Research Digest Solving economic models with machine-learning tools

In Deep learning for solving dynamic economic models, published in the Journal of Monetary Economics, ESCP Business School Professor Pablo Winant, along with Lilia Maliar and Serguei Maliar, propose using artificial intelligence (AI) technology to solve dynamic economic models.

Why study this

Many interesting economic problems are too challenging to solve by traditional computational methods; these problems include high-dimensional heterogenous-agent models, large-scale central banking models, life-cycle models and expensive nonlinear estimation procedures. The authors show that they may be solved by using the same AI technology, software and hardware that led to groundbreaking applications in data science. Specifically, the researchers introduce a deep learning (DL) method that solves dynamic economic models by reformulating them as nonlinear regression equations.


  • The authors show how to cast dynamic economic models into the form of expectation functions that are suitable for deep learning platforms (such as TensorFlow or PyTorch). 
  • Specifically, the three fundamental objects of economic dynamics that are reformulated as expectation functions are: lifetime reward functions, Bellman equations and Euler equations. 
  • The key ingredients of their DL method are multilayer neural networks and stochastic gradient training methods.
  • Neural networks (artificial neurons, or collections of connected nodes) are useful for handling multicollinearity and are linearly scalable. 
  • An all-in-one (AiO) expectation operator facilitates the approximation of integrals in Monte Carlo simulation and reduces costs dramatically.

Our solution method is tractable in models with at least 1000 agents (2,001 state variables) on a serial desktop computer!

Key insight

The authors cast an entire economic model into the state-of-the-art deep learning framework and construct a solution on simulated points by using the stochastic gradient descent method. 


In this paper, the authors solve dynamic economic models by taking advantage of ubiquitous, well-developed, optimized modern data-science tools. The DL approach seems particularly promising in that it can be used to solve models with thousands of state variables without resorting to a simplifying assumption about the economy's state space, an analysis that had been infeasible up til now.

Final takeaway

“The solution framework we introduce is not tied to neural networks but can be used with any approximating family (e.g., polynomials, splines, radial basis functions). However, neural networks possess several features that make them an excellent match for high-dimensional applications; namely, they are linearly scalable, robust to ill-conditioning, capable of model reduction and well suited for approximating highly nonlinear environments including kinks, discontinuities, discrete choices, switching.”


Lilia Maliar Lilia Maliar Professor of Economics at The Graduate Center (CUNY), Research Fellow at CEPR, and Visiting Fellow at the Hoover Institution (Stanford)
Serguei Maliar Serguei Maliar Associate Professor in Economics, Santa Clara University
Pablo Winant Pablo Winant Associate Professor of Economics at ESCP Business School