Intergenerational Discounting and Market Rate of Return in ... 2013...Intergenerational Discounting...

Intergenerational Discounting and Market Rate of Return in OLG

version of RICE Model

Oleg Lugovoy (EDF, RANE)

Andrey Polbin (RANE)

IEW 2013

Outline

Brief introduction to IAM and motivation of current research

Description of the OLG model

Key results of the model

Conclusions and further dimensions of research

Integrated Assessment Modeling

Economic block Gross output Damages from climate change Abatement costs where - emissions control rates Output net of damages and costs Climate block Carbon cycle Temperature Emissions Radiative forcing

γ 1-γ, , , ,Y =A K LR R

R T R T R T R T

( )( )-12AT AT, 1, 2Ω = 1+π T +π TR T R T T

2θ, 1, , ,Λ =θ μR T R T R T

[0,1]tµ ∈net, , , , , , +1Y =(1-Λ )Ω Y =C +K -(1-δ )KR T R T R T R T R T R T R T

AT UP LOM =(M ,M ,M )'T T T T

AT LOT =(T ,T )'T T T

Land, , ,E =σ (1-μ )Y +ET R T R T R T R

R∑

( ) ( ){ }AT AT EX2 2 1750F =η log M -log M +FT T T

Integrated Assessment Modeling

Regional welfare:

where is the social discount rate, is the elasticity of marginal utility consumption.

Social planner problem:

where is the weight of the region in the social welfare

function. The widely used approach to constraction SW is Negishi weighting.

1,1

(1 ) 1R TR

ttT

CW N

θ

ρ θ

− = + − ∑

These parameters determine the real interest rates

ρ θ

maxSP R R

RW Wϕ= →∑

Rϕ

Integrated Assessment Modeling There is an international debate on an appropriate

discounting in climate-economy modeling. Nordhaus among others calibrates the pure rate for social

time preferences to 1.5% per year, and elasticity of marginal utility of consumption equals to 2 to reproduce observable returns on capital. As a result, the “optimal” emissions reductions follow a “policy ramp” in which policies involve modest rates of emissions reductions in the near term, followed by sharp reductions in the medium and long terms.

Critique: the use of high time discount rates is inconsistent with classical utilitarianism, which holds that equal weights should be attached to the welfare of present and future generations (Arrow, Broome, Cline, Ramsey).

Integrated Assessment Modeling • Stern among others calibrates the pure rate of time

preferences equals to 0.1 percent per year and the inverse of the inter-temporal elasticity of substitution equals to 1 (logarithmic utility function) and concludes about the need for extreme immediate actions in reduction emissions of GHG.

• Critique: the use of high time discount rates is inconsistent with observable market returns on capital, saving rates, capital-output ratios (Dasgupta, Nordhaus, Wietzman)

Integrated Assessment Modeling • In this study: we introduce overlapping generations in RICE

model and consider competitive equilibrium • OLG framework provides two discount rates for investments

in physical capital and analyzing climate policy

Model structure

Households Firms Climate block Governments

Model structure: households

Each adult individual lives seven periods of ten years, works first five periods and then retires

We don’t consider bequest and pension system in this simple framework

Individuals make savings over the first five periods of life to ensure consumption in old age.

Model structure: households

A newborn generation's problem consists of maximizing an inter-temporal utility function:

subject to lifetime income:

where are the assets of individual of age group g at the

beginning of period t , is the labor earnings

1 17, , 1

,1

1ˆ1 1

GR G T G

R TG

CU

θ

ρ θ

− −+ −

=

= + − ∑

, , , 1, 1 , , , , ,(1 )R T G R T G R T G R T R T GС lend W r lend+ ++ = + +

, ,R T Glend

, ,R T GW

Individual rate of time preferences

Model structure: firms and governments

Firms maximize profits

The welfare function of the government in the each region is the sum of discounted utilities of all generations, as measured from the moment of birth:

, , , ,- - - maxnet KR T R T R T T R T TY w L R Kπ = >

, 11

(1 ) T G TTT

W Pop Uρ ==

+∑Social discount rate

Calibration and numerical results

Most of the parameters are the same as in the paper: Ortiz et al., 2011. DICER: a tool for analyzing climate policies. Energy Economics 33(S1), S42-S49.

Eight regions We fix the inverse of the inter-temporal elasticity of

substitution to 2, then we chose the value for the pure rate of time preferences equal to 2.5 to ensure that returns on capital compatible with ILA version of the model

Solution concept: Nash equilibrium

For demonstration of the discounting issue we consider Nash equilibrium solution.

Government in each region sets regional emission control rate maximizing own social welfare treating emission control rates of the other regions as a given

Two policy scenarios: social discount rate equals to 1.5% per year and 0% per year

Regional emission control rates Emission control rates

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1T1 T3 T5 T7 T9

T11 T13 T15 T17 T19

USA discount=1.5%

USA discount=0%

OECD1 discount=1.5%

OECD1 discount=0%

CHINA discount=1.5%

CHINA discount=0%

INDIA discount=1.5%

INDIA discount=0%

Regional emission control rates Emission control rates

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1T1 T3 T5 T7 T9

T11 T13 T15 T17 T19

OECD2 discount=1.5%

OECD2 discount=0%

FOREST discount=1.5%

FOREST discount=0%

FSU_EE discount=1.5%

FSU_EE discount=0%

ROW discount=1.5%

ROW discount=0%

Regional emissions of industrial GHG.

GHG emissions

0

0.5

1

1.5

2

2.5

3

3.5T1 T3 T5 T7 T9

T11 T13 T15 T17 T19

billi

ons t

on p

er y

ear

USA discount=1.5%

USA discount=0%

OECD1 discount=1.5%

OECD1 discount=0%

CHINA discount=1.5%

CHINA discount=0%

INDIA discount=1.5%

INDIA discount=0%

Regional emissions of industrial GHG.

GHG emissions

0

0.5

1

1.5

2

2.5

3

3.5T1 T3 T5 T7 T9

T11 T13 T15 T17 T19

billi

ons

ton

per

year

OECD2 discount=1.5%

OECD2 discount=0%

FOREST discount=1.5%

FOREST discount=0%

FSU_EE discount=1.5%

FSU_EE discount=0%

ROW discount=1.5%

ROW discount=0%

Global mean temperature change

0

1

2

3

4

5

6

7T1 T2 T3 T4 T5 T6 T7 T8 T9

T10 T11 T12 T13 T14 T15 T16 T17 T18 T19 T20

degr

ees C

elsiu

s

discount=1.5%

discount=0%

Real returns on capital

Real returns on capital

0

1

2

3

4

5

6

7

8T1 T3 T5 T7 T9

T11 T13 T15 T17 T19

% p

er y

ear

USA discount=1.5%

USA discount=0%

OECD1 discount=1.5%

OECD1 discount=0%

CHINA discount=1.5%

CHINA discount=0%

INDIA discount=1.5%

INDIA discount=0%

Real returns on capital

Real returns on capital

0

2

4

6

8

10

12T1 T3 T5 T7 T9

T11 T13 T15 T17 T19

% p

er y

ear

OECD2 discount=1.5%

OECD2 discount=0%

FOREST discount=1.5%

FOREST discount=0%

FSU_EE discount=1.5%

FSU_EE discount=0%

ROW discount=1.5%

ROW discount=0%

Capital-output ratio

Capital-output ratio

1.5

1.7

1.9

2.1

2.3

2.5

2.7

2.9T1 T3 T5 T7 T9

T11 T13 T15 T17 T19

USA discount=1.5%

USA discount=0%

OECD1 discount=1.5%

OECD1 discount=0%

CHINA discount=1.5%

CHINA discount=0%

INDIA discount=1.5%

INDIA discount=0%

Capital-output ratio

Capital-output ratio

1.5

1.7

1.9

2.1

2.3

2.5

2.7

2.9T1 T3 T5 T7 T9

T11 T13 T15 T17 T19

OECD2 discount=1.5%

OECD2 discount=0%

FOREST discount=1.5%

FOREST discount=0%

FSU_EE discount=1.5%

FSU_EE discount=0%

ROW discount=1.5%

ROW discount=0%

Solution concept: grand coalition

• Global social planner sets emission control rates maximizing social welfare function:

• We set weights and add condition of equalization of marginal abatement costs

Two policy scenarios: grand coalition vs Nash equilibrium. Social discount rate equals to per 0% per year

maxSP R R

RW Wϕ= →∑

1Rϕ =

Emission control rates in grand coalition

Emission control rates

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1T1 T3 T5 T7 T9

T11 T13 T15 T17 T19

USA coalition

USA Nash

OECD1 coalition

OECD1 Nash

CHINA coalition

CHINA Nash

INDIA coalition

INDIA Nash

Emission control rates in grand coalition

Emission control rates

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1T1 T3 T5 T7 T9

T11 T13 T15 T17 T19

OECD2 coalition

OECD2 Nash

FOREST coalition

FOREST Nash

FSU_EE coalition

FSU_EE Nash

ROW coalition

ROW Nash

Global mean temperature change in grand coalition

0

1

2

3

4

5

6

7T1 T2 T3 T4 T5 T6 T7 T8 T9

T10 T11 T12 T13 T14 T15 T16 T17 T18 T19 T20

degr

ees C

elsiu

s

Coalition

Nash

Welfare gains of different generations from grand coalition

Welfare gains

-10

-5

0

5

10

15

20

25

30

T(-6)

T(-4)

T(-2) T1 T3 T5 T7 T9

T11 T13 T15 T17 T19

period of birth

per

cen

t o

f co

nsu

mp

tio

n

USA

OECD1

CHINA

INDIA

OECD2

FOREST

FSU_EE

ROW

Conclusions OLG framework provides two discount rates for investments

in physical capital and analyzing climate policy It is possible to rationalize more radical emissions reduction

side by side with observable market returns on capital Regional and OLG specification of the model allows to

investigate regional-specific policies and to analyze welfare gains and losses of different generations in different regions in comparison to alternative policies

Further research: game-theoretic solution of coalitions formation

Thank you for your attention!

Oleg Lugovoy olugovoy@gmail.com

Andrey Polbin

apolbin@gmail.com