IDEAS home Printed from https://ideas.repec.org/p/tky/fseres/2009cf620.html

Computing Densities and Expectations in Stochastic Recursive Economies: Generalized Look-Ahead Techniques

Author

Listed:
  • Richard Anton Braun

    (Faculty of Economics, University of Tokyo)

  • Huiyu Li

    (Graduate School of Economics, University of Tokyo)

  • John Stachurski

    (Institute of Economic Research, Kyoto University)

Abstract

We propose a generalized look-ahead estimator for computing densities and expectations in economic models. We provide conditions under which the estimator converges globally with probability one, and exhibit the asymptotic distribution of the error. Our estimator is more efficient than other Monte Carlo based approaches. Numerical experiments indicate that the estimator can provide large increases in accuracy and speed relative to traditional methods. Particular applications we consider are the stochastic growth model and an income fluctuation problem.

Suggested Citation

  • Richard Anton Braun & Huiyu Li & John Stachurski, 2009. "Computing Densities and Expectations in Stochastic Recursive Economies: Generalized Look-Ahead Techniques," CIRJE F-Series CIRJE-F-620, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2009cf620
    as

    Download full text from publisher

    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2009/2009cf620.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    2. Shane G. Henderson & Peter W. Glynn, 2001. "Computing Densities for Markov Chains via Simulation," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 375-400, May.
    3. Aubhik Khan & Julia K. Thomas, 2008. "Idiosyncratic Shocks and the Role of Nonconvexities in Plant and Aggregate Investment Dynamics," Econometrica, Econometric Society, vol. 76(2), pages 395-436, March.
    4. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
    5. Anthony A Smith & Fatih Guvenen, 2006. "What Do Labor and Consumption Data Jointly Tell About Labor Income Risk?," 2006 Meeting Papers 500, Society for Economic Dynamics.
    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. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(3), pages 659-684.
    8. 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.
    9. John Stachurski, 2008. "Continuous State Dynamic Programming via Nonexpansive Approximation," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 141-160, March.
    10. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    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. John Stachurski & Huiyu Li & Richard Anton Braun, 2009. "Computing Densities in Stochastic Recursive Economies: Generalized Look-Ahead Techniques," 2009 Meeting Papers 975, Society for Economic Dynamics.
    2. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    3. Huiyu Li, 2015. "Numerical Policy Error Bounds for $$\eta $$ η -Concave Stochastic Dynamic Programming with Non-interior Solutions," Computational Economics, Springer;Society for Computational Economics, vol. 46(2), pages 171-187, August.
    4. Richard Anton Braun & Huiyu Li & John Stachurski, 2009. "Computing Densities: A Conditional Monte Carlo Estimator," CARF F-Series CARF-F-181, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    5. Takefumi Yamazaki, 2018. "Accuracy and speed of the solution methods for sovereign default models: The stable performance of the Tauchen method and cubic spline interpolation," Public Policy Review, Policy Research Institute, Ministry of Finance Japan, vol. 14(4), pages 641-662, July.
    6. Athreya, Kartik B., 2014. "Big Ideas in Macroeconomics: A Nontechnical View," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262019736, December.
    7. Marlon Azinovic-Yang & Jan v{Z}emliv{c}ka, 2025. "Deep Learning in the Sequence Space," Papers 2509.13623, arXiv.org, revised Mar 2026.
    8. Angeletos, George-Marios & Calvet, Laurent-Emmanuel, 2006. "Idiosyncratic production risk, growth and the business cycle," Journal of Monetary Economics, Elsevier, vol. 53(6), pages 1095-1115, September.
    9. Noh-Sun Kwark & Eunseong Ma, 2016. "Entrepreneurship and Income Distribution Dynamics: Why Are Top Income Earners Unaffected by Business Cycles?," Working Papers 1608, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy).
    10. Keyvan Eslami & Thomas Phelan, 2025. "The Art of Temporal Approximation: An Investigation into Numerical Solutions to Discrete- and Continuous-Time Problems in Economics," Computational Economics, Springer;Society for Computational Economics, vol. 65(3), pages 1505-1547, March.
    11. 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.
    12. Juessen, Falko & Linnemann, Ludger & Schabert, Andreas, 2016. "Default Risk Premia On Government Bonds In A Quantitative Macroeconomic Model," Macroeconomic Dynamics, Cambridge University Press, vol. 20(1), pages 380-403, January.
    13. Buera, Francisco J. & Shin, Yongseok, 2011. "Self-insurance vs. self-financing: A welfare analysis of the persistence of shocks," Journal of Economic Theory, Elsevier, vol. 146(3), pages 845-862, May.
    14. Robert Kirkby Author-Email: robertkirkby@gmail.com|, 2017. "Convergence of Discretized Value Function Iteration," Computational Economics, Springer;Society for Computational Economics, vol. 49(1), pages 117-153, January.
    15. Anagnostopoulos Alexis & Tang Xin, 2015. "Evaluating linear approximations in a two-country model with occasionally binding borrowing constraints," The B.E. Journal of Macroeconomics, De Gruyter, vol. 15(1), pages 43-91, January.
    16. Pál, Jenő & Stachurski, John, 2013. "Fitted value function iteration with probability one contractions," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 251-264.
    17. Pascal, Julien, 2024. "Artificial neural networks to solve dynamic programming problems: A bias-corrected Monte Carlo operator," Journal of Economic Dynamics and Control, Elsevier, vol. 162(C).
    18. Hintermaier, Thomas & Koeniger, Winfried, 2010. "The method of endogenous gridpoints with occasionally binding constraints among endogenous variables," Journal of Economic Dynamics and Control, Elsevier, vol. 34(10), pages 2074-2088, October.
    19. Marlon Azinovic-Yang & Jan Zemlicka, 2025. "Deep Learning in the Sequence Space," CERGE-EI Working Papers wp802, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    20. Foss, Sergey & Shneer, Vsevolod & Thomas, Jonathan P. & Worrall, Tim, 2018. "Stochastic stability of monotone economies in regenerative environments," Journal of Economic Theory, Elsevier, vol. 173(C), pages 334-360.

    More about this item

    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:tky:fseres:2009cf620. 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: CIRJE administrative office (email available below). General contact details of provider: https://edirc.repec.org/data/ritokjp.html .

    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.