Nonlocal Solutions to Dynamic Equilibrium Models: The Approximate Stable Manifolds Approach

This study presents a method for constructing a sequence of approximate solutions of increasing accuracy to general equilibrium models on nonlocal domains. The method is based on a technique originated from dynamical systems theory. The approximate solutions are constructed employing the Contraction Mapping Theorem and the fact that solutions to general equilibrium models converge to a steady state. The approach allows deriving the a priori and a posteriori approximation errors of the solutions. Under certain nonlocal conditions we prove the convergence of the approximate solutions to the true solution and hence the Stable Manifold Theorem. We also show that the proposed approach can be treated as a rigorous proof of convergence for the extended path algorithm to the true solution in a class of nonlinear rational expectation models.