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Annual Review of Resource Economics

Volume 13, 2021

Understanding the Improbable: A Survey of Fat Tails in Environmental Economics

Abstract

We survey the growing literature on fat-tailed distributions in environmental economics. We then examine the theoretical and statistical properties of such distributions, focusing especially on when these properties are likely to arise in environmental problems. We find that a number of variables are fat tailed in environmental economics, including the climate sensitivity, natural disaster impacts, spread of infectious diseases, and stated willingness to pay. We argue that different fat-tailed distributions arise from common pathways. Finally, we review the literature on the policy implications of fat-tailed distributions and controversies over their interpretation. We conclude that the literature has made great strides in demonstrating when fat tails matter for optimal environmental policy. Yet, much is less well understood, including how alternative policies affect fat-tailed distributions, the optimal policy in a computational economy with many fat-tailed problems, and how to account for imprecision in empirical tests for fat tails.

Keyword(s): climate sensitivity, dismal theorem, environmental economics, existence value, fat tails, infectious disease, JEL I18, JEL Q51, JEL Q54, JEL Q58, natural disasters
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2021-10-05
2024-04-18
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Literature Cited

  1. Adamowicz W, Louviere J, Williams M. 1994. Combining revealed and stated preference methods for valuing environmental amenities. J. Environ. Econ. Manag. 26:3271–92
     [Google Scholar]
  2. Allen MR, Frame DJ. 2007. Call off the quest. Science 318:5850582–83
     [Google Scholar]
  3. Armour KC, Bitz CM, Roe GH. 2013. Time-varying climate sensitivity from regional feedbacks. J. Clim. 26:134518–34
     [Google Scholar]
  4. Atreya A, Ferreira S, Kriesel W. 2013. Forgetting the flood? An analysis of the flood risk discount over time. Land Econ 89:4577–96
     [Google Scholar]
  5. Bakkensen LA, Barrage L. 2017. Flood risk belief heterogeneity and coastal home price dynamics: Going under water? NBER Work. Rep. 23854. https://www.nber.org/papers/w23854
  6. Bakkensen LA, Mendelsohn RO. 2016. Risk and adaptation: evidence from global hurricane damages and fatalities. J. Assoc. Environ. Resour. Econ. 3:3555–87
     [Google Scholar]
  7. Ball F, Mollison D, Scalia-Tomba G. 1997. Epidemics with two levels of mixing. Ann. Appl. Probab. 7:146–89
     [Google Scholar]
  8. Bansal S, Grenfell BT, Meyers LA. 2007. When individual behaviour matters: homogeneous and network models in epidemiology. J. R. Soc. Interface 4:16879–91
     [Google Scholar]
  9. Barabási AL, Albert R 1999. Emergence of scaling in random networks. Science 286:5439509–12
     [Google Scholar]
  10. Bin O, Landry CE. 2013. Changes in implicit flood risk premiums: empirical evidence from the housing market. J. Environ. Econ. Manag. 65:3361–76
     [Google Scholar]
  11. Bistline JE. 2015. Fat-tailed uncertainty, learning, and climate policy. Clim. Change Econ. 6:2 https://doi.org/10.1142/S2010007815500098
    [Crossref] [Google Scholar]
  12. Bjørnstad ON, Finkenstädt BF, Grenfell BT. 2002. Dynamics of measles epidemics: estimating scaling of transmission rates using a time series SIR model. Ecol. Monogr. 72:2169–84
     [Google Scholar]
  13. Born P, Viscusi WK. 2006. The catastrophic effects of natural disasters on insurance markets. J. Risk Uncertain. 33:1–255–72
     [Google Scholar]
  14. Botzen WW, van den Bergh JC. 2009. Bounded rationality, climate risks, and insurance: Is there a market for natural disasters?. Land Econ 85:2265–78
     [Google Scholar]
  15. Boyle K 2003. Contingent valuation in practice. A Primer on Non-Market Valuation PA Champ, KJ Boyle, TC Brown 111–70 Dordrecht, Neth: Kluwer Acad.
     [Google Scholar]
  16. Brauer F 2008. Compartmental models in epidemiology. Mathematical Epidemiology F Brauer, P van den Driessche, J Wu19–79 Berlin: Springer
     [Google Scholar]
  17. Browne MJ, Hoyt RE. 2000. The demand for flood insurance: empirical evidence. J. Risk Uncertain. 20:3291–306
     [Google Scholar]
  18. Calel R, Stainforth DA, Dietz S. 2015. Tall tales and fat tails: the science and economics of extreme warming. Clim. Change 132:1127–41
     [Google Scholar]
  19. Castillo E, Hadi AS. 1997. Fitting the generalized Pareto distribution to data. J. Am. Stat. Assoc. 92:4401609–20
     [Google Scholar]
  20. Cent. Dis. Control Prev 2000. Measles outbreak—Netherlands, April 1999-January 2000. Morb. Mortal. Wkly. Rep. 49:14299–303
     [Google Scholar]
  21. Chang S, Pierson E, Koh PW, Gerardin J, Redbird B et al. 2021. Mobility network models of COVID-19 explain inequalities and inform reopening. Nature 589:784082–87
     [Google Scholar]
  22. Chaouche A, Bacro JN. 2006. Statistical inference for the generalized Pareto distribution: maximum likelihood revisited. Commun. Stat. Theory Methods 35:5785–802
     [Google Scholar]
  23. Chapman CR. 2004. The hazard of near-Earth asteroid impacts on earth. Earth Planet. Sci. Lett. 222:11–15
     [Google Scholar]
  24. Conte MN, Gordon M, Sims CB. 2020. Fat-tailed contact rate distribution linked to more intense COVID-19 outbreak Work. Pap., Fordham Univ. New York:
  25. Conte MN, Kelly DL. 2018. An imperfect storm: Fat-tailed tropical cyclone damages, insurance, and climate policy. J. Environ. Econ. Manag. 92:677–706
     [Google Scholar]
  26. Conte MN, Kelly DL. 2020. How beliefs change following a natural disaster: evidence from wind insurance data Work. Pap., Univ Miami:
  27. Coronese M, Lamperti F, Keller K, Chiaromonte F, Roventini A 2019. Evidence for sharp increase in the economic damages of extreme natural disasters. PNAS 116:4321450–55
     [Google Scholar]
  28. Costello CJ, Neubert MG, Polasky SA, Solow AR 2010. Bounded uncertainty and climate change economics. PNAS 107:188108–10
     [Google Scholar]
  29. Cox DR, Snell EJ. 1968. A general definition of residuals. J. R. Stat. Soc. B 30:2248–65
     [Google Scholar]
  30. Cribari-Neto F, Vasconcellos KL 2002. Nearly unbiased maximum likelihood estimation for the beta distribution. J. Stat. Comput. Simul. 72:2107–18
     [Google Scholar]
  31. Das B, Resnick SI. 2008. QQ plots, random sets and data from a heavy tailed distribution. Stoch. Models 24:1103–32
     [Google Scholar]
  32. Davison AC, Smith RL. 1990. Models for exceedances over high thresholds. J. R. Stat. Soc. B 52:3393–425
     [Google Scholar]
  33. de Zea Bermudez P, Kotz S 2010. Parameter estimation of the generalized Pareto distribution—part I. J. Stat. Plan. Inference 140:61353–73
     [Google Scholar]
  34. Del Castillo J, Daoudi J. 2009. Estimation of the generalized Pareto distribution. Stat. Probab. Lett. 79:5684–88
     [Google Scholar]
  35. Desvousges WH, Johnson FR, Dunford RW, Hudson SP, Wilson KN, Boyle KJ 1993. Measuring natural resource damages with contingent valuation: tests of validity and reliability. Contingent Valuation: A Critical Assessment JA Hausman 91–164 Bingley, UK: Emerald Group
     [Google Scholar]
  36. Dezso Z, Barbasi A. 2002. Halting viruses in scale-free networks. Phys. Rev. E 65:5055103
     [Google Scholar]
  37. Dietz S. 2011. High impact, low probability? An empirical analysis of risk in the economics of climate change. Clim. Change 108:3519–41
     [Google Scholar]
  38. Embrechts P, Klüppelberg C, Mikosch T. 2013. Modelling Extremal Events for Insurance and Finance New York: Springer Sci. & Bus.
  39. Embrechts P, McNeal A, Frey R. 2005. Quantitative Risk Management: Concepts, Techniques, and Tools Princeton, NJ: Princeton Univ. Press
  40. Firth D. 1993. Bias reduction of maximum likelihood estimates. Biometrika 80:127–38
     [Google Scholar]
  41. Fitzpatrick LG, Kelly DL. 2017. Probabilistic stabilization targets. J. Assoc. Environ. Resour. Econ. 4:2611–57
     [Google Scholar]
  42. Forest CE, Stone PH, Sokolov AP, Allen MR, Webster MD. 2002. Quantifying uncertainties in climate system properties with the use of recent observations. Science 295:113–17
     [Google Scholar]
  43. Gabaix X. 1999. Zipf's law for cities: an explanation. Q. J. Econ. 114:3739–67
     [Google Scholar]
  44. Gallagher J. 2014. Learning about an infrequent event: evidence from flood insurance take-up in the United States. Am. Econ. J. Appl. Econ. 6:3206–33
     [Google Scholar]
  45. Ghosh S, Resnick S. 2010. A discussion on mean excess plots. Stoch. Proc. Appl. 120:81492–517
     [Google Scholar]
  46. Giles DE, Feng H, Godwin RT. 2016. Bias-corrected maximum likelihood estimation of the parameters of the generalized Pareto distribution. Commun. Stat. Theory Methods 45:82465–83
     [Google Scholar]
  47. Gregory JM, Stouffer RJ, Raper SC, Stott PA, Rayner NA. 2002. An observationally based estimate of the climate sensitivity. J. Clim. 15:3117–21
     [Google Scholar]
  48. Grenfell BT, Bjørnstad ON, Finkenstädt BF. 2002. Dynamics of measles epidemics: scaling noise, determinism, and predictability with the TSIR model. Ecol. Monogr. 72:2185–202
     [Google Scholar]
  49. Grimshaw SD. 1993. Computing maximum likelihood estimates for the generalized Pareto distribution. Technometrics 35:2185–91
     [Google Scholar]
  50. Guzzetti F, Ardizzone F, Cardinali M, Rossi M, Valigi D. 2009. Landslide volumes and landslide mobilization rates in Umbria, central Italy. Earth Planet. Sci. Lett. 279:3–4222–29
     [Google Scholar]
  51. Haab TC, McConnell KE. 2002. Valuing Environmental and Natural Resources: The Econometrics of Non-Market Valuation Cheltenham, UK: Edward Elgar
  52. Hanley N, Wright RE, Adamowicz V. 1998. Using choice experiments to value the environment. Environ. Resour. Econ. 11:3–4413–28
     [Google Scholar]
  53. Hegerl GC, Crowley TJ, Hyde WT, Frame DJ. 2006. Climate sensitivity constrained by temperature reconstructions over the past seven centuries. Nature 440:1029–32
     [Google Scholar]
  54. Held IM, Winton M, Takahashi K, Delworth T, Zeng F, Vallis GK. 2010. Probing the fast and slow components of global warming by returning abruptly to preindustrial forcing. J. Clim. 23:92418–27
     [Google Scholar]
  55. Hethcote HW, Yorke JA. 1984. Gonorrhea Transmission Dynamics and Control Lect. Notes Biomath. Vol. 56 Berlin: Springer Verlag
  56. Hogg RV, Klugman SA. 2009. Loss Distributions Hoboken, NJ: John Wiley & Sons
  57. Horowitz J, Lange A. 2014. Cost-benefit analysis under uncertainty—a note on Weitzman's dismal theorem. Energy Econ 42:201–3
     [Google Scholar]
  58. Hosking JR, Wallis JR. 1987. Parameter and quantile estimation for the generalized Pareto distribution. Technometrics 29:3339–49
     [Google Scholar]
  59. Huber M, Knutti R. 2012. Anthropogenic and natural warming inferred from changes in Earth's energy balance. Nat. Geosci. 5:131–36
     [Google Scholar]
  60. Hwang IC, Reynès F, Tol RS. 2013. Climate policy under fat-tailed risk: an application of dice. Environ. Resour. Econ. 56:3415–36
     [Google Scholar]
  61. Hwang IC, Reynès F, Tol RS. 2017. The effect of learning on climate policy under fat-tailed risk. Resour. Energy Econ. 48:1–18
     [Google Scholar]
  62. Hwang IC, Tol RSJ, Hofkes MW. 2016. Fat-tailed risk about climate change and climate policy. Energy Policy 89:25–35
     [Google Scholar]
  63. IPCC (Intergov. Panel Clim. Change) 2007. Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the IPCC S Solomon, D Qin, M Manning, M Marquis, K Averyt et al. Cambridge, UK: Cambridge Univ. Press
  64. Kampas A, White B. 2004. Administrative costs and instrument choice for stochastic non-point source pollutants. Environ. Resour. Econ. 27:109–33
     [Google Scholar]
  65. Karp LS. 2009. Sacrifice, discounting and climate policy: five questions CESifo Work. Pap2761 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1458887
  66. Kayaratna K, McKitrick R, Kreutzer D. 2017. Empirically constrained climate sensitivity and the social cost of carbon. Clim. Change Econ. 8:21750006
     [Google Scholar]
  67. Kelly DL, Kolstad CD. 1999. Bayesian learning, pollution, and growth. J. Econ. Dyn. Control 23:4491–518
     [Google Scholar]
  68. Kelly DL, Tan Z. 2015. Learning and climate feedbacks: optimal climate insurance and fat tails. J. Environ. Econ. Manag. 72:98–122
     [Google Scholar]
  69. Kousky C. 2017. Disasters as learning experiences or disasters as policy opportunities? Examining flood insurance purchases after hurricanes. Risk Anal 37:3517–30
     [Google Scholar]
  70. Kousky C. 2019. The role of natural disaster insurance in recovery and risk reduction. Annu. Rev. Resour. Econ. 11:399–418
     [Google Scholar]
  71. Kousky C, Cooke RM. 2009. The unholy trinity: fat tails, tail dependence, and micro-correlations. Tech. Rep. 09-36 Resour. Future Washington, DC:
     [Google Scholar]
  72. Krutilla JV. 1967. Conservation reconsidered. Am. Econ. Rev. 57:4777–86
     [Google Scholar]
  73. Lemoine D, Traeger CP. 2016. Economics of tipping the climate dominoes. Nat. Clim. Change 6:5514–19
     [Google Scholar]
  74. Levaggi R, Menoncin F. 2013. Optimal dynamic tax evasion. J. Econ. Dyn. Control 37:2157–67
     [Google Scholar]
  75. Lewis N, Curry J. 2018. The impact of recent forcing and ocean heat uptake data on estimates of climate sensitivity. J. Clim. 31:156051–71
     [Google Scholar]
  76. Lewis N, Curry JA. 2015. The implications for climate sensitivity of AR5 forcing and heat uptake estimates. Clim. Dyn. 45:3–41009–23
     [Google Scholar]
  77. Liljeros F, Edling C, Amaral L, Stanley H, Aberg Y. 2001. The web of human sexual networks. Nature 411:907–8
     [Google Scholar]
  78. Lloyd-Smith JO, Schreiber SJ, Kopp PE, Getz WM. 2005. Superspreading and the effect of individual variation on disease emergence. Nature 438:7066355–59
     [Google Scholar]
  79. Mahadevan L, Deutch JM. 2010. Influence of feedback on the stochastic evolution of simple climate systems. Proc. R. Soc. A 466:2116993–1003
     [Google Scholar]
  80. Malamud BD, Millington JD, Perry GL 2005. Characterizing wildfire regimes in the United States. PNAS 102:134694–99
     [Google Scholar]
  81. Malamud BD, Turcotte DL. 2006. The applicability of power-law frequency statistics to floods. J. Hydrol. 322:1–4168–80
     [Google Scholar]
  82. Martin IW, Pindyck RS. 2015. Averting catastrophes: the strange economics of Scylla and Charybdis. Am. Econ. Rev. 105:102947–85
     [Google Scholar]
  83. May RM, Lloyd AL. 2001. Infection dynamics on scale-free networks. Phys. Rev. E 64:6066112
     [Google Scholar]
  84. McFadden D, Leonard G 1993. Issues in the contingent valuation of environmental goods: Methodologies for data collection and analysis. Contingent Valuation: A Critical Assessment JA Hausman 165–215 New York: North-Holland
     [Google Scholar]
  85. Menoncin F, Nembrini S. 2018. Stochastic continuous time growth models that allow for closed form solutions. J. Econ. 124:3213–41
     [Google Scholar]
  86. Meyers LA, Pourbohloul B, Newman ME, Skowronski DM, Brunham RC. 2005. Network theory and SARS: predicting outbreak diversity. J. Theor. Biol. 232:171–81
     [Google Scholar]
  87. Michel-Kerjan EO. 2010. Catastrophe economics: the national flood insurance program. J. Econ. Perspect. 24:4165–86
     [Google Scholar]
  88. Millner A. 2013. On welfare frameworks and catastrophic climate risks. J. Environ. Econ. Manag. 65:2310–25
     [Google Scholar]
  89. Muller NZ, Mendelsohn R. 2009. Efficient pollution regulation: getting the prices right. Am. Econ. Rev. 99:51714–39
     [Google Scholar]
  90. Newbold SC, Daigneault A. 2009. Climate response uncertainty and the benefits of greenhouse gas emissions reductions. Environ. Resour. Econ. 44:3351–77
     [Google Scholar]
  91. Newman ME. 2002. Spread of epidemic disease on networks. Phys. Rev. E 66:1016128
     [Google Scholar]
  92. Nordhaus WD. 2011. The economics of tail events with an application to climate change. Rev. Environ. Econ. Policy 5:2240–57
     [Google Scholar]
  93. Nordhaus WD. 2017. Revisiting the social cost of carbon. PNAS 114:71518–23
     [Google Scholar]
  94. Ott W. 1990. A physical explanation of the lognormality of pollution concentrations. J. Air Waste Manag. Assoc. 40:1378–83
     [Google Scholar]
  95. Parsons G, Myers K 2017. Fat tails and truncated bids in contingent valuation: an application to an endangered shorebird species. Contingent Valuation of Environmental Goods D McFadden, K Train 17–42 Cheltenham, UK: Edward Elgar
     [Google Scholar]
  96. Pastor-Satorras R, Vespignani A 2002. Epidemic dynamics in finite size scale-free networks. Phys. Rev. E 65:3035108
     [Google Scholar]
  97. Picard P. 2008. Natural disaster insurance and the equity-efficiency trade-off. J. Risk Insur. 75:117–38
     [Google Scholar]
  98. Pindyck RS. 2011. Fat tails, thin tails, and climate change policy. Rev. Environ. Econ. Policy 5:258–74
     [Google Scholar]
  99. Poutanen SM, Low DE, Henry B, Finkelstein S, Rose D et al. 2003. Identification of severe acute respiratory syndrome in Canada. N. Engl. J. Med. 348:201995–2005
     [Google Scholar]
  100. Pycroft J, Vergano L, Hope C, Paci D, Ciscar JC. 2011. A tale of tails: uncertainty and the social cost of carbon dioxide. Economics 5:2011–22
     [Google Scholar]
  101. Pyle DM 2015. Sizes of volcanic eruptions. The Encyclopedia of Volcanoes H Sigurdsson 257–64 Amsterdam: Academic
     [Google Scholar]
  102. Roe GH, Baker MB. 2007. Why is climate sensitivity so unpredictable?. Science 318:5850629–32
     [Google Scholar]
  103. Roe GH, Bauman Y. 2013. Climate sensitivity: Should the climate tail wag the policy dog?. Clim. Change 117:4647–62
     [Google Scholar]
  104. Schwartz SE. 2012. Determination of Earth's transient and equilibrium climate sensitivities from observations over the twentieth century: strong dependence on assumed forcing. Surv. Geophys. 33:3–4745–77
     [Google Scholar]
  105. Seller C, Stoll JR, Chavas JP. 1985. Validation of empirical measures of welfare change: a comparison of nonmarket techniques. Land Econ 61:2156–75
     [Google Scholar]
  106. Shaman J, Karspeck A. 2012. Forecasting seasonal outbreaks of influenza. PNAS 109:5020425–30
     [Google Scholar]
  107. Sheldon TL, Zhan C. 2019. The impact of natural disasters on US home ownership. J. Assoc. Environ. Resour. Econ. 6:61169–203
     [Google Scholar]
  108. Shen Z, Ning F, Zhou W, He X, Lin C et al. 2004. Superspreading SARS events, Beijing, 2003. Emerg. Infect. Dis 10:2256–60
     [Google Scholar]
  109. Shirley MD, Rushton SP. 2005. The impacts of network topology on disease spread. Ecol. Complex. 2:3287–99
     [Google Scholar]
  110. Skeie RB, Berntsen T, Aldrin M, Holden M, Myhre G. 2014. A lower and more constrained estimate of climate sensitivity using updated observations and detailed radiative forcing time series. Earth Syst. Dyn. 5:1139–75
     [Google Scholar]
  111. Weinkle J, Landsea C, Collins D, Musulin R, Crompton RP et al. 2018. Normalized hurricane damage in the continental United States 1900–1917. Nat. Sustain. 1:808–13
     [Google Scholar]
  112. Weitzman ML. 2009a. Additive damages, fat-tailed climate dynamics, and uncertain discounting. Economics 3:2009–39
     [Google Scholar]
  113. Weitzman ML. 2009b. On modeling and interpreting the economics of catastrophic climate change. Rev. Econ. Stat. 91:11–19
     [Google Scholar]
  114. Weitzman ML. 2009c. Some basic economics of extreme climate change Work. Pap., Harvard Univ. Cambridge, MA: http://scholar.harvard.edu/files/weitzman/files/basiceconomicsclimatechange.pdf?m=1360041775
  115. Weitzman ML. 2011. Fat-tailed uncertainty in the economics of catastrophic climate change. Rev. Environ. Econ. Policy 5:2275–92
     [Google Scholar]
  116. Weitzman ML. 2014. Fat tails and the social cost of carbon. Am. Econ. Rev. 104:5544–46
     [Google Scholar]
  117. Wong F, Collins JJ 2020. Evidence that coronavirus superspreading is fat-tailed. PNAS 117:4729416–18
     [Google Scholar]
  118. Zhang J, Stephens MA. 2009. A new and efficient estimation method for the generalized Pareto distribution. Technometrics 51:3316–25
     [Google Scholar]
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