This course, taught by Ken Judd, introduces computational approaches for solving economic models. It focuses on a broad range of numerical methods and then applies them to economic problems. We formulate economic problems in computationally tractable forms and use numerical analysis techniques to solve them. We will study examples of computational techniques in the current economic literature as well as discuss areas of economic analysis where numerical analysis may be useful in future research of dynamic economic problems. The substantive applications will cover a wide range of problems including public finance, macroeconomics, game theory, mechanism design, econometrics, finance, and industrial organization.

The lectures will be given 18:00 CET (9:00am PST). They will be streamed using Zoom. They will also be recorded and put on the web. Exact details will be posted later. Ken Judd will deliver the lectures except where noted otherwise below.

We begin with an overview of the necessary numerical analysis and approximation theory. First, we review standard numerical analysis - interpolation and approximation techniques, numerical optimization, numerical solutions to systems of linear and nonlinear equations, numerical integration, and basic solution techniques for ordinary and partial differential equations. We also discuss perturbation methods useful in economics.

Second, there will be an emphasis on applications related to current research areas. We will discuss methods for solving dynamic programming problems, as well as dynamic stochastic equilibrium models. We will solve for optimal incentive mechanisms using numerical optimization.

The course aims to acquaint students with the range of techniques that have been useful in economic analysis as well as expose students to techniques that have potential use in economic applications. I want to develop a basic understanding of numerical methods, demonstrate their use in economic examples, show how existing techniques fit into the broader numerical literature, and point the students to potentially useful numerical techniques.

It is best if students have a good undergraduate background in mathematics (such as calculus, linear algebra, eigenvalues and eigenvectors) and are familiar with static optimization theory (such as Lagrangians and Kuhn-Tucker conditions) as well as basic dynamic optimization theory. I will also presume some experience with graduate level economics, however any student who is interested in the course and has taken either Masters or PhD courses in econometrics, microeconomics, and macroeconomics will be able to follow the course.

Doing computation is the only way to learn computation. The course grade will be based on computational exercises assigned every week along with term projects. I encourage you to work in groups of two or three.

Students will need to know use some computational language. My recommendation is that you use Python, Matlab, or R. Students are welcome to use FORTRAN, C, or C++. Statistical software such as TSP, Eviews, RATS, and SAS are not acceptable. The US Federal Reserve uses Eviews but I expect more of you. Don’t even ask about Excel. If you do not know any suitable language, I recommend that you learn Matlab or Python. Both are adequate for this course and useful in research. Matlab is the most used language in economics. Python is a more complex programming language but much better in terms of long-run value and flexibility. See the QuantEcon project of Sargent and Stachurski.

In operations research, the popular languages are GAMS and AMPL. They are is easy to learn and allows you to access the best numerical software through the NEOS website. NEOS time is FREE, reflecting the “Wisconsin idea”! If there is interest, I will have a couple of optional tutorial sessions on AMPL (sorry, I don’t know GAMS).

I will use Mathematica in my lectures and some classnotes. It allows one to use symbolic methods, has good graphics and is overall more flexible than Matlab. It is free for UZH students. All students will be asked to download the free CDF player; it will allow you to run my examples on your laptops.

The text is Numerical Methods in Economics by Judd, published by MIT Press. I will be particularly appreciative of any comments you may have on the text (typos, lack of clarity, etc.) since I am beginning to prepare the second edition.

I am working on a second edition. As we progress, I will (hopefully) have drafts on the course website of chapters for the second edition.

If you have any questions, feel free to contact Ken or open a new issue on Github (check if your question has maybe already been asked and answered).