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Deep Learning Solutions to Master Equations for Continuous Time Heterogeneous Agent Macroeconomic Models

Author

Listed:
  • Zhouzhou Gu

    (Princeton University)

  • Mathieu Laurière

    (NYU Shanghai, NYU-ECNU Institute of Mathematical Sciences)

  • Sebastian Merkel

    (University of Exeter)

  • Jonathan Payne

    (Princeton University)

Abstract

We propose a new global solution algorithm for continuous time heterogeneous agent economies with aggregate shocks. First, we approximate the state space so that equilibrium in the economy can be characterized by one high, but finite, dimensional partial differential equation. Second, we approximate the value function using neural networks and solve the differential equation using deep learning tools. We refer to the solution as an Economic Model Informed Neural Network (EMINN). The main advantage of this technique is that it allows us to find global solutions to high dimensional, non-linear problems. We demonstrate our algorithm by solving two canonical models in the macroeconomics literature: the Aiyagari (1994) model and the Krusell and Smith (1998) model.

Suggested Citation

  • Zhouzhou Gu & Mathieu Laurière & Sebastian Merkel & Jonathan Payne, 2023. "Deep Learning Solutions to Master Equations for Continuous Time Heterogeneous Agent Macroeconomic Models," Working Papers 2023-19, Princeton University. Economics Department..
    • Handle: RePEc:pri:econom:2023-19
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    More about this item

    Keywords

    Heterogeneous agents; computational methods; deep learning; inequality; mean field games; continuous time methods; aggregate shocks; global solution;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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