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Dynamic Programming with State-Dependent Discounting

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  • John Stachurski
  • Junnan Zhang

Abstract

This paper extends the core results of discrete time infinite horizon dynamic programming to the case of state-dependent discounting. We obtain a condition on the discount factor process under which all of the standard optimality results can be recovered. We also show that the condition cannot be significantly weakened. Our framework is general enough to handle complications such as recursive preferences and unbounded rewards. Economic and financial applications are discussed.

Suggested Citation

  • John Stachurski & Junnan Zhang, 2019. "Dynamic Programming with State-Dependent Discounting," Papers 1908.08800, arXiv.org, revised Oct 2020.
    • Handle: RePEc:arx:papers:1908.08800
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    1. Justiniano, Alejandro & Primiceri, Giorgio E. & Tambalotti, Andrea, 2010. "Investment shocks and business cycles," Journal of Monetary Economics, Elsevier, vol. 57(2), pages 132-145, March.
    2. Gauti B. Eggertsson, 2011. "What Fiscal Policy Is Effective at Zero Interest Rates?," NBER Chapters, in: NBER Macroeconomics Annual 2010, volume 25, pages 59-112, National Bureau of Economic Research, Inc.
    3. Patrick J. Kehoe & Virgiliu Midrigan & Elena Pastorino, 2018. "Evolution of Modern Business Cycle Models: Accounting for the Great Recession," Journal of Economic Perspectives, American Economic Association, vol. 32(3), pages 141-166, Summer.
    4. John Y. Campbell, 1986. "Bond and Stock Returns in a Simple Exchange Model," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 785-803.
    5. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09j003nctkn is not listed on IDEAS
    6. Karen Kopecky & Richard Suen, 2010. "Finite State Markov-chain Approximations to Highly Persistent Processes," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(3), pages 701-714, July.
    7. Michael Woodford, 2011. "Simple Analytics of the Government Expenditure Multiplier," American Economic Journal: Macroeconomics, American Economic Association, vol. 3(1), pages 1-35, January.
    8. Timothy S. Hills & Taisuke Nakata, 2018. "Fiscal Multipliers at the Zero Lower Bound: The Role of Policy Inertia," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 50(1), pages 155-172, February.
    9. Edi Karni & Itzhak Zilcha, 2000. "Saving behavior in stationary equilibrium with random discounting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(3), pages 551-564.
    10. Andreas Fagereng & Martin Blomhoff Holm & Benjamin Moll & Gisle Natvik, 2019. "Saving Behavior Across the Wealth Distribution: The Importance of Capital Gains," NBER Working Papers 26588, National Bureau of Economic Research, Inc.
    11. Alejandro Justiniano & Giorgio E. Primiceri, 2008. "The Time-Varying Volatility of Macroeconomic Fluctuations," American Economic Review, American Economic Association, vol. 98(3), pages 604-641, June.
    12. Frank Schorfheide & Dongho Song & Amir Yaron, 2018. "Identifying Long‐Run Risks: A Bayesian Mixed‐Frequency Approach," Econometrica, Econometric Society, vol. 86(2), pages 617-654, March.
    13. repec:hal:wpspec:info:hdl:2441/eu4vqp9ompqllr09j003nctkn is not listed on IDEAS
    14. Timothy S. Hills & Taisuke Nakata & Sebastian Schmidt, 2016. "The Risky Steady State and the Interest Rate Lower Bound," Finance and Economics Discussion Series 2016-9, Board of Governors of the Federal Reserve System (U.S.).
    15. Jean‐Marc Robin, 2011. "On the Dynamics of Unemployment and Wage Distributions," Econometrica, Econometric Society, vol. 79(5), pages 1327-1355, September.
    16. Rui Albuquerque & Martin Eichenbaum & Victor Xi Luo & Sergio Rebelo, 2016. "Valuation Risk and Asset Pricing," Journal of Finance, American Finance Association, vol. 71(6), pages 2861-2904, December.
    17. Martin Beraja & Erik Hurst & Juan Ospina, 2019. "The Aggregate Implications of Regional Business Cycles," Econometrica, Econometric Society, vol. 87(6), pages 1789-1833, November.
    18. Stephen Williamson, 2019. "Low real interest rates and the zero lower bound," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 31, pages 36-62, January.
    19. Higashi, Youichiro & Hyogo, Kazuya & Takeoka, Norio, 2009. "Subjective random discounting and intertemporal choice," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1015-1053, May.
    20. R. Vijay Krishna & Philipp Sadowski, 2014. "Dynamic Preference for Flexibility," Econometrica, Econometric Society, vol. 82(2), pages 655-703, March.
    21. Dan Cao, 2018. "Recursive Equilibrium in Krusell and Smith (1998)," Working Papers gueconwpa~18-18-13, Georgetown University, Department of Economics.
    22. Isabel Correia & Emmanuel Farhi & Juan Pablo Nicolini & Pedro Teles, 2013. "Unconventional Fiscal Policy at the Zero Bound," American Economic Review, American Economic Association, vol. 103(4), pages 1172-1211, June.
    23. Saijo, Hikaru, 2017. "The uncertainty multiplier and business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 78(C), pages 1-25.
    24. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September.
    25. David González-Sánchez & Fernando Luque-Vásquez & J. Adolfo Minjárez-Sosa, 2019. "Zero-Sum Markov Games with Random State-Actions-Dependent Discount Factors: Existence of Optimal Strategies," Dynamic Games and Applications, Springer, vol. 9(1), pages 103-121, March.
    26. Lawrence Christiano & Martin Eichenbaum & Sergio Rebelo, 2011. "When Is the Government Spending Multiplier Large?," Journal of Political Economy, University of Chicago Press, vol. 119(1), pages 78-121.
    27. Mehra, Rajnish & Sah, Raaj, 2002. "Mood fluctuations, projection bias, and volatility of equity prices," Journal of Economic Dynamics and Control, Elsevier, vol. 26(5), pages 869-887, May.
    28. Albuquerque, Rui & Eichenbaum, Martin & Papanikolaou, Dimitris & Rebelo, Sergio, 2015. "Long-run bulls and bears," Journal of Monetary Economics, Elsevier, vol. 76(S), pages 21-36.
    29. Anmol Bhandari & David Evans & Mikhail Golosov & Thomas J. Sargent, 2013. "Taxes, Debts, and Redistributions with Aggregate Shocks," NBER Working Papers 19470, National Bureau of Economic Research, Inc.
    30. J. J. McCall, 1970. "Economics of Information and Job Search," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 84(1), pages 113-126.
    31. Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, vol. 50(2), pages 326-345, April.
    32. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    33. Per Krusell & Toshihiko Mukoyama & Aysegul Sahin & Anthony A. Smith, Jr., 2009. "Revisiting the Welfare Effects of Eliminating Business Cycles," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 12(3), pages 393-402, July.
    34. Lawrence J. Christiano & Roberto Motto & Massimo Rostagno, 2014. "Risk Shocks," American Economic Review, American Economic Association, vol. 104(1), pages 27-65, January.
    35. Robert Shimer, 2005. "The Cyclical Behavior of Equilibrium Unemployment and Vacancies," American Economic Review, American Economic Association, vol. 95(1), pages 25-49, March.
    36. Robert E. Hall, 2017. "High Discounts and High Unemployment," American Economic Review, American Economic Association, vol. 107(2), pages 305-330, February.
    37. V. Filipe Martins-da-Rocha & Yiannis Vailakis, 2010. "Existence and Uniqueness of a Fixed Point for Local Contractions," Econometrica, Econometric Society, vol. 78(3), pages 1127-1141, May.
    38. Youichiro Higashi & Kazuya Hyogo & Norio Takeoka & Hiroyuki Tanaka, 2017. "Comparative impatience under random discounting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(3), pages 621-651, March.
    39. Gauti B. Eggertsson & Michael Woodford, 2003. "The Zero Bound on Interest Rates and Optimal Monetary Policy," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 34(1), pages 139-235.
    40. Lucas, Robert Jr. & Prescott, Edward C., 1974. "Equilibrium search and unemployment," Journal of Economic Theory, Elsevier, vol. 7(2), pages 188-209, February.
    41. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
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    1. Dynamic Programming with State-Dependent Discounting
      by Christian Zimmermann in NEP-DGE blog on 2019-09-25 22:14:42

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