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

Author

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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.

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  • 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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    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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