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A Theory of Average Growth Rate Indices

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  • Alexander Alexeev
  • Mikhail Sokolov

Abstract

This paper develops an axiomatic theory of an economic variable average growth rate (average rate of change) measurement. The structures that we obtain generalize the conventional measures for average rate of growth (such as the difference quotient, the continuously compounded growth rate, etc.) to an arbitrary domain of the underlying variable and comprise various models of growth. These structures can be described with the help of intertemporal choice theory by means of parametric families of time preference relations on the 'prize-time' space with a parameter representing the subjective discount rate.

Suggested Citation

  • Alexander Alexeev & Mikhail Sokolov, 2013. "A Theory of Average Growth Rate Indices," EUSP Department of Economics Working Paper Series Ec-05/13, European University at St. Petersburg, Department of Economics.
  • Handle: RePEc:eus:wpaper:ec0513
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    References listed on IDEAS

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    1. Basu, Kaushik, 1983. "Cardinal utility, utilitarianism, and a class of invariance axioms in welfare analysis," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 193-206, December.
    2. Fishburn, Peter C & Rubinstein, Ariel, 1982. "Time Preference," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(3), pages 677-694, October.
    3. David Promislow, S. & Spring, David, 1996. "Postulates for the internal rate of return of an investment project," Journal of Mathematical Economics, Elsevier, vol. 26(3), pages 325-361.
    4. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
    5. Fishburn, Peter C, 1973. "A Mixture-Set Axiomatization of Conditional Subjective Expected Utility," Econometrica, Econometric Society, vol. 41(1), pages 1-25, January.
    6. Thomas Epper & Helga Fehr-Duda & Adrian Bruhin, 2011. "Viewing the future through a warped lens: Why uncertainty generates hyperbolic discounting," Journal of Risk and Uncertainty, Springer, vol. 43(3), pages 169-203, December.
    7. Read, Daniel, 2001. "Is Time-Discounting Hyperbolic or Subadditive?," Journal of Risk and Uncertainty, Springer, vol. 23(1), pages 5-32, July.
    8. Uri Benzion & Amnon Rapoport & Joseph Yagil, 1989. "Discount Rates Inferred from Decisions: An Experimental Study," Management Science, INFORMS, vol. 35(3), pages 270-284, March.
    9. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 573-597.
    10. Thistle, Paul D., 1993. "Negative Moments, Risk Aversion, and Stochastic Dominance," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(02), pages 301-311, June.
    11. Dubra, Juan, 2009. "A theory of time preferences over risky outcomes," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 576-588, September.
    12. Marc Scholten & Daniel Read, 2006. "Discounting by Intervals: A Generalized Model of Intertemporal Choice," Management Science, INFORMS, vol. 52(9), pages 1424-1436, September.
    13. Ok, Efe A. & Masatlioglu, Yusufcan, 2007. "A theory of (relative) discounting," Journal of Economic Theory, Elsevier, vol. 137(1), pages 214-245, November.
    14. Bleichrodt, Han & Rohde, Kirsten I.M. & Wakker, Peter P., 2009. "Non-hyperbolic time inconsistency," Games and Economic Behavior, Elsevier, vol. 66(1), pages 27-38, May.
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    Cited by:

    1. Alexander Alekseev & Mikhail Sokolov, 2016. "Portfolio Return Relative to a Benchmark," EUSP Department of Economics Working Paper Series Ec-04/16, European University at St. Petersburg, Department of Economics.
    2. Aleksandr G. Alekseev & Mikhail V. Sokolov, 2016. "Benchmark-based evaluation of portfolio performance: a characterization," Annals of Finance, Springer, vol. 12(3), pages 409-440, December.

    More about this item

    Keywords

    average growth rate; average rate of change; time preferences; discounting;

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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