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Exact Present Solution with Consistent Future Approximation: A Gridless Algorithm to Solve Stochastic Dynamic Models

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  • Den Haan, Wouter
  • Rendahl, Pontus
  • Kobielarz, Michal

Abstract

This paper proposes an algorithm that finds model solutions at a particular point in the state space by solving a simple system of equations. The key step is to characterize future behavior with a Taylor series expansion of the current period's behavior around the contemporaneous values for the state variables. Since current decisions are solved from the original model equations, the solution incorporates nonlinearities and uncertainty. The algorithm is used to solve the model considered in Coeurdacier, Rey, and Winant (2011), which is a challenging model because it has no steady state and uncertainty is necessary to keep the model well behaved. We show that our algorithm can generate accurate solutions even when the model series are quite volatile. The solutions generated by the risky-steady-state algorithm proposed in Coeurdacier, Rey, and Winant (2011), in contrast, is shown to be not accurate.

Suggested Citation

  • Den Haan, Wouter & Rendahl, Pontus & Kobielarz, Michal, 2015. "Exact Present Solution with Consistent Future Approximation: A Gridless Algorithm to Solve Stochastic Dynamic Models," CEPR Discussion Papers 10999, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:10999
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    References listed on IDEAS

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    1. Gary Chamberlain & Charles A. Wilson, 2000. "Optimal Intertemporal Consumption Under Uncertainty," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(3), pages 365-395, July.
    2. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2011. "Numerically stable and accurate stochastic simulation approaches for solving dynamic economic models," Quantitative Economics, Econometric Society, vol. 2(2), pages 173-210, July.
    3. den Haan, Wouter J & Marcet, Albert, 1990. "Solving the Stochastic Growth Model by Parameterizing Expectations," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 31-34, January.
    4. Nicolas Coeurdacier & Helene Rey & Pablo Winant, 2011. "The Risky Steady State," American Economic Review, American Economic Association, vol. 101(3), pages 398-401, May.
    5. 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.
    6. repec:hal:wpspec:info:hdl:2441/c8dmi8nm4pdjkuc9g704ld0h3 is not listed on IDEAS
    7. repec:hal:spmain:info:hdl:2441/c8dmi8nm4pdjkuc9g704ld0h3 is not listed on IDEAS
    8. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
    9. den Haan, Wouter J., 1995. "The term structure of interest rates in real and monetary economies," Journal of Economic Dynamics and Control, Elsevier, vol. 19(5-7), pages 909-940.
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    Cited by:

    1. Hoffmann, Mathias & Krause, Michael & Tillmann, Peter, 2019. "International capital flows, external assets and output volatility," Journal of International Economics, Elsevier, vol. 117(C), pages 242-255.

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    More about this item

    Keywords

    Risky steady state; Solution methods;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E10 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - General
    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production
    • F41 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Open Economy Macroeconomics

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