Solving DSGE models with incomplete markets by perturbation

Abstract

DSGE models with incomplete markets (with one or many assets) are typically challenging to solve due to their lack of stable dynamics as risk goes to zero. To bypass this difficulty, I propose to first approximate the local dynamics of a tractable auxiliary model and then apply regular perturbation to some of the parameters to reach the model of interest. This method is easy to implement with available packages and allows researchers to solve a wide class of DSGE models around a large subset of the state-space while still relying on the implicit function theorems. Exploiting these properties, the paper develops a simple algorithm to find an auxiliary model whose deterministic steady state equals the stochastic steady state of the model of interest and builds the perturbation solution around this point. The lead application extends the two-period, multi-asset model of Coeurdacier and Gourinchas (2016, JME) to an infinite horizon setup. The calibrated model with bonds and equities delivers a large level of equity home bias and a natural link between trade and financial openness, with external asset positions comparable to the data. However, the model generates excessive risk-sharing and counterfactual co-movements of gross capital flows.