IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2201.10673.html
   My bibliography  Save this paper

Robust Comparative Statics for the Elasticity of Intertemporal Substitution

Author

Listed:
  • Joel P. Flynn
  • Lawrence D. W. Schmidt
  • Alexis Akira Toda

Abstract

We study a general class of consumption-savings problems with recursive preferences. We characterize the sign of the consumption response to arbitrary shocks in terms of the product of two sufficient statistics: the elasticity of intertemporal substitution between contemporaneous consumption and continuation utility (EIS), and the relative elasticity of the marginal value of wealth (REMV). Under homotheticity, the REMV always equals one, so the propensity of the agent to save or dis-save is always signed by the relationship of the EIS with unity. We apply our results to derive comparative statics in classical problems of portfolio allocation, consumption-savings with income risk, and entrepreneurial investment. Our results suggest empirical identification strategies for both the value of the EIS and its relationship with unity.

Suggested Citation

  • Joel P. Flynn & Lawrence D. W. Schmidt & Alexis Akira Toda, 2022. "Robust Comparative Statics for the Elasticity of Intertemporal Substitution," Papers 2201.10673, arXiv.org.
    • Handle: RePEc:arx:papers:2201.10673
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2201.10673
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    2. Massimiliano Croce, Mariano, 2014. "Long-run productivity risk: A new hope for production-based asset pricing?," Journal of Monetary Economics, Elsevier, vol. 66(C), pages 13-31.
    3. Weil, Philippe, 1989. "The equity premium puzzle and the risk-free rate puzzle," Journal of Monetary Economics, Elsevier, vol. 24(3), pages 401-421, November.
    4. 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..
    5. Nengjiu Ju & Jianjun Miao, 2012. "Ambiguity, Learning, and Asset Returns," Econometrica, Econometric Society, vol. 80(2), pages 559-591, March.
    6. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    7. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    8. , & ,, 2011. "Intertemporal substitution and recursive smooth ambiguity preferences," Theoretical Economics, Econometric Society, vol. 6(3), September.
    9. Havranek, Tomas & Horvath, Roman & Irsova, Zuzana & Rusnak, Marek, 2015. "Cross-country heterogeneity in intertemporal substitution," Journal of International Economics, Elsevier, vol. 96(1), pages 100-118.
    10. Philippe Weil, 1993. "Precautionary Savings and the Permanent Income Hypothesis," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(2), pages 367-383.
    11. repec:bla:jfinan:v:59:y:2004:i:4:p:1481-1509 is not listed on IDEAS
    12. Pierre-Olivier Gourinchas & Jonathan A. Parker, 2002. "Consumption Over the Life Cycle," Econometrica, Econometric Society, vol. 70(1), pages 47-89, January.
    13. Campbell, John Y. & Giglio, Stefano & Polk, Christopher & Turley, Robert, 2018. "An intertemporal CAPM with stochastic volatility," Journal of Financial Economics, Elsevier, vol. 128(2), pages 207-233.
    14. Campbell, John Y, 1993. "Intertemporal Asset Pricing without Consumption Data," American Economic Review, American Economic Association, vol. 83(3), pages 487-512, June.
    15. Felipe S. Iachan & Plamen T. Nenov & Alp Simsek, 2021. "The Choice Channel of Financial Innovation," American Economic Journal: Macroeconomics, American Economic Association, vol. 13(2), pages 333-372, April.
    16. A. Sandmo, 1970. "The Effect of Uncertainty on Saving Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(3), pages 353-360.
    17. Takashi Hayashi, 2005. "Intertemporal substitution, risk aversion and ambiguity aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(4), pages 933-956, June.
    18. Matthew Smith & Danny Yagan & Owen Zidar & Eric Zwick, 2019. "Capitalists in the Twenty-First Century," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 134(4), pages 1675-1745.
    19. Greg Kaplan & Giovanni L. Violante, 2014. "A Model of the Consumption Response to Fiscal Stimulus Payments," Econometrica, Econometric Society, vol. 82(4), pages 1199-1239, July.
    20. Toda, Alexis Akira, 2014. "Incomplete market dynamics and cross-sectional distributions," Journal of Economic Theory, Elsevier, vol. 154(C), pages 310-348.
    21. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
    22. Jerusalem D. Levhari & T. N. Srinivasan, 1969. "Optimal Savings under Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(2), pages 153-163.
    23. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    24. Itamar Drechsler & Amir Yaron, 2011. "What's Vol Got to Do with It," The Review of Financial Studies, Society for Financial Studies, vol. 24(1), pages 1-45.
    25. Robert J. Barro, 2009. "Rare Disasters, Asset Prices, and Welfare Costs," American Economic Review, American Economic Association, vol. 99(1), pages 243-264, March.
    26. Sebastian Di Tella, 2017. "Uncertainty Shocks and Balance Sheet Recessions," Journal of Political Economy, University of Chicago Press, vol. 125(6), pages 2038-2081.
    27. Epstein, Larry G., 1988. "Risk aversion and asset prices," Journal of Monetary Economics, Elsevier, vol. 22(2), pages 179-192, September.
    28. repec:hal:spmain:info:hdl:2441/8686 is not listed on IDEAS
    29. Georg Kaltenbrunner & Lars A. Lochstoer, 2010. "Long-Run Risk through Consumption Smoothing," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 3190-3224, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Julian Thimme, 2017. "Intertemporal Substitution In Consumption: A Literature Review," Journal of Economic Surveys, Wiley Blackwell, vol. 31(1), pages 226-257, February.
    2. Segal, Gill, 2019. "A tale of two volatilities: Sectoral uncertainty, growth, and asset prices," Journal of Financial Economics, Elsevier, vol. 134(1), pages 110-140.
    3. Hengjie Ai & Ravi Bansal, 2016. "Risk Preferences and The Macro Announcement Premium," NBER Working Papers 22527, National Bureau of Economic Research, Inc.
    4. Hui Chen & Nengjiu Ju & Jianjun Miao, 2014. "Dynamic Asset Allocation with Ambiguous Return Predictability," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(4), pages 799-823, October.
    5. Julian Thimme & Clemens Völkert, 2015. "High order smooth ambiguity preferences and asset prices," Review of Financial Economics, John Wiley & Sons, vol. 27(1), pages 1-15, November.
    6. Nengjiu Ju & Jianjun Miao, 2012. "Ambiguity, Learning, and Asset Returns," Econometrica, Econometric Society, vol. 80(2), pages 559-591, March.
    7. Thimme, Julian & Völkert, Clemens, 2015. "High order smooth ambiguity preferences and asset prices," Review of Financial Economics, Elsevier, vol. 27(C), pages 1-15.
    8. Rhys Bidder & Ian Dew-Becker, 2016. "Long-Run Risk Is the Worst-Case Scenario," American Economic Review, American Economic Association, vol. 106(9), pages 2494-2527, September.
    9. Isoré, Marlène & Szczerbowicz, Urszula, 2017. "Disaster risk and preference shifts in a New Keynesian model," Journal of Economic Dynamics and Control, Elsevier, vol. 79(C), pages 97-125.
    10. Sumru Altug & Cem Cakmakli & Fabrice Collard & Sujoy Mukerji & Han Ozsoylev, 2020. "Ambiguous Business Cycles: A Quantitative Assessment," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 38, pages 220-237, October.
    11. Jianjun Miao & Bin Wei & Hao Zhou, 2019. "Ambiguity Aversion and the Variance Premium," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 1-36, June.
    12. Hening Liu & Yuzhao Zhang, 2022. "Financial Uncertainty with Ambiguity and Learning," Management Science, INFORMS, vol. 68(3), pages 2120-2140, March.
    13. Turnovsky, Stephen J. & Smith, William T., 2006. "Equilibrium consumption and precautionary savings in a stochastically growing economy," Journal of Economic Dynamics and Control, Elsevier, vol. 30(2), pages 243-278, February.
    14. Langlais, Eric, 1995. "A measure of the sensitivity of saving to interest rate uncertainty with non-expected preferences," Economics Letters, Elsevier, vol. 48(3-4), pages 325-330, June.
    15. 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..
    16. David K. Backus & Bryan R. Routledge & Stanley E. Zin, 2005. "Exotic Preferences for Macroeconomists," NBER Chapters, in: NBER Macroeconomics Annual 2004, Volume 19, pages 319-414, National Bureau of Economic Research, Inc.
    17. Danilo Cascaldi-Garcia & Cisil Sarisoy & Juan M. Londono & Bo Sun & Deepa D. Datta & Thiago Ferreira & Olesya Grishchenko & Mohammad R. Jahan-Parvar & Francesca Loria & Sai Ma & Marius Rodriguez & Ilk, 2023. "What Is Certain about Uncertainty?," Journal of Economic Literature, American Economic Association, vol. 61(2), pages 624-654, June.
    18. Ghosh, Gagan & Liu, Heng, 2021. "Sequential auctions with ambiguity," Journal of Economic Theory, Elsevier, vol. 197(C).
    19. Sumru Altug & Cem Cakmakli & Fabrice Collard & Sujoy Mukerji & Han Ozsoylev, 2020. "Ambiguous Business Cycles: A Quantitative Assessment," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 38, pages 220-237, October.
    20. Zhao, Guihai, 2017. "Confidence, bond risks, and equity returns," Journal of Financial Economics, Elsevier, vol. 126(3), pages 668-688.

    More about this item

    JEL classification:

    • D15 - Microeconomics - - Household Behavior - - - Intertemporal Household Choice; Life Cycle Models and Saving

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2201.10673. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.