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

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Author Info
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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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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C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
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  2. Krusell, Per & Smith, Anthony A., 1997. "Income And Wealth Heterogeneity, Portfolio Choice, And Equilibrium Asset Returns," Macroeconomic Dynamics, Cambridge University Press, vol. 1(02), pages 387-422, June. [Downloadable!]
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  3. Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, vol. 73(6), pages 1939-1976, November. [Downloadable!] (restricted)
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  4. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
  5. Pedro Silos, 2005. "Housing, portfolio choice, and the macroeconomy," Working Paper 2005-21, Federal Reserve Bank of Atlanta. [Downloadable!]
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  6. 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. [Downloadable!] (restricted)
  7. Francisco Gomes & Alexander Michaelides, 2008. "Asset Pricing with Limited Risk Sharing and Heterogeneous Agents," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 21(1), pages 415-448, January. [Downloadable!] (restricted)
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  8. 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. [Downloadable!] (restricted)
  9. Michael Reiter, 2006. "Solving Heterogeneous-Agent Models by Projection and Perturbation," Economics Working Papers 972, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
  10. Eric R Young, 2005. "Approximate Aggregation," Computing in Economics and Finance 2005 141, Society for Computational Economics. [Downloadable!]
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  1. 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. [Downloadable!] (restricted)
  2. Den Haan, Wouter, 2008. "Comparison of Solutions to the Incomplete Markets Model with Aggregate Uncertainty," CEPR Discussion Papers 7019, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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