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

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  • 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.

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Bibliographic Info

Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 6971.

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Date of creation: Sep 2008
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Handle: RePEc:cpr:ceprdp:6971

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Keywords: approximations; numerical solutions; simulations;

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References

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  1. 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.
  2. Silos, Pedro, 2007. "Housing, portfolio choice and the macroeconomy," Journal of Economic Dynamics and Control, Elsevier, vol. 31(8), pages 2774-2801, August.
  3. Manuel S. Santos & Adrian Peralta-Alva, 2003. "Accuracy of Simulations for Stochastic Dynamic Models," Levine's Bibliography 666156000000000264, UCLA Department of Economics.
  4. Storesletten, Kjetil & Telmer, Chris & Yaron, Amir, 2001. "Asset Pricing with Idiosyncratic Risk and Overlapping Generations," CEPR Discussion Papers 3065, C.E.P.R. Discussion Papers.
  5. Makoto Nakajima, 2010. "Business cycles in the equilibrium model of labor market search and self-insurance," Working Papers 10-24, Federal Reserve Bank of Philadelphia.
  6. Per Krusell & Anthony A. Smith, Jr., . "Income and Wealth Heterogeneity, Portfolio Choice, and Equilibrium Asset Returns," GSIA Working Papers 1997-45, Carnegie Mellon University, Tepper School of Business.
  7. Den Haan, Wouter J., 1997. "Solving Dynamic Models With Aggregate Shocks And Heterogeneous Agents," Macroeconomic Dynamics, Cambridge University Press, vol. 1(02), pages 355-386, June.
  8. Krusell, P & Smith Jr, A-A, 1995. "Income and Wealth Heterogeneity in the Macroeconomic," RCER Working Papers 399, University of Rochester - Center for Economic Research (RCER).
  9. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
  10. 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.
  11. Eric R Young, 2005. "Approximate Aggregation," Computing in Economics and Finance 2005 141, Society for Computational Economics.
  12. Gomes, Francisco J & Michaelides, Alexander, 2007. "Asset Pricing with Limited Risk Sharing and Heterogeneous Agents," CEPR Discussion Papers 6136, C.E.P.R. Discussion Papers.
  13. Michael Reiter, 2006. "Solving heterogeneous-agent models by projection and perturbation," Economics Working Papers 972, Department of Economics and Business, Universitat Pompeu Fabra.
  14. Jose-Victor Rios-Rull, 1997. "Computation of equilibria in heterogeneous agent models," Staff Report 231, Federal Reserve Bank of Minneapolis.
  15. 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.
  16. Michael Reiter, 2000. "Estimating The Accuracy Of Numerical Solutions To Dynamic Optimization Problems," Computing in Economics and Finance 2000 254, Society for Computational Economics.
  17. 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.
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Citations

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Cited by:
  1. 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.
  2. Volker Tjaden & Ralph Lütticke & Lien Pham & Christian Bayer, 2013. "Household Income Risk, Nominal Frictions, and Incomplete Markets," 2013 Meeting Papers 1270, Society for Economic Dynamics.
  3. 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.
  4. Emi Nakamura & Jón Steinsson, 2010. "Monetary Non-Neutrality in a Multisector Menu Cost Model," The Quarterly Journal of Economics, MIT Press, vol. 125(3), pages 961-1013, August.
  5. Jianjun Miao & Pengfei Wang, . "Does Lumpy Investment Matter for Business Cycles?," Boston University - Department of Economics - Working Papers Series wp2010-002, Boston University - Department of Economics.
  6. Francisco Covas & Shigeru Fujita, 2007. "Private risk premium and aggregate uncertainty in the model of uninsurable investment risk," Working Papers 07-30, Federal Reserve Bank of Philadelphia.
  7. Joseph S. Vavra, 2013. "Inflation Dynamics and Time-Varying Volatility: New Evidence and an Ss Interpretation," NBER Working Papers 19148, National Bureau of Economic Research, Inc.
  8. Rüdiger Bachmann & Christian Bayer, 2011. "Investment Dispersion and the Business Cycle," NBER Working Papers 16861, National Bureau of Economic Research, Inc.
  9. Fatih Guvenen, 2011. "Macroeconomics With Heterogeneity: A Practical Guide," NBER Working Papers 17622, National Bureau of Economic Research, Inc.
  10. Immo Schott, 2013. "Startups, Credit, and the Jobless Recovery," 2013 Meeting Papers 340, Society for Economic Dynamics.
  11. Gian Luca Clementi & Berardino Palazzo, 2013. "Entry, Exit, Firm Dynamics, and Aggregate Fluctuations," NBER Working Papers 19217, National Bureau of Economic Research, Inc.

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