ADAPTATION TO CLIMATE CHANGE AND ECONOMIC ......ADAPTATION TO CLIMATE CHANGE AND ECONOMIC GROWTH IN...

ADAPTATION TO CLIMATE CHANGE AND ECONOMIC GROWTH IN DEVELOPING COUNTRIES

ANTONY MILLNER & SIMON DIETZ

GRANTHAM RESEARCH INSTITUTE

LONDON SCHOOL OF ECONOMICS

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

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

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


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

INTERACTION BETWEEN ADAPTIVE CAPITAL AND CLIMATE CHANGE


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

MODEL EQUATIONS


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”.

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


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)

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


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


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


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)


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


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


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


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


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.


ADDITIONAL MATERIALS


MODEL PARAMETERS – BASE CASE CALIBRATION


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


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


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


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


ADAPTATION TO CLIMATE CHANGE AND ECONOMIC ......ADAPTATION TO CLIMATE CHANGE AND ECONOMIC GROWTH IN...

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