Exploiting MIT Shocks in Heterogeneous-Agent Economies: The Impulse Response as a Numerical Derivative

57 Pages Posted: 2 Jan 2018

See all articles by Timo Boppart

Timo Boppart

Stockholm University - Institute for International Economic Studies (IIES); University of Zurich - Department of Economics

Per Krusell

Princeton University - Department of Economics; Stockholm University - Institute for International Economic Studies (IIES); Centre for Economic Policy Research (CEPR)

Kurt Mitman

IIES

Multiple version iconThere are 2 versions of this paper

Date Written: December 2017

Abstract

We propose a new method for computing equilibria in heterogeneous-agent models with aggregate uncertainty. The idea relies on an assumption that linearization offers a good approximation; we share this assumption with existing linearization methods. However, unlike those methods, the approach here does not rely on direct derivation of first-order Taylor terms. It also does not use recursive methods, whereby aggregates and prices would be expressed as linear functions of the state, usually a very high-dimensional object (such as the wealth distribution). Rather, we rely merely on solving nonlinearly for a deterministic transition path: we study the equilibrium response to a single, small "MIT shock" carefully. We then regard this impulse response path as a numerical derivative in sequence space and hence provide our linearized solution directly using this path. The method can easily be extended to the case of many shocks and computation time rises linearly in the number of shocks. We also propose a set of checks on whether linearization is a good approximation. We assert that our method is the simplest and most transparent linearization technique among currently known methods. The key numerical tool required to implement it is value-function iteration, using a very limited set of state variables.

Keywords: computation, Heterogeneous Agents, linearization, MIT shock.

Suggested Citation

Boppart, Timo and Krusell, Per L. and Mitman, Kurt, Exploiting MIT Shocks in Heterogeneous-Agent Economies: The Impulse Response as a Numerical Derivative (December 2017). CEPR Discussion Paper No. DP12520. Available at SSRN: https://ssrn.com/abstract=3095570

Timo Boppart (Contact Author)

Stockholm University - Institute for International Economic Studies (IIES) ( email )

Stockholm, SE-10691
Sweden

University of Zurich - Department of Economics ( email )

Z├╝rich, CH-8006
Switzerland

Per L. Krusell

Princeton University - Department of Economics ( email )

111 Fisher Hall
Princeton, NJ
United States
609-258-4003 (Phone)
609-258-6419 (Fax)

HOME PAGE: http://rincewind.iies.su.se/%7Ekrusell/

Stockholm University - Institute for International Economic Studies (IIES) ( email )

Stockholm, SE-10691
Sweden
+46 0 8 16 30 73 (Phone)
+46 0 8 16 41 77 (Fax)

HOME PAGE: http://rincewind.iies.su.se/%7Ekrusell/

Centre for Economic Policy Research (CEPR)

London
United Kingdom

Kurt Mitman

IIES ( email )

Stockholm, SE-10691
Sweden

HOME PAGE: http://kurtmitman.com

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