Merging Deep Learning Neural Networks with the Stochastic Parameterized Expectations Algorithm for Solving Nonlinear Rational Expectations Models

This paper proposes a novel framework that integrates Deep Learning Neural Networks into the Stochastic Parameterized Expectations Algorithm (DLNN-PEA) to solve nonlinear rational expectations models. This method enhances traditional PEA-based solvers by employing a deep neural expectations operator that captures complex nonlinearities and asymmetries. The DLNN-PEA is implemented in Matlab R2024b. It combines deep learning approximation with the standard expectation-iteration structure of the PEA, replacing the conventional shallow ANN-based operator with a deeper architecture that improves both accuracy and stability. The methodology is applied to the stochastic Neoclassical Growth Model, where the DLNN-PEA is trained to approximate conditional expectations and decision rules under uncertainty. The results show rapid convergence, reduced boundary-related issues, and stable performance even in high-volatility environments. Compared with ANN-PEA, deep architectures exhibit greater robustness and adaptability, making them suitable for economic models characterized by stronger nonlinearities and richer state dynamics. Beyond the benchmark model, the proposed framework is well-suited for medium-scale DSGE models, nonlinear monetary policy environments, and macro-financial simulations involving high-dimensional state spaces. These features make DLNN-PEA a practical tool for applied macroeconomic analysis and model-based policy evaluation.