Expected Utility and Catastrophic Risk in a Stochastic Economy-Climate Model

M. Ikefuji, R.J.A. Laeven, J.R. Magnus, C.H.M. Muris

Research output: Working paperDiscussion paperOther research output

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Abstract

In the context of extreme climate change, we ask how to conduct expected utility analysis in the presence of catastrophic risks. Economists typically model decision making under risk and uncertainty by expected util- ity with constant relative risk aversion (power utility); statisticians typi- cally model economic catastrophes by probability distributions with heavy tails. Unfortunately, the expected utility framework is fragile with respect to heavy-tailed distributional assumptions. We specify a stochastic economy- climate model with power utility and explicitly demonstrate this fragility. We derive necessary and sufficient compatibility conditions on the utility function to avoid fragility and solve our stochastic economy-climate model for two examples of such compatible utility functions. We further develop and implement a procedure to learn the input parameters of our model and show that the model thus specified produces quite robust optimal policies. The numerical results indicate that higher levels of uncertainty (heavier tails) lead to less abatement and consumption, and to more investment, but this effect is not unlimited.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages42
Volume2010-122
Publication statusPublished - 2010

Publication series

NameCentER Discussion Paper
Volume2010-122

Fingerprint

Climate
Expected utility
Catastrophic risk
Power utility
Utility function
Fragility
Heavy tails
Decision making under risk
Compatibility
Uncertainty
Utility analysis
Constant relative risk aversion
Risk and uncertainty
Economics
Probability distribution
Abatement
Optimal policy
Decision making under uncertainty
Economists
Catastrophe

Keywords

  • Economy-climate models
  • Catastrophe
  • Expected utility
  • Heavy tails
  • Power utility

Cite this

Ikefuji, M., Laeven, R. J. A., Magnus, J. R., & Muris, C. H. M. (2010). Expected Utility and Catastrophic Risk in a Stochastic Economy-Climate Model. (CentER Discussion Paper; Vol. 2010-122). Tilburg: Econometrics.
Ikefuji, M. ; Laeven, R.J.A. ; Magnus, J.R. ; Muris, C.H.M. / Expected Utility and Catastrophic Risk in a Stochastic Economy-Climate Model. Tilburg : Econometrics, 2010. (CentER Discussion Paper).
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Ikefuji, M, Laeven, RJA, Magnus, JR & Muris, CHM 2010 'Expected Utility and Catastrophic Risk in a Stochastic Economy-Climate Model' CentER Discussion Paper, vol. 2010-122, Econometrics, Tilburg.

Expected Utility and Catastrophic Risk in a Stochastic Economy-Climate Model. / Ikefuji, M.; Laeven, R.J.A.; Magnus, J.R.; Muris, C.H.M.

Tilburg : Econometrics, 2010. (CentER Discussion Paper; Vol. 2010-122).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Expected Utility and Catastrophic Risk in a Stochastic Economy-Climate Model

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AU - Laeven, R.J.A.

AU - Magnus, J.R.

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N1 - Pagination: 42

PY - 2010

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N2 - In the context of extreme climate change, we ask how to conduct expected utility analysis in the presence of catastrophic risks. Economists typically model decision making under risk and uncertainty by expected util- ity with constant relative risk aversion (power utility); statisticians typi- cally model economic catastrophes by probability distributions with heavy tails. Unfortunately, the expected utility framework is fragile with respect to heavy-tailed distributional assumptions. We specify a stochastic economy- climate model with power utility and explicitly demonstrate this fragility. We derive necessary and sufficient compatibility conditions on the utility function to avoid fragility and solve our stochastic economy-climate model for two examples of such compatible utility functions. We further develop and implement a procedure to learn the input parameters of our model and show that the model thus specified produces quite robust optimal policies. The numerical results indicate that higher levels of uncertainty (heavier tails) lead to less abatement and consumption, and to more investment, but this effect is not unlimited.

AB - In the context of extreme climate change, we ask how to conduct expected utility analysis in the presence of catastrophic risks. Economists typically model decision making under risk and uncertainty by expected util- ity with constant relative risk aversion (power utility); statisticians typi- cally model economic catastrophes by probability distributions with heavy tails. Unfortunately, the expected utility framework is fragile with respect to heavy-tailed distributional assumptions. We specify a stochastic economy- climate model with power utility and explicitly demonstrate this fragility. We derive necessary and sufficient compatibility conditions on the utility function to avoid fragility and solve our stochastic economy-climate model for two examples of such compatible utility functions. We further develop and implement a procedure to learn the input parameters of our model and show that the model thus specified produces quite robust optimal policies. The numerical results indicate that higher levels of uncertainty (heavier tails) lead to less abatement and consumption, and to more investment, but this effect is not unlimited.

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KW - Expected utility

KW - Heavy tails

KW - Power utility

M3 - Discussion paper

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Ikefuji M, Laeven RJA, Magnus JR, Muris CHM. Expected Utility and Catastrophic Risk in a Stochastic Economy-Climate Model. Tilburg: Econometrics. 2010. (CentER Discussion Paper).