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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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RSMG http://www.uq.edu.au/economics/rsmg/index.htm

Quiggin http://www.uq.edu.au/economics/johnquiggin

WebLog http://johnquiggin.com

Web Sites

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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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•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

• 50 per cent reduction in global emissions

• Income share of energy*elasticity*tax-rate^2

• 0.04*1*1=0.04

Stabilization: modest uncertainty

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•Should be evaluated relative to stabilisation

•Stern vs Nordhaus & Boyer

•Differences relate mostly to discounting

•Neither deals well with uncertainty

Costs of doing nothing

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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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•Appealing

• Normatively plausible axioms

•Tractable

• Models of asset pricing, discounting

•Empirically unsatisfactory

• Allais, Ellsberg 'paradoxes'

• Equity premium puzzle

The expected utility model

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• 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!

Implications

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•r = δ + η*g

• 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.

Discounting under EU

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•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)

Stern's parameter values

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•Given percentage change in income equally valuable at all income levels

•Ideal for simple analysis over long periods with uncertain growth rates

Log utility

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•Covers any event that renders all calculations irrelevant

•Stern uses 0.001, arguably should be higher

Extinction

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•Widely used

•No obvious justification in social choice

•Overlapping generations problem

•Small probability of extinction

Inherent discounting

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•‘Future generations’ are alive today

• Not ‘current vs future generations’ but ‘older vs younger cohorts’

Overlapping generations problem

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•Equal treatment of contemporaries

• Equal value on lifetime utility

•Overlapping generations create an unbroken chain

• Implies no inherent discounting

Inherent discounting violates standard norms

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Overlapping generations model

•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

• 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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•Stern's choice fit well with some observations (market rates of interest)

•Badly with others (average returns to capital)

Market comparisons

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•Rate of return to equity much higher than for bonds

•Can't be explained by EU under

• Plausible risk aversion

• Perfect capital markets

• Intertemporally separable utility

•Key assumptions of EU discounting theory

Equity premium puzzle

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•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

Reasons for favoring low r

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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

• Hyperbolic discounting (Nordhaus & Boyer)

• Rank-dependent probability (Prospect theory)

•Non-EU models allow more flexibility, but more problematic for welfare analysis

• Dynamic inconsistency

• Maybe not a big problem in this case

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•Uncertainty still problematic

•Catastrophic risk poorly understood

•Presumption in favour of early action

Concluding comments