Stochastic Extended Path

The Stochastic Extended Path (SEP) method enhances the traditional Extended Path technique by integrating numerical methods to estimate conditional expectations. In contrast to the deterministic Extended Path, which presumes that future shocks will align with their expected values, SEP accommodates stochastic non-linearity by performing integration over future shocks. We employ numerical techniques, including Gaussian quadrature and unscented transforms, to efficiently approximate integrals while alleviating the challenges posed by the curse of dimensionality. To further enhance accuracy, we propose a hybrid strategy that merges SEP with perturbation methods to effectively address long-run uncertainty effects. We evaluate the performance of SEP in an asset pricing model with a closed-form solution and demonstrate the methodology using a Real Business Cycle (RBC) model featuring irreversible investment.