This paper provides first and second-order approximation methods for the solution of non-linear dynamic stochastic models in which the exogenous state variables follow conditionally linear stochastic processes displaying time-varying risk. The first-order approximation is consistent with a...

This paper undertakes a Bayesian analysis of optimal monetary policy for the U.K. We estimate a suite of monetary-policy models that include both forward- and backward-looking representations as well as large- and small-scale models. We find an optimal simple Taylor-type rule that accounts for...

We investigate the behavior of asset prices in a typical New Keynesian macro model. Using a second-order approximation, we examine bond and equity returns, the equity risk premium, and the behavior of the real and nominal term structure. As documented in the literature, our results suggest that...