IDEAS home Printed from https://ideas.repec.org/a/eee/ecmode/v23y2006i3p492-505.html
   My bibliography  Save this article

Indeterminacy in a log-linearized neoclassical growth model with quasi-geometric discounting

Author

Listed:
  • Maliar, Lilia
  • Maliar, Serguei

Abstract

This paper studies the properties of solutions to a log-linearized version of the neoclassical growth model with quasi-geometric discounting. We show that after the log-linearization, the model has indeterminacy and multiplicity of equilibria even though the original non-linear model has a unique interior solution. Specifically, in both the deterministic and stochastic cases, the log-linearized model has a continuum of steady states. In the deterministic case, there is a unique log-linear policy function leading to each steady state, while in the stochastic case, there is a continuum of log-linear policy functions, associated with each steady state. Hence, the standard log-linearization method cannot be applied for solving models with quasi-geometric discounting.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Maliar, Lilia & Maliar, Serguei, 2006. "Indeterminacy in a log-linearized neoclassical growth model with quasi-geometric discounting," Economic Modelling, Elsevier, vol. 23(3), pages 492-505, May.
    • Handle: RePEc:eee:ecmode:v:23:y:2006:i:3:p:492-505
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0264-9993(06)00015-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Per Krusell & Anthony A. Smith, Jr., 2003. "Consumption--Savings Decisions with Quasi--Geometric Discounting," Econometrica, Econometric Society, vol. 71(1), pages 365-375, January.
    2. Krusell, Per & Kuruscu, Burhanettin & Smith, Anthony Jr., 2002. "Equilibrium Welfare and Government Policy with Quasi-geometric Discounting," Journal of Economic Theory, Elsevier, vol. 105(1), pages 42-72, July.
    3. Thaler, Richard H, 1990. "Saving, Fungibility, and Mental Accounts," Journal of Economic Perspectives, American Economic Association, vol. 4(1), pages 193-205, Winter.
    4. Thaler, Richard H & Shefrin, H M, 1981. "An Economic Theory of Self-Control," Journal of Political Economy, University of Chicago Press, vol. 89(2), pages 392-406, April.
    5. David I. Laibson & Andrea Repetto & Jeremy Tobacman, 1998. "Self-Control and Saving for Retirement," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 29(1), pages 91-196.
    6. Caillaud, Bernard & Jullien, Bruno, 2000. "Modelling time-inconsistent preferences," European Economic Review, Elsevier, vol. 44(4-6), pages 1116-1124, May.
    7. Lilia Maliar & Serguei Maliar, 2003. "Solving The Neoclassical Growth Model With Quasi-Geometric Discounting: Non-Linear Euler-Equation Models," Working Papers. Serie AD 2003-23, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    8. Harris, Christopher & Laibson, David, 2001. "Dynamic Choices of Hyperbolic Consumers," Econometrica, Econometric Society, vol. 69(4), pages 935-957, July.
    9. Lilia Maliar & Serguei Maliar, 2005. "Solving the Neoclassical Growth Model with Quasi-Geometric Discounting: A Grid-Based Euler-Equation Method," Computational Economics, Springer;Society for Computational Economics, vol. 26(2), pages 163-172, October.
    10. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 573-597.
    11. George-Marios Angeletos & David Laibson & Andrea Repetto & Jeremy Tobacman & Stephen Weinberg, 2001. "The Hyberbolic Consumption Model: Calibration, Simulation, and Empirical Evaluation," Journal of Economic Perspectives, American Economic Association, vol. 15(3), pages 47-68, Summer.
    12. Robert J. Barro, 1999. "Ramsey Meets Laibson in the Neoclassical Growth Model," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(4), pages 1125-1152.
    13. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
    14. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Richard Dennis & Oleg Kirsanov, 2020. "Monetary Policy when Preferences are Quasi-Hyperbolic," Working Papers 2020_05, Business School - Economics, University of Glasgow.

    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. Maliar, Lilia & Maliar, Serguei, 2006. "The Neoclassical Growth Model with Heterogeneous Quasi-Geometric Consumers," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(3), pages 635-654, April.
    2. Lilia Maliar & Serguei Maliar, 2016. "Ruling Out Multiplicity of Smooth Equilibria in Dynamic Games: A Hyperbolic Discounting Example," Dynamic Games and Applications, Springer, vol. 6(2), pages 243-261, June.
    3. Lilia Maliar & Serguei Maliar, 2003. "Heterogeneity In The Degree Of Quasi-Geometric Discounting: The Distributional Implications," Working Papers. Serie AD 2003-28, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    4. Breugelmans, E. & Campo, K. & Gijsbrechts, E., 2005. "Shelf sequence and proximity effects on online grocery choices," Research Memorandum 053, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    5. Kirill Borissov & Mikhail Pakhnin & Ronald Wendner, 2020. "Naive Agents with Quasi-hyperbolic Discounting and Perfect Foresight," EUSP Department of Economics Working Paper Series 2020/03, European University at St. Petersburg, Department of Economics.
    6. Chatterjee, Satyajit & Eyigungor, Burcu, 2016. "Continuous Markov equilibria with quasi-geometric discounting," Journal of Economic Theory, Elsevier, vol. 163(C), pages 467-494.
    7. Liya Liu & Yingjie Niu & Yuanping Wang & Jinqiang Yang, 2020. "Optimal consumption with time-inconsistent preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 785-815, October.
    8. Christopher Harris & David Laibson, 2013. "Instantaneous Gratification," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(1), pages 205-248.
    9. Lilia Maliar & Serguei Maliar, 2003. "Solving The Neoclassical Growth Model With Quasi-Geometric Discounting: Non-Linear Euler-Equation Models," Working Papers. Serie AD 2003-23, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    10. Anke Gerbe & Kirsten I.M. Rohde, 2010. "Risk and Preference Reversals in Intertemporal Choice," Post-Print hal-00911832, HAL.
    11. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2013. "Ambiguous Survival Beliefs and Hyperbolic Discounting in a Life-Cycle Model," VfS Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79878, Verein für Socialpolitik / German Economic Association.
    12. Gerber, Anke & Rohde, Kirsten I.M., 2010. "Risk and preference reversals in intertemporal choice," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 654-668, December.
    13. Chen Lian, 2021. "Mistakes in Future Consumption, High MPCs Now," NBER Working Papers 29517, National Bureau of Economic Research, Inc.
    14. Chen, Shumin & Luo, Dan & Yao, Haixiang, 2024. "Optimal investor life cycle decisions with time-inconsistent preferences," Journal of Banking & Finance, Elsevier, vol. 161(C).
    15. Tyson, Christopher J., 2008. "Management of a capital stock by Strotz's naive planner," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2214-2239, July.
    16. Hanming Fang & Dan Silverman, 2009. "Time-Inconsistency And Welfare Program Participation: Evidence From The Nlsy," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 50(4), pages 1043-1077, November.
    17. Hammond, Peter J & Zank, Horst, 2013. "Rationality and Dynamic Consistency under Risk and Uncertainty," The Warwick Economics Research Paper Series (TWERPS) 1033, University of Warwick, Department of Economics.
    18. Lilia Maliar & Serguei Maliar, 2004. "Quasi‐geometric discounting: A closed‐form solution under the exponential utility function," Bulletin of Economic Research, Wiley Blackwell, vol. 56(2), pages 201-206, April.
    19. S. Nageeb Ali, 2011. "Learning Self-Control," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(2), pages 857-893.
    20. Kevin X.D. Huang & Zheng Liu & John Qi Zhu, 2015. "Temptation and Self‐Control: Some Evidence and Applications," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 47(4), pages 581-615, June.

    More about this item

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

    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:eee:ecmode:v:23:y:2006:i:3:p:492-505. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/30411 .

    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.