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Small noise methods for risk-sensitive/robust economies

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  • Anderson, Evan W.
  • Hansen, Lars Peter
  • Sargent, Thomas J.

Abstract

We provide small noise expansions for the value function and decision rule for the recursive risk-sensitive preferences specified by Hansen and Sargent (1995), Hansen et al. (1999), and Tallarini (2000). We use the expansions (1) to provide a fast method for approximating solutions of dynamic stochastic problems and (2) to quantify the effects on decisions of uncertainty and concerns about robustness to misspecification.

Suggested Citation

  • Anderson, Evan W. & Hansen, Lars Peter & Sargent, Thomas J., 2012. "Small noise methods for risk-sensitive/robust economies," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 468-500.
    • Handle: RePEc:eee:dyncon:v:36:y:2012:i:4:p:468-500
    DOI: 10.1016/j.jedc.2011.11.007
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    1. Fair, Ray C & Taylor, John B, 1983. "Solution and Maximum Likelihood Estimation of Dynamic Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 51(4), pages 1169-1185, July.
    2. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-396, March.
    3. Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Solving DSGE models with perturbation methods and a change of variables," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2509-2531, December.
    4. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    5. Baoline Chen & Peter A. Zadrozny, 2003. "Higher-Moments in Perturbation Solution of the Linear-Quadratic Exponential Gaussian Optimal Control Problem," Computational Economics, Springer;Society for Computational Economics, vol. 21(1_2), pages 45-64, February.
    6. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, December.
    7. Ray Fair, 2003. "Optimal Control and Stochastic Simulation of Large Nonlinear Models with Rational Expectations," Computational Economics, Springer;Society for Computational Economics, vol. 21(3), pages 245-256, June.
    8. Lars Peter Hansen & John C. Heaton & Nan Li, 2008. "Consumption Strikes Back? Measuring Long-Run Risk," Journal of Political Economy, University of Chicago Press, vol. 116(2), pages 260-302, April.
    9. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    10. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Permanent Income and Pricing," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 3, pages 33-81, World Scientific Publishing Co. Pte. Ltd..
    11. Santos, Manuel S., 1994. "Smooth dynamics and computation in models of economic growth," Journal of Economic Dynamics and Control, Elsevier, vol. 18(3-4), pages 879-895.
    12. Judd, Kenneth L., 1996. "Approximation, perturbation, and projection methods in economic analysis," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 12, pages 509-585, Elsevier.
    13. Lars Peter Hansen & Thomas J. Sargent, 2007. "Introduction to Robustness," Introductory Chapters, in: Robustness, Princeton University Press.
    14. TallariniJr., Thomas D., 2000. "Risk-sensitive real business cycles," Journal of Monetary Economics, Elsevier, vol. 45(3), pages 507-532, June.
    15. Williams, Noah, 2004. "Small noise asymptotics for a stochastic growth model," Journal of Economic Theory, Elsevier, vol. 119(2), pages 271-298, December.
    16. Pascal J. Maenhout, 2004. "Robust Portfolio Rules and Asset Pricing," Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 951-983.
    17. Judd, Kenneth L. & Guu, Sy-Ming, 1997. "Asymptotic methods for aggregate growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 1025-1042, June.
    18. Lars Peter Hansen & Thomas J Sargent, 2014. "A Quartet of Semigroups for Model Specification, Robustness, Prices of Risk, and Model Detection," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 4, pages 83-143, World Scientific Publishing Co. Pte. Ltd..
    19. Hansen, Lars Peter & Heaton, John & Lee, Junghoon & Roussanov, Nikolai, 2007. "Intertemporal Substitution and Risk Aversion," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 61, Elsevier.
    20. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1.
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    Cited by:

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    3. Anderson, Evan W. & Brock, William & Sanstad, Alan H., 2016. "Robust Consumption and Energy Decisions," 2017 Allied Social Sciences Association (ASSA) Annual Meeting, January 6-8, 2017, Chicago, Illinois 250117, Agricultural and Applied Economics Association.
    4. Kwon, Hyosung & Miao, Jianjun, 2017. "Three types of robust Ramsey problems in a linear-quadratic framework," Journal of Economic Dynamics and Control, Elsevier, vol. 76(C), pages 211-231.
    5. Cho, In-Koo & Kasa, Kenneth, 2014. "An escape time interpretation of robust control," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 1-12.
    6. Nicole Bauerle & Anna Ja'skiewicz, 2015. "Stochastic Optimal Growth Model with Risk Sensitive Preferences," Papers 1509.05638, arXiv.org.
    7. Agliardi, Elettra & Xepapadeas, Anastasios, 2022. "Temperature targets, deep uncertainty and extreme events in the design of optimal climate policy," Journal of Economic Dynamics and Control, Elsevier, vol. 139(C).
    8. Kasa, Kenneth & Lei, Xiaowen, 2018. "Risk, uncertainty, and the dynamics of inequality," Journal of Monetary Economics, Elsevier, vol. 94(C), pages 60-78.
    9. Anmol Bhandari & David Evans & Mikhail Golosov & Thomas J. Sargent, 2018. "Inequality, Business Cycles, and Monetary-Fiscal Policy," Working Papers 18-26, New York University, Leonard N. Stern School of Business, Department of Economics.
    10. Brock, William & Xepapadeas, Anastasios, 2021. "Regional climate policy under deep uncertainty: robust control and distributional concerns," Environment and Development Economics, Cambridge University Press, vol. 26(3), pages 211-238, June.
    11. Balbus, Łukasz & Jaśkiewicz, Anna & Nowak, Andrzej S., 2015. "Stochastic bequest games," Games and Economic Behavior, Elsevier, vol. 90(C), pages 247-256.
    12. Ellison, Martin & Sargent, Thomas J., 2012. "Welfare cost of business cycles in economies with individual consumption risk," Bank of Finland Research Discussion Papers 25/2012, Bank of Finland.
    13. Ellison, Martin & Sargent, Thomas J., 2012. "Welfare cost of business cycles in economies with individual consumption risk," Research Discussion Papers 25/2012, Bank of Finland.
    14. William Brock & Anastasios Xepapadeas, 2020. "Spatial Environmental and Resource Economics," DEOS Working Papers 2002, Athens University of Economics and Business.
    15. Boyarchenko, Nina, 2012. "Ambiguity shifts and the 2007–2008 financial crisis," Journal of Monetary Economics, Elsevier, vol. 59(5), pages 493-507.
    16. Bäuerle, Nicole & Jaśkiewicz, Anna, 2018. "Stochastic optimal growth model with risk sensitive preferences," Journal of Economic Theory, Elsevier, vol. 173(C), pages 181-200.
    17. Jaśkiewicz, Anna & Nowak, Andrzej S., 2014. "Stationary Markov perfect equilibria in risk sensitive stochastic overlapping generations models," Journal of Economic Theory, Elsevier, vol. 151(C), pages 411-447.
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    19. Martin Ellison & Thomas J. Sargent, 2015. "Welfare Cost of Business Cycles with Idiosyncratic Consumption Risk and a Preference for Robustness," American Economic Journal: Macroeconomics, American Economic Association, vol. 7(2), pages 40-57, April.
    20. Lee, Sang Seok & Luk, Paul, 2018. "The Asian Financial Crisis and international reserve accumulation: A robust control approach," Journal of Economic Dynamics and Control, Elsevier, vol. 90(C), pages 284-309.

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    More about this item

    Keywords

    Computational economics; Recursive utility; Perturbation methods; Stochastic growth model;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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