Semi-Global Solutions to DSGE Models: Perturbation around a Deterministic Path

TL;DR

This paper introduces a perturbation-based method to construct semi-global solutions for DSGE models by expanding around deterministic paths, enabling solutions that are global in state variables.

Contribution

It develops a recursive approach for higher-order terms in the expansion and a backward recursion method for solving linear rational expectations models with time-varying parameters.

Findings

Solutions are global in state variables if the deterministic path is global.

Higher order terms are obtained recursively from linear models.

Conditions for existence of solutions are established.

Abstract

This study proposes an approach based on a perturbation technique to construct global solutions to dynamic stochastic general equilibrium models (DSGE). The main idea is to expand a solution in a series of powers of a small parameter scaling the uncertainty in the economy around a solution to the deterministic model, i.e. the model where the volatility of the shocks vanishes. If a deterministic path is global in state variables, then so are the constructed solutions to the stochastic model, whereas these solutions are local in the scaling parameter. Under the assumption that a deterministic path is already known the higher order terms in the expansion are obtained recursively by solving linear rational expectations models with time-varying parameters. The present work also proposes a method rested on backward recursion for solving general systems of linear rational expectations models with time-varying parameters and determines the conditions under which the solutions of the method exist.