Intergenerational equity, risk and
climate modeling
Paper presented by John Quiggin*
Thirteenth Annual Conference on Global Economic
Analysis
Penang, Malaysia, 9-11 June 2010
* Australian Research Council Federation Fellow
* Risk and Sustainable Management Group, Schools of Economics and
Political Science,University of Queensland
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Web Sites
RSMG
http://www.uq.edu.au/economics/rsmg/ind
ex.htm
Quiggin
http://www.uq.edu.au/economics/johnquig
gin
WebLog http://johnquiggin.com
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Modelling climate change
• Policy decisions now, outcomes over
next century
• Stabilization, Business as Usual, Wait
and See
• Time and uncertainty
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Stabilization: modest
uncertainty
• Estimated cost 0-4 per cent of 2050 NWI
• Lower bound of 0 (some regrets)
• Upper bound ‘all renewables’, 10 per cent
• Back of the envelope calculation
•
•
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50 per cent reduction in global emissions
Income share of energy*elasticity*tax-rate^2
0.04*1*1=0.04
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Costs of doing nothing
• Should be evaluated relative to
stabilisation
• Stern vs Nordhaus & Boyer
• Differences relate mostly to discounting
• Neither deals well with uncertainty
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Time, risk, equity
• Closely related problems
• Outcomes differentiated by dates, states
of nature, persons
• All conflated in standard discussions of
discounting
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The expected utility model
• Appealing
•
Normatively plausible axioms
•
Models of asset pricing, discounting
• Tractable
• Empirically unsatisfactory
•
•
Allais, Ellsberg 'paradoxes'
Equity premium puzzle
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Implications
•
•
•
•
Assuming rising incomes, a dollar of extra
income is worth less in the future than it is
today
Under uncertainty, a dollar of extra income
in a bad state of nature is worth more than a
dollar in a good state of nature
Transferring income from rich to poor people
improves aggregate welfare
Same function captures all three!
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Discounting under EU
• r = δ + η*g
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•
•
•
r is the rate of discount
η is the elasticity of substitution for
consumption,
g is the rate of growth of consumption per
person
δ is the inherent discount rate.
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Stern's parameter values
• δ = 0.001 (no inherent discounting)
• η = 1 (log utility)
• g varies but generally around 0.02
• Implies r=0.021 (2.1 per cent)
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Log utility
• Given percentage change in income
equally valuable at all income levels
• Ideal for simple analysis over long
periods with uncertain growth rates
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Extinction
• Covers any event that renders all
calculations irrelevant
• Stern uses 0.001, arguably should be
higher
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Inherent discounting
• Widely used
• No obvious justification in social choice
• Overlapping generations problem
• Small probability of extinction
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Overlapping generations
problem
• ‘Future generations’ are alive today
• Not ‘current vs future generations’ but
‘older vs younger cohorts’
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Inherent discounting violates
standard norms
• Equal treatment of contemporaries
•
Equal value on lifetime utility
• Overlapping generations create an
unbroken chain
•
Implies no inherent discounting
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Overlapping generations
model
•
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All generations live two periods
Additively separable utilitarian preferences
•
•
•
Can include inherent discounting of own
consumption
V = u(c1)+βu(c2)
Social choices over utility profiles for T
generations
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No discounting proposition
• Assumptions
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•
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Pareto optimality
Independence
Utilitarianism for contemporaries
• Conclusion: Maximize sum over
generations of lifetime utility Σt V
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Sketch proof
Any transfer within generations that
increases lifetime utility V increases social
welfare (Pareto optimality)
Any transfer between currently living
generations that increases aggregate V
increases social welfare (Utilitarianism
within periods)
General result follows from Independence
(+ Transitivity)
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Key implication
• Preferences including inherent
discounting justify transfers from
consumption in old age to consumption
in youth within a generation
• Don’t justify transfers from later-born to
earlier-born cohorts
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Market comparisons
• Stern's choice fit well with some
observations (market rates of interest)
• Badly with others (average returns to
capital)
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Equity premium puzzle
• Rate of return to equity much higher than
for bonds
• Can't be explained by EU under
•
•
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Plausible risk aversion
Perfect capital markets
Intertemporally separable utility
• Key assumptions of EU discounting
theory
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Reasons for favoring low r
• Bond rate is most plausible market rate
• Price of environmental services likely to
rise in bad states
• Standard procedures don't take
adequate account of tails of distribution
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Implications for modelling
• Need for explicit modelling of uncertainty
and learning
• Need to model right-hand tail of damage
distribution
• Representation of time and state of
nature in discounting
• EU vs non-EU
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Explicit modelling of
uncertainty
• At least three possible damage states
•
Median, High, Catastrophic
• Learning over time
• A complex control problem
•
Monte Carlo?
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Right-hand tail
• Equilibrium warming above 6 degrees
(Weitzman iconic value)
• Poorly represented in current models
• Account for large proportion of expected
loss
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State-contingent discounting
• Bad states, low discount rates
• Negative growth path, negative discount
rates
• Over long periods, these may dominate
welfare calculations (Newell and Pizer)
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EU vs non-EU
• Non-EU treatment of time and risk
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Hyperbolic discounting (Nordhaus & Boyer)
Rank-dependent probability (Prospect
theory)
• Non-EU models allow more flexibility, but
more problematic for welfare analysis
•
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Dynamic inconsistency
Maybe not a big problem in this case
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Concluding comments
• Uncertainty still problematic
• Catastrophic risk poorly understood
• Presumption in favour of early action
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