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. It is possible to make separate arguments or assumptions that allow use of first-order approximations in these contexts, but the usual reliance on local approximation being generally locally accurate does not apply to these contexts. It is therefore of some interest to have an algorithm available that will produce second-order accurate approximations to the solutions to DSGE’s from a straightforward second-order expansion of the model’s equilibrium equations. Matlab code that does this is available at eco-072399b.princeton.edu/yftp/gensys2/, where the current version of this paper will also be found.