a global economy-climate model with high regional resolution · markets capital flows with a...
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A Global Economy-Climate Model with
High Regional Resolution
Per KrusellIIES, University of Goteborg, CEPR, NBER
Anthony A. Smith, Jr.Yale University, NBER
March 2014
WORK-IN-PROGRESS!!!
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Overall goals of the paper
1. Push out the frontier in “integrated-assessment” modelling(beyond Nordhaus’s DICE and RICE).
2. Build a quantitative model of global economy-climateinteractions featuring:
◮ a full microfoundation to permit standard welfare analysis;◮ a very large number of regions;◮ uncertainty about climatic, meteorological, and other shocks;◮ a high degree of region-specific detail; and◮ rich economic interactions between regions (e.g., trade and
insurance).
3. Use the model to provide quantitative evaluations of thedistributional effects of climate-related policies.
4. Study the effects of heterogeneous policy (differential carbontaxes or differential tariffs on “carbon content”).
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Outline
◮ Regional data on GDP and temperature.
◮ A baseline model with (exogenous) temperature shocks.
◮ Calibration and results.
◮ The model with economy-climate feedback.
◮ Calibration and results.
◮ Tax experiments.
◮ Future steps.
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Weather and climate
◮ Weather: stochastic fluctuations in temperature around atrend.
◮ Climate: the average of weather.
◮ Secular trends in climate stemming from carbon emissions.
◮ Cyclical and secular movements in temperature both affecteconomic outcomes (via changes in total factor productivity,or TFP).
◮ First incorporate weather, then add climate.
◮ To be completed: secular trend in the variance of shocks totemperature.
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Geographical structure
I The unit of analysis is a 1◦ × 1◦ cell containing land.
I Nordhaus’s G-Econ database: GDP and population for allsuch cells in 1990, 1995, 2000, and 2005.
I ∼ 17, 000 cells are economically active and ∼ 2, 000 of theseinclude more than one country. The economic model then has∼ 19, 000 “regions” (or cell-countries).
I Matsuura and Willmott: gridded (0.5◦ × 0.5◦) annualterrestrial temperature data for 1900–2008, aggregated to∼ 25, 000 1◦ × 1◦ cells.
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Number of economically active cells
Num
ber
Latitude−90 −60 −30 0 30 60 89
0
100
200
285
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Share of world GDP in 1990
Sha
re (
perc
enta
ge)
Latitude−90 −60 −30 0 30 60 89
0
2
4
6
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Share of world population in 1990
Sha
re (
perc
enta
ge)
Latitude−90 −60 −30 0 30 60 89
0
1
2
3.2
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GCP per capita in 1990
GC
P p
er c
apita
Latitude−56 −30 0 30 60 84
1
10
20
30
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Global average land temperature (by year)
Year1901 1920 1940 1960 1980 2008
8.8
9.2
9.6
10
10.3
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Regional GDP and temperature: panel evidence
◮ Follow Dell, Jones, and Olken (2009), but use cells ratherthan countries as the unit of analysis:
yit = φ1Tit + log(Ait)
∆ log(Ait) = gi + φ2Tit + time fixed effects + error
◮ Main Dell et al regression:
git = gi + φ1 ·Tit − Ti ,t−5
5+ φ2 · 5
−1
4∑
j=0
Ti ,t−j + stuff,
where git is average annual growth rate in GDP per capitaover the last 5 years.
◮ φ1 is a “level” effect and φ2 is a “growth-rate” effect.
◮ Captures effects of temperature “shocks”, not changingclimate.
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Panel results
φ1 φ2 # cells
All cells −1.65 (0.11) −0.09 (0.07) 17181Pop. > 50K in 1990 −1.79 (0.24) 0.35 (0.13) 6665High income in 1990 −1.81 (0.12) −0.13 (0.08) 8580Low income in 1990 −0.58 (0.21) 1.37 (0.14) 8581
High income, pop. > 50K −3.62 (0.41) 0.42 (0.20) 2151Low income, pop. > 50K −0.58 (0.28) 0.47 (0.18) 4514
Need to:
◮ account for measurement error using Nordhaus’s estimates;
◮ check robustness to aggregation of cells.
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A global equilibrium model with shocks to temperature
◮ Temperature shocks are embedded in a global macroeconomicmodel that builds on:
1. Bewley-Huggett-Aiyagari: a continuum of “regions”, or pointson the globe, hit by shocks and interacting in limited financialmarkets; and
2. Castro-Covas-Angeletos: each region is an “entrepreneur”endowed with a (region-specific) production technology.
◮ Preferences of the consumer/entrepreneur in region i :E0
∑∞t=0
βt U(cit), where cit is consumption expenditures.
◮ Technology: yit = exp(−θzit) F (kit ,AitLit , eit), where: yit isGDP; kit is the physical capital stock; eit is (carbon) energy incoal equivalents; and Ait is labor productivity.
◮ θ captures economic “damages” caused by deviations, zit , ofregional temperature from its expected value.
◮ Ait grows at a constant rate; the vector {zit} is stochastic.
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Markets
◮ Capital flows with a one-year lag subject to (regional)restrictions on borrowing.
◮ Labor supply is fixed and immobile.
◮ No equity or insurance markets, but regions can self-insure bytrading a risk-free bond in a global market.
◮ Each region has a nontrivial portfolio problem: invest in itsown physical capital and/or take a position in the bondmarket.
◮ Energy is produced at a constant marginal cost, which equalsthe price of energy in a perfectly competitive global energymarket.
◮ Remark : The model allows for adaptation in the form ofmovements of resources in response to productivity differencesacross regions (and it allows for “leakage” in response todifferential carbon policy).
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Dynamic program of a typical region
◮ Region-specific state variables: wealth, ω; trend inproductivity, A; regional temperature shock, z . Aggregatestate variables: global capital, k ; (weighted) averagetemperature shock, z.
◮ v(ω, z ,A, k , z) =maxk′,b′ [U(c) + βEz ′,z ′|z ,z v(ω
′, z ′,A′, k ′, z ′)], subject to:
c = ω − k ′ − q(k , z)b′
ω′ = maxe′
[exp(−θz ′) F (k ′,A′, e′)− pe′)] + (1− δ)k ′ + b′
A′ = (1 + g)A
b′ ≥ b(k ′)
k ′ = H(k , z)
and a conditional distribution for (z ′, z ′) given (z , z).
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Approximate aggregation
◮ Definition of equilibrium: the bond-pricing function q clearsthe bond market and the optimal decisions of the regionsgenerate H and the density f (z ′|z).
◮ Use global capital and (weighted) average shock as statevariables rather than full joint distribution over capital andshocks.
◮ Use algorithm from Krusell and Smith (1997): guess on(q,H, f ); solve for decision rules; simulate evolution of thedistribution, allowing the bond price to deviate in each periodfrom the bond pricing function so as to clear the bond market;update guesses for (q,H, f ).
◮ In the calibrated economy, regions can make very accurateforecasts of current and future interest rates (and globalenergy emissions) using the limited set of state variables.
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Calibration
◮ Annual model with log period utility.
◮ Discount factor of 0.985 and annual depreciation rate of 10%.
◮ Can borrow up to b(k ′) = γ(δ − 1)k ′; set γ = 0.1.
◮ Production function is CES in kα(AL)1−α and Be, withelasticity 0.1.
◮ Annual growth rate of labor-augmenting productivity is 1%.
◮ Initial distribution of region-specific capital and level ofproductivity chosen to: (1) match regional GDP per capita in1990 and; (2) equalize the marginal product of capital acrossregions.
◮ Price of “coal” and B chosen to match: (1) total carbonemissions in 1990; and (2) energy share of 5% along abalanced growth path.
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A stochastic process for regional temperature
◮ Use gridded temperature data to estimate a stochastic processfor regional temperature.
◮ An exercise in (empirical) statistical downscaling.
◮ The downscaling model:
Tit = Ti + f (ℓi ;ψ1)Tt + zit
zit = ρzi ,t−1 + νit
var(νit) = σ2ν
corr(νit , νjt) = g(d(i , j);ψ2)
◮ Allows for: (i) region-specific dependence of regionaltemperature on global temperature; (ii) autocorrelation; and(iii) spatial correlation.
◮ Estimates: ρ = 0.41, σν = 0.72.
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Change in regional temperature(in response to a 1−degree increase in global temperature)
Cha
nge
in te
mpe
ratu
re
Latitude−90 −60 −30 0 30 60 90
.26
.5
1
1.5
2
2.5
3
3.6
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Spatial correlation of temperature shocks
Cor
rela
tion
Distance (000s of kilometers)0 1 2 3 4 5 6
0
.25
.5
.75
1
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Standard deviation of temperature shock (by year)
Year1901 1920 1940 1960 1980 2008
.43
.6
.8
1
1.2
1.42
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Standard deviation of regional temperature shock
Sta
ndar
d de
viat
ion
Latitude−90 −60 −30 0 30 60 90
.02
.5
1
1.5
2
2.5
3
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Evidence of ARCH in temperature shocks
◮ In a pooled regression, coefficient on the lagged squaredtemperature residual in an ARCH(1) model is 0.34.
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Calibrating the damage parameter
I Use indirect inference (a way of implementing simulationestimation).
I Choose θ so that simulated data from the equilibrium modelreplicates the regression coefficients in the panel regressionsusing the observed data on GDP and temperature at theregional level.
I Result: θ ≈ 0.02—a 1-degree shock to temperature reducesTFP (temporarily) by 2%.
I Regression coefficients from the model: ϕ1 = −1.72% (leveleffect), ϕ2 = −0.27% (growth-rate effect); compare to−1.65% and −0.09% in the observed data.
I Future work: allow θ to vary across different types of regions.
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Aggregate fluctuations from idiosyncratic shocks
◮ GDP is highly concentrated spatially: top 1% of regions (192cells) produce 44% of world GDP; top 15% of regions (2840cells) produce 90% of world GDP.
◮ Temperature shocks are correlated in space.
◮ Implication: using the calibrated damage parameter, regionaltemperature shocks produce aggregate fluctuations in worldGDP (and in the world interest rate): coefficient of variationof world GDP is 0.5%.
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The climate-economy model
◮ Global temperature (as a deviation from preindustrial level) isgiven by:
T = λlog(S/S)
log 2,
where S is the stock of carbon in the atmosphere and λ is“climate sensitivity” (we set λ = 3).
◮ Introduce feedback from carbon emissions to economicactivity: S → T → TFP via a Nordhaus-style “damage”function, G (T ):
G (T ) =1
1 + 0.00284T 2.
◮ The stock of carbon evolves according to the physical laws ofthe carbon cycle. At some known time in the future (140years), “green” energy replaces carbon energy.
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A simple model of the carbon cycle
◮ The total stock of atmospheric carbon, St , is the sum of apermanent stock, S1t , and a (slowly) depreciating stock, S2t :St = S1t + S2t .
◮ S1t = 0.25Et + S1,t−1, where Et is total carbon emissions.
◮ S2t = 0.36(1 − 0.25)Et + 0.998S2,t−1.
◮ Half-life of a freshly-emitted unit of carbon is 30 years;half-life of the depreciating stock (given no new emissions) is300 years.
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Dynamic program of a typical region with feedback
◮ Two new aggregate state variables: current carbon stocks.
◮ vt(ω, z ,A, k , z ,S1,S2) =maxk′,b′ [U(c) + βEz ′,z ′|z ,z vt+1(ω
′, z ′,A′, k ′, z ′,S ′1,S
′2)], s.t.
c = ω − k ′ − qt(k , z ,S1,S2)b′
ω′ = maxe′
[G (f (ℓ)T (S)) exp(−θz ′) F (k ′,A′, e′)− pe′)] +
(1− δ)k ′ + b′
A′ = (1 + g)A
b′ ≥ b(k ′)
k ′ = Ht(k , z ,S1,S2)
S ′1 = φ1Et+1(k
′, z ′,S) + S1
S ′2 = φ2Et+1(k
′, z ′,S) + φ3S2
and a (time-varying) conditional distribution for (z ′, z ′) given(z , z).
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Hard computational problem
◮ Heterogeneity + portfolio problem with occasionally bindingborrowing constraint + aggregate uncertainty + transition.
◮ A recursive competitive equilibrium is a fixed point in a set ofof functions indexed by time: {qt ,Ht ,Et}.
◮ Simplification #1: the “constrained” and “unconstrained”problems (nearly) separate and the constrained decision rule is(nearly) linear.
◮ Simplification #2: the functions {qt ,Ht ,Et} are (nearly)linear.
◮ But fair to say that the computational model goes wellbeyond what’s been done in macro so far . . .
◮ . . . and solves problems (stemming from forward-lookingbehavior) that natural scientists do not have to face!
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Imagine how much harder physics would be if electrons hadfeelings!
–Richard Feynman
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Computational algorithm
◮ Solve steady-state problem after total stock of carbon hassettled down (at date T ).
◮ Guess on (time-varying) coefficients of aggregate functions.
◮ Solve a typical’s region problem backwards from T , obtaining(time-varying) decision rules.
◮ Simulate the global economy forwards N times.
◮ Use simulated data to confirm coefficients. (Perturb thedistribution at each point in time to calculate estimates ofslope coefficients; “connect” these over time using a spline.)
◮ Check forecasting accuracy of each function.
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Results from computational model
◮ Comparing equilibrium outcomes: one region vs. manyregions.
◮ Distributions of gains/losses in two tax experiments:
1. All regions impose a tax on carbon emissions.2. Only U.S. regions impose a tax.
◮ To be completed:◮ Distribution of gains/losses from climate change (i.e., compareλ > 0 to λ = 0).
◮ Graphs of evolution of global resource allocation (i.e., capital)under the various scenarios.
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Bond price
Year1990 2130 2990
.974408
.978377
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Detrended global output
Year1990 2130 2990
26.4286
30.8034
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Detrended global capital stock
Year1990 2130 2990
71.8858
83.3325
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Detrended global energy use (in gigatons of carbon)
Gig
aton
s of
car
bon
Year1990 2130 2990
8.8826
9.45835
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Stock of atmospheric carbon (gigatons)
Gig
aton
s of
car
bon
Year1990 2130 2990
714.521
2027.45
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Global temperature(degrees centigrade above pre−industrial temperature)
Deg
rees
cen
tigra
de
Year1990 2130 2990
.779914
5.52453
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Global temperature(degrees centigrade above pre−industrial temperature)
Deg
rees
cen
tigra
de
Year1990 2010 2030 2050 2070 2090
.779914
4.05805
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Percentage share of world GDP at latitude of 52 degrees (north)
Sha
re o
f GD
P (
perc
ent)
Year1990 2130 2290
2.405
2.684
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Percentage share of world GDP at equator
Sha
re o
f GD
P (
perc
ent)
Year1990 2130 2290
.1098
.127
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Bond price (one vs. many regions)
Year1990 2130 2290
.974408
.978377
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Detrended global output (one vs. many regions)
Year1990 2130 2290
26.4286
30.8034
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Trend in global temperature (one vs. many regions)
Deg
rees
cen
tigra
de
Year1990 2130 2290
.895314
5.42534
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A regional tax on carbon emissions
◮ Next-period wealth given by:
maxe′
[G (f (ℓ)T (S))] exp(−θz ′) F (k ′,A′, e′)− p(1 + τ)e′)] +
(1− δ)k ′ + b +D
◮ In equilibrium, the region-specific lump-sum subsidy, D, equalstotal tax receipts in that region (imagine a continuum ofidentical entrepreneurs in each region).
◮ In the experiments, set τ = 1, either for the whole world orjust for the U.S.
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Percentage change in detrended global output (tax vs. no tax)
Per
cent
age
chan
ge
Year1990 2130 2290
−.543906
0
1.02141
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Percentage change in global energy use (tax vs. no tax)
Per
cent
age
chan
ge
Year1990 2130 2290
−7.21303
0.464219
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Change in global temperature (tax vs. no tax)
Deg
rees
cen
tigra
de
Year1990 2130 2290
−.206646
−.002131
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Welfare gain (in percent consumption)(all regions taxed)
Wel
fare
gai
n
Latitude−90 −60 −30 0 30 60 89
−.2
0
.25
.5
.75
1.1
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Welfare gain from deviating (in percent consumption)(all other regions taxed)
Wel
fare
gai
n
Latitude−90 −60 −30 0 30 60 89
.213
.261
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Histogram of welfare gains by region (in percent consumption)(all regions taxed vs. none taxed)
Fre
quen
cy
Welfare gain−.167 0 1.007
0
.173
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Histogram of welfare gains by region (in percent consumption)(only U.S. taxed vs. none taxed)
Fre
quen
cy
Welfare gain−.177 0 .255
0
.173
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Summary welfare measures
◮ Average welfare gain across regions, all taxed vs. none taxed:0.070%.
◮ Average welfare gain across regions, only U.S. taxed vs. nonetaxed: 0.043%.
◮ Population-weighted welfare gain, all taxed vs. none taxed:0.039% (compare to 0.1% in one-region world).
◮ Population-weighted welfare gain, only U.S. taxed vs. nonetaxed: 0.041%.
◮ Fraction of world population gaining, all taxed vs. none taxed:0.66.
◮ Fraction of world population gaining, only U.S. taxed vs. nonetaxed: 0.95.
◮ Fraction of world population gaining, only U.S. taxed vs. alltaxed: 0.53
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Next steps
◮ Introduce additional sources of heterogeneity: heteroskedasticshocks, region-specific damage functions. (Easy to parallelizecomputation of decision rules and simulation of multipleglobes.)
◮ Introduce time-varying variance of temperature shocks.
◮ Extensions:◮ Precipitation as well as temperature.◮ Additional risk-sharing mechanisms within some groups of
regions (within a country, say).◮ Additional interactions between regions: trade, migration.