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

Timo Boppart, Per Krusell and Kurt Mitman

No 24138, NBER Working Papers from National Bureau of Economic Research, Inc

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.

JEL-codes: C68 E1 (search for similar items in EconPapers)
Date: 2017-12
New Economics Papers: this item is included in nep-cmp and nep-dge
Note: EFG ME
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Citations: View citations in EconPapers (9)

Published as Timo Boppart & Per Krusell & Kurt Mitman, 2018. "Exploiting MIT Shocks in Heterogeneous-Agent Economies: The Impulse Response as a Numerical Derivative," Journal of Economic Dynamics and Control, .

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Related works:
Journal Article: Exploiting MIT shocks in heterogeneous-agent economies: the impulse response as a numerical derivative (2018)
Working Paper: Exploiting MIT Shocks in Heterogeneous-Agent Economies: The Impulse Response as a Numerical Derivative (2017)
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