Incomplete Markets, Heterogeneity and Macroeconomic Dynamics
This paper solves a real business cycle model with heterogeneous agents and uninsurable income risk using perturbation methods. A second order accurate characterization of agent's optimal decision rules is given, which renders the implications of aggregation for macroeconomic dynamics transparent. The role of cross-sectional holdings of capital in determining equilibrium dynamics can be directly assessed. Analysis discloses that an individual's optimal saving decisions are almost linear in their own capital stock giving rise to permanent income consumption behavior. This provides an explanation for the approximate aggregation properties of this model documented by Krusell and Smith (1998): the distribution of capital does not affect aggregate dynamics. While the variance-covariance properties of endogenous variables are almost entirely determined by first order dynamics, the second order dynamics, which capture properties of the wealth distribution, are nonetheless important for an individual's mean consumption and saving decisions and therefore the mean equilibrium capital stock. Policy evaluation exercises therefore need to take account of these higher order terms.
The authors thank seminar participants at the Australian National University, Columbia University, CREI-Universitat Pompeu Fabra, Duke University, Federal Reserve Bank of Atlanta, Federal Reserve Board of Governors, Indiana University, the New York Federal Reserve Bank Workshop on Monetary Policy, the North American Summer Meeting of the Econometric Society, Ohio State University and the San Francisco Federal Reserve Bank for comments and Stefania Albanesi, George-Marios Angeletos, Jesus Fernandez-Villaverde, Marc Giannoni, Wouter den Haan, Jinill Kim, John Leahy, Albert Marcet, Tony Smith and Mike Woodford for comments and useful discussions. The usual caveat applies. Financial support from the PER Student-Faculty Summer Grant is gratefully acknowledged. The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research.