Deep learning for solving dynamic economic models

Deep learning for solving dynamic economic models

This notebook solves a version of Krusell and Smith’s (1998) heterogenous-agent model with idiosyncrastic and aggregate shocks, incomplete markets and borrowing constraints. It uses a deep learning Euler-equation method introduced by Maliar, Maliar and Winant (2018) in the paper “Deep learning for solving dynamic economic models”, Journal of Monetary Economics 122, pp 76-101. https://lmaliar.ws.gc.cuny.edu/files/2021/09/JME2021.pdf

We show a version of the Euler equation method that minimizes the sum of squared residuals in the equilibrium conditions. See https://deepecon.org for documentation, updates and the other versions of the deep learning method (Bellman equation and life-time reward).

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Abstract

We introduce a unified deep learning method that solves dynamic economic models by casting them into nonlinear regression equations. We derive such equations for three fundamental objects of economic dynamics – lifetime reward functions, Bellman equations and Euler equations. We estimate the decision functions on simulated data using a stochastic gradient descent method. We introduce an all-in-one integration operator that facilitates approximation of high-dimensional integrals. We use neural networks to perform model reduction and to handle multicollinearity. Our deep learning method is tractable in large-scale problems, e.g., Krusell and Smith (1998). We provide a TensorFlow code that accommodates a variety of applications.

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How to Execute this Notebook (with conda)

Install miniconda on your computer

  1. Open a Terminal (MacOS) or the Anaconda Prompt (Windows)
  2. At a command line, change the working directory to the one where you want to install
    • On MacOS/unix, if you install in the /tmp directory, the repo will disappear at reboot:
    • cd /tmp
  3. git clone https://github.com/marcmaliar/deep-learning-euler-method-krusell-smith/ --recursive
  4. cd deep-learning-euler-method-krusell-smith
  5. conda env create -f ./binder/environment.yml --prefix ./condaenv
    • This creates ./condaenv inside your clone of the repo, containing dependencies.
  6. conda run --prefix ./condaenv pip install jupyterlab
  7. conda run --prefix ./condaenv jupyter-lab

Metadata

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Key Value
cff-version 1.2.0
message If you use this software, please cite it using the metadata from this file.
type software
authors {"given-names"=>"Lilia", "family-names"=>"Maliar", "affiliation"=>"a The Graduate Center, City University of New York, CEPR, and Hoover Institution, Stanford University"}
{"given-names"=>"Serguei", "family-names"=>"Maliar", "affiliation"=>"Santa Clara University"}
{"given-names"=>"Pablo", "family-names"=>"Winant", "affiliation"=>"ESCP Business School and CREST/Ecole Polytechnique"}
identifiers {"type"=>"doi", "value"=>"10.1016/j.jmoneco.2021.07.004"}
abstract We introduce a unified deep learning method that solves dynamic economic models by casting them into nonlinear regression equations. We derive such equations for three fundamental objects of economic dynamics – lifetime reward functions, Bellman equations and Euler equations. We estimate the decision functions on simulated data using a stochastic gradient descent method. We introduce an all-in-one integration operator that facilitates approximation of high-dimensional integrals. We use neural networks to perform model reduction and to handle multicollinearity. Our deep learning method is tractable in large-scale problems, e.g., Krusell and Smith (1998). We provide a TensorFlow code that accommodates a variety of applications.
keywords Artificial intelligence
Machine learning
Deep learning
Neural network
Stochastic gradient
Dynamic models
Model reduction
Dynamic programming
Bellman equation
Euler equation
Value function
references {"type"=>"article", "authors"=>[{"family-names"=>"Krusell", "given-names"=>"Per"}, {"family-names"=>"Smith, Jr.", "given-names"=>"Anthony A."}], "title"=>"Income and Wealth Heterogeneity in the Macroeconomy", "doi"=>"10.1086/250034", "date-released"=>#, "publisher"=>{"name"=>"Journal of Political Economy"}}
remark-version v1.0.0
remark-name DeepLearningKrusselSmith
github_repo_url https://github.com/marcmaliar/deep-learning-euler-method-krusell-smith/
notebooks code/python/Main_KS.ipynb
tags
date