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Nonlinear and stable perturbation-based approximations

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  • Den Haan, Wouter J.
  • De Wind, Joris

Abstract

Users of regular higher-order perturbation approximations can face two problems: policy functions with odd oscillations and simulated data that explode. We propose a perturbation-based approximation that (i) does not have odd shapes, (ii) generates stable time paths, and (iii) avoids the drawbacks that hamper the pruned perturbation approach of Kim et al. (2008). For models with nontrivial nonlinearities, we find that our alternative and the pruned perturbation approximations give a good qualitative insight in the nonlinear aspects of the true solution, but can differ from the true solution in some quantitative aspects, especially during severe peaks and troughs.

Suggested Citation

  • Den Haan, Wouter J. & De Wind, Joris, 2012. "Nonlinear and stable perturbation-based approximations," Journal of Economic Dynamics and Control, Elsevier, vol. 36(10), pages 1477-1497.
  • Handle: RePEc:eee:dyncon:v:36:y:2012:i:10:p:1477-1497
    DOI: 10.1016/j.jedc.2012.05.001
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    References listed on IDEAS

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    1. Marcus Hagedorn & Iourii Manovskii, 2008. "The Cyclical Behavior of Equilibrium Unemployment and Vacancies Revisited," American Economic Review, American Economic Association, vol. 98(4), pages 1692-1706, September.
    2. Stephan Fahr & Frank Smets, 2010. "Downward Wage Rigidities and Optimal Monetary Policy in a Monetary Union," Scandinavian Journal of Economics, Wiley Blackwell, vol. 112(4), pages 812-840, December.
    3. Fair, Ray C & Taylor, John B, 1983. "Solution and Maximum Likelihood Estimation of Dynamic Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 51(4), pages 1169-1185, July.
    4. Christopher A. Pissarides & Barbara Petrongolo, 2001. "Looking into the Black Box: A Survey of the Matching Function," Journal of Economic Literature, American Economic Association, vol. 39(2), pages 390-431, June.
    5. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    6. Deaton, Angus, 1991. "Saving and Liquidity Constraints," Econometrica, Econometric Society, vol. 59(5), pages 1221-1248, September.
    7. Jesus Fernandez-Villaverde & Pablo Guerron-Quintana & Juan F. Rubio-Ramirez & Martin Uribe, 2011. "Risk Matters: The Real Effects of Volatility Shocks," American Economic Review, American Economic Association, vol. 101(6), pages 2530-2561, October.
    8. Doh, Taeyoung, 2011. "Yield curve in an estimated nonlinear macro model," Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages 1229-1244, August.
    9. Gagnon, Joseph E, 1990. "Solving the Stochastic Growth Model by Deterministic Extended Path," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 35-36, January.
    10. 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.
    11. Den Haan, Wouter J. & Kaltenbrunner, Georg, 2009. "Anticipated growth and business cycles in matching models," Journal of Monetary Economics, Elsevier, vol. 56(3), pages 309-327, April.
    12. Lombardo, Giovanni, 2010. "On approximating DSGE models by series expansions," Working Paper Series 1264, European Central Bank.
    13. 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.
    14. Collard, Fabrice & Juillard, Michel, 2001. "Accuracy of stochastic perturbation methods: The case of asset pricing models," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 979-999, June.
    15. Martin Møller Andreasen, 2008. "Non-linear DSGE Models, The Central Difference Kalman Filter, and The Mean Shifted Particle Filter," CREATES Research Papers 2008-33, Department of Economics and Business Economics, Aarhus University.
    16. Robert E. Hall, 2005. "Employment Fluctuations with Equilibrium Wage Stickiness," American Economic Review, American Economic Association, vol. 95(1), pages 50-65, March.
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    More about this item

    Keywords

    Accuracy; Nonlinear numerical solutions;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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