Sequence-Space Jacobians of Life-Cycle Models

The sequence-space Jacobian (SSJ) method of Auclert et al. (2021a) has made heterogeneous-agent models far easier to solve, fueling an explosion of applications. But even SSJ strains against capacity constraints when state spaces grow very large, as in economies with overlapping generations of heterogeneous agents (HA-OLG). We show how to exploit the special properties of age—finite planning horizons and deterministic transitions between ages—to compute the Jacobians of a general class of HA-OLG models orders of magnitude faster. We provide rigorous proofs, age-specific Jacobians that decompose aggregate dynamics across cohorts, an application to the dynamic general-equilibrium effects of secularly declining birth rates, and an accessible cookbook for adopting our method.