Climate Change Around the World Per Krusell Institute for International Economic Studies, NBER, CEPR Anthony A. Smith, Jr. Yale University, NBER
The Society for Economic Measurement’s Third Conference Keynote Address Thessalonki, Greece July 8, 2016
The project I
Construct global model of economy-climate interactions featuring a high degree of geographic resolution (1◦ × 1◦ regions).
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Use the model as a laboratory to quantify the distributional effects of climate change and climate policy.
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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?
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Related to small new literature on spatial equilibrium models of climate change: Desmet and Rossi-Hansberg; Krusell and Hassler; Brock, Engstr¨om, and Xepapadeas.
The data
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Unit of analysis: 1◦ × 1◦ cells containing land.
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The model contains ∼ 19, 000 regions (or cell-countries).
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Matsuura and Willmott: gridded (0.5◦ × 0.5◦ ) monthly terrestrial temperature data for 1900–2008.
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Nordhaus’s G-Econ database: gross domestic product (GDP) and population for all such cells in 1990, 1995, 2000, and 2005.
Average temperature (1901-1920) 30.8
80 26
60 23.8
40 20.4
Latitude
20 14.7
0 8.7
-20 2.9
-40 -2.2
-60 -8.9
-80 -64.7
-180
-120
-60
0
Longitude
60
120
180
Global average land temperature (by year) 10.3
10
9.6
9.2
8.8 1901
1920
1940
1960 Year
1980
2008
Log of GDP in 1990 6.6
80 0.9
60 -0.1
40 -1.1
Latitude
20 -2
0 -2.9
-20 -3.7
-40 -4.6
-60 -6
-80 -9.2
-180
-120
-60
0
Longitude
60
120
180
Natural-science background I: the climate I
Energy balance (inflow from the Sun equals outflow from the Earth) determines the Earth’s temperature.
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“Forcing”, F , from CO2 in the atmosphere (relative to pre-industrial) is: ¯ ln(S/S) , F =η ln(2) where S = 840GtC and S¯ = 600GtC are current and pre-industrial stocks.
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Equilibrium temperature, T (relative to pre-industrial), is: T = κF = λ
¯ ln(S/S) , ln(2)
where κ depends on various feedback effects. I
λ ≈ 3 ± 1.5 is “climate sensitivity”.
Natural-science background II: the carbon cycle I
Carbon cycle: how emissions of CO2 enter/exit atmosphere.
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Key: emissions spread globally very quickly (“global externality”). Depreciation structure of atmospheric CO2 :
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smooth, but very slow; some stays “forever” in atmosphere nonlinear but linear approximation okay.
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Emissions: 10GtC/year; ∆St ≈ 4.5GtC/year.
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Estimated remaining carbon: oil + gas = 300GtC, coal much bigger (> 3,000GtC?). So coal is key!
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To summarize: emissions → carbon in atmosphere → forcing → temperature.
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Bad if higher T causes “damages”: the mother of all externalities (Stern).
Integrated assessment models I I
Pioneered by Nordhaus (DICE, RICE). Quantitative theory, computational. Key components: I I I
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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: I I I
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 (2014)
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? I
Answer given by complex global and regional climate models. But not feasible (yet) to combine these with economic model.
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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.
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Capture sensitivity of temperature in region ℓ to global temperature T in a coefficent (linear structure; standard).
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With help of climate scientists, use runs of (highly) complex climate models into the future to estimate sensitivities.
Sensitivity to changes in global temperature 5.2
80 2.2
60 1.7
40 1.4
Latitude
20 1.3
0 1.2
-20 1.1
-40 1
-60 0.8
-80 0.4
-180
-120
-60
0
Longitude
60
120
180
Our damage specification What are the damages in region ℓ as a result of global warming? I
Damage measurements: overall the weakest part of quantitative climate-economy models, especially for regional damages.
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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:
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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 (2014) also use a common U-shape in a spatial application.
Nordhaus’s damage function (percentage of GDP) 7 6
Percentage
5 4 3 2 1 0 0
1
2 3 Temperature
4
5
Damage function: productivity vs. temperature 1
Fraction of optimum
.75
.5
.25
.02 −32
−20
−10 0 11.6 Temperature (degrees centigrade)
20
32
Share of world GDP vs. temperature
Share of GDP
4.53732
0 −32
−20
−10 0 11.6 Temperature (degrees centigrade)
20
32
Share of world population vs. temperature
Share of population
5.67524
0 −32
−20
−10 0 11.6 Temperature (degrees centigrade)
20
32
Share of world GDP vs. productivity (as a fraction of optimum)
Share of GDP
21.8995
.010076 .25
.5
.75 Productivity
.9
.995
Share of world population vs. productivity (as a fraction of optimum)
Share of population
10.6286
.005168 .25
.5
.75 Productivity
.9
.995
Damage coefficient x 100 (at temperature in 1901-1920) 100
80 96.5
60 87.6
40 76
Latitude
20 65.5
0 57.2
-20 50.6
-40 40.9
-60 16.5
-80 2
-180
-120
-60
0
Longitude
60
120
180
The economic model I
Forward-looking consumers and firms in each region determine their consumption, saving, and energy use. No migration.
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Neoclassical production technologies, different TFPs both exogenously and due to climate.
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Energy as an input: coal, produced locally, at constant marginal cost (no profits).
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Coal slowly, exogenously replaced by (same-cost) green energy. Market structure: two cases.
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Autarky (regions only linked via emission externality). Unrestricted borrowing/lending (world interest rate clears market).
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Summary: like Aiyagari (1994) and our previous work, though no shocks in this version.
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Adaptation: consumption smoothing and, in case with international markets, capital mobility (“leakage”).
Regional problem In a recursive equilibrium, region ℓ solves ¯ S; ℓ) = I vt (ω, A, k, maxk ′ ,b′ [U(c) + β vt+1 (ω ′ , A′ , k¯ ′ , S ′ ; ℓ)], s.t. ¯ S)b ′ c = ω − k ′ − qt (k, ω ′ = max [F (k ′ , (1 − D(Tℓ (S ′ )))A′ , e ′ ) − pe ′ )] + ′ e
(1 − δ)k ′ + b ′ A′ = (1 + g )A ¯ S) k¯ ′ = Ht (k, ( ) ′ ¯ S . S = Φt k, I
Can be interpreted as decentralized equilibrium.
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Set up to deal with shocks, aggregate and/or local.
Calibration I I
Annual time step, log utility, discount factor β = 0.985. Production function in region ℓ: CES in kℓα ((1 − Dℓ )Aℓ L)1−α and energy eℓ , with: I I I I
share parameter θ; elasticity = (1 − ρ)−1 (set ρ = 0 for now); α = 0.36; Aℓ grows at rate g = 1%.
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Capital depreciates at rate δ = 6%.
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Initial distribution of region-specific capital, kℓ , and level of productivity, Aℓ , chosen to: (1) match regional GDP per capita in 1990 and; (2) equalize MPKs across regions.
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Price of coal and θ chosen to match: (1) total carbon emissions in 1990; and (2) energy share of 6% along a balanced growth path.
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Green energy replaces coal slowly (logistic).
Fraction of carbon emissions abated 1
Fraction
.75
.5
.25
0 1990
2090
2190 Year
2290
Carbon cycle
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The total stock of atmospheric carbon, St , is the sum of a permanent stock, S1t , and a (slowly) depreciating stock, S2t : St = S1t + S2t .
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S1t = 0.25Et + S1,t−1 , where Et is total carbon emissions.
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S2t = 0.36(1 − 0.25)Et + 0.998S2,t−1 .
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Half-life of a freshly-emitted unit of carbon is 30 years; half-life of the depreciating stock (given no new emissions) is 300 years.
Computation I
Richard Feynman: Imagine how much harder physics would be if electrons had feelings!
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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:
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exogenous TFP wealth/capital ℓ captures entire path of future regional TFP endogenous to climate (this feature NOT one-dimensional); I I I
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we don’t actually solve 19,235 DP problems but so much heterogeneity that we need to solve 700 DPs and then nonlinearly interpolate decision rules between 700 “types”.
Fortran 90 + OpenMP with 20 cores: less than five minutes.
Experiments
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Laissez-faire.
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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
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Climate change affects regions very differently. Stakes big at regional level.
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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).
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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)
Gigatons of carbon
13.7765
0 1990
2090
2190 Year
2290
2390
Optimal carbon tax (dollars per GtC)
Dollars
1158.2
49.3421 2288
1990 Year
Global emissions of atmospheric carbon (in gigatons) (taxes vs. no taxes; free capital movement)
Gigatons of carbon
13.7765
0 1990
2090
2190 Year
2290
2390
Gigatons of atmospheric carbon (no taxes; free capital movement)
Gigatons of carbon
1607.5
768.754 1990
2090
2190 Year
2290
2390
Gigatons of atmospheric carbon (taxes vs. no taxes; free capital movement)
Gigatons of carbon
1607.5
768.115 1990
2090
2190 Year
2290
2390
Temperature (degrees centrigrade above pre−indudstrial) (no taxes; free capital movement)
Degrees centigrade
4.40464
1.21195 1990
2090
2190 Year
2290
2390
Temperature (degrees centrigrade above pre−indudstrial) (taxes vs. no taxes; free capital movement)
Degrees centigrade
4.40464
1.20835 1990
2090
2190 Year
2290
2390
World GDP (trillions of dollars; detrended) (no taxes; free capital movement)
Trillions of dollars
30.5506
28.2934 1990
2090
2190 Year
2290
2390
World GDP (trillions of dollars; detrended) (taxes vs. no taxes; free capital movement)
Trillions of dollars
30.5506
28.2934 1990
2090
2190 Year
2290
2390
World consumption (trillions of dollars; detrended) (no taxes; free capital movement)
Trillions of dollars
21.7
19.9 1990
2090
2190 Year
2290
2390
World consumption (trillions of dollars; detrended) (taxes vs. no taxes; free capital movement)
Trillions of dollars
21.7
19.9 1990
2090
2190 Year
2290
2390
movie: temperature, laissez-faire
Temperature in 2000 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
Temperature in 2010 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
Temperature in 2020 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
Temperature in 2030 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
Temperature in 2040 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
Temperature in 2050 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
Temperature in 2060 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
Temperature in 2070 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
Temperature in 2080 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
Temperature in 2090 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
Temperature in 2100 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
Temperature in 2110 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
Temperature in 2120 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
Temperature in 2130 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
Temperature in 2140 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
Temperature in 2150 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
Temperature in 2160 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
Temperature in 2170 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
Temperature in 2180 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
Temperature in 2190 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
Temperature in 2200 35.7
80 30.3
60 28.1
40 24.8
Latitude
20 19.2
0 13.6
-20 9.1
-40 5.2
-60 -0.2
-80 -29.5
-180
-120
-60
0
Longitude
60
120
180
movie: 1 minus damage coefficient, laissez-faire
Damage coefficient (x 100) in 2000 100
80 98.1
60 92.6
40 83.2
Latitude
20 70.2
0 56.2
-20 45.9
-40 38.1
-60 32.2
-80 2
-180
-120
-60
0
Longitude
60
120
180
Damage coefficient (x 100) in 2010 100
80 98.1
60 92.6
40 83.2
Latitude
20 70.2
0 56.2
-20 45.9
-40 38.1
-60 32.2
-80 2
-180
-120
-60
0
Longitude
60
120
180
Damage coefficient (x 100) in 2020 100
80 98.1
60 92.6
40 83.2
Latitude
20 70.2
0 56.2
-20 45.9
-40 38.1
-60 32.2
-80 2
-180
-120
-60
0
Longitude
60
120
180
Damage coefficient (x 100) in 2030 100
80 98.1
60 92.6
40 83.2
Latitude
20 70.2
0 56.2
-20 45.9
-40 38.1
-60 32.2
-80 2
-180
-120
-60
0
Longitude
60
120
180
Damage coefficient (x 100) in 2040 100
80 98.1
60 92.6
40 83.2
Latitude
20 70.2
0 56.2
-20 45.9
-40 38.1
-60 32.2
-80 2
-180
-120
-60
0
Longitude
60
120
180
Damage coefficient (x 100) in 2050 100
80 98.1
60 92.6
40 83.2
Latitude
20 70.2
0 56.2
-20 45.9
-40 38.1
-60 32.2
-80 2
-180
-120
-60
0
Longitude
60
120
180
Damage coefficient (x 100) in 2060 100
80 97.9
60 92.4
40 83.1
Latitude
20 70.6
0 56.6
-20 46.1
-40 38.2
-60 32.3
-80 2
-180
-120
-60
0
Longitude
60
120
180
Damage coefficient (x 100) in 2070 100
80 97.9
60 92.4
40 83.1
Latitude
20 70.6
0 56.6
-20 46.1
-40 38.2
-60 32.3
-80 2
-180
-120
-60
0
Longitude
60
120
180
Damage coefficient (x 100) in 2080 100
80 97.9
60 92.4
40 83.1
Latitude
20 70.6
0 56.6
-20 46.1
-40 38.2
-60 32.3
-80 2
-180
-120
-60
0
Longitude
60
120
180
Damage coefficient (x 100) in 2090 100
80 97.9
60 92.4
40 83.1
Latitude
20 70.6
0 56.6
-20 46.1
-40 38.2
-60 32.3
-80 2
-180
-120
-60
0
Longitude
60
120
180
Damage coefficient (x 100) in 2100 100
80 97.9
60 92.4
40 83.1
Latitude
20 70.6
0 56.6
-20 46.1
-40 38.2
-60 32.3
-80 2
-180
-120
-60
0
Longitude
60
120
180
Damage coefficient (x 100) in 2110 100
80 97.9
60 92.4
40 83.1
Latitude
20 70.6
0 56.6
-20 46.1
-40 38.2
-60 32.3
-80 2
-180
-120
-60
0
Longitude
60
120
180
Damage coefficient (x 100) in 2120 100
80 97.9
60 92.4
40 83.1
Latitude
20 70.6
0 56.6
-20 46.1
-40 38.2
-60 32.3
-80 2
-180
-120
-60
0
Longitude
60
120
180
Damage coefficient (x 100) in 2130 100
80 97.9
60 92.4
40 83.1
Latitude
20 70.6
0 56.6
-20 46.1
-40 38.2
-60 32.3
-80 2
-180
-120
-60
0
Longitude
60
120
180
Damage coefficient (x 100) in 2140 100
80 97.9
60 92.4
40 83.1
Latitude
20 70.6
0 56.6
-20 46.1
-40 38.2
-60 32.3
-80 2
-180
-120
-60
0
Longitude
60
120
180
Damage coefficient (x 100) in 2150 100
80 97.9
60 92.4
40 83.1
Latitude
20 70.6
0 56.6
-20 46.1
-40 38.2
-60 32.3
-80 2
-180
-120
-60
0
Longitude
60
120
180
Damage coefficient (x 100) in 2160 100
80 97.9
60 92.4
40 83.1
Latitude
20 70.6
0 56.6
-20 46.1
-40 38.2
-60 32.3
-80 2
-180
-120
-60
0
Longitude
60
120
180
Damage coefficient (x 100) in 2170 100
80 97.9
60 92.4
40 83.1
Latitude
20 70.6
0 56.6
-20 46.1
-40 38.2
-60 32.3
-80 2
-180
-120
-60
0
Longitude
60
120
180
Damage coefficient (x 100) in 2180 100
80 97.9
60 92.4
40 83.1
Latitude
20 70.6
0 56.6
-20 46.1
-40 38.2
-60 32.3
-80 2
-180
-120
-60
0
Longitude
60
120
180
Damage coefficient (x 100) in 2190 100
80 97.9
60 92.4
40 83.1
Latitude
20 70.6
0 56.6
-20 46.1
-40 38.2
-60 32.3
-80 2
-180
-120
-60
0
Longitude
60
120
180
Damage coefficient (x 100) in 2200 100
80 97.9
60 92.4
40 83.1
Latitude
20 70.6
0 56.6
-20 46.1
-40 38.2
-60 32.3
-80 2
-180
-120
-60
0
Longitude
60
120
180
movie: percentage change in gdp, laissez-faire
Percentage change in GDP: 2000 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2010 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2020 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2030 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2040 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2050 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2060 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2070 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2080 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2090 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2100 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2110 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2120 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2130 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2140 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2150 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2160 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2170 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2180 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2190 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2200 vs. 1990 2678.6
80 271.3
60 97.4
40 36.3
Latitude
20 0.4
0 -17
-20 -28.9
-40 -35.7
-60 -43
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
movie: distribution of percentage changes in GDP
Distribution of percentage change in GDP: 2000 vs. 1990
Fraction
.377281
0 −80
0
100 Percentage change in GDP
200
Distribution of percentage change in GDP: 2010 vs. 1990
Fraction
.405043
0 −80
0
100 Percentage change in GDP
200
Distribution of percentage change in GDP: 2020 vs. 1990
Fraction
.258799
0 −80
0
100 Percentage change in GDP
200
Distribution of percentage change in GDP: 2030 vs. 1990
Fraction
.248245
0 −80
0
100 Percentage change in GDP
200
Distribution of percentage change in GDP: 2040 vs. 1990
Fraction
.184078
0 −80
0
100 Percentage change in GDP
200
Distribution of percentage change in GDP: 2050 vs. 1990
Fraction
.18385
0 −80
0
100 Percentage change in GDP
200
Distribution of percentage change in GDP: 2060 vs. 1990
Fraction
.147369
0 −80
0
100 Percentage change in GDP
200
Distribution of percentage change in GDP: 2070 vs. 1990
Fraction
.150234
0 −80
0
100 Percentage change in GDP
200
Distribution of percentage change in GDP: 2080 vs. 1990
Fraction
.139922
0 −80
0
100 Percentage change in GDP
200
Distribution of percentage change in GDP: 2090 vs. 1990
Fraction
.132043
0 −80
0
100 Percentage change in GDP
200
Distribution of percentage change in GDP: 2100 vs. 1990
Fraction
.128358
0 −80
0
100 Percentage change in GDP
200
Distribution of percentage change in GDP: 2110 vs. 1990
Fraction
.11835
0 −80
0
100 Percentage change in GDP
200
Distribution of percentage change in GDP: 2120 vs. 1990
Fraction
.119074
0 −80
0
100 Percentage change in GDP
200
Distribution of percentage change in GDP: 2130 vs. 1990
Fraction
.119431
0 −80
0
100 Percentage change in GDP
200
Distribution of percentage change in GDP: 2140 vs. 1990
Fraction
.115568
0 −80
0
100 Percentage change in GDP
200
Distribution of percentage change in GDP: 2150 vs. 1990
Fraction
.113538
0 −80
0
100 Percentage change in GDP
200
Distribution of percentage change in GDP: 2160 vs. 1990
Fraction
.110828
0 −80
0
100 Percentage change in GDP
200
Distribution of percentage change in GDP: 2170 vs. 1990
Fraction
.108643
0 −80
0
100 Percentage change in GDP
200
Distribution of percentage change in GDP: 2180 vs. 1990
Fraction
.10878
0 −80
0
100 Percentage change in GDP
200
Distribution of percentage change in GDP: 2190 vs. 1990
Fraction
.10868
0 −80
0
100 Percentage change in GDP
200
Distribution of percentage change in GDP: 2200 vs. 1990
Fraction
.108799
0 −80
0
100 Percentage change in GDP
200
movie: level change in gdp, laissez-faire
Change in GDP (in millions of $): 2000 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
Change in GDP (in millions of $): 2010 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
Change in GDP (in millions of $): 2020 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
Change in GDP (in millions of $): 2030 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
Change in GDP (in millions of $): 2040 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
Change in GDP (in millions of $): 2050 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
Change in GDP (in millions of $): 2060 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
Change in GDP (in millions of $): 2070 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
Change in GDP (in millions of $): 2080 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
Change in GDP (in millions of $): 2090 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
Change in GDP (in millions of $): 2100 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
Change in GDP (in millions of $): 2110 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
Change in GDP (in millions of $): 2120 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
Change in GDP (in millions of $): 2130 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
Change in GDP (in millions of $): 2140 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
Change in GDP (in millions of $): 2150 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
Change in GDP (in millions of $): 2160 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
Change in GDP (in millions of $): 2170 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
Change in GDP (in millions of $): 2180 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
Change in GDP (in millions of $): 2190 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
Change in GDP (in millions of $): 2200 vs. 1990 70273.7
80 157.8
60 45
40 7.6
Latitude
20 0.1
0 -4.8
-20 -22.9
-40 -87
-60 -377.2
-80 -92042.7
-180
-120
-60
0
Longitude
60
120
180
movie: percentage change in gdp, taxes
Percentage change in GDP: 2000 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2010 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2020 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2030 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2040 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2050 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2060 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2070 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2080 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2090 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2100 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2110 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2120 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2130 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2140 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2150 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2160 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2170 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2180 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2190 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
Percentage change in GDP: 2200 vs. 1990 2678.6
80 228.4
60 81.2
40 26.2
Latitude
20 -3
0 -19.5
-20 -30.2
-40 -36.5
-60 -43.6
-80 -86.8
-180
-120
-60
0
Longitude
60
120
180
pictures: winners and losers from tax
Welfare gains from taxation (with free capital movement) 10.4
80 3.9
60 3.1
40 2.4
Latitude
20 1.2
0 -0.2
-20 -2.8
-40 -6.4
-60 -13.5
-80 -36.1
-180
-120
-60
0
Longitude
60
120
180
Welfare gains from taxation (in autarky) 10.4
80 3.9
60 3.1
40 2.4
Latitude
20 1.2
0 -0.2
-20 -2.8
-40 -6.4
-60 -13.5
-80 -36.1
-180
-120
-60
0
Longitude
60
120
180
Welfare gains from taxation (with free movement) (as a percentage of consumption)
Fraction
.127495
0 −30
−20
−10 Percentage of consumption
0
10
Welfare gains from taxation (in autarky) (as a percentage of consumption)
Fraction
.108378
0 −30
−20
−10 Percentage of consumption
0
10
Difference in gains from taxation (autarky vs. free movement) (as a percentage of consumption)
Fraction
.393553
0 12.808
−.008447 Percentage of consumption
Welfare changes from tax: summary measures
I
One region = one vote: 56% gain.
I
One person = one vote: 84% gain.
I
One dollar = one vote: 68% gain.
I
Average gain across all regions: −2.11% (of consumption).
I
Average gain weighted by regional GDP: 0.60%.
I
Average gain weighted by regional population: 1.74%.
I
World consumption path: gain of 0.37%.
Welfare changes from tax in U.S. and China only
I
One region = one vote: 56% gain (vs. 56%).
I
One person = one vote: 83% gain (vs. 84%).
I
One dollar = one vote: 69% gain (vs. 68%).
I
Average gain across all regions: −0.55% (vs. −2.11%).
I
Average gain weighted by GDP: 0.16% (vs. 0.60%).
I
Average gain weighted by population: 0.44% (vs. 1.74%).
I
World consumption path: gain of 0.10% (vs. 0.37%).
I
27% of regions in U.S. gain (vs. 41%).
I
27% of regions in China gain (vs. 36%).
I
60% of regions in rest of world gain (vs. 58%).
picture: welfare gains from free capital movement (laissez-faire, then taxes)
Welfare gains from free capital movement (without taxes) (as a percentage of consumption)
Fraction
.339343
0 19.9441
−.000096 Percentage of consumption
Welfare gains from free capital movement (with taxes) (as a percentage of consumption)
Fraction
.458428
0 19.9539
−.00612 Percentage of consumption
movie: distribution of mpks
Distribution of marginal product of capital in 1999 (triangle = unweighted; circle = weighted by GDP) .234596
0 .0692
.08524 Marginal product of capital
.1155
Distribution of marginal product of capital in 2009 (triangle = unweighted; circle = weighted by GDP) .225781
0 .0692
.08514 Marginal product of capital
.1155
Distribution of marginal product of capital in 2019 (triangle = unweighted; circle = weighted by GDP) .22969
0 .0692
.08507 Marginal product of capital
.1155
Distribution of marginal product of capital in 2029 (triangle = unweighted; circle = weighted by GDP) .251976
0 .0692
.08501 Marginal product of capital
.1155
Distribution of marginal product of capital in 2039 (triangle = unweighted; circle = weighted by GDP) .252178
0 .0692
.08495 Marginal product of capital
.1155
Distribution of marginal product of capital in 2049 (triangle = unweighted; circle = weighted by GDP) .254956
0 .0692
.0849 Marginal product of capital
.1155
Distribution of marginal product of capital in 2059 (triangle = unweighted; circle = weighted by GDP) .241803
0 .0692
.08485 Marginal product of capital
.1155
Distribution of marginal product of capital in 2069 (triangle = unweighted; circle = weighted by GDP) .262373
0 .0692
.08481 Marginal product of capital
.1155
Distribution of marginal product of capital in 2079 (triangle = unweighted; circle = weighted by GDP) .258922
0 .0692
.08478 Marginal product of capital
.1155
Distribution of marginal product of capital in 2089 (triangle = unweighted; circle = weighted by GDP) .259884
0 .0692
.08477 Marginal product of capital
.1155
Distribution of marginal product of capital in 2099 (triangle = unweighted; circle = weighted by GDP) .261026
0 .0692
.08477 Marginal product of capital
.1155
Distribution of marginal product of capital in 2109 (triangle = unweighted; circle = weighted by GDP) .270779
0 .0692
.0848 Marginal product of capital
.1155
Distribution of marginal product of capital in 2119 (triangle = unweighted; circle = weighted by GDP) .25717
0 .0692
.08485 Marginal product of capital
.1155
Distribution of marginal product of capital in 2129 (triangle = unweighted; circle = weighted by GDP) .269914
0 .0692
.08491 Marginal product of capital
.1155
Distribution of marginal product of capital in 2139 (triangle = unweighted; circle = weighted by GDP) .270324
0 .0692
.08499 Marginal product of capital
.1155
Distribution of marginal product of capital in 2149 (triangle = unweighted; circle = weighted by GDP) .272621
0 .0692
.08507 Marginal product of capital
.1155
Distribution of marginal product of capital in 2159 (triangle = unweighted; circle = weighted by GDP) .287492
0 .0692
.08515 Marginal product of capital
.1155
Distribution of marginal product of capital in 2169 (triangle = unweighted; circle = weighted by GDP) .27098
0 .0692
.08522 Marginal product of capital
.1155
Distribution of marginal product of capital in 2179 (triangle = unweighted; circle = weighted by GDP) .263406
0 .0692
.08528 Marginal product of capital
.1155
Distribution of marginal product of capital in 2189 (triangle = unweighted; circle = weighted by GDP) .226704
0 .0692
.08533 Marginal product of capital
.1155
Conclusions
Take-away: I
Results from our model: climate change is about relative effects much more than about average effects!
I
In particular, large disagreements about taxes (so large transfer payments needed to compensate those losing from carbon tax).
I
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
I
On one hand, damages “too local” and symmetric: no common aggregate damages. There are potentially such effects: I
I I
I
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: I
More on heterogeneous taxes.
I
How does climate change influence migration pressure at borders? Easy to compute. (PICTURE!)
I
Sea-level rise and coastal damages (straightforward to incorporate).
Applications: I
Temperature shocks; can be problematic at higher T s because of extreme weather events (developed new computational tools to handle aggregate uncertainty + transition).
I
Rising volatility as globe warms.
I
Agricultural sector and food supplies (includes adding precipitation).
I
...
Log of lifetime wealth (per effective unit of labor) 657.2
80 162.8
60 118.8
40 101
Latitude
20 88.9
0 82.7
-20 78.3
-40 75.9
-60 73.1
-80 56.5
-180
-120
-60
0
Longitude
60
120
180
