Please note that the CGDE Special Course on Computational Economics taught by Kenneth Judd (Stanford University, https://kenjudd.org/) at Leipzig University had to be rescheduled. The course will now take place on the following dates:
- November 17–21, 2025 (no class on November 19 due to a public holiday)
- December 1–5, 2025
Registration
The registration deadline is November 4, 2025 (capacity is limited).
To register, please send an e-mail to steger@wifa.uni-leipzig.de
(Subject: Registration Computational Economics)
Important: If you have already registered for the original course dates, please register again for the new dates.
Course contents
Week 1 (4 days)
- Day 1: Elementary methods
- Day 2: Optimization and equations
- Day 3: Approximation and quadrature
- Day 4: Projection methods and dynamic programming
Week 2 (5 days)
- Day 5: Advanced approximation methods
- Day 6: Solutions for perfect foresight models
- Day 7: Solutions for rational expectations models
- Day 8: Empirical applications
- Day 9: Survey of current advanced work
Schedule
The initial plan will have four sessions each day:
09:30 – 10:30 class
10:30 – 10:45 coffee break
10:45 – 12:15 class
12:15 – 13:30 lunch
13:30 – 14:45 class
14:45 – 15:00 coffee break
15:00 – 16:30 class
There may be adjustments in the times after we begin. Most of the sessions will be lectures. Some may be time for discussions of exercises.
Topics
Week one presents the basic ideas behind methods for optimization, equation solving, approximation and functional problems. Week two examines more advanced methods and applications. Students’ preference will be accommodated to the extent possible.
Monday, Nov. 17: Elementary methods
Computational power is exploding, but still not enough to accomplish anyone’s goals. Organizing a computer program is basically an economics problem: managing scarce resources including CPUs, RAM, GPUs, and communication across processors. Computer arithmetic is not perfect. We examine general concepts of computational errors, and rates of convergence. Many numerical methods reduce to solving a sequence of linear systems of equations. We define the general notion of a condition number.
Reference: Chapters 1, 2, and 3 in textbook.
Tuesday, Nov. 18: Optimization and equations
Optimization is the foundation of economics and econometrics. We study the basic methods for unconstrained and constrained optimization. The concept of equilibrium leads to equations and their numerical methods.
Reference: Chapters 4 and 5 in textbook.
Thursday, Nov. 20: Approximation and quadrature
We often need to approximate unknown functions. Methods include interpolation, regression, and shape-preserving approximation. Integration is essential for computing expectations. Monte Carlo simulation methods are often used, but quasi-Monte Carlo methods are far better asymptotically.
Reference: Chapters 6-9 in textbook.
Friday, Nov. 21: Projection methods and dynamic programming
Dynamic economic problems lead to functional equations, such as differential equations and operators in Banach spaces. Solutions to deterministic and stochastic dynamic economic problems use approximation, integration, and optimization methods. Applications to savings-consumption problems and portfolio problems
Reference: Chapters 11 and 12 in textbook.
Monday, Dec. 1: Advanced approximation methods
Advanced multidimensional approximation methods including splines, LAD and Lasso fits, radial basis functions and neural networks. Taylor series approximations to find numerical solutions of equations, linearizing around a steady state, simple bifurcation methods.
Tuesday, Dec. 2: Solutions for perfect foresight models
Finite-difference methods for differential equations. Shooting and reverse shooting. Parametric methods.
Wednesday, Dec. 3: Solutions for rational expectations models
NLCEQ by Cai and Judd. The methods developed by Judd, Maliar and Maliar. Machine learning methods.
Thursday, Dec. 4: Empirical applications
Calibration. Maximum likelihood and method of moments. Confidence sets.
Friday, Dec. 5: Survey of current advanced work
Optimal taxation. Nash equilibria of dynamic games. Hyperbolic preferences.
Grading
tba
Textbook
The textbook will be Numerical Methods in Economics by Ken Judd
References
Lectures will also be based on the following papers which are available at https://kenjudd.org/published-papers/. The most important ones are in bold.
Surveys
“Computational Economics and Economic Theory: Complements or Substitutes?”. Journal of Economic Dynamics and Control, 1997, 21 (6), 907-942.
“Approximation, Perturbation, and Projection Solution Methods in Economics”. Handbook of Computational Economics. 1996.
Climate Economics
“The Social Cost of Carbon with Economic and Climate Risks” (with Yongyang Cai and Thomas S. Lontzek). Journal of Political Economy, December-2019. (Acknowledged as co-author in lead footnote.)
“Stochastic integrated assessment of climate tipping points indicates the need for strict climate policy” (with Yongyang Cai, Timothy M. Lenton, and Thomas S. Lontzek). Nature Climate Change, March-2015, 5. DOI 10.1038/NCLIMATE2570
“Open science is necessary” (with Yongyang Cai and Thomas S. Lontzek). Nature Climate Change, May-2012, 2 (5) 299.
“Environmental tipping points significantly affect the cost-benefit assessment of climate policies” (with Yongyang Cai, Timothy M. Lenton, Thomas S. Lontzek, and Daiju Narita). The Proceedings of the National Academy of Sciences, April-2015, 112 (15) 4606-4611.
“Statistical Approximation of High-Dimensional Climate Models” (with Alena Miftakhova, Thomas S. Lontzek, and Karl Schmedders). Journal of Econometrics, January-2020.
Perturbation Methods
“Short-run Analysis of Fiscal Policy in a Simple Perfect Foresight Model”. Journal of Political Economy, April 1985, 93 (21), 298-319. (pdf)
“Solving an Incomplete Markets Model With a Large Cross-Section of Agents” (with Thomas M. Mertens). Journal of Economic Dynamics & Control 91 (2018) 349–368. DOI: 10.1016/j.jedc.2018.01.025
“Asymptotic Methods for Asset Market Equilibrium Analysis” (with Sy-Ming Guu ). Economic Theory, 2001, 18 127-157.
“Perturbation Solution Methods for Economic Growth Models” (with Sy-Ming Guu), in Hal Varian ed., Economic and Financial Modelling with Mathematica, (Springer-Verlag Publishers: New York, Dec-1992, pp. 80-103.
Dynamic Programming
“Solving dynamic programming problems on a computational grid” (with Yongyang Cai, Greg Thain, and Stephen J. Wright). Computational Economics, February-2014, 45 (261-284). DOI: 10.1007/s10614-014-9419-x.
“Advances in Numerical Dynamic Programming and New Applications” (with Yongyang Cai). Chapter 8, Handbook of Computational Economics, Volume 3 (2014). DOI: 10.1016/B978-0-444-52980-0.00008-6
“Shape-preserving dynamic programming” (with Yongyang Cai). Mathematical Methods of Operations Research, 2012, 77 (3), 407-421.
“Dynamic programming with Hermite approximation” (with Yongyang Cai). Mathematical Methods of Operations Research (2015) 81:245–267. DOI: 10.1007/s00186-015-0495-z.
“Dynamic programming with shape-preserving rational spline Hermite interpolation” (with Yongyang Cai). Economics Letters, 2012, 117 (1) 161-164.
“Stable and efficient computational methods for dynamic programming” (with Yongyang Cai). Journal of the European Economic Association, 2010, 8(2-3), 626-634.
Parallel Computing
“Harnessing Parallelism in Multicore Clusters with the All-Pairs and Wavefront Abstractions” (with Li Yu, Christopher Moretti, Scott Emrich, and Douglas Thain), 2009.
“Harnessing parallelism in multicore clusters with the All-Pairs, Wavefront, and Makeflow abstractions” (with Li Yu, Christopher Moretti, Andrew Thrasher, Scott Emrich, and Douglas Thain) Cluster Comput (2010) 13: 243–256 DOI 10.1007/s10586-010-0134-7
Projection Methods
“Projection Methods for Solving Aggregate Growth Models,” Journal of Economic Theory, December-1992, 58 410-452.
“Solving Large-Scale Rational-Expectations Models,” (with Jess Gaspar). Macroeconomic Dynamics, 1997, 1 45-75.
“The parametric path method: an alternative to Fair-Taylor and L-B-J for solving perfect foresight models”. Journal of Economic Dynamics and Control, August-2002, 26 (9-10), 1557-1583.
“Merging simulation and projection approaches to solve high-dimensional problems with an application to a new Keynesian model” (with Lilia Maliar and Serguei Maliar). Quantitative Economics 6 (2015), 1–47. (informative footnote on p.43)
“A nonlinear certainty equivalent approximation method for dynamic stochastic problems” (with Yongyang Cai). Quantitative Economics, 2017, 8, 117-147.
“Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain” (with Lilia Maliar, Serguei Maliar, and Rafael Valero). Journal of Economic Dynamics & Control 44 (2014) 92–123. DOI: 10.1016/j.jedc.2014.03.003. (pdf)
“Computational suite of models with heterogeneous agents II: Multi-country real business cycle models” (with Wouter J. Den Hann, and Michel Juillard) Journal of Economic Dynamics and Control, 2011, 35 (2), 175-17.
“Solving the multi-country real business cycle model using ergodic set methods” (with Serguei Maliar Lilia Maliar). Journal of Economic Dynamics and Control, 2011, 35 (2) 207-228.
Optimal Taxation a la Mirrlees
“Stabilized Optimization Via an NCL Algorithm” (with Ding Ma, Dominique Orban, and Michael A. Saunders). In: Al-Baali, M., Grandinetti, L., Purnama, A. (eds) Numerical Analysis and Optimization. NAO 2017. Springer Proceedings in Mathematics & Statistics, vol 235. Springer, Cham. DOI: 10.1007/978-3-319-90026-1_8