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Sequence-Space Jacobians of Life-Cycle Models

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Abstract

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.

Suggested Citation

  • Bence Bardóczy & Akshay Shanker & Mateo Velásquez-Giraldo, 2026. "Sequence-Space Jacobians of Life-Cycle Models," Finance and Economics Discussion Series 2026-046, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgfe:103447
    DOI: 10.17016/FEDS.2026.046
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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D15 - Microeconomics - - Household Behavior - - - Intertemporal Household Choice; Life Cycle Models and Saving

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