Embed Size (px)
Citation preview
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
