Calculating and Using Second Order Accurate Solution of Discrete Time Dynamic Equilibrium Models

It is now widely understood how to obtain first-order accurate approximations to the solution to a dynamic, stochastic general equilibrium model (DSGE model). Such solutions are fairly easy to construct and useful for a wide variety of purposes. They are likely to be accurate enough to be a basis for fitting the models to data, for example. However, for some purposes first-order accuracy is not enough. This is true in particular for comparing welfare across policies that do not have first-order effects on the model's deterministic steady state, for example. It is also true for attempts to study asset pricing in the context of DSGE models. This paper describes the algorithm for computing a second order approximation and shows how to apply it to calculating forecasts and impulse responses in dynamic models and to evaluating welfare in DSGE models. It points out some necessary regularity conditions for application of the method and discusses the sense in which the approximate solutions are locally accurate