The Accuracy of Perturbation Methods to Solve Small Open Economy Models

This paper presents the evaluation of the canonical RBC models for small-open economies described in Schmitt-Grohé and Uribe (2003) when the solution is obtained by perturbation methods up to a third-order approximation. The models are evaluated in terms of accuracy of solution, ergodic moments, and local responses in extreme regions of the state vector. Results show that the gains from non-linear solutions are significant in terms of accuracy and with respect to the outcome of simulations: when compared to the linear approximation of the equilibrium conditions, non-linear solution generates very different dynamics of the stationary-inducing devices and smaller responses of consumption and output if the economy is in a state of low capital. However, changes in the main allocations of the economy when using different solution methods appear only locally and under significant increases in the volatility of the economy.