.2 2
8 6 4 2 Damage coefficient (x 1) in 26 1 97.9 92.4 83.1-2 7.6 56.6-4 -6-8 -18-12 -6 6 12 18 46.1 38.2 32.3 2
8 6 4 2 Damage coefficient (x 1) in 27 1 97.9 92.4 83.1-2 7.6 56.6-4 -6-8 -18-12 -6 6 12 18 46.1 38.2 32.3 2
8 6 4 2 Damage coefficient (x 1) in 28 1 97.9 92.4 83.1-2 7.6 56.6-4 -6-8 -18-12 -6 6 12 18 46.1 38.2 32.3 2
8 6 4 2 Damage coefficient (x 1) in 29 1 97.9 92.4 83.1-2 7.6 56.6-4 -6-8 -18-12 -6 6 12 18 46.1 38.2 32.3 2
8 6 4 2 Damage coefficient (x 1) in 21 1 97.9 92.4 83.1-2 7.6 56.6-4 -6-8 -18-12 -6 6 12 18 46.1 38.2 32.3 2
8 6 4 2 Damage coefficient (x 1) in 211 1 97.9 92.4 83.1-2 7.6 56.6-4 -6-8 -18-12 -6 6 12 18 46.1 38.2 32.3 2
8 6 4 2 Damage coefficient (x 1) in 212 1 97.9 92.4 83.1-2 7.6 56.6-4 -6-8 -18-12 -6 6 12 18 46.1 38.2 32.3 2
8 6 4 2 Damage coefficient (x 1) in 213 1 97.9 92.4 83.1-2 7.6 56.6-4 -6-8 -18-12 -6 6 12 18 46.1 38.2 32.3 2
8 6 4 2 Damage coefficient (x 1) in 214 1 97.9 92.4 83.1-2 7.6 56.6-4 -6-8 -18-12 -6 6 12 18 46.1 38.2 32.3 2
8 6 4 2 Damage coefficient (x 1) in 215 1 97.9 92.4 83.1-2 7.6 56.6-4 -6-8 -18-12 -6 6 12 18 46.1 38.2 32.3 2
8 6 4 2 Damage coefficient (x 1) in 216 1 97.9 92.4 83.1-2 7.6 56.6-4 -6-8 -18-12 -6 6 12 18 46.1 38.2 32.3 2
8 6 4 2 Damage coefficient (x 1) in 217 1 97.9 92.4 83.1-2 7.6 56.6-4 -6-8 -18-12 -6 6 12 18 46.1 38.2 32.3 2
8 6 4 2 Damage coefficient (x 1) in 218 1 97.9 92.4 83.1-2 7.6 56.6-4 -6-8 -18-12 -6 6 12 18 46.1 38.2 32.3 2
8 6 4 2 Damage coefficient (x 1) in 219 1 97.9 92.4 83.1-2 7.6 56.6-4 -6-8 -18-12 -6 6 12 18 46.1 38.2 32.3 2
8 6 4 2 Damage coefficient (x 1) in 22 1 97.9 92.4 83.1-2 7.6 56.6-4 -6-8 -18-12 -6 6 12 18 46.1 38.2 32.3 2
movie: percentage change in gdp, laissez-faire animation: www.econ.yale.edu/smith/pctgdp1.mp4
8 6 4 2 Percentage change in GDP: 2 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
8 6 4 2 Percentage change in GDP: 21 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
8 6 4 2 Percentage change in GDP: 22 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
8 6 4 2 Percentage change in GDP: 23 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
8 6 4 2 Percentage change in GDP: 24 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
8 6 4 2 Percentage change in GDP: 25 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
8 6 4 2 Percentage change in GDP: 26 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
8 6 4 2 Percentage change in GDP: 27 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
8 6 4 2 Percentage change in GDP: 28 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
8 6 4 2 Percentage change in GDP: 29 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
8 6 4 2 Percentage change in GDP: 21 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
8 6 4 2 Percentage change in GDP: 211 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
8 6 4 2 Percentage change in GDP: 212 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
8 6 4 2 Percentage change in GDP: 213 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
8 6 4 2 Percentage change in GDP: 214 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
8 6 4 2 Percentage change in GDP: 215 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
8 6 4 2 Percentage change in GDP: 216 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
8 6 4 2 Percentage change in GDP: 217 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
8 6 4 2 Percentage change in GDP: 218 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
8 6 4 2 Percentage change in GDP: 219 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
8 6 4 2 Percentage change in GDP: 22 vs. 199 2678.6 271.3 97.4 36.3-2.4-17 -4-6 -8-18 -12-6 6 12 18-28.9-35.7-43 -86.8
movie: distribution of percentage changes in GDP animation: www.econ.yale.edu/smith/distpctgdp1.mp4
Distribution of percentage change in GDP: 2 vs. 199.377281 Fraction 8 1 2 Percentage change in GDP
Distribution of percentage change in GDP: 21 vs. 199.4543 Fraction 8 1 2 Percentage change in GDP
Distribution of percentage change in GDP: 22 vs. 199.258799 Fraction 8 1 2 Percentage change in GDP
Distribution of percentage change in GDP: 23 vs. 199.248245 Fraction 8 1 2 Percentage change in GDP
Distribution of percentage change in GDP: 24 vs. 199.18478 Fraction 8 1 2 Percentage change in GDP
Distribution of percentage change in GDP: 25 vs. 199.18385 Fraction 8 1 2 Percentage change in GDP
Distribution of percentage change in GDP: 26 vs. 199.147369 Fraction 8 1 2 Percentage change in GDP
Distribution of percentage change in GDP: 27 vs. 199.15234 Fraction 8 1 2 Percentage change in GDP
Distribution of percentage change in GDP: 28 vs. 199.139922 Fraction 8 1 2 Percentage change in GDP
Distribution of percentage change in GDP: 29 vs. 199.13243 Fraction 8 1 2 Percentage change in GDP
Distribution of percentage change in GDP: 21 vs. 199.128358 Fraction 8 1 2 Percentage change in GDP
Distribution of percentage change in GDP: 211 vs. 199.11835 Fraction 8 1 2 Percentage change in GDP
Distribution of percentage change in GDP: 212 vs. 199.11974 Fraction 8 1 2 Percentage change in GDP
Distribution of percentage change in GDP: 213 vs. 199.119431 Fraction 8 1 2 Percentage change in GDP
Distribution of percentage change in GDP: 214 vs. 199.115568 Fraction 8 1 2 Percentage change in GDP
Distribution of percentage change in GDP: 215 vs. 199.113538 Fraction 8 1 2 Percentage change in GDP
Distribution of percentage change in GDP: 216 vs. 199.11828 Fraction 8 1 2 Percentage change in GDP
Distribution of percentage change in GDP: 217 vs. 199.18643 Fraction 8 1 2 Percentage change in GDP
Distribution of percentage change in GDP: 218 vs. 199.1878 Fraction 8 1 2 Percentage change in GDP
Distribution of percentage change in GDP: 219 vs. 199.1868 Fraction 8 1 2 Percentage change in GDP
Distribution of percentage change in GDP: 22 vs. 199.18799 Fraction 8 1 2 Percentage change in GDP
movie: level change in gdp, laissez-faire
8 6 4 2 Change in GDP (in millions of $): 2 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
8 6 4 2 Change in GDP (in millions of $): 21 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
8 6 4 2 Change in GDP (in millions of $): 22 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
8 6 4 2 Change in GDP (in millions of $): 23 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
8 6 4 2 Change in GDP (in millions of $): 24 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
8 6 4 2 Change in GDP (in millions of $): 25 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
8 6 4 2 Change in GDP (in millions of $): 26 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
8 6 4 2 Change in GDP (in millions of $): 27 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
8 6 4 2 Change in GDP (in millions of $): 28 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
8 6 4 2 Change in GDP (in millions of $): 29 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
8 6 4 2 Change in GDP (in millions of $): 21 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
8 6 4 2 Change in GDP (in millions of $): 211 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
8 6 4 2 Change in GDP (in millions of $): 212 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
8 6 4 2 Change in GDP (in millions of $): 213 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
8 6 4 2 Change in GDP (in millions of $): 214 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
8 6 4 2 Change in GDP (in millions of $): 215 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
8 6 4 2 Change in GDP (in millions of $): 216 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
8 6 4 2 Change in GDP (in millions of $): 217 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
8 6 4 2 Change in GDP (in millions of $): 218 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
8 6 4 2 Change in GDP (in millions of $): 219 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
8 6 4 2 Change in GDP (in millions of $): 22 vs. 199 7273.7 157.8 45 7.6-2.1-4.8-4 -6-8 -18-12 -6 6 12 18-22.9-87 -377.2-9242.7
movie: percentage change in gdp, taxes
8 6 4 2 Percentage change in GDP: 2 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
8 6 4 2 Percentage change in GDP: 21 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
8 6 4 2 Percentage change in GDP: 22 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
8 6 4 2 Percentage change in GDP: 23 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
8 6 4 2 Percentage change in GDP: 24 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
8 6 4 2 Percentage change in GDP: 25 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
8 6 4 2 Percentage change in GDP: 26 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
8 6 4 2 Percentage change in GDP: 27 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
8 6 4 2 Percentage change in GDP: 28 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
8 6 4 2 Percentage change in GDP: 29 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
8 6 4 2 Percentage change in GDP: 21 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
8 6 4 2 Percentage change in GDP: 211 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
8 6 4 2 Percentage change in GDP: 212 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
8 6 4 2 Percentage change in GDP: 213 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
8 6 4 2 Percentage change in GDP: 214 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
8 6 4 2 Percentage change in GDP: 215 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
8 6 4 2 Percentage change in GDP: 216 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
8 6 4 2 Percentage change in GDP: 217 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
8 6 4 2 Percentage change in GDP: 218 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
8 6 4 2 Percentage change in GDP: 219 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
8 6 4 2 Percentage change in GDP: 22 vs. 199 2678.6 228.4 81.2 26.2-2 -3-19.5-4 -6-8 -18-12 -6 6 12 18-3.2-36.5-43.6-86.8
pictures: winners and losers from tax
8 6 4 2 Welfare gains from taxation (with free capital movement) 1.4 3.9 3.1 2.4-2 1.2 -.2-4 -6-8 -18-12 -6 6 12 18-2.8-6.4-13.5-36.1
8 6 4 2 Welfare gains from taxation (in autarky) 1.4 3.9 3.1 2.4-2 1.2 -.2-4 -6-8 -18-12 -6 6 12 18-2.8-6.4-13.5-36.1
Welfare gains from taxation (with free movement) (as a percentage of consumption).127495 Fraction 3 2 1 1 Percentage of consumption
Welfare gains from taxation (in autarky) (as a percentage of consumption).18378 Fraction 3 2 1 1 Percentage of consumption
Difference in gains from taxation (autarky vs. free movement) (as a percentage of consumption).393553 Fraction.8447 12.88 Percentage of consumption
Welfare changes from tax: summary measures One region = one vote: 56% gain. One person = one vote: 84% gain. One dollar = one vote: 68% gain. Average gain across all regions: 2.11% (of consumption). Average gain weighted by regional GDP:.6%. Average gain weighted by regional population: 1.74%. World consumption path: gain of.37%.
Welfare changes from tax in U.S. and China only One region = one vote: 56% gain (vs. 56%). One person = one vote: 83% gain (vs. 84%). One dollar = one vote: 69% gain (vs. 68%). Average gain across all regions:.55% (vs. 2.11%). Average gain weighted by GDP:.16% (vs..6%). Average gain weighted by population:.44% (vs. 1.74%). World consumption path: gain of.1% (vs..37%). 27% of regions in U.S. gain (vs. 41%). 27% of regions in China gain (vs. 36%). 6% of regions in rest of world gain (vs. 58%).
8 6 4 2 Percentage of population in favor of carbon tax (by country) 1 88.5 77.4 66.3-2 55.2 44-4 -6-8 -18-12 -6 6 12 18 32.9 21.8 1.7
8 6 4 2 Welfare gain from carbon tax (as a percentage of consumption) 4.8 3.2 2.4 1.7-2.9.7-4 -6-8 -18-12 -6 6 12 18-1.5-3.8-4.7-18.8
picture: welfare gains from free capital movement (laissez-faire, then taxes)
Welfare gains from free capital movement (without taxes) (as a percentage of consumption).339343 Fraction.96 19.9441 Percentage of consumption
Welfare gains from free capital movement (with taxes) (as a percentage of consumption).458428 Fraction.612 19.9539 Percentage of consumption
movie: distribution of mpks animation: www.econ.yale.edu/smith/distmpk1.mp4
Distribution of marginal product of capital in 1999 (triangle = unweighted; circle = weighted by GDP).234596.692.8524.1155 Marginal product of capital
Distribution of marginal product of capital in 29 (triangle = unweighted; circle = weighted by GDP).225781.692.8514.1155 Marginal product of capital
Distribution of marginal product of capital in 219 (triangle = unweighted; circle = weighted by GDP).22969.692.857.1155 Marginal product of capital
Distribution of marginal product of capital in 229 (triangle = unweighted; circle = weighted by GDP).251976.692.851.1155 Marginal product of capital
Distribution of marginal product of capital in 239 (triangle = unweighted; circle = weighted by GDP).252178.692.8495.1155 Marginal product of capital
Distribution of marginal product of capital in 249 (triangle = unweighted; circle = weighted by GDP).254956.692.849.1155 Marginal product of capital
Distribution of marginal product of capital in 259 (triangle = unweighted; circle = weighted by GDP).24183.692.8485.1155 Marginal product of capital
Distribution of marginal product of capital in 269 (triangle = unweighted; circle = weighted by GDP).262373.692.8481.1155 Marginal product of capital
Distribution of marginal product of capital in 279 (triangle = unweighted; circle = weighted by GDP).258922.692.8478.1155 Marginal product of capital
Distribution of marginal product of capital in 289 (triangle = unweighted; circle = weighted by GDP).259884.692.8477.1155 Marginal product of capital
Distribution of marginal product of capital in 299 (triangle = unweighted; circle = weighted by GDP).26126.692.8477.1155 Marginal product of capital
Distribution of marginal product of capital in 219 (triangle = unweighted; circle = weighted by GDP).27779.692.848.1155 Marginal product of capital
Distribution of marginal product of capital in 2119 (triangle = unweighted; circle = weighted by GDP).25717.692.8485.1155 Marginal product of capital
Distribution of marginal product of capital in 2129 (triangle = unweighted; circle = weighted by GDP).269914.692.8491.1155 Marginal product of capital
Distribution of marginal product of capital in 2139 (triangle = unweighted; circle = weighted by GDP).27324.692.8499.1155 Marginal product of capital
Distribution of marginal product of capital in 2149 (triangle = unweighted; circle = weighted by GDP).272621.692.857.1155 Marginal product of capital
Distribution of marginal product of capital in 2159 (triangle = unweighted; circle = weighted by GDP).287492.692.8515.1155 Marginal product of capital
Distribution of marginal product of capital in 2169 (triangle = unweighted; circle = weighted by GDP).2798.692.8522.1155 Marginal product of capital
Distribution of marginal product of capital in 2179 (triangle = unweighted; circle = weighted by GDP).26346.692.8528.1155 Marginal product of capital
Distribution of marginal product of capital in 2189 (triangle = unweighted; circle = weighted by GDP).22674.692.8533.1155 Marginal product of capital
Conclusions Take-away: Results from our model: climate change is about relative effects much more than about average effects! In particular, large disagreements about taxes (so large transfer payments needed to compensate those losing from carbon tax). Methodological insight: we thought the market structure (because it admits more or less adaptation) would be important for the results, but it isn t.
Some caveats On one hand, damages too local and symmetric: no common aggregate damages. There are potentially such effects: world technology development (level or growth) can be impacted; biodiversity, ocean acidification,... ; spillovers through trade, migration, tourism,... On other hand, maybe not enough regional heterogeneity yet (rural vs. urban, manufacturing vs. agriculture,... ).
Near-future follow-up Within present model/paper: More on heterogeneous taxes. How does climate change influence migration pressure at borders? Easy to compute. (PICTURE!) Sea-level rise and coastal damages (straightforward to incorporate). Applications: Temperature shocks; can be problematic at higher T s because of extreme weather events (developed new computational tools to handle aggregate uncertainty + transition). Rising volatility as globe warms. Agricultural sector and food supplies (includes adding precipitation)....
8 6 4 2 Log of lifetime wealth (per effective unit of labor) 657.2 162.8 118.8 11-2 88.9 82.7-4 -6-8 -18-12 -6 6 12 18 78.3 75.9 73.1 56.5