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Stochastic Extended Path

Author

Listed:
  • Adjemian, Stéphane
  • Juillard, Michel

Abstract

The Extended Path (EP) method solves DSGE models under certainty equivalence, capturing nonlinearities and occasionally binding constraints but ignoring the role of uncertainty. We propose the Stochastic Extended Path (SEP), which restores this channel by computing conditional expectations with quadrature and unscented transforms. To avoid the exponential explosion of a full tree of future shocks, we introduce a sparse tree representation that scales linearly with the horizon. We further develop a hybrid SEP, combining SEP with perturbation corrections to capture long-run effects of volatility at low cost. Accuracy is benchmarked in an asset pricing model with a closed-form solution, where hybrid SEP outperforms perturbation methods. We then illustrate the approach in an RBC model with a lower bound on investment.

Suggested Citation

  • Adjemian, Stéphane & Juillard, Michel, 2025. "Stochastic Extended Path," Dynare Working Papers 84, CEPREMAP, revised Sep 2025.
    • Handle: RePEc:cpm:dynare:084
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    References listed on IDEAS

    as
    1. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    2. Guerrieri, Luca & Iacoviello, Matteo, 2015. "OccBin: A toolkit for solving dynamic models with occasionally binding constraints easily," Journal of Monetary Economics, Elsevier, vol. 70(C), pages 22-38.
    3. David R.F. Love, 2009. "Accuracy of Deterministic Extended-Path Solution Methods for Dynamic Stochastic Optimization Problems in Macroeconomics," Working Papers 0907, Brock University, Department of Economics.
    4. 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.
    Full references (including those not matched with items on IDEAS)

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