Representing Catastrophic Risks ina Climate-Economy Model*

Richard B. HowarthEnvironmental Studies Program

Dartmouth College

Presentation to the Conference onSustainable Growth in the 21st Century

The New School, April 25, 2014

* Based on joint work with Michael Gerst and Mark Borsuk1

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Introduction

The Framework Convention on Climate Change (1992) calls for stabilizing greenhouse gas concentrations to prevent “dangerous anthropogenic interference” with the earth’s climate

• The Copenhagen Accord (2009) stipulates limiting climate change to a 2C increase in mean global temperature

• Based on Nordhaus’ DICE-2007 model, achieving this goal would require a carbon price that rose from $19 to $210 per tonne-CO2e over the next century

Supporting rationale: Future generations have a right to protection from potentially catastrophic harms

• The 2C target is a pragmatic, judgment-based standard for curtailing characterized risks and “unknown unknowns”

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Since the early 1990s, economists such as Nordhaus (1992, 2008) have argued that deep cuts in greenhouse gas emissions are inconsistent with maximizing social welfare (but see Cline, 1992)

• DICE-2007 employs a revealed preference approach to match observed returns on capital investments and the rate of economic growth

• Qualitative conclusions:

1. The expected damages of climate change are relatively small, at least in the next century or so

2. Decision-makers are too impatient to justify major short-run investments in “climate capital” (my term)

• Thus, DICE-2007 supports relatively low carbon prices as socially optimal ($11 per tonne-CO2e in 2015)

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Weitzman (2009) argues that climate change policy should be driven not by expected (or average) economic costs but by society’s aversion to potentially catastrophic environmental impacts

• These costs, Weitzman suggests, are poorly represented in the current generation of climate-economy models (see also Pindyck, 2013)

• Why that’s true is complicated. The demands for analytical and numerical tractability drive the way models are specified and solved. What’s tractable can then loop back and affect the narrative framing of policy evaluation

My strategy for this talk:

1. Explore Weitzman’s conjecture in a version of DICE-2007 adapted to evaluate potentially catastrophic risks

2. Examine the consequences to the social cost of carbon

Uncertainty and DICE

The base version of DICE-2007 maximizes a social welfare function defined in terms of population (Nt) and per capita consumption (ct):

α = elasticity of marginal utility = 2

ρ = pure rate of time preference = 1.5% per year

Why these parameters? When this function is optimized under the assumption of perfect foresight, these values match:

1. The observed rate of economic growth

2. The observed 6% annual rate of return on (risky) financial investments

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0

1 )1/(1

1

t

ttt cNW

What’s wrong with these values?

• This model predicts that there should be minimal differences in the returns paid by safe and risky financial assets

• Yet real-world data establish that safe investments pay real (inflation-corrected) returns of just 1% per year. So the Nordhaus calibration understates observed risk aversion

Barro’s (2006) solution – work with a baseline economic model that accounts for investment risk premia and “rare economic disasters”

• Ding et al. (2012) – values of α = 5.6 and ρ = 1.5% simultaneously explain the returns on safe and risky assets and the observed (uncertain) rate of economic growth

• Why this matters – our analysis implies relatively high risk aversion (but see Atkinson et al., 2009)

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How does this change in preferences affect climate stabilization policies? To find out, Gerst et al. (2013) constructed a stochastic version of DICE-2007. (See also Howarth et al., 2014)

Our analysis:

1.Replaces DICE’s deterministic Ramsey growth model with a Lucas-Mehra-Prescott specification in which baseline growth follows a random walk

• [Technicality – We bound and scale the utility function so that welfare = 0 when consumption is driven down or below subsistence]

2.Draws on Nordhaus’ assumptions concerning the distributions over uncertain parameters

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One exception:

• Nordhaus (2008) assumes that climate sensitivity (the level of climate change caused by a doubling of greenhouse gas concentations) follows a normal distribution with mean 3°C and a standard error of 1.1°C

• Roe and Baker (2007), in contrast, find that climate sensitivity follows a fat-tailed distribution with a 20% chance of a value >5°C and a 4% chance of a value >10°C (see also Weitzman, 2007)

• We consider both possibilities but consider Roe and Baker more plausible given the state of the scientific literature

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Policy Scenarios:Median CO2 Emissions (109 tonnes/year)

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Probability of a Consumption Collapse (through 2400)

0 0.2 0.4 0.610

-8

10-6

10-4

10-2

Emissions mitigation level in year 2050

Pro

bability

of cata

str

ophe

Fat-tailed S

Thin-tailed S

Fat-tailed Sdeterministic

Fat-tailed

Thin-tailed

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Net Benefits of Climate Stabilization(% change in levelized consumption)

Emissions control rate in 2050

Gerst et al. calibration

NordhausCalibration

0 0% 0%0.1 179% 0.54%

0.2 289% 0.59%0.3 355% 0.58%0.4 374% 0.54%

0.5 377% 0.45%0.6 376% 0.28%0.7 375% 0.06%0.8 374% -0.21%0.9 372% -0.56%

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The Social Cost of Carbon($/tonne-CO2e)

Emissions control rate in 2050

Gerst et al. calibration

Nordhauscalibration

0 25,697 11.270.1 1,103 10.570.2 117 10.480.3 14.1 10.410.4 4.15 10.330.5 4.15 10.260.6 4.19 10.200.7 4.24 10.140.8 4.30 10.080.9 4.39 10.01

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Conclusions and Policy Implications

These results suggest that:

1. Climate stabilization generates large net economic benefits by reducing the risk of low-probability, catastrophic impacts

2. The “social cost of carbon” – i.e., the marginal external cost of carbon emissions – depends sensitively on the emissions pathway

The bad news – it’s computationally intractable to compute a unique, “optimal” value for the SCC in a model like this

• The good news – social welfare is nearly invariant across policy scenarios that achieve the goal of climate stabilization

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One way forward:

• Solve for the set of policies that minimizes the cost of achieving a specified climate stabilization target – say the 2C temperature limit set forth in the Copenhagen Accord

• Employ the resulting marginal cost estimates as shadow prices for use in Regulatory Impact Analysis

• In DICE-2007, this implies a carbon price that rises from about $19 to $210 per tonne-CO2e over the next century (see Nordhaus, 2010)

• Relatively small price signals can set the economy on course towards a stable climate future, thereby meeting the goals set by the UNFCCC and the Copenhagen Accord