Econ 561bYale UniversitySpring 2010Prof. Tony SmithSyllabus forCOMPUTATIONAL METHODS FOR ECONOMIC DYNAMICSECON 561bCourse Objectives: Most of the dynamic models used in modern quantitative researchin economics do not have analytical (closed-form) solutions. For this reason, the computerhas become an indispensable tool for conducting research in economics. The goal of thisset of lectures is to provide an introduction to computational tools for conducting numericalanalysis of dynamic economic models. These tools have applications in all areas of economics,including macroeconomics, labor economics, industrial organization, financial economics,public finance, and political economy.Contact InformationOffice: 28 Hillhouse, Room 306Office phone: (203) 432-3583Email address: [email protected] Web site: www.econ.yale.edu/smith/econ561aOffice hours: by appointment (or just stop by and see if I am free)Class Meetings: The course meets on Mondays and Wednesdays from 10:30AM to 11:50AMin Room 106 (28 Hillhouse). This is a half-semester (seven-week) course; the last lecture ison Wednesday, February 24.Prerequisites: This course is designed for graduate students in economics who have takenfirst-year graduate courses in microeconomics, macroeconomics, and econometrics. No priorknowledge of either numerical methods or computer programming is assumed, but somefamiliarity with a programming language would prove helpful.1Texts: The lectures will be largely self-contained, but there are several good texts thatprovide useful complements to the material in the lectures. An especially valuable book is:Numerical Recipes in Fortran 77: The Art of Scientific Computing, Second Edition (Volume1 of Fortran Numerical Recipes) by William H. Press, Saul A. Teukolsky, William T. Vet-terling, and Brian P. Flannery (Cambridge University Press, 1992). This book is availableonline (for free) at: www.nrbook.com/a/bookfpdf.php. Its companion, Numerical Recipes inFortran 90: The Art of Parallel Scientific Computing, Second Edition (Volume 2 of FortranNumerical Recipes), is also available online at: www.nrbook.com/a/bookf90pdf.php. (Note:The third edition of Numerical Recipes, with code available entirely in C++, is availableonline to o—with a paid subscription—at www.nr.com. The third edition covers a few moretopics than the second edition, but its text overlaps substantially with the second edition.)Other useful books include:• Applied Computational Economics and Finance by Mario J. Miranda and Paul L.Fackler (MIT Press, 2002).• Numerical Methods in Economics by Kenneth L. Judd (MIT Press, 1998).• Dynamic Economics: Quantitative Methods and Applications by J´erˆome Adda andRussell Cooper (MIT Press, 2003).• Computational Methods for the Study of Dynamic Economies, edited by Ramon Ma-rimon and Andrew Scott (Oxford University Press, 1999).• Handbook of Computational Economics (Volume 1), edited by Hans M. Amman, DavidA. Kendrick, and John Rust (North-Holland, 1996).Exercises: The best (and really the only) way to learn numerical methods is to use themin actual problems. Accordingly, each week of lectures will be accompanied by a set ofproblems for students to solve. It is highly recommended that students attempt to workthese problems!2SCHEDULE OF LECTURESWeek 1Introduction (built around some simple examples from economics, including the stochastic-growth model and a canonical consumption-savings model).General considerations in numerical analysis: convergence, roundoff error, truncation error.Numerical differentiation.Root-finding in one or more dimensions: bisection, secant method, Newton’s method, fixed-point iteration, Gauss-Jacobi, Gauss-Seidel, Brent’s method.Suggested readings:Chapters 1, 5.7, and 9 in Numerical Recipes; Appendix 2A, Chapter 3, and Chapter 5.6 inMiranda and Fackler; Chapters 1, 2, 5, and 7.7 in Judd.Huggett, M. (1993), “The Risk-Free Rate in Heterogeneous-Agents, Incomplete MarketsEconomies,” Journal of Economic Dynamics and Control 17, 953–969.Taylor, J.B. and H. Uhlig (1990), “Solving Nonlinear Stochastic Growth Models: A Com-parison of Alternative Solution Methods,” Journal of Business and Economic Statistics 8,1–18.Week 2Minimization in one or more dimensions: golden section search, Brent’s method with orwithout derivatives, simplex method, Newton-Raphson, variable metric methods.Suggested readings: Chapter 10 in Numerical Recipes; Chapter 5 in Miranda and Fackler;Chapter 4 in Judd.3Week 3Interpolation and approximation of functions: linear interpolation in several dimensions,cubic splines, polynomial interpolation, orthogonal polynomials.Suggested readings: Chapters 3 and 6 in Numerical Recipes; Chapter 5 in Miranda andFackler; Chapter 6 in Judd.Week 4Numerical integration: cubic spline integration, Gaussian quadrature, Monte Carlo integra-tion, integration of multivariate normal densities.Suggested readings: Chapters 4 and 7 in Numerical Recipes; Chapter 5 in Miranda andFackler; Chapters 7 and 8 in Judd.Week 5Numerical dynamic programming: value iteration, Euler equation methods, rules of thumb,perturbation methods, parameterized expectations, linear-quadratic (first-order) and second-order methods.Suggested readings:Chapters 7, 8, and 9 in Miranda and Fackler; Chapters 12, 13, 16, and 17 in Judd.Benitez-Silva, H., G. Hall, G. Hitsch, G. Pauletto, and J. Rust (2005), “A Comparison of Dis-crete and Parametric Approximation Methods for Continuous-State Dynamic ProgrammingProblems,” manuscript (ms.cc.sunysb.edu/∼hbenitezsilv/dpa2005.pdf).Christiano, L.J. and J.D.M. Fisher (2000), “Algorithms for Solving Dynamic Models withOccasionally Binding Constraints,” Journal of Economic Dynamics and Control 24, 1179–1232.Coleman, W.J. II (1990), “Solving the Stochastic Growth Model by Policy Function Itera-tion,” Journal of Business and Economic Statistics 8, 27–29.Keane, M.P. and K. Wolpin (1994), “The Solution and E stimation of Discrete Choice Dy-4namic Programming Models by Simulation and Interpolation: Monte Carlo Evidence,” TheReview of Economics and Statistics 76, 648–672.Kim, J., S. Kim, E. Schaumburg, and C.A. Sims (2008), “Calculating and Using SecondOrder Accurate Solutions of Discrete Time Dynamic Equilibrium Models,” Journal of Eco-nomic Dynamics and Control 32, 3397–3414.Schmitt-Groh´e, S. and M. Ur´ıbe (2004), “Solving Dynamic General Equilibrium Models Us-ing a Second-Order Approximation to the Policy