Climate Change Around the World

Transcription

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

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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

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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