Deep Learning Methods

Lecture 10 · 2026-05-26 / 06-02 (AI solution methods, parts 1 & 2)

Solving dynamic economic models with deep learning. Part 1 starts from the machine-learning toolkit (neural networks, loss functions, stochastic gradient descent, automatic differentiation) and, using a consumption–savings model with a borrowing constraint, introduces three ways to recast a dynamic model as a loss function (lifetime utility, Euler-equation residual, Bellman residual); the occasionally binding constraint is handled with the Fischer–Burmeister function, and the all-in-one expectation operator collapses the nested expectations into a single layer of Monte Carlo, yielding an end-to-end JAX implementation of the Euler-residual method. Part 2 carries the same toolkit (FB + AiO + Adam + autodiff) to a Krusell–Smith model with aggregate shocks: a single neural network takes the entire cross-sectional distribution directly as a state input and is solved globally in JAX/Equinox via vmap, with checks on the decision rule, the ergodic distribution, and whether approximate aggregation holds.

Materials

• Part 1 — Deep Learning Methods: HTML · PDF · Notebook
• Part 2 — Deep Learning for Krusell–Smith: HTML · PDF · Notebook

Readings

• Maliar, Maliar & Winant (2021), “Deep Learning for Solving Dynamic Economic Models,” JME 122, 76–101. (primary slide reference)
• Han, Yang & E (2021), “DeepHAM: A Global Solution Method for Heterogeneous Agent Models with Aggregate Shocks,” forthcoming in Quantitative Economics.
• Maliar & Maliar (2022), “Deep Learning Classification: Modeling Discrete Labor Choice,” JEDC 135.
• Gu, Laurière, Merkel & Payne (2024), “Global Solutions to Master Equations for Continuous Time Heterogeneous Agent Macroeconomic Models.”
• Achdou, Han, Lasry, Lions & Moll (2022), “Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach,” RES 89(1), 45–86.