A General Method for Comparative Dynamics in Continuous‐Time Models

Abstract

This paper develops a general and applicable method for the computation of comparative dynamics in continuous‐time perfect foresight models. The key technique in our method is the Jordan decomposition of the Jacobian matrix. This enables us to derive analytical solutions when dealing with high‐dimensional systems with repeated eigenvalues. In an application, we compute comparative dynamics of an unanticipated expansionary monetary policy in scenarios with and without repeated eigenvalues. We find that the short‐run effects on the social welfare are opposite in the two scenarios, while the long‐run effects are similar.

Keywords: Jordan decomposition, Laplace transforms, multidimensional dynamic models