On Approximating DSGE Models By Series Expansions
The authors show how to use a simple perturbation method to solve non-linear rational expectation models. Drawing from the applied mathematics literature they propose a method consisting of series expansions of the non-linear system around a known solution. The variables are represented in terms of their orders of approximation with respect to a perturbation parameter. The final solution, therefore, is the sum of the different orders. This approach links to formal arguments the idea that each order of approximation is solved recursively taking as given the lower order of approximation.