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PENN STATE 2025 LECTURES ON NUMERICAL METHODS
KEN JUDD
Lecture Schedule
I will be visiting the Penn State University Department of Economics from March 17 to March 28, 2025. I will give four lectures on topics in computational methods. All times are 6:00 – 7:30 p.m. Dates and locations are
Tuesday, March 18 – 105 Chambers
Thursday, March 20 – 105 Rackley
Tuesday, March 25 – 105 Chambers
Thursday, March 27 – 105 Rackley
On Friday, March 21, Carlos Rangel will lead a class on using the high-performance computing cluster at PSU. It will meet in 413 Kern at 3:30pm.
Lecture Topics
1: Structural Estimation: NFXP vs MPEC vs Surrogate
We first compare methods for structural estimation.
The first comparison is the Nested Fixed Point method and the MPEC (constrained optimization) approach.
Nested Methods and a Superior Alternative
The SJ papers are versions of the Su-Judd paper on MPEC, a small piece of which was published in Econometrica as a note. Here are the four versions of Su-Judd, leading to the 2012 Econometrica paper.
2007 SJ Working paper Nov07
2008 SJ Original submission to ECTA
2010 SJ First revision for ECTA
2012 SuJudd_ECTA2012
The third approach is the surrogate function approach. Markus Trunschke, Gregor Reich, Carlos Rangel and I have applied the surrogate method to the Zurcher bus model. The idea is to approximate the function which gives the likelihood as a function of the parameters, and then to use that approximation (the “surrogate”) to find the maximum likelihood estimate. This is now feasible due to the easy access to massively parallel hardware.
2: BLP and Parametric Bootstrap Inference
NFXP vs MPEC
Nevo’s A Research Assistant’s Guide to Random Coefficients Discrete Choice Models of Demand describes the BLP model and a commonly used computational method. Che-Lin and I looked at Nevo’s code and found some obvious weaknesses. In particular, the stopping rules were too loose. I had Che-Lin use MPEC to solve the Nevo problem. He found a better value for the objective and was happy because he was trained as a computational mathematician. I told him that was not enough, and that he should check to see if Nevo’s estimate was statistically different than his result. It was. I decided my job was done. Che-Lin went on to write a paper with Dube and Fox.
AMPL code for MPEC applied to BLP.
Dubé, Fox, & Su (2012) compares Nevo to an MPEC approach
Dubé, Fox, Su Appendix
Quadrature vs Monte Carlo integration
Skrainka-Judd (2012) and Rangel-Judd (2025) show that Monte Carlo integration can lead to serious problems for estimating BLP models, and argues that that numerical quadrature formulas are far more accurate and reliable. The Skrainka-Judd paper demonstrated some basic points, but was never finished.
Carlos Rangel and I are doing a systematic evaluation of quadrature rules and BLP, with a focus on both point estimation and inference. This lecture will discuss the importance of integration rules in BLP models along with using parametric bootstrapping (possible because of massively parallel computing) to do inference.
3: Discrete-state Dynamic Programming
Discrete-state dynamic programming is often used in economics. Value function iteration is the most common method but much faster methods are available.
4: Solving for Nash equilibria
Games in IO are often solved using Gauss-Jacobi (as in Pakes-Maguire) or Gauss-Seidel (as in many other papers) iteration. That was the best way 30 years ago. However, it is now possible to use far faster nonlinear equation methods to solve such problems.
Office Hours:
I will also be available for office visits. I ask that you first send me something written that describes the computational aspects of what you are working on or want to work on. Do not assume that I have read the papers related to your research. You should be able to explain the mathematical and computational structure of your problems in a way that I can understand without knowing published economic papers (which are often poorly written).
Basically, the part of your research I can help with is the computational methods you use. Feel free to send me your writeup NOW so that I will be acquainted with your work when we meet.
Looking forward to seeing you soon.