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Stochastic extended path

Author

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  • 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, 2026. "Stochastic extended path," Journal of Economic Dynamics and Control, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:dyncon:v:182:y:2026:i:c:s0165188925001939
    DOI: 10.1016/j.jedc.2025.105227
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    References listed on IDEAS

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