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

  • Den Haan, Wouter

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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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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  1. Yann Algan & Olivier Allais & Wouter J Den Haan, 2010. "Solving the incomplete markets model with aggregate uncertainty using parameterized cross-sectional distributions," Sciences Po publications info:hdl:2441/72lkhuq5cm8, Sciences Po.
  2. Yann Algan & Olivier Allais & Wouter J Den Haan, 2007. "Solving Heterogeneous-agent Models with Parameterized Cross-sectional Distributions," Sciences Po publications 6062, Sciences Po.
  3. Michael Reiter, 2000. "Estimating The Accuracy Of Numerical Solutions To Dynamic Optimization Problems," Computing in Economics and Finance 2000 254, Society for Computational Economics.
  4. 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.
  5. Per Krusell & Anthony A. Smith, Jr., . "Income and Wealth Heterogeneity in the Macroeconomy," GSIA Working Papers 1997-37, Carnegie Mellon University, Tepper School of Business.
  6. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
  7. Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, vol. 73(6), pages 1939-1976, November.
  8. 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.
  9. Storesletten, Kjetil & Telmer, Chris & Yaron, Amir, 2002. "Asset pricing with idiosyncratic risk and overlapping generations," Seminar Papers 703, Stockholm University, Institute for International Economic Studies.
  10. Den Haan, Wouter & Rendahl, Pontus, 2008. "Solving the Incomplete Markets Model with Aggregate Uncertainty using Explicit Aggregation," CEPR Discussion Papers 6963, C.E.P.R. Discussion Papers.
  11. Jose-Victor Rios-Rull, 1997. "Computation of equilibria in heterogeneous agent models," Staff Report 231, Federal Reserve Bank of Minneapolis.
  12. 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.
  13. Francisco Gomes & Alexander Michaelides, 2008. "Asset Pricing with Limited Risk Sharing and Heterogeneous Agents," Review of Financial Studies, Society for Financial Studies, vol. 21(1), pages 415-448, January.
  14. 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.
  15. Eric R Young, 2005. "Approximate Aggregation," Computing in Economics and Finance 2005 141, Society for Computational Economics.
  16. 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.
  17. 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.
  18. Silos, Pedro, 2007. "Housing, portfolio choice and the macroeconomy," Journal of Economic Dynamics and Control, Elsevier, vol. 31(8), pages 2774-2801, August.
  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.
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