We introduce the market resources method (MRM) for solving dynamic optimization problems. MRM extends Carroll's (2006) endogenous grid point method (EGM) for problems with more than one control variable using policy function iteration. The MRM algorithm is simple to implement and provides...

I construct risk-sensitive approximations of policy functions of DSGE models around the stochastic steady state and ergodic mean that are linear in the state variables. The method requires only the solution of linear equations using standard perturbation output to construct the approximation and...

We present the first necessary and sufficient conditions for the existence of a unique perfect-foresight solution, returning to a given steady-state, in an otherwise linear model with occasionally binding constraints. We derive further conditions on the existence of a solution in such models,...

This paper presents and compares Newton-based methods from the applied mathematics literature for solving the matrix quadratic that underlies the recursive solution of linear DSGE models. The methods are compared using nearly 100 different models from the Macroeconomic Model Data Base (MMB) and...

This paper presents and compares Bernoulli iterative approaches for solving linear DSGE models. The methods are compared using nearly 100 different models from the Macroeconomic Model Data Base (MMB) and different parameterizations of the monetary policy rule in the medium-scale New Keynesian...

This paper develops and implements a backward and forward error analysis of and condition numbers for the numerical stability of the solutions of linear dynamic stochastic general equilibrium (DSGE) models. Comparing seven different solution methods from the literature, I demonstrate an...

This paper applies structure preserving doubling methods to solve the matrix quadratic underlying the recursive solution of linear DSGE models. We present and compare two Structure-Preserving Doubling Algorithms (SDAs) to other competing methods - the QZ method, a Newton algorithm, and an...

This paper demonstrates a failure of standard, generalized Schur (orQZ) decomposition based solutions methods for linear dynamic stochastic general equilibrium (DSGE) models when there is insufficient eigenvalue separation about the unit circle. The significance of this is demonstrated in a...

We prove that standard regularity and saddle stability assumptions for linear approximations are sufficient to guarantee the existence of a unique solution for all undetermined coefficients of nonlinear perturbations of arbitrary order to discrete time DSGE models. We derive the perturbation...

We introduce a nonlinear infinite moving average as an alternative to the standard state-space policy function for solving nonlinear DSGE models. Perturbation of the nonlinear moving average policy function provides a direct mapping from a history of innovations to endogenous variables,...