Journal of Risk and Uncertainty

, Volume 38, Issue 2, pp 87–94 | Cite as

A note on uncertainty and discounting in models of economic growth

  • Kenneth J. ArrowEmail author


The implications of uncertainty for appropriate discounting in models of economic growth have been studied at some length, notably, (Review of Economic Studies, 36:153–163; 1969) and (Journal of Public Economics, 85:149–166; 2002). A detailed account has now appeared in Journal of Risk and Uncertainty, 37:141–169; 2008, sections 4 and 5 (pp. 160–166). One interesting, if perhaps minor, aspect is that under certain circumstances, there appeared to be no solution or at least no satisfactory one. More importantly, the formulas are usually given for the log normal case and are somewhat complicated and hard to interpret intuitively. I show here that assuming a general distribution for returns to capital gives simpler and more understandable results.


Uncertainty Discount rate Intertemporal optimization Relative risk aversion 


C61 D9 H43 O41 



Preparation of this study was made possible by a grant from the William and Flora Hewlett Foundation. I am indebted for many discussions with Partha Dasgupta on the role of uncertainty in climate change problems.


  1. Bernoulli, D. (1738). Specimen theoriae novae de mensura sortis. Comentarii academiae scientiararum imperialis Petropolitanae, 5, 175–192; translated as, (1954). Exposition of a new theory on the measurement of risk, Econometrica, 22, 23–36.Google Scholar
  2. Dasgupta, P. (2008). Discounting climate change. Journal of Risk and Uncertainty, 37, 141–169.CrossRefGoogle Scholar
  3. Gollier, C. (2002). Discounting an uncertain future. Journal of Public Economics, 85, 149–166.CrossRefGoogle Scholar
  4. Gollier, C. (2008). Discounting with fat-tailed economic growth. Journal of Risk and Uncertainty, 37, 171–186.CrossRefGoogle Scholar
  5. Levhari, D., & Srinivasan, T. N. (1969). Optimal savings under uncertainty. Review of Economic Studies, 36, 153–163.CrossRefGoogle Scholar
  6. Menger, K. (1934). Das Unsicherheitsmoment in der Wertlehre. Betrachtungen im Anschluss an das sogennante Petersburger Spiel. Zeitschrift für Nationalökonomie, 5, 459–485.CrossRefGoogle Scholar
  7. Rothschild, M., & Stiglitz, J. (1970). Increasing risk: I. Definition. Journal of Economic Theory, 2, 225–243.CrossRefGoogle Scholar
  8. Weitzman, M. L. (forthcoming). On models of interpreting the economics of catastrophic climate change. Review of Economics and Statistics.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of EconomicsStanford UniversityStanfordUSA

Personalised recommendations