University of Illinois Department of Economics
Spring 1998 Roger Koenker
This course is a research seminar in semiparametric methods in
econometrics. The objective of the course from a student viewpoint
should be to write a research paper of potentially publishable quality,
either as an exploratory venture directed toward finding a thesis topic,
or as an opportunity to explore a new area in some depth just for the
fun of it.
The course will be organized as an informal seminar. There will be no text per se, but there will be a considerable range of readings from the current literature. There will be no exams only a required term paper, and there will be periodic student presentations of course material. The topics covered in the course can be tailored somewhat to student demand. There are a few topics in which I have a current research interest, and for which I think there might be some scope for constructive interaction in a course of this type. I will try to encourage toward these topics in an effort to increase effective collaboration among students in the course. Not surprisingly, many of these topics have some connection to quantile regression, although in some cases this connection is rather speculative.
In the first class I will try to describe and motivate the topics I have identified and provide some basic bibliography.
In the second week I would like to get down to business by discussing a group of recent papers on estimating treatment effects. This is a topic on which there is considerable recent activity by both econometricians and statisticians and I believe that it is worthwhile for the entire class to take a close look at a few of these papers. I have prepared a xeroxed collection of papers which will be distributed through Up Close, one of the campus copy centers.
In the third week I would like to reconsider some classical readings on instrumental variable methods focusing on the connection between LIML canonical correlation and some related eigenvalue problems. The objective will be to begin to forge a link between the treatment effect discussion of the previous week and this older literature which would eventually result in a more refined approach to IV methods for quantile regression.
In the fourth week I will discuss some recent developments on numerical methods for quantile regression, and raise some questions about my ongoing project to revise the software distribution for Splus for quantile regression. This discussion is likely to focus on extensions of existing methods for inference.
In subsequent weeks there will be a sequence of mini-lectures by students to report progress on their research. Since the scope for these presentations will be rather severely constrained by the size of the class, I am investigating schemes which would enable students to ``present'' research results on lab web pages. This would enable us to share bibliography, software and other materials in an efficient and timely manner. I hope to provide some tutorial material on this in the first weeks of class. to provide some tutorial material on this in the first weeks of class. Some basic material related to the course, including this document, is available on the web at http://www.econ.uiuc.edu/ roger/courses/478/478.html. There will also be an expanded version of the bibliography which appears below which will be available on the web. One of the byproducts of the course will be an expanded version of this bibliography.
I would strongly recommend that you to begin to learn LATEXand Splus as part of the research process. Some (hopefully helpful) hints on this are available in my paper ``Reproducible Econometrics'' which I will distribute in class. The book by (Venables and Ripley, 1997) is highly recommended for Splus. (Lamport, 1994) is the definitive introduction to LATEX.
I would like to devote some time to what I regard as important open research problems in quantile regression. These might include some of the following:
The time seems right for another look at the pros and cons of various nonparametric methods currently available in the literature. In particular, I would like to compare current kernel methods with the sieve-like methods of the (Fenton and Gallant, 1996; Gallant and Tauchen, 1997) SNP approach and the log-spline methods of (Stone, Hansen, Kooperberg, and Truong, 1997) and others. There are some interesting current applications to options pricing which might be an interesting case study here.
There is an interesting new book by a political scientist (King, 1997) on the ecological regression fallacy which draws interesting parallels to current work on the statistical theory of image processing and tomography, and is also connected to current advances in spatial statistics, see for example (Small, 1997). There are interesting connections to density estimation, nonparametric quantile regression and other topics which are suggested by these developments.
There is still considerable scope for drawing together methods for estimating transformation models using a variety of techniques closely associated with some of the topics listed above. Here there are also deeper theoretical issues relating to adaptive estimation. Single index models have a large literature in econometrics, see e.g. (Chaudhuri, Doksum, and Samarov, 1997; Stoker, 1992) Survival analysis is an important application in this context, as is the connection to discrete choice models. There are also interesting connections to rank statistics, see (Gutenbrunner, 1997; Han, 1987).