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On time-consistent policy rules for heterogeneous discounting programs

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  • Drugeon, Jean-Pierre
  • Wigniolle, Bertrand

Abstract

This article considers a new concept of social optimum for an economy populated by agents with heterogeneous discount factors. It is based upon an approach that constrains decision rules to be temporally consistent: these are stationary and unequivocally ruled by the state variable. For agents who differ only in their discount factors and have equal weights in the planner’s objective, the temporally-consistent optimal solution produces identical consumption for the agents at all time periods. In the long run, the capital stock is determined by a modified golden rule that corresponds to an average-like summation of all discount factors. The general argument is illustrated by various two-agent examples that allow for an explicit determination of the temporally consistent decision rules. Interestingly, this temporally consistent solution can be simply recovered from the characterization of a social planner’s problem with variable discounting and can also be decentralized as a competitive equilibrium through the use of various instruments.

Suggested Citation

  • Drugeon, Jean-Pierre & Wigniolle, Bertrand, 2016. "On time-consistent policy rules for heterogeneous discounting programs," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 174-187.
  • Handle: RePEc:eee:mateco:v:63:y:2016:i:c:p:174-187
    DOI: 10.1016/j.jmateco.2016.01.006
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    1. Cuong Le Van & Yiannis Vailakis, 2003. "Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 743-771, November.
    2. Becker, Robert & Zilcha, Itzhak, 1997. "Stationary Ramsey Equilibria under Uncertainty," Journal of Economic Theory, Elsevier, vol. 75(1), pages 122-140, July.
    3. Harris, Christopher & Laibson, David, 2001. "Dynamic Choices of Hyperbolic Consumers," Econometrica, Econometric Society, vol. 69(4), pages 935-957, July.
    4. Per Krusell & Anthony A. Smith, Jr., 2003. "Consumption--Savings Decisions with Quasi--Geometric Discounting," Econometrica, Econometric Society, vol. 71(1), pages 365-375, January.
    5. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 185-199.
    6. Robert A. Becker, 2012. "Optimal growth with heterogeneous agents and the twisted turnpike: An example," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(1), pages 27-47, March.
    7. Robert A. Becker, 1980. "On the Long-Run Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 95(2), pages 375-382.
    8. Mitra, Tapan, 1979. "On Optimal Economic Growth with Variable Discount Rates: Existence and Stability Results," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(1), pages 133-145, February.
    9. Epstein, Larry G, 1987. "The Global Stability of Efficient Intertemporal Allocations," Econometrica, Econometric Society, vol. 55(2), pages 329-355, March.
    10. Becker, Robert A. & Foias, Ciprian, 2007. "Strategic Ramsey equilibrium dynamics," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 318-346, April.
    11. Sorger, Gerhard, 2002. "On the Long-Run Distribution of Capital in the Ramsey Model," Journal of Economic Theory, Elsevier, vol. 105(1), pages 226-243, July.
    12. Coles, Jeffrey Link, 1985. "Equilibrium Turnpike Theory with Constant Returns to Scale and Possible Heterogeneous Discount Factors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 671-679, October.
    13. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
    14. Coles, Jeffrey L., 1986. "Equilibrium turnpike theory with time-separable utility," Journal of Economic Dynamics and Control, Elsevier, vol. 10(3), pages 367-394, September.
    15. Cuong Le Van & Yiannis Vailakis, 2003. "Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment," Post-Print halshs-00119095, HAL.
    16. Epstein, Larry G., 1987. "A simple dynamic general equilibrium model," Journal of Economic Theory, Elsevier, vol. 41(1), pages 68-95, February.
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    Cited by:

    1. Jean-Pierre Drugeon & Bertrand Wigniolle, 2017. "On Time-Consistent Collective Choice with Heterogeneous Quasi- Hyperbolic Discounting," PSE Working Papers halshs-01662833, HAL.
    2. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2018. "On uniqueness of time-consistent Markov policies for quasi-hyperbolic consumers under uncertainty," Journal of Economic Theory, Elsevier, vol. 176(C), pages 293-310.
    3. Jean-Pierre Drugeon & Bertrand Wigniolle, 2017. "On impatience, temptation and Ramsey’s conjecture," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 73-98, January.
    4. Mikhail Pakhnin, 2021. "Collective Choice with Heterogeneous Time Preferences," CESifo Working Paper Series 9141, CESifo.
    5. Jean-Pierre Drugeon & Bertrand Wigniolle, 2021. "On Markovian collective choice with heterogeneous quasi-hyperbolic discounting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1257-1296, November.

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    More about this item

    Keywords

    Time-consistent policy rules; Heterogeneous discounting programs;

    JEL classification:

    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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