Sequence-Space Jacobian – IKC

Lecture 9 · 2026-05-19

The lecture begins with the intertemporal Keynesian cross (IKC), showing that the matrix of intertemporal marginal propensities to consume (iMPCs) \(\mathbf{M}\) is a sufficient statistic for the macroeconomic response of heterogeneous-agent models to fiscal policy, and compares its shape and the implied fiscal multipliers across alternative consumption models (RA, TA, HA). It then contrasts the state-space and sequence-space representations and introduces the sequence-space Jacobian (SSJ) method: linearizing the model around the steady state, solving for impulse responses via Jacobian matrices, and conducting estimation and local-determinacy testing. Finally, using the Krusell–Smith model as an example, it explains how the fake-news algorithm rapidly constructs the Jacobian of the heterogeneous-agent block.

Materials

Readings

  • Auclert, Bardóczy, Rognlie & Straub (2021), “Using the Sequence-Space Jacobian to Solve and Estimate Heterogeneous-Agent Models,” Econometrica 89(5), 2379–2419.
  • Auclert, Rognlie & Straub, “The Intertemporal Keynesian Cross.”
  • Code repository: https://github.com/shade-econ/sequence-jacobian