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Parameterized Expectations Algorithm and the Moving Bounds

Author

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  • Maliar, Lilia
  • Maliar, Serguei

Abstract

The Parameterized Expectations Algorithm (PEA) is a powerful tool for solving nonlinear stochastic dynamic models. However, it has an important shortcoming: it is not a contraction mapping technique and thus does not guarantee a solution will be found. We suggest a simple modification that enhances the convergence property of the algorithm. The idea is to rule out the possibility of (ex)implosive behavior by artificially restricting the simulated series within certain bounds. As the solution is refined along the iterations, the bounds are gradually removed. The modified PEA can systematically converge to the stationary solution starting from the nonstochastic steady state.

Suggested Citation

  • Maliar, Lilia & Maliar, Serguei, 2003. "Parameterized Expectations Algorithm and the Moving Bounds," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 88-92, January.
    • Handle: RePEc:bes:jnlbes:v:21:y:2003:i:1:p:88-92
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    Cited by:

    1. Lilia Maliar & Serguei Maliar, 2006. "Capital-Skill Complementarity And Steady-State Growth," Working Papers. Serie AD 2006-15, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    2. Maliar, Lilia & Maliar, Serguei, 2005. "Solving nonlinear dynamic stochastic models: an algorithm computing value function by simulations," Economics Letters, Elsevier, vol. 87(1), pages 135-140, April.
    3. Michael Creel, 2008. "Using Parallelization to Solve a Macroeconomic Model: A Parallel Parameterized Expectations Algorithm," Computational Economics, Springer;Society for Computational Economics, vol. 32(4), pages 343-352, November.
    4. Lilia Maliar & Serguei Maliar, 2004. "Preference shocks from aggregation: time series data evidence," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 37(3), pages 768-781, August.
    5. Gary S. Anderson, 2018. "Reliably Computing Nonlinear Dynamic Stochastic Model Solutions: An Algorithm with Error Formulas," Finance and Economics Discussion Series 2018-070, Board of Governors of the Federal Reserve System (U.S.).
    6. Ángel Gavilán & Juan A. Rojas, 2009. "Solving Portfolio Problems with the Smolyak-Parameterized Expectations Algorithm," Working Papers 0838, Banco de España.
    7. Jesús Fernández-Villaverde & Galo Nuño & Jesse Perla, 2024. "Taming the Curse of Dimensionality: Quantitative Economics with Deep Learning," NBER Working Papers 33117, National Bureau of Economic Research, Inc.
    8. Shaw, Philip, 2014. "A nonparametric approach to solving a simple one-sector stochastic growth model," Economics Letters, Elsevier, vol. 125(3), pages 447-450.
    9. Giulia Piccillo & Poramapa Poonpakdee, 2023. "Ambiguous Business Cycles, Recessions and Uncertainty: A Quantitative Analysis," CESifo Working Paper Series 10646, CESifo.
    10. Vytautas Valaitis & Alessandro T. Villa, 2024. "A machine learning projection method for macro‐finance models," Quantitative Economics, Econometric Society, vol. 15(1), pages 145-173, January.
    11. Kenneth Judd & Lilia Maliar & Serguei Maliar, 2009. "Numerically Stable Stochastic Simulation Approaches for Solving Dynamic Economic Models," NBER Working Papers 15296, National Bureau of Economic Research, Inc.
    12. Maliar, Lilia & Maliar, Serguei & Valli, Fernando, 2010. "Solving the incomplete markets model with aggregate uncertainty using the Krusell-Smith algorithm," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 42-49, January.
    13. Paul Pichler, 2005. "Evaluating Approximate Equilibria of Dynamic Economic Models," Vienna Economics Papers 0510, University of Vienna, Department of Economics.
    14. Florian Böser & Chiara Colesanti Senni, 2020. "Emission-based Interest Rates and the Transition to a Low-carbon Economy," CER-ETH Economics working paper series 20/337, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    15. Maliar, Serguei & Maliar, Lilia & Judd, Kenneth, 2011. "Solving the multi-country real business cycle model using ergodic set methods," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 207-228, February.
    16. Pérez, Javier J. & Sánchez, A. Jesús, 2009. "Alternatives to initialize the Parameterized Expectations Algorithm," Economics Letters, Elsevier, vol. 102(2), pages 116-118, February.
    17. Lilia Maliar & Serguei Maliar, 2005. "Parameterized Expectations Algorithm: How to Solve for Labor Easily," Computational Economics, Springer;Society for Computational Economics, vol. 25(3), pages 269-274, June.
    18. Rhys Bidder & Kalin Nikolov & Tony Yates, "undated". "Self-confirming Inflation Persistence," CDMA Conference Paper Series 0908, Centre for Dynamic Macroeconomic Analysis.
    19. Alex Clymo & Andrea Lanteri & Alessandro Villa, 2023. "Capital and Labor Taxes with Costly State Contingency," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 51, pages 943-964, December.

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