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On Learning and Growth

Author

Listed:
  • Leonard J. Mirman
  • Kevin Reffett
  • Marc Santugini

Abstract

We study optimal growth under learning. We extend the Mirman-Zilcha stochastic growth results characterizing optimal programs for general utility and production functions to the case of learning. We then use recursive methods to study the effect of learning on the dynamic program by considering the case of iso-elastic utility and linear production, for general distributions of the random shocks and beliefs (i.e., without the use of conjugate priors), for any horizon. Finally, we address the issue of experimentation by providing a solution to an infinite-horizon optimal dynamic program.

Suggested Citation

  • Leonard J. Mirman & Kevin Reffett & Marc Santugini, 2013. "On Learning and Growth," Cahiers de recherche 1336, CIRPEE.
    • Handle: RePEc:lvl:lacicr:1336
    as

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    File URL: http://www.cirpee.org/fileadmin/documents/Cahiers_2013/CIRPEE13-36.pdf
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    Other versions of this item:

    • Leonard J. Mirman & Kevin Reffett & Marc Santugini, 2016. "On learning and growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(4), pages 641-684, April.

    References listed on IDEAS

    as
    1. Philippe Aghion & Patrick Bolton & Christopher Harris & Bruno Jullien, 1991. "Optimal Learning by Experimentation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(4), pages 621-654.
    2. Sanford J. Grossman & Richard E. Kihlstrom & Leonard J. Mirman, 1977. "A Bayesian Approach to the Production of Information and Learning By Doing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(3), pages 533-547.
    3. Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2008. "A qualitative approach to Markovian equilibrium in infinite horizon economies with capital," Journal of Economic Theory, Elsevier, vol. 139(1), pages 75-98, March.
    4. Fishman, Arthur & Gandal, Neil, 1994. "Experimentation and learning with networks effects," Economics Letters, Elsevier, vol. 44(1-2), pages 103-108.
    5. Easley, David & Kiefer, Nicholas M, 1989. "Optimal Learning with Endogenous Data," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(4), pages 963-978, November.
    6. Wieland, Volker, 2000. "Learning by doing and the value of optimal experimentation," Journal of Economic Dynamics and Control, Elsevier, vol. 24(4), pages 501-534, April.
    7. William A. Brock & Leonard J. Mirman, 2001. "Optimal Economic Growth And Uncertainty: The Discounted Case," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 1, pages 3-37, Edward Elgar Publishing.
    8. Beck, Gunter W. & Wieland, Volker, 2002. "Learning and control in a changing economic environment," Journal of Economic Dynamics and Control, Elsevier, vol. 26(9-10), pages 1359-1377, August.
    9. Mirman, Leonard J & Samuelson, Larry & Urbano, Amparo, 1993. "Monopoly Experimentation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(3), pages 549-563, August.
    10. Creane, Anthony, 1994. "Experimentation with Heteroskedastic Noise," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 275-286, March.
    11. Balvers, Ronald J & Cosimano, Thomas F, 1990. "Actively Learning about Demand and the Dynamics of Price Adjustment," Economic Journal, Royal Economic Society, vol. 100(402), pages 882-898, September.
    12. Bertocchi, Graziella & Spagat, Michael, 1998. "Growth under uncertainty with experimentation," Journal of Economic Dynamics and Control, Elsevier, vol. 23(2), pages 209-231, September.
    13. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-1406, November.
    14. El-Gamal, Mahmoud A. & Sundaram, Rangarajan K., 1993. "Bayesian economists ... Bayesian agents : An alternative approach to optimal learning," Journal of Economic Dynamics and Control, Elsevier, vol. 17(3), pages 355-383, May.
    15. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 11(3), pages 329-339, December.
    16. Leonard Mirman & Olivier Morand & Kevin Reffett, "undated". "A Qualitative Theory of Markovian Equilibrium in Infinite Horizon Economies with Capital," Working Papers 2133376, Department of Economics, W. P. Carey School of Business, Arizona State University.
    17. Koulovatianos, Christos & Mirman, Leonard J. & Santugini, Marc, 2009. "Optimal growth and uncertainty: Learning," Journal of Economic Theory, Elsevier, vol. 144(1), pages 280-295, January.
    18. Mirman, Leonard J. & Zilcha, Itzhak, 1977. "Characterizing optimal policies in a one-sector model of economic growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 14(2), pages 389-401, April.
    19. Trefler, Daniel, 1993. "The Ignorant Monopolist: Optimal Learning with Endogenous Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(3), pages 565-581, August.
    20. Prescott, Edward C, 1972. "The Multi-Period Control Problem Under Uncertainty," Econometrica, Econometric Society, vol. 40(6), pages 1043-1058, November.
    21. Manjira Datta & Leonard J. Mirman & Edward E. Schlee, 2002. "Optimal Experimentation in Signal Dependent Decision Problems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(2), pages 577-608, May.
    22. Kiefer, Nicholas M & Nyarko, Yaw, 1989. "Optimal Control of an Unknown Linear Process with Learning," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(3), pages 571-586, August.
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    Cited by:

    1. La Torre, Davide & Marsiglio, Simone & Mendivil, Franklin & Privileggi, Fabio, 2016. "Fractal Attractors and Singular Invariant Measures in Two-Sector Growth Models with Random Factor Shares," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201620, University of Turin.
    2. Fu, Wentao & Le Riche, Antoine, 2021. "Endogenous growth model with Bayesian learning and technology selection," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 58-71.

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    More about this item

    Keywords

    Brock-Mirman environment; Dynamic programming; Euler equation; Experimentation; Learning; Optimal growth;
    All these keywords.

    JEL classification:

    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • D9 - Microeconomics - - Micro-Based Behavioral Economics
    • E2 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment

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