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

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.

Using the Sequence‐Space Jacobian to Solve and Estimate Heterogeneous‐Agent Models

“…This application uses the equivalence of impulse responses with the moving‐average (MA) representation of the model with aggregate shocks. This equivalence, in turn, follows immediately from the certainty equivalence property of first‐order perturbation methods such as ours (see, e.g., Simon (1956), Theil (1957), Judd and Guu (1993), and Boppart, Krusell, and Mitman (2018)).…”

“…As pointed out by Boppart, Krusell, and Mitman (2018), the formulation in equation (33) is useful to simulate sample paths for aggregate variables generated by any model, including a heterogeneous‐agent model. Assume impulse responses have been computed with truncation horizon T .…”

Integrated Epi-Econ Assessment

“…We have chosen not to model this uncertainty explicitly at this point. However, we believe that it can be studied straightforwardly using recent computational methods, at least to a first order: see Boppart et al (2018). I.e., it is possible to examine how information shocks (say, about an epidemiological parameter) at different points in time affect the economic and epidemiological evolution; these effects would depend on when they hit, but the methods allow for such analysis.…”

Validation and Calibration of an Agent-Based Model: A Surrogate Approach

“…Recent evidence proves that HAMs provide empirical results that outperform conventional capital asset pricing models or arbitrage models, which makes this theory one of the representative theories of behavioural nance. We choose heterogeneous agent models as an ideal investigatory instance for two reasons: they have been widely studied by nancial researchers and they o er a proper number of parameters [26][27][28]. is section will rst brie y describe the heterogeneous trader pricing model, then use the model to test the of performance of our method, and nally report the evaluation and comparison results.…”