Solving nonlinear rational expectations models by parameterized expectations: convergence to stationary solutions

This paper develops the Parameterized Expectations Approach (PEA) for solving nonlinear dynamic stochastic models with rational expectations. The method can be applied to a variety of models, including models with strong nonlinearities, sub-optimal equilibria, and many continuous state variables. In this approach, the conditional expectations in the equilibrium conditions are approximated by finite-dimensional classes of functional forms. The approach is highly efficient computationally because it incorporates endogenous oversampling and Monte-Carlo integration, and it does not impost a discrete grid on the state variables or the stochastic shocks. We prove that PEA can approximate the correct solution with arbitrary accuracy on the ergodic set by increasing the size of the Monte-Carlo simulations and the dimensionality of the approximating family of functions.