02691cam a22003257 4500001000700000003000500007005001700012006001900029007001500048008004100063100001900104245015100123260006600274300005700340490004200397500001900439520132200458530006001780538007201840538003601912588002501948690008701973690007502060700001802135700001802153710004202171830007702213856003802290856003702328w24138NBER20200807233239.0m o d cr cnu||||||||200807s2017 mau fo 000 0 eng d1 aBoppart, Timo.10aExploiting MIT Shocks in Heterogeneous-Agent Economies:bThe Impulse Response as a Numerical Derivative /cTimo Boppart, Per Krusell, Kurt Mitman. aCambridge, Mass.bNational Bureau of Economic Researchc2017. a1 online resource:billustrations (black and white);1 aNBER working paper seriesvno. w24138 aDecember 2017.3 aWe 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. aHardcopy version available to institutional subscribers aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web.0 aPrint version record 7aC68 - Computable General Equilibrium Models2Journal of Economic Literature class. 7aE1 - General Aggregative Models2Journal of Economic Literature class.1 aKrusell, Per.1 aMitman, Kurt.2 aNational Bureau of Economic Research. 0aWorking Paper Series (National Bureau of Economic Research)vno. w24138.40uhttp://www.nber.org/papers/w2413840uhttp://dx.doi.org/10.3386/w24138