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Solving the Stochastic Growth Model by Linear-Quadratic Approximation

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  • McGrattan, Ellen R

Abstract

I describe a method that can be used to approximate the solution of the stochastic growth model. The method relies on approximating the return and transition functions of the original problem by taking second-order and first-order Taylor expansions around the steady state of the system. The result is the optimal linear regulator problem.

Suggested Citation

  • McGrattan, Ellen R, 1990. "Solving the Stochastic Growth Model by Linear-Quadratic Approximation," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 41-44, January.
    • Handle: RePEc:bes:jnlbes:v:8:y:1990:i:1:p:41-44
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    Cited by:

    1. Jean-Bernard Chatelain & Kirsten Ralf, 2024. "Wealth in the Quadratic Loss Function of the Ramsey Malinvaud Cass Koopmans Model of Optimal Savings," Revue d'économie politique, Dalloz, vol. 134(3), pages 371-390.
    2. Jinill Kim & Sunghyun Henry Kim, 2007. "Two Pitfalls of Linearization Methods," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(4), pages 995-1001, June.
    3. Jose Maria Da Rocha & Diego Restuccia, 2002. "Aggregate Employment Fluctuations and Agricultural Share," Working Papers diegor-02-02, University of Toronto, Department of Economics.
    4. S. Sirakaya & Stephen Turnovsky & M. Alemdar, 2006. "Feedback Approximation of the Stochastic Growth Model by Genetic Neural Networks," Computational Economics, Springer;Society for Computational Economics, vol. 27(2), pages 185-206, May.
    5. Judd, Kenneth L., 1996. "Approximation, perturbation, and projection methods in economic analysis," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 12, pages 509-585, Elsevier.
    6. Karp, Larry & Zhang, Jiangfeng, 2001. "Bayesian Learning and the Regulation of Greenhouse Gas Emissions," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt2fr0783c, Department of Agricultural & Resource Economics, UC Berkeley.
    7. Reiter, Michael, 1997. "Chow's method of optimal control," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 723-737, May.
    8. Benigno, Pierpaolo & Woodford, Michael, 2006. "Optimal taxation in an RBC model: A linear-quadratic approach," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1445-1489.
    9. Feigenbaum, James, 2008. "Information shocks and precautionary saving," Journal of Economic Dynamics and Control, Elsevier, vol. 32(12), pages 3917-3938, December.
    10. Taylor, John B & Uhlig, Harald, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 1-17, January.
    11. Maldonado, Wilfredo L. & Moreira, Humberto Luiz Ataíde, 2006. "Solving Euler Equations: Classical Methods and the C¹ Contraction Mapping Method Revisited," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 60(2), November.
    12. Jose Maria Da Rocha & Diego Restuccia, 2002. "The Role of Agriculture in Aggregate Business Cycle Fluctuations," Working Papers diegor-02-04, University of Toronto, Department of Economics.
    13. Jose Maria Da Rocha & Diego Restuccia, 2006. "The Role of Agriculture in Aggregate Business Cycles," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(3), pages 455-482, July.
    14. Anagnostopoulos Alexis & Tang Xin, 2015. "Evaluating linear approximations in a two-country model with occasionally binding borrowing constraints," The B.E. Journal of Macroeconomics, De Gruyter, vol. 15(1), pages 43-91, January.
    15. Huber, Johannes & Meyer-Gohde, Alexander & Saecker, Johanna, 2023. "Solving linear DSGE models with structure-preserving doubling methods," IMFS Working Paper Series 195, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).

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