Econ 561bYale UniversitySpring 2004Prof. Tony SmithSyllabus forCOMPUTATIONAL METHODS FOR ECONOMIC DYNAMICSECON 561bCourse Objectives: The goals of this course are to teach students the basic tools ofnumerical analysis and to illustrate how these tools can be used to address analyticallyintractable problems in economics and econometrics. The underlying theme of this courseis that computational methods belong in every economist’s toolkit. These methods can beused not only to explore the theoretical implications of economic models in the absence ofanalytical solutions, but also to assess the quantitative importance of the various forces atplay in an economic model. Thus computation can help to advance both theoretical andempirical work in economics. In order to teach students how to wield computational toolsin an informed and intelligent way, this course endeavors to explain not only when and howto use various numerical algorithms but also how and why they work; in other words, thecourse opens up the “black boxes”.Another theme of this course is that computational methods are vital to all types ofresearch in economics, from the most theoretical to the most applied. To this end, the sub-stantive applications in the course are drawn from a wide range of fields, including macroe-conomics, finance, game theory, industrial organization, public finance, contract theory, andeconometrics. The course will pay special attention to dynamic economic problems, includ-ing methods for solving stochastic dynamic programming problems, for computing equilibriawith heterogeneous firms and consumers, and for estimating the parameters of dynamic eco-nomic models.Contact InformationOffice: 28 Hillhouse, Room 306Office phone: (203) 432-3583Email address: [email protected] web site: fasttone.gsia.cmu.edu/econ561bOffice hours: Thursdays from 10AM–noon, or by appointmentClass Me etings: The course meets on Mondays from 4PM to 5:20PM in Room B8 (28Hillhouse) and Wednesdays from 4PM to 5:20PM in Room 106 (28 Hillhouse).1Texts: The required textbooks for this course are: Numerical Methods in Economics byKenneth L. Judd (MIT Press, 1998) and Numerical Recipes in Fortran 77 (Second Edition)by William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery(Cambridge University Press, 1992). Both of these books are available in the Yale bookstore.Students who are familiar with the C or C++ programming languages may want to useversions of Numerical Recipes geared towards these languages. Numerical Recipes in Fortran90: The Art of Parallel Scientific Computing is a useful companion volume to NumericalRecipes in Fortran 77 ; in addition to using a more modern version (or standard) of theFortran programming language, this book shows how to write Fortran programs that takeadvantage of parallel computing. The Numerical Recipes books are also available online at:www.nr.com.Other (optional) books that students might find useful are: the Handbook of Computa-tional Economics (Volume 1), edited by Hans M. Amman, David A. Kendrick, and JohnRust (North-Holland, 1996); Computational Methods for the Study of Dynamic Economies,edited by Ramon Marimon and Andrew Scott (Oxford University Press, 1999); Frontiers ofBusiness Cycle Research, edited by Thomas F. C ooley (Princeton University Press, 1995);and Dynamic Economics: Quantitative Methods and Applications by J´erˆome Adda and Rus-sell Cooper (MIT Press, 2003).Grading: Occasional problem sets will constitute 30% of the course grade and a project(described in more detail below) will constitute 70% of the course grade.Students may use any programming language to complete the problem sets, includingFortran, C, Matlab, and Gauss. If you do not already know a programming language, Matlabis probably the easiest to learn. If you want to do state-of-the-art research using compu-tational methods, however, you will need ultimately to learn a fast high-level programminglanguage such as Fortran or C. This course will not teach programming per se, but it willteach and emphasize general principles of programming, such as simplic ity, clarity, structure,replicability, and testing. Since one of the goals of this course is to teach students what isgoing on inside the “black boxes” of numerical algorithms, students are asked to avoid theuse of such black boxes except for routine tasks.The project will consist of the application of computational methods to a problem ineconomics or econometrics. This problem could be original research, perhaps as a first steptowards a Ph.D. dissertation. However, the problem need not consist of original research:one acceptable option for the project is, in fact, to attempt to replicate the computationalresults in an existing paper.The written report for the project should consist of three parts: a brief description ofthe problem, a detailed description of the computational methods used to solve the problem(including a copy of the code), and a thorough description of the numerical results.2COURSE OUTLINE1 Basic numerical methods• Introduction (built around the Huggett-Aiyagari model; see references in Section 3 be-low); general considerations in numerical analysis (convergence, roundoff error, trun-cation error), numerical differentiation.[Judd: Chapters 1, 2, and 7.7; Numerical Recipes: Chapters 1 and 5.7]• Root-finding in one or more dimensions (bisection, secant method, Newton’s method,fixed-point iteration, Gauss-Jacobi, Gauss-Seidel, Brent’s method).[Judd: Chapter 5; Numerical Recipes: Chapter 9]• Minimization in one or more dimensions (golden section search, Brent’s method with orwithout derivatives, simplex method, Newton-Raphson, conjugate gradient methods,variable metric methods, simulated annealing).[Judd: Chapter 4; Numerical Recipes: Chapter 10]• Interpolation and approximation of functions (linear interpolation in several dimen-sions, cubic splines, polynomial interpolation, searching a table, orthogonal polynomi-als).[Judd: Chapter 6; Numerical Recipes: Chapters 3 and 6]• Random numbers, simulation, and intro duction to asymptotic theory.[Judd: Chapter 8; Numerical Recipes: Chapter 7]• Integration (cubic spline integration, Gaussian quadrature, Monte Carlo integration,integration of multivariate normal densities).[Judd: Chapter 7; Numerical Recipes: Chapter 4]2 Numerical dynamic programming• Linear-quadratic methods– Uhlig, H. (1999), “A Toolkit for Analysing Nonlinear Dynamic Stochastic