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Parameterized Expectations Algorithm and the Moving Bounds

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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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    1. Christiano, Lawrence J. & Fisher, Jonas D. M., 2000. "Algorithms for solving dynamic models with occasionally binding constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(8), pages 1179-1232, July.
    2. Miranda, Mario J & Helmberger, Peter G, 1988. "The Effects of Commodity Price Stabilization Programs," American Economic Review, American Economic Association, vol. 78(1), pages 46-58, March.
    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. Wright, Brian D & Williams, Jeffrey C, 1982. "The Economic Role of Commodity Storage," Economic Journal, Royal Economic Society, vol. 92(367), pages 596-614, September.
    5. Wouter J. Den Haan & Albert Marcet, 1994. "Accuracy in Simulations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(1), pages 3-17.
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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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.).
    7. 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.
    8. Ángel Gavilán & Juan A. Rojas, 2009. "Solving Portfolio Problems with the Smolyak-Parameterized Expectations Algorithm," Working Papers 0838, Banco de España.
    9. Jesús Fernández-Villaverde & Galo Nuño & Jesse Perla, 2024. "Taming the curse of dimensionality: quantitative economics with deep learning," Working Papers 2444, Banco de España.
    10. Shaw, Philip, 2014. "A nonparametric approach to solving a simple one-sector stochastic growth model," Economics Letters, Elsevier, vol. 125(3), pages 447-450.
    11. Giulia Piccillo & Poramapa Poonpakdee, 2023. "Ambiguous Business Cycles, Recessions and Uncertainty: A Quantitative Analysis," CESifo Working Paper Series 10646, CESifo.
    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. 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.
    14. 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.
    15. Paul Pichler, 2005. "Evaluating Approximate Equilibria of Dynamic Economic Models," Vienna Economics Papers 0510, University of Vienna, Department of Economics.
    16. 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.
    17. Pérez, Javier J. & Sánchez, A. Jesús, 2009. "Alternatives to initialize the Parameterized Expectations Algorithm," Economics Letters, Elsevier, vol. 102(2), pages 116-118, February.
    18. 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.
    19. Rhys Bidder & Kalin Nikolov & Tony Yates, "undated". "Self-confirming Inflation Persistence," CDMA Conference Paper Series 0908, Centre for Dynamic Macroeconomic Analysis.

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