Recursive Solution Of Heterogeneous Agent Models
AbstractThe paper presents a method for the recursive solution of models with a continuum of heterogeneous agents. Following Krusell and Smith (1998) and others, it is assumed that the wealth distribution in the economy can be represented, to a sufficient degree of accuracy, by a finite number of statistics. The method then uses a discretization of the state space on a finite grid. The method combines shape-preserving interpolation of the value function in endogenous variables with a simplicial linear interpolation in nonlinear transformations of other state variables. A shape-preserving interpolation scheme is developed that is particularly suitable for value functions that arise from capital accumulation problems. This interpolation scheme leads to an algorithm that - is stable - achieves a high level of accuracy with a relatively low computational effort. A computational advantage of the method is that it can be easily parallelized. The method is illustrated by an application to a standard model of heterogeneous agents that face uninsurable income risk, with endogenous labor supply and aggregate as well as idiosyncratic risk. The accuracy of the solution is investigated by a technique developed in Reiter (2000) which measures the optimizing agents' value loss which arises from using the numerical rather than the exact solution. While the main focus of the paper is on the stability and accuracy of the method, it also pays attention to the efficient implementation of the algorithm and investigates acceleration schemes to speed up the backward iterations. It is shown that a reasonably accurate solution can be obtained on a personal computer in a few minutes. References: Krusell, P. and Smith, A.A., Jr., Income and Wealth Heterogeneity in the Macroeconomy, JPE Vol. 106, 867-96, 1998 Reiter, M.: Estimating the Accuracy of Numerical Solutions to Dynamic Optimization Problems, Universitat Pompeu Fabra, 2000
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Bibliographic InfoPaper provided by Society for Computational Economics in its series Computing in Economics and Finance 2001 with number 167.
Date of creation: 01 Apr 2001
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recursive computation; interpolation; heterogenous agents models;
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- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
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- Olivier Allais & Wouter J Den Haan & Yann Algan, 2007.
"Solving Heterogeneous-agent Models with Parameterized Cross-sectional Distributions,"
Sciences Po publications
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- 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.
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- Algan, Yann & Allais, Olivier & Den Haan, Wouter, 2007. "Solving Heterogeneous-Agent Models with Parameterized Cross-Sectional Distributions," CEPR Discussion Papers 6062, C.E.P.R. Discussion Papers.
- Yann Algan & Olivier Allais & Wouter J. Den Haan, 2008. "Solving heterogenous-agent models with parameterized cross-sectional distributions," Working Papers 9149, Institut National de la Recherche Agronomique, France.
- Olivier Allais & Wouter J Den Haan & Yann Algan, 2006. "Solving Heterogeneous-agent Models with Parameterized Cross-sectional Distributions," Sciences Po publications 2006 - 46, Sciences Po.
- Michael Reiter, 2006.
"Solving heterogeneous-agent models by projection and perturbation,"
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972, Department of Economics and Business, Universitat Pompeu Fabra.
- 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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