IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v163y2016icp900-924.html
   My bibliography  Save this article

Seeking ergodicity in dynamic economies

Author

Listed:
  • Kamihigashi, Takashi
  • Stachurski, John

Abstract

In estimation and calibration studies, the convergence of time series sample averages plays a central role. At the same time, a significant number of economic models do not satisfy the classical ergodicity conditions. Motivated by existing work on asymptotics of stochastic economic models, we develop a new set of results on limits of sample moments and other sample averages using an order-theoretic approach. Our results include a condition that is necessary and sufficient for convergence over a broad class of moment functions. We discuss implications, sufficient conditions and a range of economic applications.

Suggested Citation

  • Kamihigashi, Takashi & Stachurski, John, 2016. "Seeking ergodicity in dynamic economies," Journal of Economic Theory, Elsevier, vol. 163(C), pages 900-924.
    • Handle: RePEc:eee:jetheo:v:163:y:2016:i:c:p:900-924
    DOI: 10.1016/j.jet.2016.03.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053116000405
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2016.03.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Kamihigashi, Takashi & Stachurski, John, 2012. "An order-theoretic mixing condition for monotone Markov chains," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 262-267.
    2. Christopher D. Carroll, 1997. "Buffer-Stock Saving and the Life Cycle/Permanent Income Hypothesis," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(1), pages 1-55.
    3. Samaniego, Roberto M., 2008. "Can technical change exacerbate the effects of labor market sclerosis," Journal of Economic Dynamics and Control, Elsevier, vol. 32(2), pages 497-528, February.
    4. Jess Benhabib & Alberto Bisin & Shenghao Zhu, 2011. "The Distribution of Wealth and Fiscal Policy in Economies With Finitely Lived Agents," Econometrica, Econometric Society, vol. 79(1), pages 123-157, January.
    5. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    6. , & ,, 2014. "Stochastic stability in monotone economies," Theoretical Economics, Econometric Society, vol. 9(2), May.
    7. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    8. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-781, July.
    9. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-952, July.
    10. 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.
    11. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 11(3), pages 329-339, December.
    12. Greenwood Jeremy & Huffman Gregory W., 1995. "On the Existence of Nonoptimal Equilibria in Dynamic Stochastic Economies," Journal of Economic Theory, Elsevier, vol. 65(2), pages 611-623, April.
    13. Razin, Assaf & Yahav, Joseph A, 1979. "On Stochastic Models of Economic Growth," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(3), pages 599-604, October.
    14. Owen, Ann L. & Weil, David N., 1998. "Intergenerational earnings mobility, inequality and growth," Journal of Monetary Economics, Elsevier, vol. 41(1), pages 71-104, February.
    15. Steven N. Durlauf, 1993. "Nonergodic Economic Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(2), pages 349-366.
    16. Cabrales, Antonio & Hopenhayn, Hugo A., 1997. "Labor-market flexibility and aggregate employment volatility," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 46(1), pages 189-228, June.
    17. Zhang, Yuzhe, 2007. "Stochastic optimal growth with a non-compact state space," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 115-129, February.
    18. Thomas F. Cooley & Vincenzo Quadrini, 2001. "Financial Markets and Firm Dynamics," American Economic Review, American Economic Association, vol. 91(5), pages 1286-1310, December.
    19. Tapan Mitra & Luigi Montrucchio & Fabio Privileggi, 2003. "The nature of the steady state in models of optimal growth under uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(1), pages 39-71, December.
    20. William A. Brock & Steven N. Durlauf, 2001. "Discrete Choice with Social Interactions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(2), pages 235-260.
    21. Jess Benhabib & Chetan Dave, 2014. "Learning, Large Deviations and Rare Events," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(3), pages 367-382, July.
    22. Hansen, Lars Peter & Sargent, Thomas J., 2010. "Wanting Robustness in Macroeconomics," Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 20, pages 1097-1157, Elsevier.
    23. de Hek, Paul A, 1999. "On Endogenous Growth under Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 727-744, August.
    24. 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.
    25. Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, vol. 73(6), pages 1939-1976, November.
    26. Roger E. A. Farmer & Daniel F. Waggoner & Tao Zha, 2009. "Indeterminacy in a forward‐looking regime switching model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(1), pages 69-84, March.
    27. Kamihigashi, Takashi, 2007. "Stochastic optimal growth with bounded or unbounded utility and with bounded or unbounded shocks," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 477-500, April.
    28. Philippe Aghion & Patrick Bolton, 1997. "A Theory of Trickle-Down Growth and Development," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(2), pages 151-172.
    29. 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.
    30. Esteban Rossi-Hansberg & Mark L. J. Wright, 2007. "Establishment Size Dynamics in the Aggregate Economy," American Economic Review, American Economic Association, vol. 97(5), pages 1639-1666, December.
    31. Thomas Piketty, 1997. "The Dynamics of the Wealth Distribution and the Interest Rate with Credit Rationing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(2), pages 173-189.
    32. Morand, Olivier F. & Reffett, Kevin L., 2007. "Stationary Markovian equilibrium in overlapping generation models with stochastic nonclassical production and Markov shocks," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 501-522, April.
    33. Olivier F. Morand & Kevin L. Reffett, 2005. "Stationary Markovian Equilibrium in Overlapping Generation Models with Stochastic Nonclassical Production," Working papers 2005-52, University of Connecticut, Department of Economics.
    34. Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, vol. 73(6), pages 1939-1976, November.
    35. Kazuo Nishimura & John Stachurski, 2012. "Stability of Stochastic Optimal Growth Models: A New Approach," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 289-307, Springer.
    36. Bhattacharya, Rabi & Majumdar, Mukul, 2001. "On a Class of Stable Random Dynamical Systems: Theory and Applications," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 208-229, January.
    37. Ljungqvist, Lars & Sargent, Thomas J., 2012. "Recursive Macroeconomic Theory, Third Edition," MIT Press Books, The MIT Press, edition 3, volume 1, number 0262018748, April.
    38. Nirei, Makoto, 2006. "Threshold behavior and aggregate fluctuation," Journal of Economic Theory, Elsevier, vol. 127(1), pages 309-322, March.
    39. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
    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. David Staines, 2023. "Stochastic Equilibrium the Lucas Critique and Keynesian Economics," Papers 2312.16214, arXiv.org, revised Jun 2024.
    2. Kenichiro McAlinn & Kosaku Takanashi, 2021. "Convergence of Computed Dynamic Models with Unbounded Shock," Papers 2103.06483, arXiv.org.
    3. Bäuerle, Nicole & Jaśkiewicz, Anna, 2018. "Stochastic optimal growth model with risk sensitive preferences," Journal of Economic Theory, Elsevier, vol. 173(C), pages 181-200.
    4. Robert Kirkby, 2016. "Value Function Iteration Toolkit: In Matlab, on the GPU," EcoMod2016 9122, EcoMod.
    5. Robert Kirkby, 2017. "A Toolkit for Value Function Iteration," Computational Economics, Springer;Society for Computational Economics, vol. 49(1), pages 1-15, January.

    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. Takashi Kamihigashi & John Stachurski, 2014. "Interlinkage between Real Exchange rate and Current Account Behaviors: Evidence from India," Working Papers 2014-86, Department of Research, Ipag Business School.
    2. Takashi Kamihigashiw & John Stachurski, 2014. "Seeking Ergodicity in Dynamic Economies," Working Papers 2014-402, Department of Research, Ipag Business School.
    3. repec:ipg:wpaper:2014-086 is not listed on IDEAS
    4. Takashi Kamihigashi & John Stachurski, 2011. "Existence, Stability and Computation of Stationary Distributions: An Extension of the Hopenhayn-Prescott Theorem," Discussion Paper Series DP2011-32, Research Institute for Economics & Business Administration, Kobe University.
    5. Takashi Kamihigashi & John Stachurski, 2014. "Stability Analysis for Random Dynamical Systems in Economics," Discussion Paper Series DP2014-35, Research Institute for Economics & Business Administration, Kobe University.
    6. Takashi Kamihigashi & John Stachurski, 2011. "Stability of Stationary Distributions in Monotone Economies," ANU Working Papers in Economics and Econometrics 2011-561, Australian National University, College of Business and Economics, School of Economics.
    7. , & ,, 2014. "Stochastic stability in monotone economies," Theoretical Economics, Econometric Society, vol. 9(2), May.
    8. Takashi Kamihigashi & John Stachurski, 2012. "Existence, Uniqueness and Stability of Stationary Distributions: An Extension of the Hopenhayn-Prescott Theorem," Discussion Paper Series DP2012-27, Research Institute for Economics & Business Administration, Kobe University.
    9. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, April.
    10. Cai, Yiyong & Kamihigashi, Takashi & Stachurski, John, 2014. "Stochastic optimal growth with risky labor supply," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 167-176.
    11. Jaime McGovern & Olivier Morand & Kevin Reffett, 2013. "Computing minimal state space recursive equilibrium in OLG models with stochastic production," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 623-674, November.
    12. Lars J. Olson & Santanu Roy, 2006. "Theory of Stochastic Optimal Economic Growth," Springer Books, in: Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), Handbook on Optimal Growth 1, chapter 11, pages 297-335, Springer.
    13. Datta, Manjira & Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2005. "Markovian equilibrium in infinite horizon economies with incomplete markets and public policy," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 505-544, August.
    14. Manuel S. Santos & Adrian Peralta-Alva, 2012. "Analysis of Numerical Errors," Working Papers 2012-6, University of Miami, Department of Economics.
    15. Thomas J. Sargent & John Stachurski, 2024. "Dynamic Programming: Finite States," Papers 2401.10473, arXiv.org.
    16. Tapan Mitra & Santanu Roy, 2023. "Stochastic growth, conservation of capital and convergence to a positive steady state," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 311-351, July.
    17. 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.
    18. Santos, Manuel S., 2003. "Simulation-based estimation of dynamic models with continuous equilibrium solutions," UC3M Working papers. Economics we034716, Universidad Carlos III de Madrid. Departamento de Economía.
    19. Takashi Kamihigashi & John Stachurski, 2009. "Asymptotics Of Stochastic Recursive Economies Under Monotonicity," KIER Working Papers 666, Kyoto University, Institute of Economic Research.
    20. Zhang, Yuzhe, 2007. "Stochastic optimal growth with a non-compact state space," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 115-129, February.
    21. Zhigang Feng & Jianjun Miao & Adrian Peralta‐Alva & Manuel S. Santos, 2014. "Numerical Simulation Of Nonoptimal Dynamic Equilibrium Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(1), pages 83-110, February.

    More about this item

    Keywords

    Ergodicity; Monotonicity; Calibration;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    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:jetheo:v:163:y:2016:i:c:p:900-924. 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/622869 .

    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.