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Model Uncertainty in Climate Change Economics: A Review and Proposed Framework for Future Research

Environmental and Resource Economics volume 77, pages 475–501 (2020)Cite this article

Abstract

We review recent models of choices under uncertainty that have been proposed in the economic literature. In particular, we show how different concepts and methods of economic decision theory can be directly useful for problems in environmental economics. The framework we propose is general and can be applied in many different fields of environmental economics. To illustrate, we provide a simple application in the context of an optimal mitigation policy under climate change.

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Notes

  1. See, for example, Pindyck (2007, 2013b), Heal and Millner (2014), Convery and Wagner (2015), Millner et al. (2013); and Berger et al. (2017).

  2. The SCC is the damages caused by emitting carbon. According to Burke et al (2016, p. 292), the SCC estimates the “monetized change in social welfare over all future time from emitting one more tonne of carbon today, conditional on a specific trajectory of future global emissions and economic and demographic growth.”

  3. See Arrow (1951), Hansen (2014), Marinacci (2015); and Hansen and Marinacci (2016) for a discussion, and Aydogan et al. (2018) for empirical evidence.

  4. A model probabilizes uncertainty using “analogies with canonical random mechanisms that serve as benchmark” (Marinacci 2015, p. 1000). So, we can regard random mechanisms as the thermometers of probability.

  5. The notion of “a true model” is a methodologically delicate one that here we take in a pragmatic sense. It permits, inter alia, to abstract from model misspecification issues (a decision-theoretic attempt to model these issues is in Cerreia-Vioglio et al. (2020).

  6. As is usual, we write \(a\succsim b\) if the decision maker prefers action a to action b (i.e., either strictly prefers action a to action b, \(a\succ b\), or is indifferent between the two, \(a\sim b\)).

  7. The state that obtained is possibly not observable. In a dynamic setting, ex post observability becomes a key modelling issue (see Battigalli et al. 2019).

  8. The differences observed in the projection of the climate response to \({\hbox {CO}}_{2}\) emissions are due to different reasons such as different transient climate responses or carbon sensitivities as explained in the Supplementary Information of Matthews et al. (2009).

  9. DICE stands for Dynamic Integrated Climate and Economy (Nordhaus 1993; Nordhaus and Sztorc 2013). The damage function presented in Eq. (4) is the one in the DICE code in Nordhaus and Sztorc (2013). It is a slight variant of the version of the quadratic form presented in the theoretical description of DICE, in which climate damages are bounded to \(100\%\) (i.e., climate change is assumed to only reduce current income, but may not destroy pre-existing assets). At low temperature increases, the two versions are virtually identical.

  10. For an overview of these studies, see Pindyck (2013a), and Heal and Millner (2014).

  11. Models used for projections of future temperature increases are those whose results on transient climate response are reported in the IPCC fifth assessment report. The hypothesis that current nationally determined contributions are projected beyond 2030 is made here for these projections. See Bosetti et al. (2017) for more details.

  12. That is, \(\delta _{\theta }\left( \theta \right) =1\) and \(\delta _{\theta } \left( \theta ^{\prime } \right) =0\) if \(\theta ^{\prime }\ne \theta\).

  13. To ease matters, we restrict our attention to finite state and model spaces. Integrals with respect to probability density functions would arise without such assumption.

  14. Note that these decision criteria have axiomatic behavioral foundations that clarify their nature. We refer interested readers to Gilboa and Marinacci (2013).

  15. The unanimity criterion (13) is based on the general form of Bewley’s (2002) model studied by Gilboa et al. (2010) but it is conceptually different in that here \({\varTheta }\times {\varSigma }\) is posited.

  16. See Klibanoff et al. (2005), who show that \(\lambda\) can be interpreted as the coefficient of absolute of ambiguity aversion.

  17. The gross level of output and the abatement costs are also potentially uncertain. However, because we focus on the type of uncertainty described previously, here we do not consider these additional sources of uncertainty.

  18. In this example, the consequence function is simply the net output computed as \(\rho (a,\varepsilon ,\theta )=\frac{Y_{{\text {gross}}}-C(a)}{ 1+D(a,\varepsilon ,\theta )}\), where \(Y_{{\text {gross}}}\) is the gross output, \(D(a,\varepsilon ,\theta )\) represents the damages associated with climate change, and C(a) is the abatement cost. Both damages and costs depend on the action taken (a represents the level of GHG emissions). The abatement cost function is assumed to be nearly cubic as in Nordhaus and Sztorc (2013). The von Neumann-Morgernstern utility function u used is a power function, with a constant relative risk aversion coefficient of 1.5.

  19. A certainty equivalent is nothing but a monotonic transformation of an expected utility.

  20. In this example, the model uncertainty aversion function v is also a power function, with a constant relative model uncertainty aversion coefficient of 15. The prior distribution remains the uniform one.

References

  • Arrow KJ (1951) Alternative approaches to the theory of choice in risk-taking situations. Econometrica 19:404–437

    Google Scholar 

  • Athanassoglou S, Xepapadeas A (2012) Pollution control with uncertain stock dynamics: when, and how, to be precautious. J Environ Econ Manag 63(3):304–320

    Google Scholar 

  • Aydogan I, Berger L, Bosetti V, Liu N (2018) Three layers of uncertainty and the role of model misspecification: an experiment. IGIER working papers series, Bocconi University (WP623)

  • Battigalli P, Francetich A, Lanzani G, Marinacci M (2019) Learning and self-confirming long-run biases. J Econ Theory 183:740–785

    Google Scholar 

  • Beck M, Krueger T (2016) The epistemic, ethical, and political dimensions of uncertainty in integrated assessment modeling. Wiley Interdiscip Rev Clim Change 7(5):627–645

    Google Scholar 

  • Berger L (2016) The impact of ambiguity and prudence on prevention decisions. Theor Decis 80(3):389–409. https://doi.org/10.1007/s11238-015-9512-1

    Article  Google Scholar 

  • Berger L, Bosetti V (2020) Are policymakers ambiguity averse? Econ J 130:331–355

    Google Scholar 

  • Berger L, Emmerling J, Tavoni M (2017) Managing catastrophic climate risks under model uncertainty aversion. Manag Sci 63(3):749–765. https://doi.org/10.1287/mnsc.2015.2365

    Article  Google Scholar 

  • Bewley TF (2002) Knightian decision theory. Part I. Decis Econ Finance 25(2):79–110

    Google Scholar 

  • Bosetti V, Weber E, Berger L, Budescu DV, Liu N, Tavoni M (2017) COP21 climate negotiators’ responses to climate model forecasts. Nat Clim Change 7(3):185–191

    Google Scholar 

  • Bradley R, Helgeson C, Hill B (2017) Climate change assessments: confidence, probability, and decision. Philos Sci 84(3):500–522

    Google Scholar 

  • Brock WA, Hansen LP (2018) Wrestling with uncertainty in climate economic models. University of Chicago, Becker Friedman Institute for Economics Working Paper 2019–71

    Google Scholar 

  • Broome J (2012) Climate Matters: Ethics in a Warming World (Norton Global Ethics Series). WW Norton & Company, New York City

    Google Scholar 

  • Burke M, Craxton M, Kolstad C, Onda C, Allcott H, Baker E, Barrage L, Carson R, Gillingham K, Graff-Zivin J et al (2016) Opportunities for advances in climate change economics. Science 352(6283):292–293

    Google Scholar 

  • Cerreia-Vioglio S (2016) Objective rationality and uncertainty averse preferences. Theor Econ 11(2):523–545

    Google Scholar 

  • Cerreia-Vioglio S, Maccheroni F, Marinacci M, Montrucchio L (2011) Uncertainty averse preferences. J Econ Theory 146(4):1275–1330

    Google Scholar 

  • Cerreia-Vioglio S, Maccheroni F, Marinacci M, Montrucchio L (2013) Classical subjective expected utility. Proc Nat Acad Sci 110(17):6754–6759

    Google Scholar 

  • Cerreia-Vioglio S, Lars HP, Maccheroni F, Marinacci M (2020) Making decisions under model misspecification. Mimeo, New York

    Google Scholar 

  • Chambers RG, Melkonyan T (2017) Ambiguity, reasoned determination, and climate-change policy. J Environ Econ Manag 81:74–92

    Google Scholar 

  • Convery FJ, Wagner G (2015) Managing uncertain climates: some guidance for policy makers and researchers. Rev Environ Econ Policy 9:304–320

    Google Scholar 

  • Deser C, Phillips A, Bourdette V, Teng H (2012) Uncertainty in climate change projections: the role of internal variability. Clim Dyn 38(3):527–546

    Google Scholar 

  • Drouet L, Bosetti V, Tavoni M (2015) Selection of climate policies under the uncertainties in the fifth assessment report of the IPCC. Nat Clim Change 5:937–940

    Google Scholar 

  • Dupuis P, Ellis RS (1997) A weak convergence approach to the theory of large deviations, vol 902. Wiley, New York

    Google Scholar 

  • Ellsberg D (1961) Risk, ambiguity, and the Savage axioms. Q J Econ 75:643–669

    Google Scholar 

  • Friedlingstein P, Cox P, Betts R, Bopp L, Von Bloh W, Brovkin V, Cadule P, Doney S, Eby M, Fung I et al (2006) Climate-carbon cycle feedback analysis: results from the C4MIP model intercomparison. J Clim 19(14):3337–3353

    Google Scholar 

  • Ghirardato P, Maccheroni F, Marinacci M (2004) Differentiating ambiguity and ambiguity attitude. J Econ Theory 118(2):133–173

    Google Scholar 

  • Gilboa I, Marinacci M (2013) Ambiguity and the Bayesian paradigm. In: Acemoglu D, Arellano M, Dekel E (eds) Advances in economics and econometrics: theory and applications, tenth world congress of the econometric society. Cambridge University Press, New York

    Google Scholar 

  • Gilboa I, Schmeidler D (1989) Maxmin expected utility with a non-unique prior. J Math Econ 18(2):141–154

    Google Scholar 

  • Gilboa I, Postlewaite AW, Schmeidler D (2008) Probability and uncertainty in economic modeling. J Econ Perspect 22(3):173–188

    Google Scholar 

  • Gilboa I, Postlewaite A, Schmeidler D (2009) Is it always rational to satisfy Savage’s axioms? Econ Philos 25(03):285–296

    Google Scholar 

  • Gilboa I, Maccheroni F, Marinacci M, Schmeidler D (2010) Objective and subjective rationality in a multiple prior model. Econometrica 78(2):755–770

    Google Scholar 

  • Gilboa I, Postlewaite A, Schmeidler D (2012) Rationality of belief or: why Savage’s axioms are neither necessary nor sufficient for rationality. Synthese 187(1):11–31

    Google Scholar 

  • Hansen LP (2014) Nobel lecture: uncertainty outside and inside economic models. J Polit Econ 122(5):945–987

    Google Scholar 

  • Hansen LP, Marinacci M (2016) Ambiguity aversion and model misspecification: an economic perspective. Stat Sci 31:511–515

    Google Scholar 

  • Hansen LP, Sargent TJ (2001) Robust control and model uncertainty. Am Econ Rev 91(2):60–66

    Google Scholar 

  • Hansen LP, Sargent TJ (2007) Recursive robust estimation and control without commitment. J Econ Theory 136(1):1–27

    Google Scholar 

  • Hansen LP, Sargent TJ (2008) Robustness. Princeton University Press, Princeton

    Google Scholar 

  • Hansen J, Sato M, Ruedy R, Lo K, Lea DW, Medina-Elizade M (2006) Global temperature change. Proc Nat Acad Sci 103(39):14,288–14,293

    Google Scholar 

  • Heal G, Millner A (2014) Uncertainty and decision in climate change economics. Rev Environ Econ Policy 8(1):120–137

    Google Scholar 

  • Hill B (2013) Confidence and decision. Games Econ Behav 82:675–692

    Google Scholar 

  • Howard P (2014) Omitted damages: what’s missing from the social cost of carbon. The cost of carbon project

  • Howard P, Sterner T, et al (2014) Loaded dice: refining the meta-analysis approach to calibrating climate damage functions. In: 2014 annual meeting, Minneapolis, Minnesota, Agricultural and Applied Economics Association, p 169952

  • IPCC (2007) Climate change 2007: mitigation of climate change. [B. Metz, O. R. Davidson, P.R. Bosch, R. Dave, L. A. Meyer (eds.)] Cambridge, UK, and New York: Cambridge University Press

  • IPCC (2013) Climate change 2013: the physical science basis. [Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P.M. Midgley (eds.)]. Cambridge, UK and New York: Cambridge University Press, 1535 pp

  • IPCC (2014a) Climate change 2014: impacts, adaptation, and vulnerability. [Field, C.B., V.R. Barros, D.J. Dokken, K.J. Mach, M.D. Mastrandrea, T.E. Bilir, M. Chatterjee, K.L. Ebi, Y.O. Estrada, R.C. Genova, B. Girma, E.S. Kissel, A.N. Levy, S. MacCracken, P.R. Mastrandrea, L.L. White]. New York: Cambridge University Press, 1132 pp

  • IPCC (2014b) Climate change 2014: synthesis report. [Core Writing Team, R.K. Pachauri and L.A. Meyer (eds.)]. IPCC, Geneva, Switzerland, 151 pp

  • Keynes JM (1921) A treatise on probability. Macmillan and Co, London

    Google Scholar 

  • Keynes JM (1936) The general theory of employment, interest, and money. Harcourt, Brace, New York

    Google Scholar 

  • Klibanoff P, Marinacci M, Mukerji S (2005) A smooth model of decision making under ambiguity. Econometrica 73:1849–1892

    Google Scholar 

  • Knight F (1921) Risk, uncertainty, and profit. Houghton Mifflin, Boston

    Google Scholar 

  • Koopmans TC (1947) Measurement without theory. Rev Econ Stat 29(3):161–172

    Google Scholar 

  • Kunreuther H, Heal G, Allen M, Edenhofer O, Field CB, Yohe G (2013) Risk management and climate change. Nat Clim Change 3(5):447–450

    Google Scholar 

  • Lange A, Treich N (2008) Uncertainty, learning and ambiguity in economic models on climate policy: some classical results and new directions. Clim Change 89(1):7–21

    Google Scholar 

  • Lemoine D, Traeger CP (2016) Ambiguous tipping points. J Econ Behav Organ 132:5–18

    Google Scholar 

  • Maccheroni F, Marinacci M, Rustichini A (2006) Ambiguity aversion, robustness, and the variational representation of preferences. Econometrica 74(6):1447–1498

    Google Scholar 

  • Mäki U (2011) Models and the locus of their truth. Synthese 180(1):47–63

    Google Scholar 

  • Marinacci M (2015) Model uncertainty. J Eur Econ Assoc 13(6):1022–1100. https://doi.org/10.1111/jeea.12164

    Article  Google Scholar 

  • Marschak J (1953) Economic measurements for policy and prediction. In: Hood W, Koopmans TJ (eds) Studies in econometric method. Wiley, New York, pp 1–26

    Google Scholar 

  • Marschak J, Radner R (1972) Economic theory of teams. Yale University Press, New Haven

    Google Scholar 

  • Matthews HD, Gillett NP, Stott PA, Zickfeld K (2009) The proportionality of global warming to cumulative carbon emissions. Nature 459(7248):829–832

    Google Scholar 

  • Meinshausen M, Meinshausen N, Hare W, Raper SC, Frieler K, Knutti R, Frame DJ, Allen MR (2009) Greenhouse-gas emission targets for limiting global warming to 2 c. Nature 458(7242):1158–1162

    Google Scholar 

  • Millner A, Dietz S, Heal G (2013) Scientific ambiguity and climate policy. Environ Resour Econ 55(1):21–46

    Google Scholar 

  • Mukerji S (2009) Foundations of ambiguity and economic modelling. Econ Philos 25(03):297–302

    Google Scholar 

  • von Neumann J, Morgenstern O (1947) Theory of games and economic behavior, 2nd edn. Princeton University Press, Princeton

    Google Scholar 

  • Nordhaus WD (1993) Optimal greenhouse-gas reductions and tax policy in the dice model. Am Econ Rev 83:313–317

    Google Scholar 

  • Nordhaus W, Sztorc P (2013) Dice 2013r: introduction and user’s manual. Retrieved November

  • Pindyck R (2007) Uncertainty in environmental economics. Rev Environ Econ Policy 1(1):45

    Google Scholar 

  • Pindyck RS (2013a) Climate change policy: what do the models tell us? J Econ Lit 51(3):860–72

    Google Scholar 

  • Pindyck RS (2013b) The climate policy dilemma. Rev Environ Econ Policy 7(2):219–237

    Google Scholar 

  • Pindyck RS (2015) The use and misuse of models for climate policy. Technial report, National Bureau of Economic Research

  • Rezai A, van der Ploeg R (2017) Climate policies under climate model uncertainty: max-min and min-max regret. Energy Econ 68:4–16

    Google Scholar 

  • Rudik I (2020) Optimal climate policy when damages are unknown. Am Econ J Econ Policy 12(2):340–373

    Google Scholar 

  • Savage LJ (1951) The theory of statistical decision. J Am Stat Assoc 46(253):55–67

    Google Scholar 

  • Savage L (1954) The foundations of statistics, 2nd edn. Wiley, New York, p 1972

    Google Scholar 

  • Schmeidler D (1989) Subjective probability and expected utility without additivity. Econometrica 57(3):571–587

    Google Scholar 

  • Stern N et al (2016) Current climate models are grossly misleading. Nature 530:407–409

    Google Scholar 

  • Wakker PP (2010) Prospect theory: for risk and ambiguity. Cambridge University Press, Cambridge

    Google Scholar 

  • Wald A (1950) Statistical decision functions. Wiley, New York

    Google Scholar 

  • Weitzman M (2009) On modeling and interpreting the economics of catastrophic climate change. Rev Econ Stat 91(1):1–19

    Google Scholar 

  • Weitzman ML (2012) GHG targets as insurance against catastrophic climate damages. J Public Econ Theory 14(2):221–244 00066

    Google Scholar 

  • Xepapadeas A, Yannacopoulos A (2017) Spatially structured deep uncertainty, robust control, and climate change policies. Mimeo, New York

    Google Scholar 

Download references

Acknowledgements

We are grateful to Valentina Bosetti, Laurent Drouet, Johannes Emmerling and Phoebe Koundouri for helpful comments and discussions. We acknowledge audiences at the 23rd conference of the European Association of Environmental and Resource Economists and at the 6th World Congress of Environmental and Resource Economists for their helpful comments.

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Authors and Affiliations

  1. CNRS, IESEG School of Management, Univ. Lille, UMR 9221 - LEM, 59000, Lille, France

    Loïc Berger

  2. RFF-CMCC European Institute on Economics and the Environment (EIEE), Centro Euro-Mediterraneo sui Cambiamenti Climatici, 20123, Milan, Italy

    Loïc Berger

  3. Department of Decision Sciences and IGIER, Universita Bocconi, 20136, Milan, Italy

    Massimo Marinacci

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  1. Loïc Berger
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Correspondence to Loïc Berger.

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This work was supported by the AXA Chair in Risk at Bocconi University, the European Research Council (ERC) under the European Union’s [Seventh Framework Programme (FP7-2007-2013)] (Grant Agreement No. 336703) and [Horizon 2020 research and innovation programme] (Grant Agreement No. 670337), and the French Agence Nationale de la Recherche (ANR), under Grants ANR-17-CE03-0008-01.

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Berger, L., Marinacci, M. Model Uncertainty in Climate Change Economics: A Review and Proposed Framework for Future Research. Environ Resource Econ 77, 475–501 (2020). https://doi.org/10.1007/s10640-020-00503-3

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Keywords

  • Ambiguity
  • Non-expected utility
  • Model uncertainty
  • Climate change

JEL Classification

  • D81
  • Q54