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ADAPTATION TO CLIMATE CHANGE AND ECONOMIC GROWTH IN DEVELOPING COUNTRIES
ANTONY MILLNER & SIMON DIETZ
GRANTHAM RESEARCH INSTITUTE
LONDON SCHOOL OF ECONOMICS
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STYLIZED FACTS
Developing countries, particularly in sub-Saharan Africa, are highly vulnerable to climate change:
• Geographic location • High sensitivity (e.g. share of GDP in agriculture) • Low adaptive capacity (e.g. finance, institutions, information)
Even if (and that’s a BIG “if”) we get effective mitigation, climate change will occur due to long residence time of atmospheric CO2. Macro & Climate, LSE , Dec. 2012
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THIS PAPER IN A NUTSHELL
How should developing countries adapt to climate change? • “Development is the best form of adaptation” – i.e. invest as usual in
productive capital • “Development is contingent on adaptation” – i.e. invest to ‘climate-proof’
productive capital Towards adjudicating between these positions, we:
• Construct a fully dynamic, easy to interpret, analytical model of adaptation as an investment problem at the macro level
• Apply the model empirically to Sub-Saharan Africa, with extensive sensitivity analysis
We find that in most contingencies it will be optimal to grow the stock of adaptive capital rapidly over the next 50 years.
Macro & Climate, LSE , Dec. 2012
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MODEL SETUP Modified Ramsey-Cass-Koopmans growth model (cf. DICE) Two capital stocks
• ‘Vulnerable capital’ – productive, but damaged by CC • ‘Adaptive capital’ – unproductive in the absence of CC, but reduces CC
damages to vulnerable capital output Two controls
• Consumption/investment in vulnerable capital • Investment in adaptive capital
Exogenous temperature change (small developing country/region), population and TFP Convex cost of investment in adaptive capital Captures barriers to adapting quickly such as planning costs, policy delays and corruption
Macro & Climate, LSE , Dec. 2012
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MODEL SETUP II
max
c(t),I(t)
Z T
0L(t)U(c(t))e�⇢tdt
KA = I � �AKA
Vulnerable capital KV:
KV = A(t)D(KA, X(t))F (KV , L(t))� �V KV � cL(t)�Q(I)
TFP Damages = D(Adaptive capital, Exogenous Temperature)
GDP Depreciation
Consumption
Adaptation costs
Adaptive capital KA:
Social Planner’s Objective:
Adaptive investment Depreciation Macro & Climate, LSE , Dec. 2012
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INTERACTION BETWEEN ADAPTIVE CAPITAL AND CLIMATE CHANGE
Macro & Climate, LSE , Dec. 2012
All interactions are captured by the modified damage multiplier:
D(KA, X) : R+ ⇥ R+ ! [0, 1]
We assume: 1. D is decreasing in X (climate change is ‘bad’).
2. KA unproductive in the absence of climate change (i.e. D(KA,0) = 1) 3. D is increasing and concave in KA.
4. “Productivity” of the marginal unit of KA is increasing in X, i.e. @2D
@KA@X> 0
Temperature Adaptive capital
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MODEL EQUATIONS
Macro & Climate, LSE , Dec. 2012
State equations:
Euler equations (follow from Maximum principle):
Terminal conditions:
4 dimensional coupled nonlinear system. We are interested in the transient (not steady state) regime
c =c
⌘(c)[A(t)D(KA, X(t))FKV � �V � ⇢]
I =Q0(I)
Q00(I)[A(t)D(KA, X(t))FKV � �V + �A]�
1
Q00(I)A(t)Da(KA, X(t))F (KV , L(t))
KV = A(t)D(KA, X(t))F (KV , L(t))� �V KV � cL(t)�Q(I)
KA = I � �AKA
Pick values for KV (T ),KA(T )
Ramsey eqn
Capital adjustment eqn: Make marginal products of KA & KV more equal, but not “too fast”.
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DEPENDENCE OF OPTIMAL INVESTMENT RULE ON CAPITAL (NO ADJUSTMENT COSTS)
Implications: • The strong “adapt through development” position is probably not optimal. • Richer economies respond proportionately less to changes in KV but may
respond proportionately more to changes in X if the damage reduction effect of a marginal unit of adaptive capital outweighs its effect on the returns to adaptive investment.
I = RX(KV ,KA, X)X +RV (KV ,KA, X)KV + �AKA
Macro & Climate, LSE , Dec. 2012
For simplicity, assume: • Q(I) = I, i.e. no adjustment costs. • Depreciation rates of two types of capital are equal.
Remark:
Proposition: RX is an increasing (decreasing) function of KV when ✏a,a < ✏X,a(✏a,a > ✏X,a)
RV is decreasing in KV
If X > 0 and KV > 0, then I > 0 (since RV > 0 and RX > 0)
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FULL DYNAMIC SIMULATIONS FOR SUB-SAHARAN AFRICA
Why Sub-Saharan Africa? • Small emitter of carbon: reasonable to assume climate
change is exogenous • Highly vulnerable to climate change
Close the model:
• Choose sensible functional forms for: D(KA,X), F(KV,L), Q(I) and U(c)
• Calibrate model parameters based on IAM literature
Note calibration takes into account: 1. Flow adaptation 2. Relationship between income and damages
Macro & Climate, LSE , Dec. 2012
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0 50 100 150 200 250 3000
5
10
15
20
25
t
Dam
ages
as
% G
DP
0 50 100 150 200 250 3000
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
t
Cost
s of
ada
ptive
inve
stm
ent a
s %
GDP
BAU − grossBAU − residual2CO2 − gross
2CO2 − residual
1.5CO2 − gross
1.5CO2 − residual
BAU2CO21.5CO2
BASE CASE : COSTS & BENEFITS
Same order of magnitude as AD-WITCH model.
Damages as % GDP Investment Costs as % GDP
Macro & Climate, LSE , Dec. 2012
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WELFARE VS. CLIMATE SENSITIVITY WITH AND WITHOUT ADAPTATION
1.5 2 2.5 3 3.5 4 4.5 5 5.5 65250
5300
5350
5400
5450
5500
5550
Climate Sensitivity (°C)
Sta
tionary
equiv
ale
nt consum
ption (
2005 U
SD
)
BAU − adapt2CO
2 − adapt
1.5CO2 − adapt
BAU − no adapt2CO
2 − no adapt
1.5CO2 − no adapt
Macro & Climate, LSE , Dec. 2012
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0 50 100 150 200 250 3000
1000
2000
3000
4000
5000
6000
t
KV / K
A
BAU
2CO2
1.5CO2
BASE CASE: RATIO OF VULNERABLE TO ADAPTIVE CAPITAL AS FUNCTION OF TIME (BOTH CHOSEN OPTIMALLY)
Macro & Climate, LSE , Dec. 2012
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ROBUSTNESS OF CAPITAL RATIO TRAJECTORY The qualitative ‘U-shaped’ dependence of the capital ratio on time is robust to plausible changes in the values of: 1. Adjustment cost parameter 2. Rate of growth of TFP 3. Pure rate of time preference 4. Elasticity of Marginal Utility 5. Climate sensitivity and emissions pathway It is NOT robust to changes in: 1. An ‘Adaptation Effectiveness’ parameter 2. Initial stock of adaptive capital
Macro & Climate, LSE , Dec. 2012
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SENSITIVITY TO ADJUSTMENT COSTS: DIFFERENCE IN GROWTH RATES OF VULNERABLE AND ADAPTIVE CAPITAL VS. ADJUSTMENT COST PARAMETER
1 2 3 4 5
x 10−11
−0.055
−0.05
−0.045
−0.04
−0.035
q
Diffe
rence in a
vera
ge g
row
th r
ate
s (
0−
50 y
ears
)
1 2 3 4 5
x 10−11
−9
−8
−7
−6
−5
−4
−3
−2
−1
0x 10
−3
q
Diffe
rence in a
vera
ge g
row
th r
ate
s (
50−
100 y
ears
)
BAU2CO
2
1.5CO2
BAU2CO
2
1.5CO2
First 50 years Second 50 years
Macro & Climate, LSE , Dec. 2012
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CAPITAL RATIO FOR LOW ADAPTATION EFFECTIVENESS
0 50 100 150 200 250 3000
2000
4000
6000
8000
10000
12000
14000
t
KV / K
A
BAU
2CO2
1.5CO2
Macro & Climate, LSE , Dec. 2012
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SENSITIVITY TO ADAPTATION EFFECTIVENESS WELFARE VS. ADAPTATION EFFECTIVENESS PARAMETER
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.35400
5450
5500
5550
β2
Sta
tio
na
ry e
qu
iva
len
t co
nsu
mp
tio
n (
20
05
US
D)
BAU2CO
2
1.5CO2
Macro & Climate, LSE , Dec. 2012
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CONCLUSIONS Developed a simple, transparent model for informing policy discussions. In most plausible cases, we find that it is optimal to grow the stock of adaptive capital rapidly over the next 50 years. This conclusion is robust to changes in the values of all model parameters, except:
• i) Effectiveness of adaptation • ii) Initial stock of adaptive capital (which is probably very low)
These are the parameters we should focus on pinning down empirically. Our analytics show that simple ad hoc prescriptions are almost certainly wrong: Everything depends on empirical details. Caveats: Uncertainty & Learning, Thresholds, Extreme Events, Institutions, etc., etc.
Macro & Climate, LSE , Dec. 2012
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ADDITIONAL MATERIALS
Macro & Climate, LSE , Dec. 2012
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MODEL PARAMETERS – BASE CASE CALIBRATION
Macro & Climate, LSE , Dec. 2012
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GLOBAL TEMPERATURE TRAJECTORIES
0 100 200 300 400 5000
1
2
3
4
5
6
7
8
9
BAU
t
X
0 100 200 300 400 5000
1
2
3
4
5
6
7
8
9
2CO2
t
X
0 100 200 300 400 5000
1
2
3
4
5
6
7
8
9
1.5CO2
t
X
S = 1.5
°C
S = 3°C
S = 4.5°C
S = 6°C
Macro & Climate, LSE , Dec. 2012
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BASE CASE RESULTS: OPTIMAL CONTROLS
0 50 100 150 200 250 3000
2
4
6
8
10
12
14x 10
4
t
c
0 50 100 150 200 250 3000
20
40
60
80
100
120
140
160
180
200
t
I/L
BAU
2CO2
1.5CO2
BAU
2CO2
1.5CO2
Consumption per capita vs. time Adaptive investment per capita vs. time
Macro & Climate, LSE , Dec. 2012
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SENSITIVITY TO ADAPTATION EFFECTIVENESS: (GV – GA)
0.1 0.15 0.2 0.25 0.3−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
β2
Diffe
ren
ce
in
ave
rag
e g
row
th r
ate
s (
0−
5 y
ea
rs)
0.1 0.15 0.2 0.25 0.3−0.035
−0.03
−0.025
−0.02
−0.015
−0.01
−0.005
0
0.005
β2
Diffe
ren
ce
in
ave
rag
e g
row
th r
ate
s (
5−
50
ye
ars
)
0.1 0.15 0.2 0.25 0.3−14
−12
−10
−8
−6
−4
−2
0
2x 10
−3
β2
Diffe
ren
ce
in
ave
rag
e g
row
th r
ate
s (
50−
10
0 y
ea
rs)
BAU2CO
2
1.5CO2
BAU2CO
2
1.5CO2
BAU2CO
2
1.5CO2
Macro & Climate, LSE , Dec. 2012
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SENSITIVITY TO DISCOUNT RATE: CAPITAL RATIO
0.01 0.015 0.02 0.025 0.03 0.035200
300
400
500
600
700
800
900
1000
1100
ρ
KV(5
0)
/ K
A(5
0)
0.01 0.015 0.02 0.025 0.03 0.035200
300
400
500
600
700
800
900
1000
1100
ρ
KV(1
00)
/ K
A(1
00)
BAU2CO
2
1.5CO2
BAU2CO
2
1.5CO2
Macro & Climate, LSE , Dec. 2012