Climate Change Around the World
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1 Climate Change Around the World Per Krusell Institute for International Economic Studies, NBER, CEPR Anthony A. Smith, Jr. Yale University, NBER Walras-Bowley Lecture Econometric Society World Congress Montréal Août, 215
2
3 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?
4 The data Unit of analysis: 1 1 cells containing land. The model contains 19, regions (or cell-countries). Nordhaus s G-Econ database: gross domestic product (GDP) and population for all such cells in 199, 1995, 2, and 25. Matsuura and Willmott: gridded (.5.5 ) monthly terrestrial temperature data for
5 Global average land temperature (by year) Year
6 Nordhaus s G-Econ globe with output by regions
7
8
9 same data on our map
10 Log of GDP in Latitude Longitude
11 temperature map of the world
12 Average temperature ( ) Latitude Longitude
13 Natural-science background I: the climate What determines the earth s surface temperature, T s? Energy balance: energy in = energy out. With no atmosphere (treat the Earth as a blackbody ): πr 2 (1 α)i = 4πR 2 σt 4 s, where I is the solar flux intensity, α is Earth s albedo, R is the Earth s radius, and σ is the Stefan-Boltzmann constant. T s is the price that equilibrates the two energy flows. Plug in the constants and solve for T s : Earth too cold by 3 degrees.
14 Natural-science background I: the climate (cont d) The (single) layer model with an opaque atmosphere. Short-wave solar radiation penetrates the atmosphere, but long-wave radiation emitted by the Earth s surface does not. Energy balance for the atmosphere: energy radiated by surface = 2 energy radiated by atmosphere (depends on T 4 a ). Energy balance for the surface: incoming solar energy + energy radiated by atmosphere = energy radiated by surface (depends on T 4 s ). Solve the two equations for T s and T a : Earth s surface too warm by 18 degrees.
15 Natural-science background I: the climate (cont d) The atmosphere is semi-opaque: only part of it consists of greenhouse gases which trap long-wave radiation. 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 feedbacks not present in the (simple) layer model. λ 3 ± 1.5 is climate sensitivity.
16 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).
17 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.
18 Some relevant background from past work Model development: a number of our earlier papers on this can be viewed as pilot studies for present work in particular, Golosov, Hassler, K, and Tsyvinski (GHKT; Econometrica, 214) develops simple one-sector DSGE setting. Build present structure on earlier insights: one-region version of present model very close to GHKT.
19 Overview for remainder of talk 1. our climate modeling 2. our damage specification 3. economic model 4. calibration, computation 5. results 6. conclusions, future
20 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 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 coefficent (linear structure; standard). With help of climate scientists, use runs of (highly) complex climate models into the future to estimate sensitivities.
21 global map with estimated sensitivities: how much temperature goes up everywhere if T rises by one degree
22 Sensitivity to changes in global temperature Latitude Longitude
23 Our damage specification What are the damages in region l as a result of global warming? Damage measurements: overall, weakest part of quantitative climate-economy models, especially for regional damages. Our approach: formulate a damage function D of local temperature that is: common across all l; like Nordhaus s, a TFP drag; and U-shaped, with three parameters which are estimated to match, when aggregated across all l, the global damages estimated by Nordhaus: Nordhaus s formulation: convex three points used: at 1 degree centigrade,.3% output drag; at 2.5, 1.8%; and at 5, 6.8%. Nordhaus s global estimates not much different from those of others (IPCC has recent summary). Desmet and Rossi-Hansberg (214) also use a common U-shape in a spatial application.
24 picture of 1 minus estimated U-shaped damage function, as function of local temperature
25 Damage function: productivity vs. temperature 1.75 Fraction of optimum Temperature (degrees centigrade)
26 gdp distribution across temperatures (you see that most output is near the optimum)
27 Share of world GDP vs. temperature Share of GDP Temperature (degrees centigrade)
28 population distribution across temperatures (similar graph, but less concentrated near optimum)
29 Share of world population vs. temperature Share of population Temperature (degrees centigrade)
30 gdp distribution across 1 minus damages
31 Share of world GDP vs. productivity (as a fraction of optimum) Share of GDP Productivity
32 population distribution across 1 minus damages
33 Share of world population vs. productivity (as a fraction of optimum) Share of population Productivity
34 global map with 1 minus damage coefficients
35 Damage coefficient x 1 (at temperature in ) Latitude Longitude
36 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 tech. 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 ).
37 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 decentralized equilibrium. Set up to deal with shocks, aggregate and/or local.
38 Calibration Annual time step, log utility, δ = 1%, g = 1%, β =.985. Production function F is CES in k α ((1 D)AL) 1 α and Be, with elasticity.1 (we do robustness) and α =.36. Initial distribution of region-specific capital and level of productivity chosen to: (1) match regional GDP per capita in 199 and; (2) equalize MPK across regions. Price of coal and B chosen to match: (1) total carbon emissions in 199; and (2) energy share of 5% along a balanced growth path. Green energy replaces coal slowly (logistic).
39 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.
40 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.
41 Experiments Laissez-faire. Main policy experiment: all regions impose a modest common carbon tax, financed locally (no transfers implied). Throughout: focus on relative effects, not aggregates.
42 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 (55% of regions gain, while 45% lose). Findings almost identical for two extreme market structures (autarky and international capital markets).
43 behavior of aggregates over time
44 Gigatons of atmospheric carbon (no taxes; free capital movement) 1991 Gigatons of carbon Year
45 Gigatons of atmospheric carbon (taxes vs. no taxes; free capital movement) 1991 Gigatons of carbon Year
46 Temperature (degrees centrigrade above pre indudstrial) (no taxes; free capital movement) Degrees centigrade Year
47 Temperature (degrees centrigrade above pre indudstrial) (taxes vs. no taxes; free capital movement) Degrees centigrade Year
48 World GDP (trillions of dollars; detrended) (no taxes; free capital movement) Trillions of dollars Year
49 World GDP (trillions of dollars; detrended) (taxes vs. no taxes; free capital movement) Trillions of dollars Year
50 World consumption (trillions of dollars; detrended) (no taxes; free capital movement) Trillions of dollars Year
51 World consumption (trillions of dollars; detrended) (taxes vs. no taxes; free capital movement) Trillions of dollars Year
52 Global emissions of atmospheric carbon (in gigatons) (no taxes; free capital movement) Gigatons of carbon Year
53 Global emissions of atmospheric carbon (in gigatons) (taxes vs. no taxes; free capital movement) Gigatons of carbon Year
54 movie: distribution of mpks
55 Distribution of marginal product of capital in 1999 (triangle = unweighted; circle = weighted by GDP) Marginal product of capital
56 Distribution of marginal product of capital in 29 (triangle = unweighted; circle = weighted by GDP) Marginal product of capital
57 Distribution of marginal product of capital in 219 (triangle = unweighted; circle = weighted by GDP) Marginal product of capital
58 Distribution of marginal product of capital in 229 (triangle = unweighted; circle = weighted by GDP) Marginal product of capital
59 Distribution of marginal product of capital in 239 (triangle = unweighted; circle = weighted by GDP) Marginal product of capital
60 Distribution of marginal product of capital in 249 (triangle = unweighted; circle = weighted by GDP) Marginal product of capital
61 Distribution of marginal product of capital in 259 (triangle = unweighted; circle = weighted by GDP) Marginal product of capital
62 Distribution of marginal product of capital in 269 (triangle = unweighted; circle = weighted by GDP) Marginal product of capital
63 Distribution of marginal product of capital in 279 (triangle = unweighted; circle = weighted by GDP) Marginal product of capital
64 Distribution of marginal product of capital in 289 (triangle = unweighted; circle = weighted by GDP) Marginal product of capital
65 Distribution of marginal product of capital in 299 (triangle = unweighted; circle = weighted by GDP) Marginal product of capital
66 Distribution of marginal product of capital in 219 (triangle = unweighted; circle = weighted by GDP) Marginal product of capital
67 Distribution of marginal product of capital in 2119 (triangle = unweighted; circle = weighted by GDP) Marginal product of capital
68 Distribution of marginal product of capital in 2129 (triangle = unweighted; circle = weighted by GDP) Marginal product of capital
69 Distribution of marginal product of capital in 2139 (triangle = unweighted; circle = weighted by GDP) Marginal product of capital
70 Distribution of marginal product of capital in 2199 (triangle = unweighted; circle = weighted by GDP) Marginal product of capital
71 Distribution of marginal product of capital in 2299 (triangle = unweighted; circle = weighted by GDP) Marginal product of capital
72 movie: percentage change in gdp, laissez-faire
73 Percentage change in GDP: 2 vs Latitude Longitude
74 Percentage change in GDP: 21 vs Latitude Longitude
75 Percentage change in GDP: 22 vs Latitude Longitude
76 Percentage change in GDP: 23 vs Latitude Longitude
77 Percentage change in GDP: 24 vs Latitude Longitude
78 Percentage change in GDP: 25 vs Latitude Longitude
79 Percentage change in GDP: 26 vs Latitude Longitude
80 Percentage change in GDP: 27 vs Latitude Longitude
81 Percentage change in GDP: 28 vs Latitude Longitude
82 Percentage change in GDP: 29 vs Latitude Longitude
83 Percentage change in GDP: 21 vs Latitude Longitude
84 Percentage change in GDP: 211 vs Latitude Longitude
85 Percentage change in GDP: 212 vs Latitude Longitude
86 Percentage change in GDP: 213 vs Latitude Longitude
87 Percentage change in GDP: 214 vs Latitude Longitude
88 Percentage change in GDP: 215 vs Latitude Longitude
89 Percentage change in GDP: 216 vs Latitude Longitude
90 Percentage change in GDP: 217 vs Latitude Longitude
91 Percentage change in GDP: 218 vs Latitude Longitude
92 Percentage change in GDP: 219 vs Latitude Longitude
93 Percentage change in GDP: 22 vs Latitude Longitude
94 movie: level change in gdp, laissez-faire
95 Change in GDP (in millions of $): 2 vs Latitude Longitude
96 Change in GDP (in millions of $): 21 vs Latitude Longitude
97 Change in GDP (in millions of $): 22 vs Latitude Longitude
98 Change in GDP (in millions of $): 23 vs Latitude Longitude
99 Change in GDP (in millions of $): 24 vs Latitude Longitude
100 Change in GDP (in millions of $): 25 vs Latitude Longitude
101 Change in GDP (in millions of $): 26 vs Latitude Longitude
102 Change in GDP (in millions of $): 27 vs Latitude Longitude
103 Change in GDP (in millions of $): 28 vs Latitude Longitude
104 Change in GDP (in millions of $): 29 vs Latitude Longitude
105 Change in GDP (in millions of $): 21 vs Latitude Longitude
106 Change in GDP (in millions of $): 211 vs Latitude Longitude
107 Change in GDP (in millions of $): 212 vs Latitude Longitude
108 Change in GDP (in millions of $): 213 vs Latitude Longitude
109 Change in GDP (in millions of $): 214 vs Latitude Longitude
110 Change in GDP (in millions of $): 215 vs Latitude Longitude
111 Change in GDP (in millions of $): 216 vs Latitude Longitude
112 Change in GDP (in millions of $): 217 vs Latitude Longitude
113 Change in GDP (in millions of $): 218 vs Latitude Longitude
114 Change in GDP (in millions of $): 219 vs Latitude Longitude
115 Change in GDP (in millions of $): 22 vs Latitude Longitude
116 pictures: map (and histogram) of winners and losers from tax, full equalization (then autarky)
117 Welfare gains from taxation (with free capital movement) Latitude Longitude
118 Welfare gains from taxation (in autarchy) Latitude Longitude
119 Welfare gains from taxation (with free movement) (as a percentage of consumption) Fraction Percentage of consumption
120 Welfare gains from taxation (in autarchy) (as a percentage of consumption) Fraction Percentage of consumption
121 Welfare changes from tax: summary measures One region = one vote: 55% gain. One person = one vote: 83% gain. One dollar = one vote: 65% gain. Average gain across all regions:.81% (of consumption). Average gain weighted by regional GDP:.14%. Average gain weighted by regional population:.46%. World consumption path: gain of.3%.
122 picture: welfare gains from free capital movements (laissez-faire)
123 Welfare gains from free capital movement (without taxes) (as a percentage of consumption) Fraction Percentage of consumption
124 picture: differences in gains from taxation (autarky vs. free capital movements)
125 Difference in gains from taxation (autarchy vs. free movement) (as a percentage of consumption).3673 Fraction Percentage of consumption
126 movie: percentage change in gdp, taxes
127 Percentage change in GDP: 2 vs Latitude Longitude
128 Percentage change in GDP: 21 vs Latitude Longitude
129 Percentage change in GDP: 22 vs Latitude Longitude
130 Percentage change in GDP: 23 vs Latitude Longitude
131 Percentage change in GDP: 24 vs Latitude Longitude
132 Percentage change in GDP: 25 vs Latitude Longitude
133 Percentage change in GDP: 26 vs Latitude Longitude
134 Percentage change in GDP: 27 vs Latitude Longitude
135 Percentage change in GDP: 28 vs Latitude Longitude
136 Percentage change in GDP: 29 vs Latitude Longitude
137 Percentage change in GDP: 21 vs Latitude Longitude
138 Percentage change in GDP: 211 vs Latitude Longitude
139 Percentage change in GDP: 212 vs Latitude Longitude
140 Percentage change in GDP: 213 vs Latitude Longitude
141 Percentage change in GDP: 214 vs Latitude Longitude
142 Percentage change in GDP: 215 vs Latitude Longitude
143 Percentage change in GDP: 216 vs Latitude Longitude
144 Percentage change in GDP: 217 vs Latitude Longitude
145 Percentage change in GDP: 218 vs Latitude Longitude
146 Percentage change in GDP: 219 vs Latitude Longitude
147 Percentage change in GDP: 22 vs Latitude Longitude
148 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.
149 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,... ).
150 Near-future follow-up Within present model/paper: Heterogeneous taxes (results for tax in U.S. and China only). 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 (programming under way). Rising volatility as globe warms. Agricultural sector and food supplies (includes adding precipitation)....
151 Welfare changes from tax: summary measures One region = one vote: 55% gain (vs. 55%) One person = one vote: 62% gain (vs. 83%). One dollar = one vote: 7% gain (vs. 65%) Average gain across all regions:.18% (vs..81%). Average gain weighted by GDP:.4% (vs..14%). Average gain weighted by population:.12% (vs..46%). World consumption path: gain of.7% (vs..3%). 3% of regions in U.S. gain (vs. 42%). 7% of regions in China gain (vs. 3%). 62% of regions in ROW gain (vs. 57%).
152 Log of lifetime wealth (per effective unit of labor) Latitude Longitude
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