This paper derives a second-order approximation to the solution of a general class of discrete-time rational expectations models. The main theoretical contribution of the paper is to show that for any model belonging to the general class considered, the coefficients on the terms linear and...

We show how to use a simple perturbation method to solve non-linear rational expectation models. Drawing from the applied mathematics literature we propose a method consisting of series expansions of the non-linear system around a known solution. The variables are represented in terms of their...

This paper aims at providing macroeconomists with a detailed exposition of the New Keynesian DSGE model. Both the sticky price version and the sticky information variant are derived mathematically. Moreover, we simulate the models, also including lagged terms in the sticky price version, and...

This paper derives a fifth-order perturbation solution to DSGE models. The paper develops a new notation that reduces the notational complexity of high-order solutions and yields a faster code. The new notation consists of new matrix forms of high-order multivariate chain rules and a new...

First-order approximation methods are a standard technique for analyzing the local dynamics of dynamic stochastic general equilibrium (DSGE) models. Although for a wide class of DSGE models linear methods yield quite accurate solutions, some important economic issues such as portfolio choice and...

This paper shows how to compute a second-order accurate solution of a non-linear rational expectation model using algorithms developed for the solution of linear rational expectation models. The result is a state-space representation for the realized values of the variables of the model. This...

This paper shows how to compute a second-order-accurate solution of a non-linear rational expectation model using algorithms developed for the solution of linear rational expectation models. The result is a state-space representation for the realized values of the variables of the model. This...

We show how to use a simple perturbation method to solve non-linear rational expectation models. Drawing from the applied mathematics literature we propose a method consisting of series expansions of the non-linear system around a known solution. The variables are represented in terms of their...

Phenomena such as the Great Moderation have increased the attention of macro-economists towards models where shock processes are not (log-) normal. This paper studies a class of discrete-time rational expectations models where the variance of exogenous innovations is subject to stochastic regime...

Phenomena such as the Great Moderation have increased the attention of macro-economists towards models where shock processes are not (log-)normal. This paper studies a class of discrete-time rational expectations models where the variance of exogenous innovations is subject to stochastic regime...