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Neural Network Methods for Solving and Estimating Nonlinear Economic Models (ECO-AD-NEURALNET)

ECO-AD-NEURALNET

Description

Contacts: 
hanno.kase@ecb.europa.eu, matthias.rottner@bundesbank.de

Description:
This course introduces students to recent advances in machine learning that make it possible to globally solve and estimate macroeconomic models featuring agent heterogeneity, nonlinear constraints, and aggregate risk. The central idea is to use neural networks to approximate the policy functions of a model while treating its structural parameters as pseudo-state variables, so that the model has to be solved only once, before the estimation starts. A second neural network, the neural network particle filter, approximates the likelihood function and delivers a fast and smooth objective for maximum likelihood and Bayesian estimation. We will also discuss how a dedicated neural network can characterize the deterministic steady state, which makes it possible to estimate parameters that govern the steady state of the economy.
Building on these methodological foundations, the course follows introduces models of increasing complexity. We start with a small-scale Representative Agent New Keynesian (RANK) model, which can be extended it to account for the ZLB. We then turn to heterogeneous agent models: the economy of Krusell and Smith (1998), its two-asset extension, and a canonical Heterogeneous Agent New Keynesian (HANK) model, comparing the neural network solution with the Sequence Space Jacobian approach. Throughout the course, the lectures are accompanied by annotated Python code based on PyTorch, which students can use as a starting point for their term papers. Time permitting, we conclude with generative economic modeling, a recently developed approach that combines neural networks with conventional solution techniques to solve high-dimensional models.

Goal:
The course aims to introduce students to the research frontier on neural networks in quantitative macroeconomics.

Assessment:
It will consist of a term paper, in which students, working individually or in groups of two, apply the newly learned methods to a problem of their choice. Students will submit the paper and present their results in a seminar, which will take place virtually. The final grade will be based exclusively on the term paper and the presentation. The term paper should not exceed 15 pages in length for individual submissions and 20 pages for groups of two.

The submission deadline will be announced at a later date. Late submissions will be subject to substantial penalties.

Course Outline

1. Introduction to Neural Networks
(a) Neural Networks as Function Approximators: Architecture, Activation Functions, and the Universal Approximation Theorem
(b) Training: Loss Functions, Back-Propagation, Stochastic Gradient Descent, and Learning Rate Schedules
(c) Computation on CPUs and GPUs: Python and PyTorch

2. Solution of Macroeconomic Models with Neural Networks
(a) A General Framework: State Variables, Shocks, Policy Functions, and Equilibrium Conditions
(b) Extended Policy Functions: Parameters as Pseudo-State Variables
(c) Neural Network Solution of the Deterministic Steady State
(d) Incorporating Agent Heterogeneity

3. The Neural Network Particle Filter
(a) Likelihood Evaluation of Nonlinear Models and the Particle Filter
(b) Training a Neural Network to Approximate the Likelihood Function
(c) Maximum Likelihood and Bayesian Estimation

4. Nonlinear Representative Agent New Keynesian (RANK) Model
(a) The RANK Model as a Baseline: Solution and Estimation Step by Step
(b) Extending the Code: Policy Functions, Parameters, State Variables, Shocks, Pseudo-State Variables, and the Observation Equation
(c) Options for the Neural Network Solution and Filtering Steps
(d) The Zero Lower Bound: Global Solution and Estimation

5. Heterogeneous Agent Model Based on Krusell and Smith (1998)
(a) Mapping of the Model to the General Framework
(b) Deterministic Steady State: Asset Distribution, Individual Policy Functions, and Approximation Errors
(c) Equilibrium with Aggregate Risk: Impulse Response Functions and Approximation Errors
(d) Comparison with the Sequence Space Jacobian

6. Two-Asset Extension of the Heterogeneous Agent Model
(a) Households Holding Capital and Government Debt
(b) Adapting the Neural Network Architecture to Multiple Assets
(c) Deterministic Steady State and Equilibrium with Aggregate Risk

7. Heterogeneous Agent New Keynesian (HANK) Model
(a) Mapping of the Canonical One-Asset HANK Model to the General Framework
(b) Deterministic Steady State and Equilibrium with Aggregate Risk
(c) Comparison with the Sequence Space Jacobian under Low and High Aggregate Risk
(d) Estimation of a Nonlinear HANK Model with a Zero Lower Bound on U.S. Data

8. Generative Economic Modeling (Optional)
(a) Combining Neural Networks with Conventional Solution Techniques
(b) Training on Simplified Submodels to Circumvent the Curse of Dimensionality
(c) Application: A High-Dimensional HANK Model with an Occasionally Binding Financial Friction

Main References:
• Kase, H., L. Melosi, and M. Rottner (2022): Estimating Nonlinear Heterogeneous Agents Models with Neural Networks, CEPR Discussion Paper 17391.
• Kase, H., L. Melosi, and M. Rottner (2026): Accompanying Material: Learning Guide for “Estimating Nonlinear Heterogeneous Agent Models with Neural Networks”, Manuscript.
• Kase, H., M. Rottner, and F. Stohler (2025): Generative Economic Modeling, BIS Working Papers 1312, Bank for International Settlements.

Other References
Auclert, A., B. Bardóczy, M. Rognlie, and L. Straub (2021): Using the Sequence-Space Jacobian to Solve and Estimate Heterogeneous-Agent Models, Econometrica, 89, 2375– 2408.
Azinovic, M., L. Gaegauf, and S. Scheidegger (2022): Deep Equilibrium Nets, International Economic Review, 63, 1471–1525.
Fernández-Villaverde, J., S. Hurtado, and G. Nuño (2023): Financial Frictions and the Wealth Distribution, Econometrica, 91, 869–901.
Fernández-Villaverde, J., J. Marbet, G. Nuño, and O. Rachedi (2025): Inequality and the Zero Lower Bound, Journal of Econometrics, 249, 105819.
Fernández-Villaverde, J., G. Nuño, and J. Perla (2026): Taming the Curse of Dimensionality: Quantitative Economics with Deep Learning, Quantitative Economics, forthcoming.
Han, J., Y. Yang, and W. E (2026): DeepHAM: A Global Solution Method for Heterogeneous
Agent Models with Aggregate Shocks, Quantitative Economics, 17, 297–341.
Herbst, E. P., and F. Schorfheide (2015): Bayesian Estimation of DSGE Models, Princeton University Press, Princeton, New Jersey.
Krusell, P., and A. Smith (1998): Income and Wealth Heterogeneity in the Macroeconomy, Journal of Political Economy, 106, 867–896.
Maliar, L., and S. Maliar (2020): Deep Learning: Solving HANC and HANK Models in the Absence of Krusell-Smith Aggregation, Manuscript.
Maliar, L., S.Maliar, and P. Winant (2021): Deep Learning for Solving Dynamic Economic Models, Journal of Monetary Economics, 122, 76–101.
Scheidegger, S. (2026): Deep Learning for Solving and Estimating Dynamic Models in Economics and Finance, arXiv preprint arXiv:2605.14493.

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