Computational Topics in Economics and Econometrics Spring Semester 2003 Tuesday 12-2 Room 315 Christopher Flinn Room 302 christopher.fl[email protected]

Introduction:

The objective of this course is to develop computational modeling skills that will increase the stu- dent’s capacity for performing quantiative research in economics. The basic premise of the course is the following. To adequately explain social phenomena of interest to economists requires the use of relatively sophisticated, albeit stylized, models. These models, whether involving only the solution of individual decision rules in a dynamic context or the determination of equilibria in a general equilibrium model, can only be solved numerically. We will review techniques that allow the solution of a large class of fixed point problems, which virtually all economic problems can be cast as, and will illustrate and compare techniques in the context of diverse examples. As an integral part of the course, students will be expected to contribute problems of their own, hopefully taken from current research questions they are investigating. We will also study the use of computational-intensive techniques in econometrics. Over the past several decades there have been a lot of exciting developments in this area due to enormous increases in processor speed and affordability. Topics in this area that we will treat include general computational issues in the estimation of nonlinear models, simulation estimation methods (maximum likelihood and method of moments), bootstrap methods, and the E-M algorithm. Examples from my own and other applied economists’ research will be used to illustrate the methods where appropriate. Because applied numerical analysis is at least one-half art form, it will be extremely useful for all of us to hear from individuals who have successfully completed large research projects that required them to solve daunting computational problems in the process. As we will see, there is no single “right” way to solve most computational problems, and these speakers will share their experiences with us and the rationales for the choices they made along the way. We plan to have four of these “outside” speakers: Meta Brown (UW-Madison), Matt Dey (BLS-DOL), Donghoon Lee (NYU), and Giorgio Topa (NYU). All will be discussing research projects that involve simultaneously solving dynamic optimization and/or equilibrium problems and the estimation of primitive parameters. Since the emphasis of the course is on computation, we will be performing a number of exercises over the course of the semester. There is no requirement that all participants use the same language to perform the exercises. Probably the most frequently used languages by economists working on these types of problems are FORTRAN, Matlab, and Gauss. The “lowest level” language of the three is FORTRAN, and hence it is the most general. It has a large number of numerical analysis procedures available for use in the IMSL library. Gauss and Matlab are easier to use, quite similar in that they are both primarily matrix programming languages (that is, they are most comfortable with two-dimensional objects), and both have numerical analysis procedures built into the language itself as operators. The choice is left to you; I will try to ensure that all are available on our server.

1 Texts: Mario Miranda and Paul Fackler, Applied Computational Economics and Finance. Cambridge, MA: MIT Press, 2002. Ken Judd, Numerical Methods in Economics. Cambridge, MA: MIT Press, 1998. Christian Gourieroux and Alain Monfort, Simulation Based Econometric Methods. Louvain: CORE Lecture Series, 1994 Bradley Efron, The Jackknife, the Bootstrap, and Other Resampling Plans. Philadelphia: SIAM, 1982. The book by Miranda and Fackler will serve as the principle text for reference, though the Judd book is also very useful and provides a deeper level of coverage on a number of topics. The last two short monographs will be useful when we discuss computational approaches in econometric applications. We will also be reading a number of papers in which computational methods are either the focus of attention or a featured part of solving some applied theory or econometric problem. A list of these papers will be distributed at the beginning of class and over the course of the semester as we determine the interests of students. Course Requirements: Students will be required to complete the computational exercises assigned over the course of the semester (approximately six in all). In addition, each student is expected to complete a short paper, the focus of which will be the solution of a nontrivial computational problem in theory, econometrics, or (preferably) both. The paper should include a short motivation for the problem investigated and a detailed description of the algorithm(s) used in the course of your research (including the annotated code in an appendix). Course Schedule Four of our meetings will be held with “outside” speakers discussing their work (see above). The content of the remaining 10 meetings is as follows:

1. Preliminary Issues in Numerical Analysis and the Solution of Linear Equations

2. Solution of Nonlinear Equations

3. Finite-Dimensional Optimization Problems

4. Function Approximation

5. Differential, Integral, and Functional Equations

6. Solving Dynamic Programming Problems

7. General Issues in Nonlinear Estimation

8. Estimation Using Simulation Techniques

9. The Bootstrap and other Resampling Techniques

10. Indirect Inference; the E-M Algorithm

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