IDEAS home Printed from https://ideas.repec.org/p/cpr/ceprdp/6971.html
   My bibliography  Save this paper

Assessing the Accuracy of the Aggregate Law of Motion in Models with Heterogeneous Agents

Author

Listed:
  • Den Haan, Wouter

Abstract

This paper shows that the R² and the standard error have fatal flaws and are inadequate as accuracy tests for models with heterogeneous agents and aggregate risk. Using data from a Krusell-Smith economy, I show that approximations for the law of motion of aggregate capital for which the true standard deviation of aggregate capital is up to 14% (119%) higher than the implied value (and which are thus clearly inaccurate) can have an R² as high as 0.9999 (0.99). Key in generating a more powerful test is to not update the aggregate law of motion with the aggregated simulated individual data, but to use as the explanatory variable the value predicted by the aggregate law of motion itself.

Suggested Citation

  • Den Haan, Wouter, 2008. "Assessing the Accuracy of the Aggregate Law of Motion in Models with Heterogeneous Agents," CEPR Discussion Papers 6971, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:6971
    as

    Download full text from publisher

    File URL: https://cepr.org/publications/DP6971
    Download Restriction: CEPR Discussion Papers are free to download for our researchers, subscribers and members. If you fall into one of these categories but have trouble downloading our papers, please contact us at subscribers@cepr.org
    ---><---

    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. Den Haan, Wouter J, 1996. "Heterogeneity, Aggregate Uncertainty, and the Short-Term Interest Rate," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 399-411, October.
    2. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    3. Kjetil Storesletten & Chris Telmer & Amir Yaron, 2007. "Asset Pricing with Idiosyncratic Risk and Overlapping Generations," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(4), pages 519-548, October.
    4. Den Haan, Wouter J. & Rendahl, Pontus, 2010. "Solving the incomplete markets model with aggregate uncertainty using explicit aggregation," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 69-78, January.
    5. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2006. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871525, December.
    6. Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, vol. 73(6), pages 1939-1976, November.
    7. Algan, Yann & Allais, Olivier & Den Haan, Wouter J., 2008. "Solving heterogeneous-agent models with parameterized cross-sectional distributions," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 875-908, March.
    8. Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, vol. 73(6), pages 1939-1976, November.
    9. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    10. Eric R Young, 2005. "Approximate Aggregation," Computing in Economics and Finance 2005 141, Society for Computational Economics.
    11. Krusell, Per & Smith, Anthony A., 1997. "Income And Wealth Heterogeneity, Portfolio Choice, And Equilibrium Asset Returns," Macroeconomic Dynamics, Cambridge University Press, vol. 1(2), pages 387-422, June.
    12. Den Haan, Wouter J., 1997. "Solving Dynamic Models With Aggregate Shocks And Heterogeneous Agents," Macroeconomic Dynamics, Cambridge University Press, vol. 1(2), pages 355-386, June.
    13. repec:hal:spmain:info:hdl:2441/41rhqgovpp8hnq9i7ndtl26ltm is not listed on IDEAS
    14. Francisco Gomes & Alexander Michaelides, 2008. "Asset Pricing with Limited Risk Sharing and Heterogeneous Agents," The Review of Financial Studies, Society for Financial Studies, vol. 21(1), pages 415-448, January.
    15. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2006. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692083, December.
    16. repec:spo:wpmain:info:hdl:2441/41rhqgovpp8hnq9i7ndtl26ltm is not listed on IDEAS
    17. José-Víctor Ríos-Rull, 1997. "Computation of equilibria in heterogeneous agent models," Staff Report 231, Federal Reserve Bank of Minneapolis.
    18. Krueger, Dirk & Kubler, Felix, 2004. "Computing equilibrium in OLG models with stochastic production," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1411-1436, April.
    19. Reiter, Michael, 2009. "Solving heterogeneous-agent models by projection and perturbation," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 649-665, March.
    20. Makoto Nakajima, 2006. "Business Cycles in the Equilibrium Model of Labor Search and Self-Insurance," Computing in Economics and Finance 2006 426, Society for Computational Economics.
    21. Michael Reiter, 2000. "Estimating The Accuracy Of Numerical Solutions To Dynamic Optimization Problems," Computing in Economics and Finance 2000 254, Society for Computational Economics.
    22. Silos, Pedro, 2007. "Housing, portfolio choice and the macroeconomy," Journal of Economic Dynamics and Control, Elsevier, vol. 31(8), pages 2774-2801, August.
    23. 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.
    24. repec:cdl:ucsdec:94-03r is not listed on IDEAS
    25. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
    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. Den Haan, Wouter J., 2010. "Comparison of solutions to the incomplete markets model with aggregate uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 4-27, January.
    2. Algan, Yann & Allais, Olivier & Den Haan, Wouter J., 2008. "Solving heterogeneous-agent models with parameterized cross-sectional distributions," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 875-908, March.
    3. Ivo Bakota, 2023. "Market Clearing and Krusell-Smith Algorithm in an Economy with Multiple Assets," Computational Economics, Springer;Society for Computational Economics, vol. 62(3), pages 1007-1045, October.
    4. Young, Eric R., 2010. "Solving the incomplete markets model with aggregate uncertainty using the Krusell-Smith algorithm and non-stochastic simulations," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 36-41, January.
    5. Jonathan Heathcote & Kjetil Storesletten & Giovanni L. Violante, 2009. "Quantitative Macroeconomics with Heterogeneous Households," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 319-354, May.
    6. Marco Cozzi, 2015. "The Krusell–Smith Algorithm: Are Self-Fulfilling Equilibria Likely?," Computational Economics, Springer;Society for Computational Economics, vol. 46(4), pages 653-670, December.
    7. Schesch, Constantin, 2024. "Pseudospectral methods for continuous-time heterogeneous-agent models," Journal of Economic Dynamics and Control, Elsevier, vol. 163(C).
    8. Jesús Fernández‐Villaverde & Samuel Hurtado & Galo Nuño, 2023. "Financial Frictions and the Wealth Distribution," Econometrica, Econometric Society, vol. 91(3), pages 869-901, May.
    9. Jonathan Heathcote, 2005. "Fiscal Policy with Heterogeneous Agents and Incomplete Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(1), pages 161-188.
    10. Senbeta, Sisay, 2011. "How applicable are the new keynesian DSGE models to a typical low-income economy?," MPRA Paper 30931, University Library of Munich, Germany.
    11. Takeki Sunakawa, 2020. "Applying the Explicit Aggregation Algorithm to Heterogeneous Macro Models," Computational Economics, Springer;Society for Computational Economics, vol. 55(3), pages 845-874, March.
    12. Reiter, Michael, 2010. "Approximate and Almost-Exact Aggregation in Dynamic Stochastic Heterogeneous-Agent Models," Economics Series 258, Institute for Advanced Studies.
    13. Covas Francisco & Fujita Shigeru, 2011. "Private Equity Premium and Aggregate Uncertainty in a Model of Uninsurable Investment Risk," The B.E. Journal of Macroeconomics, De Gruyter, vol. 11(1), pages 1-36, July.
    14. Bruce Preston & Mauro Roca, 2007. "Incomplete Markets, Heterogeneity and Macroeconomic Dynamics," NBER Working Papers 13260, National Bureau of Economic Research, Inc.
    15. Cao, Dan, 2020. "Recursive equilibrium in Krusell and Smith (1998)," Journal of Economic Theory, Elsevier, vol. 186(C).
    16. Reiter, Michael, 2009. "Solving heterogeneous-agent models by projection and perturbation," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 649-665, March.
    17. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 527-724, Elsevier.
    18. Gouin-Bonenfant, Emilien & Toda, Alexis Akira, 2018. "Pareto Extrapolation: Bridging Theoretical and Quantitative Models of Wealth Inequality," University of California at San Diego, Economics Working Paper Series qt90n2h2bb, Department of Economics, UC San Diego.
    19. Xiaoliang Yang & Patrick Minford & David Meenagh, 2021. "Inequality and Economic Growth in the UK," Open Economies Review, Springer, vol. 32(1), pages 37-69, February.
    20. Christian Bayer & Ralph Luetticke, 2020. "Solving discrete time heterogeneous agent models with aggregate risk and many idiosyncratic states by perturbation," Quantitative Economics, Econometric Society, vol. 11(4), pages 1253-1288, November.

    More about this item

    Keywords

    Approximations; Numerical solutions; Simulations;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    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:cpr:ceprdp:6971. 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: the person in charge (email available below). General contact details of provider: https://www.cepr.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.