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    Local vs global solution methods in real business cycle models: a comparative analysis of perturbation, value function iteration, endogenous grids, and neural networks
    (2025-12-09) Geiger, Iasonas; Γκάιγκερ, Ιάσονας; Kospentaris, Ioannis; Pagratis, Spyridon; Alexopoulos, Angelos
    This thesis investigates and compares alternative numerical methods for solving the stochastic Real Business Cycle (RBC) model, focusing on the trade off between local analytical efficiency and global numerical accuracy. The analysis benchmarks four main approaches, Perturbation, Value Function Iteration (VFI), the Endogenous Grid Method (EGM), and Neural Network (NN)–based solvers, under a unified calibration based on Schmitt-Grohé and Uribe (2004). The Perturbation method provides a fast and analytically transparent local approximation, yet its accuracy deteriorates under large shocks or high volatility. A systematic stress test quantifies the precise boundary of its validity, establishing thresholds for when global methods are required. The global solvers, VFI and EGM, compute policy functions directly on the full state space, offering benchmark accuracy; among them, EGM achieves near-perfect equilibrium precision with substantially reduced computational cost. Building upon these, two Neural Network architectures are implemented: a hybrid NN(Global) trained via distillation from EGM followed by Euler-equation fine-tuning, and an autonomous NN(Equation) trained solely on the model’s structural conditions. Both achieve global accuracy comparable to traditional methods, with NN(Equation) showing superior robustness in the tails of the state space. While Neural Networks entail significant upfront training time, they enable instantaneous policy evaluation after convergence, introducing a “solve-once, simulate instantly” paradigm highly suitable for large-scale simulations and sensitivity analyses. The results confirm that local methods remain sufficient near the steady state, EGM constitutes the optimal benchmark for most global analyses, and Neural Networks provide a credible and powerful alternative for high-dimensional or computation-intensive macroeconomic applications.