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,...

We derive recursive representations of nonlinear moving average (NLMA) perturbations of DSGE models. As the stability of higher order NLMA representations follows directly from stability at first order, these recursive representations provide rigorous support for the practice of pruning that is...

We analyze the theoretical moments of a nonlinear approximation to real business cycle model with stochastic volatility and recursive preferences. We find that the conditional heteroskedasticity of stochastic volatility operationalizes a time-varying risk adjustment channel that induces...

We analyze the theoretical moments of a nonlinear approximation to a model of business cycles and asset pricing with stochastic volatility and recursive preferences. We find that heteroskedastic volatility operationalizes a time-varying risk adjustment channel that induces variability in...

I compare the performance of solution methods in solving a standard real business cycle model with labor market search frictions. Under the conventional calibration, the model is solved by the projection method using the Chebyshev polynomials as its basis, and the perturbation methods up to...