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Economics 331b

Integrated Assessment Modelsof Economics of Climate Change

Integrated Assessment (IA) Models of Climate Change

• What are IA model?– These are models that include the full range of

cause and effect in climate change (“end to end” modeling).

– They are necessarily interdisciplinary and involve natural and social sciences

• Major goals:– Project the impact of current trends and of policies

on important variables– Assess the costs and benefits of alternative policies– Assess uncertainties and priorities for scientific and

technology research

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Person or nation 1

Person or nation 2

Inefficient initial (no-policy) position

Bargaining region (Pareto improving)

Pareto Improvement from Climate Policy

Elements of building/using an IAM1. Economics

– Population– Inputs: energy, capital, land, …– Technology (total factor productivity)

2. Emissions of CO2 and other GHGs3. Carbon cycle, forcings, temperature, other

geophysical4. Impacts or damages5. Policies

– Emissions controls, taxes, regulations, subsidies– International strategies for global externalities

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Basic economic methodology of IA models

We will use a very simple IA model to illustrate – the Yale “DICE” model.

Last published version is 2007 in your assignmentAlso:

- Regional version (RICE-2010)- Experimental or beta DICE-2010 in Excel format

Lint will give overview of IAM in section this week.

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Simplified Equations of DICE Model (QoB, pp. 205-209) Objective Function

(1)

1

T max

tW U[c(t),L(t)]R(t) [maximize for control rate (μ) and savings rate (s)]

Economics (2) 1-U [c(t),L(t )] =L(t)[c(t) / (1- )] Utility function (3) 2

1 AT 2 AT(t)=Dam/ GDP =[1+ T (t)+ T (t) ] Damage function (4) 2

1(t) = (t) (t) Abatement cost (5) 1g gQ (t) = A(t) K(t) L(t) C(t) s(t)Q (t) Gross output (6) gnQ (t) = [1- (t)] [1- (t)] Q (t) Net output (7) g

IndE (t) = (t)[1- (t)] Q (t) Industrial emissions Geosciences (8) 11 1AT ATM (t) E(t) M (t - ) ... Atmospheric CO2 (9) 2 AT AT EXF(t) {log [M (t) / M (0)] } F (t) Radiative forcings (10) 11 AT ATT (t) T (t ) {F(t) ... Global mean temperature Key variables (in addition to standard from growth theory):

Eind = industrial CO2 emissions F = radiative forcings MAT = atmospheric concentrations CO2 Qg = output gross of damages and abatement Qn = output net of damages and abatement TAT = global mean surface temperature

Λ = abatement (mitigation) cost/ output μ = emissions control rate (fraction of uncontrolled) σ = uncontrolled emissions/ output ratio Ω = damages as fraction of output s = savings rate = I/ Q R = utility discount factor = (1+ρ)-t

Basic structure of IAMEconomic sectors (more or less elaborate):

Q = A F(K, L) = C + Iplus:

• Energy sector • Emissions• Abatement• Climate damages

Geophysical sectors:• Carbon cycle• Climate model• Impacts

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I. Economics: DICE/RICE model examplePopulation exogenous: use UN and IIASA

projections. - Should we have endogenous fertility?

Total factor productivity exogenous - Problem that technological change is endogenous,

particularly with large changes in energy pricesSavings rate optimized by country

- Use Solow-Ramsey model of optimal economic growth

Put all these together (for 12 regions j=US, EU, …)

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1gj j j j

j j j

Q (t) = A (t) K (t) L (t)

K (t)=s(t)Q (t) K (t)

Per capita GDP: history and projections

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1

10

100

1960 1980 2000 2020 2040 2060 2080 2100

Per c

apita

GDP

(200

0$ P

PP)

US WE OHI

Russia EE/FSU Japan

China India World

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Emissions trajectories:Start with data on Q, L, and E of CO2 for major

countriesEstimate population, productivity, emissions growth Project these by decade for futureThen aggregate up by twelve major regions (US, EU,

…)Constrain by global fossil fuel resources

This is probably the largest uncertainty over the long run.

Modeling Strategies (II): Emissions

CO2-GDP ratios: history

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.0

.1

.2

.3

.4

.5

.6

.7

80 82 84 86 88 90 92 94 96 98 00 02 04

ChinaRussiaUS

WorldWestern/Central Europe

CO

2-G

DP

ratio

(ton

s pe

r con

stan

t PP

P $

)

Decarbonization projections

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-

0.05

0.10

0.15

0.20

0.25

0.30

0.35

2005 2015 2025 2035 2045 2055 2065 2075 2085 2095 2105

CO2

emiss

ions

/GDP

US EU

Japan Russia

China India

Africa

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Climate modelIdea here to use “reduced form” or simplified models.As we have seen, large models have very fine

resolution and require supercomputers for solution and cannot be used in economic modeling.

We take two-layers (atmosphere, deep oceans) and decadal time steps.

Calibrated to ensemble of models in IPCC science reports.

Modeling Strategies (III): Climate Models

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Actual and predicted global temperature history

-.6

-.4

-.2

.0

.2

.4

.6

1840 1880 1920 1960 2000YEAR

T_DICE2007 T_Hadley T_GISS

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T projections multi-model comparison

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100

Glob

al m

ean

tem

pera

ture

incr

ease

(from

190

0,

◦C)

RICE-201

EMF-22

A1B

A2

B1

B2

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Modeling Strategies (IV): Impacts• Central difficulty is evaluation of the impact of

climate change on society• Two major areas:

– market economy (agriculture, manufacturing, housing, …)

– non-market sectors • human (health, recreation, …)• non-human (ecosystems, fish, trees, …)

Summary from Tol Survey

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-3

-2

-1

0

1

2

3

4

5

6

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Dam

ages

as p

erce

nt o

f out

put

Global mean temperature increase (°C)

Tol survey

Richard Tol, “The Economic Impact of Climate Change,” Journal of Economic Perspectives, Vol. 23, No. 2, Spring 2009

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Modeling Strategies (V): Abatement costs

These are the abatement cost functions we discussed in energy economics.– Some use econometric analysis of costs of reductions– Some use engineering/mathematical programming

estimates– DICE model generally uses “reduced form” estimates

of marginal costs of reduction as function of emissions reduction rate

– We will return to this later.Marginal cost of reductions

0 Reductions in energy use or CO2 emissions

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Outcome of efficientcompetitive market(however complex

but finite time)

Maximization of weighted utility function:

Economic Theory Behind Modeling

1for utility functions U; individuals i=1,...,n; locations k, uncertain states of world s,

time periods t; welfare weights

ni i i

k,s,ti

i .

W [U (c )]

=

1. Basic theorem of “markets as maximization” (Samuelson, Negishi)

2. This allows us (in principle) to calculate the outcome of a marketsystem by a constrained non-linear maximization.

How do we solve IA models?The structure of the models is the following:

We solve using various mathematical optimization techniques.

1. GAMS solver (proprietary). This takes the problem and solves it using linear programming (LP) through successive steps. It is extremely reliable.

2. Use EXCEL solver. This is available with standard EXCEL and uses various numerical techniques. It is not 100% reliable for difficult or complex problems.

3. MATHLAB. Useful if you know it.4. Genetic algorithms. Some like these.

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1

subject to initial conditions, parameters]

(The functions are production functions, climate model,carbon cycle, abatement costs, damages, and

T max

{ (t)} tmax W U[c(t),L(t)]R(t)

c(t) H[ (t),s(t);H[...]

so forth.)

Can also calculate the “shadow prices,” here the efficient carbon taxes

Remember that in a constrained optimization (Lagrangean), the multipliers have the interpretation of d[Objective Function]/dX.

So, in this problem, interpretation is MC of emissions reduction.

Optimization programs (particularly LP) will generate the shadow prices of carbon emissions in the optimal path.

For example, if we look at the DICE model, the carbon shadow price might be $30 per ton carbon ($7 per ton CO2)

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0

100

200

300

400

500

600

0 10 20 30M

argi

nal c

ost o

f Em

issio

ns R

educ

tions

($)

Period

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Applications of IA ModelsI will give an example that compares different

policies and scenarios.

1. No controls ("baseline"). No emissions controls.2. Optimal policy. Emissions and carbon prices set

for economic optimum.3. Various international agreements (Strong Kyoto ≈

Obama proposals and Copenhagen Accord)

For these, I will use latest modeling results (RICE-2010, Nordhaus, PNAS, 2010).

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Emissions Trajectories for RICE-2010

0

2

4

6

8

10

12

14

16

18

20

2005 2025 2045 2065 2085 2105

CO2

emiss

ions

(GtC

per

year

)Optimal

Baseline

Lim T<2

Copenhagen Accord

Source: Nordhaus, “Economics of Copenhagen Accord,” PNAS (US), 2010.

Concentrations profiles: RICE-2010

25

0

200

400

600

800

1,000

1,200

1,400

2005 2025 2045 2065 2085 2105 2125 2145 2165 2185 2205

Atm

osph

eric

conc

entra

tions

CO2

(ppm

) Optimal

Baseline

Lim T<2

Copenhagen Accord

Temperature profiles

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0.0

1.0

2.0

3.0

4.0

5.0

6.0

2005 2025 2045 2065 2085 2105 2125 2145 2165 2185 2205

Glob

al m

ean t

empe

ratu

re (d

egre

es C

)Optimal

Baseline

Lim T<2

Copenhagen Accord

IPCC AR4 Model Results: History and Projections

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RICE-2010model

Policy outcomes variablesOverall evaluationTwo major policy variables are

- emissions with controls- carbon tax

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Carbon prices for major scenarios

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0

100

200

300

400

500

600

700

800

900

1,000

2005 2025 2045 2065 2085 2105

Carb

on p

rice (

2005

$ pe

r ton

C)

Optimal

Lim T<2

Copenhagen Accord

Source: Nordhaus, “Economics of Copenhagen Accord,” PNAS (US), 2010.

0

50

100

150

200

250

2005 2015 2025 2035

Carb

on p

rice (

2005

$ pe

r ton

C)

Optimal

Lim T<2

Copenhagen Accord

Where are we today?

Actual equivalent global carbon price = $1 / tCO2