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An extension of quasi-hyperbolic discounting to continuous time

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  • Pan, Jinrui
  • Webb, Craig S.
  • Zank, Horst

Abstract

Two-Stage Exponential (TSE) discounting, the model developed here, generalises exponential discounting in a parsimonious way. It can be seen as an extension of Quasi-Hyperbolic discounting to continuous time. A TSE discounter has a constant rate of time preference before and after some threshold time; the switch point. If the switch point is expressed in calendar time, TSE discounting captures time consistent behaviour. If it is expressed in waiting time, TSE discounting captures time invariant behaviour. We provide preference foundations for all cases, showing how the switch point is derived endogenously from behaviour. We apply each case to Rubinstein's infinite-horizon, alternating-offers bargaining model.

Suggested Citation

  • Pan, Jinrui & Webb, Craig S. & Zank, Horst, 2015. "An extension of quasi-hyperbolic discounting to continuous time," Games and Economic Behavior, Elsevier, vol. 89(C), pages 43-55.
  • Handle: RePEc:eee:gamebe:v:89:y:2015:i:c:p:43-55
    DOI: 10.1016/j.geb.2014.11.003
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    References listed on IDEAS

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    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Takeuchi, Kan, 2011. "Non-parametric test of time consistency: Present bias and future bias," Games and Economic Behavior, Elsevier, vol. 71(2), pages 456-478, March.
    3. José Luis Montiel Olea & Tomasz Strzalecki, 2014. "Axiomatization and Measurement of Quasi-Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 129(3), pages 1449-1499.
    4. Benoît, Jean-Pierre & Ok, Efe A., 2007. "Delay aversion," Theoretical Economics, Econometric Society, vol. 2(1), pages 71-113, March.
    5. Ted O'Donoghue & Matthew Rabin, 2001. "Choice and Procrastination," The Quarterly Journal of Economics, Oxford University Press, vol. 116(1), pages 121-160.
    6. 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.
    7. Mohammed Abdellaoui & Han Bleichrodt & Olivier l’Haridon, 2013. "Sign-dependence in intertemporal choice," Journal of Risk and Uncertainty, Springer, vol. 47(3), pages 225-253, December.
    8. Jamison, Dean T. & Jamison, Julian, 2011. "Characterizing the Amount and Speed of Discounting Procedures," Journal of Benefit-Cost Analysis, Cambridge University Press, vol. 2(02), pages 1-56, April.
    9. Peter J. Hammond, 1976. "Changing Tastes and Coherent Dynamic Choice," Review of Economic Studies, Oxford University Press, vol. 43(1), pages 159-173.
    10. Geir B. Asheim, 1997. "Individual and Collective Time-Consistency," Review of Economic Studies, Oxford University Press, vol. 64(3), pages 427-443.
    11. Erzo G. J. Luttmer & Thomas Mariotti, 2003. "Subjective Discounting in an Exchange Economy," Journal of Political Economy, University of Chicago Press, vol. 111(5), pages 959-989, October.
    12. Zafer Akin, 2007. "Time inconsistency and learning in bargaining games," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 275-299, October.
    13. repec:wsi:wschap:9789813235816_0011 is not listed on IDEAS
    14. Baillon, Aurélien & Driesen, Bram & Wakker, Peter P., 2012. "Relative concave utility for risk and ambiguity," Games and Economic Behavior, Elsevier, vol. 75(2), pages 481-489.
    15. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-1668, December.
    16. John D. Hey & Gianna Lotito, 2018. "Naive, resolute or sophisticated? A study of dynamic decision making," World Scientific Book Chapters,in: Experiments in Economics Decision Making and Markets, chapter 11, pages 275-299 World Scientific Publishing Co. Pte. Ltd..
    17. Jamison Dean T. & Jamison Julian, 2011. "Characterizing the Amount and Speed of Discounting Procedures," Journal of Benefit-Cost Analysis, De Gruyter, vol. 2(2), pages 1-56, April.
    18. Veronika Köbberling & Peter P. Wakker, 2003. "Preference Foundations for Nonexpected Utility: A Generalized and Simplified Technique," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 395-423, August.
    19. Diecidue, Enrico & Schmidt, Ulrich & Zank, Horst, 2009. "Parametric weighting functions," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1102-1118, May.
    20. Christopher Harris & David Laibson, 2013. "Instantaneous Gratification," The Quarterly Journal of Economics, Oxford University Press, vol. 128(1), pages 205-248.
    21. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
    22. Mohammed Abdellaoui & ArthurE. Attema & Han Bleichrodt, 2010. "Intertemporal Tradeoffs for Gains and Losses: An Experimental Measurement of Discounted Utility," Economic Journal, Royal Economic Society, vol. 120(545), pages 845-866, June.
    23. Arthur E. Attema & Han Bleichrodt & Kirsten I. M. Rohde & Peter P. Wakker, 2010. "Time-Tradeoff Sequences for Analyzing Discounting and Time Inconsistency," Management Science, INFORMS, vol. 56(11), pages 2015-2030, November.
    24. Hayashi, Takashi, 2003. "Quasi-stationary cardinal utility and present bias," Journal of Economic Theory, Elsevier, vol. 112(2), pages 343-352, October.
    25. 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.
    26. Noor, Jawwad, 2011. "Intertemporal choice and the magnitude effect," Games and Economic Behavior, Elsevier, vol. 72(1), pages 255-270, May.
    27. repec:wsi:wschap:9789813235816_0010 is not listed on IDEAS
    28. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 443-478.
    29. Charles Blackorby & David Nissen & Daniel Primont & R. Robert Russell, 1973. "Consistent Intertemporal Decision Making," Review of Economic Studies, Oxford University Press, vol. 40(2), pages 239-248.
    30. Ok, Efe A. & Masatlioglu, Yusufcan, 2007. "A theory of (relative) discounting," Journal of Economic Theory, Elsevier, vol. 137(1), pages 214-245, November.
    31. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 185-199.
    32. Mohammed Abdellaoui & Olivier l’Haridon & Horst Zank, 2009. "Separating Curvature and Elevation: A Parametric Weighting Function," The School of Economics Discussion Paper Series 0901, Economics, The University of Manchester.
    33. John D. Hey & Luca Panaccione, 2018. "Dynamic decision making: what do people do?," World Scientific Book Chapters,in: Experiments in Economics Decision Making and Markets, chapter 10, pages 235-273 World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. repec:kap:jrisku:v:56:y:2018:i:3:d:10.1007_s11166-018-9281-7 is not listed on IDEAS
    2. Nicolas Drouhin, 2017. "Non stationary additive utility and time consistency," Working Papers halshs-01238584, HAL.
    3. Webb, Craig S., 2016. "Continuous quasi-hyperbolic discounting," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 99-106.
    4. Sebastian Schweighofer-Kodritsch, 2015. "Time Preferences and Bargaining," STICERD - Theoretical Economics Paper Series /2015/568, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    5. Nina Anchugina, 2017. "A simple framework for the axiomatization of exponential and quasi-hyperbolic discounting," Theory and Decision, Springer, vol. 82(2), pages 185-210, February.
    6. Lu, Shih En, 2016. "Self-control and bargaining," Journal of Economic Theory, Elsevier, vol. 165(C), pages 390-413.

    More about this item

    Keywords

    Discounting; Present bias; Decreasing impatience; Bargaining;

    JEL classification:

    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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