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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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    1. Adrien Auclert & Ludwig Straub & Matthew Rognlie, 2019. "Micro Jumps, Macro Humps: monetary policy and business cycles in an estimated HANK model," 2019 Meeting Papers 1449, Society for Economic Dynamics.
    2. Eva F. Janssens & Sean McCrary, 2023. "Finite-State Markov-Chain Approximations: A Hidden Markov Approach," Finance and Economics Discussion Series 2023-040, Board of Governors of the Federal Reserve System (U.S.).
    3. Josef Platzer & Marcel Peruffo, 2022. "Secular Drivers of the Natural Rate of Interest in the United States: A Quantitative Evaluation," IMF Working Papers 2022/030, International Monetary Fund.
    4. Anmol Bhandari & Thomas Bourany & David Evans & Mikhail Golosov, 2023. "A Perturbational Approach for Approximating Heterogeneous Agent Models," NBER Working Papers 31744, National Bureau of Economic Research, Inc.
    5. Marlon Azinovic-Yang & Jan Zemlicka, 2025. "Deep Learning in the Sequence Space," CERGE-EI Working Papers wp802, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    6. Richard Evans & Kerk Phillips, 2014. "OLG Life Cycle Model Transition Paths: Alternate Model Forecast Method," Computational Economics, Springer;Society for Computational Economics, vol. 43(1), pages 105-131, January.
    7. Manuel Arellano & Richard Blundell & Stéphane Bonhomme, 2017. "Earnings and Consumption Dynamics: A Nonlinear Panel Data Framework," Econometrica, Econometric Society, vol. 85, pages 693-734, May.
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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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