ENSAE Paris - École d'ingénieurs pour l'économie, la data science, la finance et l'actuariat

Advanced Methods in Computational Economics (CREST)


This course is intended to confront M.sc. and Ph.D. students in economics, finance, and related fields with recent tools developed in applied mathematics, machine learning, computational science, and the computational economics literature to solve and estimate state-of-the-art models.
The lectures will be centered around sparse grids, adaptive sparse grids, two types of machine learning methods (Gaussian Processes and Deep Neural Networks), and will be showcased in the context of application in climate change economics, macroeconomics, and finance. The lectures will be interactive, in a workshop-like style, that is, a mix of theory and actively playing with code examples (delivered in Python and deployed on a cloud computing infrastructure).



  • Graduate-level mathematics (see, e.g., "Mathematics for Machine Learning". The book is freely downloadable here: https://mml-book.github.io).
  • Solid coding skills in Python (see, e.g., https://python-programming.quantecon.org/intro.html, Sections 1 - 7).
  • Some working knowledge of recursive methods (see, e.g., Stokey et al. [1989], Ljungqvist and Sargent [2000]).



Participants who take the course for credits are expected to propose a small project where they apply some of the methods learned to an application (e.g., apply deep learning to a data set, solve a dynamic model, etc.). The deliverable that will be graded is a short write-up (4-6 pages maximum), the data set (if any), and the code on which the presented results in the report were based. The participants will have four weeks' time after the course is finished to complete the task.


Some related literature:

  • Sparse grids in general: Bungartz and Griebel [2004]
  • Sparse grids in economics: Brumm and Scheidegger [2017], Brumm et al.
  • [2021]
  • High-dimensional model representation: Yang et al. [2012]
  • High-dimensional dynamic stochastic model representation: Eftekhari and
  • Scheidegger [2020]
  • Gaussian processes in general: Rasmussen [2004]
  • Gaussian processes in economics and finance: Scheidegger and Bilionis [2019], Renner and Scheidegger [2018]
  • Active subspaces: Constantine [2015]
  • Active subspaces in economics: Scheidegger and Bilionis [2019], Kubler and Scheidegger [2018]
  • Deep learning in general: Goodfellow et al. [2016]
  • Deep equilibrium nets: Azinovic et al. [2022]
  • Deep structural estimation: Chen et al. [2021]


There will be four lectures that will cover the following topics:

Lecture 1 - Monday 14/11
Sparse Grids, Adaptive Sparse Grids, High-dimensional model reduction, and high-performance computing Python libraries (if time permits).

Lecture 2 - Thursday 17/11
Gaussian Processes, Bayesian active learning, and active subspace methods for solving dynamic stochastic models.

Lecture 3 - Monday 21/11
Deep Learning basics.

Lecture 4 - Thursday 24/11
Deep Equilibrium Nets, Deep structural estimation, and some applications to climate economics and finance.


  • Marlon Azinovic, Luca Gaegauf, and Simon Scheidegger. Deep equilibrium nets. International Economic Review, 2022. doi: https://doi.org/10.1111/iere.12575. URL  ttps://onlinelibrary.wiley.com/doi/abs/10.1111/iere.12575.
  • Johannes Brumm and Simon Scheidegger. Using adaptive sparse grids to solve high-dimensional dynamic models. Econometrica, 85(5):1575- 1612, 2017. ISSN 1468-0262. doi: 10.3982/ECTA12216. URL http://dx.doi.org/10.3982/ECTA12216.
  • Johannes Brumm, Christopher Krause, Andreas Schaab, and Simon Scheidegger. Sparse grids for dynamic economic models. Available at SSRN 3979412, 2021.
  • Hans-Joachim Bungartz and Michael Griebel. Sparse grids. Acta numerica, 13:147–269, 2004.
  • Hui Chen, Antoine Didisheim, and Simon Scheidegger. Deep structural estimation: With an application to option pricing. Available at SSRN 3782722, 2021.
  • Paul G. Constantine. Active Subspaces: Emerging Ideas for Dimension Reduction in Parameter Studies. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2015. ISBN 1611973856, 9781611973853.
  • Aryan Eftekhari and Simon Scheidegger. High-dimensional dynamic stochastic model representation. Available at SSRN 3603294 - Forthcoming in SIAM SISC, 2020.
  • Ian Goodfellow, Yoshua Bengio, and Aaron Courville. Deep Learning. MIT Press, 2016. http://www.deeplearningbook.org.
  • Felix Kubler and Simon Scheidegger. Self-justified equilibria: Existence and computation. 2018.
  • L. Ljungqvist and T.J. Sargent. Recursive macroeconomic theory. Mit Press, 2000. ISBN 9780262194518. URL http://books.google.ch/books?id=3LmXQgAACAAJ.
  • Carl Edward Rasmussen. Gaussian processes in machine learning. In Advanced lectures on machine learning, pages 63–71. Springer, 2004.
  • Philipp Renner and Simon Scheidegger. Machine learning for dynamic incentive problems. Available at SSRN 3462011, 2018. Working paper.
  • Simon Scheidegger and Ilias Bilionis. Machine learning for high-dimensional dynamic stochastic economies. Journal of Computational Science, 33:68 – 82, 2019. ISSN 1877-7503. doi: https://doi.org/10.1016/j.jocs.2019.03.004. URL http://www.sciencedirect.com/science/article/pii/S1877750318306161.
  • Nancy L. Stokey, Robert E. Lucas, and Edward C. Prescott. Recursive Methods in Economic Dynamics. Harvard University Press, 1989. ISBN 9780674750968. URL http://www.jstor.org/stable/j.ctvjnrt76.
  • Xiu Yang, Minseok Choi, Guang Lin, and George Em Karniadakis. Adaptive anova decomposition of stochastic incompressible and compressible flows. Journal of Computational Physics, 231(4):1587 – 1614, 2012. ISSN 0021-9991. doi: https://doi.org/10.1016/j.jcp.2011.10.028. URL http://www.sciencedirect.com/science/article/pii/S0021999111006280.