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

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  • Adrien Auclert
  • Bence Bardóczy
  • Matthew Rognlie
  • Ludwig Straub

Abstract

We propose a general and highly efficient method for solving and estimating general equilibrium heterogeneous-agent models with aggregate shocks in discrete time. Our approach relies on the rapid computation of sequence-space Jacobians—the derivatives of perfect-foresight equilibrium mappings between aggregate sequences around the steady state. Our main contribution is a fast algorithm for calculating Jacobians for a large class of heterogeneous-agent problems. We combine this algorithm with a systematic approach to composing and inverting Jacobians to solve for general equilibrium impulse responses. We obtain a rapid procedure for likelihood-based estimation and computation of nonlinear perfect-foresight transitions. We apply our methods to three canonical heterogeneous-agent models: a neoclassical model, a New Keynesian model with one asset, and a New Keynesian model with two assets.

Suggested Citation

  • Adrien Auclert & Bence Bardóczy & Matthew Rognlie & Ludwig Straub, 2019. "Using the Sequence-Space Jacobian to Solve and Estimate Heterogeneous-Agent Models," NBER Working Papers 26123, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:26123
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    2. Papp, Tamás K. & Reiter, Michael, 2020. "Estimating linearized heterogeneous agent models using panel data," Journal of Economic Dynamics and Control, Elsevier, vol. 115(C).
    3. Christian Bayer & Ralph Luetticke, 2019. "Shocks, Frictions, and Inequality in US Business Cycles," 2019 Meeting Papers 256, Society for Economic Dynamics.
    4. Alisdair McKay & Johannes F. Wieland, 2019. "Lumpy Durable Consumption Demand and the Limited Ammunition of Monetary Policy," NBER Working Papers 26175, National Bureau of Economic Research, Inc.
    5. Jesús Fernández-Villaverde & Samuel Hurtado & Galo Nuño, 2019. "Financial Frictions and the Wealth Distribution," NBER Working Papers 26302, National Bureau of Economic Research, Inc.
    6. Felipe Alves, 2022. "Job Ladder and Business Cycles," Staff Working Papers 22-14, Bank of Canada.
    7. Cameron Fen, 2022. "Fast Simulation-Based Bayesian Estimation of Heterogeneous and Representative Agent Models using Normalizing Flow Neural Networks," Papers 2203.06537, arXiv.org.
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    9. Achdou, Yves & Han, Jiequn & Lasry, Jean Michel & Lions, Pierre Louis & Moll, Ben, 2022. "Income and wealth distribution in macroeconomics: a continuous-time approach," LSE Research Online Documents on Economics 107422, London School of Economics and Political Science, LSE Library.
    10. Ester Faia & Marianna Kudlyak & Ekaterina Shabalina, 2021. "Dynamic Labor Reallocation with Heterogeneous Skills and Uninsured Idiosyncratic Risk," Working Paper Series 2021-16, Federal Reserve Bank of San Francisco.
    11. Jiequn Han & Yucheng Yang & Weinan E, 2021. "DeepHAM: A Global Solution Method for Heterogeneous Agent Models with Aggregate Shocks," Papers 2112.14377, arXiv.org, revised Feb 2022.
    12. Matthew D. Cocci & Mikkel Plagborg-Møller, 2021. "Standard Errors for Calibrated Parameters," Working Papers 2021-20, Princeton University. Economics Department..
    13. Alisdair McKay & Johannes F. Wieland, 2021. "Lumpy Durable Consumption Demand and the Limited Ammunition of Monetary Policy," Econometrica, Econometric Society, vol. 89(6), pages 2717-2749, November.
    14. Ben Moll, 2020. "The Research Agenda: Ben Moll on the Rich Interactions between Inequality and the Macroeconomy," EconomicDynamics Newsletter, Review of Economic Dynamics, vol. 21(2), November.
    15. Felipe Alves & Christian Bustamante & Xing Guo & Katya Kartashova & Soyoung Lee & Thomas Michael Pugh & Kurt See & Yaz Terajima & Alexander Ueberfeldt, 2022. "Heterogeneity and Monetary Policy: A Thematic Review," Discussion Papers 2022-2, Bank of Canada.

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    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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