Econ 226 Bayesian and Numerical Methods James D. Hamilton, UCSD Spring 2013 SCHEDULE Class meets Mondays and Wednesdays 8:00 - 9:20 a.m., Monday April 1 - Wednesday June 5 in SSB 107 No class Monday May 27 Office hours: Mondays 9:30 - 10:30 a.m. in Econ 307 and by appointment ([email protected]) GRADES Grades for the course will be determined as follows: 25% in-class midterm exam 8:00 - 9:20 a.m. Wednesday, April 24 40% paper proposal due 8:00 a.m. Wednesday June 5 35% in-class final exam 8:00 - 11:00 a.m. Friday June 14 (held in Econ 300) The paper proposal should be typed (double-spaced, 12-point font, 1.5 inches space on right margin). The idea is to propose a project, but not actually perform any data collection or estimation. The proposal should consist of two sections. The first briefly describes some of the related literature with a clear description of one or more previous papers and a statement of the relation or model you would propose to estimate. You do not need to propose an original model, but it should be something that has not been estimated with Bayesian methods or for which you would add something missing from previous Bayesian analysis of that model. The second section should provide a detailed description of the methods and algorithm you would use to perform Bayesian estimation of the model. Note that this second section must be self-contained-- you should not assume that the reader is familiar with the algorithms or Bayesian approach, and you will be graded based on how clearly and accurately you explain them here.BOOKS Many of the readings can be found in the following three books: Greenberg: Edward Greenberg, Introduction to Bayesian Econometrics, Cambridge University Press, Second edition, 2012. TSA: James D. Hamilton, Time Series Analysis, Princeton University Press, 1994. SSM: Chang-Jin Kim and Charles R. Nelson, State-Space Models with Regime Switching, MIT Press, 1999. In addition, copies of the slides used in some of the lectures will periodically be linked from the course web page (check for last-minute updates before class) at: http://dss.ucsd.edu/~jhamilto/Econ226.html COURSE OUTLINE I. Bayesian econometrics A. Introduction Greenberg,, Chapter 2 TSA, Section 12.1 Morris H. DeGroot (1970), Optimal Statistical Decisions, McGraw-Hill, Chapter 6, and Sections 9.1-9.6 Bradley Efron and Carl Morris (1975) “Data Analysis Using Stein’s Estimator and Its Generalizations,” Journal of the American Statistical Association vol. 70, pp. 311-319 B. Bayesian inference in the univariate regression model SSM, Sections 7.1 and 7.2 TSA, Section 12.2 Greenberg, Chapter 4 C. Statistical decision theory Greenberg, Chapter 3 Mark J. Schervish (1995), Theory of Statistics, Chapter 3, Springer-Verlag. D. Large sample results Tony Lancaster (2004), An Introduction to Modern Bayesian Econometrics, Chapter 1, Blackwell. Mark J. Schervish (1995), Theory of Statistics, Section 7.4, Springer-Verlag.E. Diffuse priors Mark J. Schervish (1995), Theory of Statistics, pp. 121-123, Springer-Verlag. DeGroot, Morris H. (1970), Optimal Statistical Decisions, Chapter 10, McGraw-Hill. F. Numerical Bayesian methods Greenberg, Chapters 5-8 Christian P. Robert and George Casella (2004), Monte Carlo Statistical Methods, Second edition, Section 2.3, Chapter 7, Section 9.1, Chapter 12. A.F.M. Smith and A.E. Gelfand (1992), “Bayesian Statistics Without Tears: A Sampling-Resampling Perspective,” American Statistician vol. 46, pp. 84-88. SSM, Sections 7.3 and 7.4 Siddhartha Chib and Edward Greenberg (1996), “Markov Chain Monte Carlo Simulation Methods in Econometrics,” Econometric Theory 12, pp. 409-431. Siddhartha Chib (1995), “Marginal Likelihood from the Gibbs Output,” Journal of the American Statistical Association, 90, pp. 1313-1321. James D. Hamilton, Daniel F. Waggoner, and Tao Zha (2007), “Normalization in Econometrics,” Econometric Reviews, vol 26, no 2-4, pp. 221-252. II. Vector autoregressions A. Introduction TSA, Section 11.6, pp. 324-336 B. Normal-Wishart priors for VARs K. Rao Kadiyala and S. Karlsson (1997) “Numerical Methods for Estimation and Inference in Bayesian VAR-models,” Journal of Applied Econometrics vol. 12, pp. 99-132. John Geweke (1988), “Antithetic Acceleration of Monte Carlo Integration in Bayesian Inference,” Journal of Econometrics vol. 38, pp. 73-89. C. Bayesian analysis of structural VARs Christopher A. Sims and Tao Zha (1998) “Bayesian Methods for Dynamic Multivariate Models,” International Economic Review vol. 39, pp. 949-968. D. Identification using inequality constraints Harald Uhlig (2005), “What Are the Effects of Monetary Policy on Output? Results from an Agnostic Identification Procedure,” Journal of Monetary Economics, 52(2), pp. 381-419. E. Integrating VARs with dynamic general equilibrium models Marco del Negro and Frank Schorfheide (2004), “Priors from General Equilibrium Models for VARS,” International Economic Review 45, pp. 643-673.F. Selecting priors for DSGEs Marco del Negro and Frank Schorfheide (2008), “Forming Priors for DSGE Models (and How It Affects the Assessment of Nominal Rigidities)”, Journal of Monetary Economics, 55, no. 7, pp. 1191-1208. III. Linear state-space models. A. State-space representation of a dynamic system TSA, Section 13.1. B. Kalman filter TSA, Section 13.2 C. Using the Kalman filter TSA, Sections 13.3-13.6 Maximo Camacho and Gabriel Perez-Quiros (2010), “Introducing the Euro-Sting: Short Term Indicator of Euro Area Growth,” Journal of Applied Econometrics, 25(4), pp. 663–694. D. Bayesian analysis of linear state-space models SSM, Chapter 8 E. Solutions to linear rational expectations models Olivier Jean Blanchard and Charles M. Kahn (1980), “The Solution of Linear Difference Models under Rational Expectations,” Econometrica 48, pp. 1305-1317. Robert G. King and Mark W. Watson (1998), “The Solution of Singular Linear Difference Systems under Rational Expectations,” International Economic Review 39, pp. 1015-1026. Paul Klein (2000), “Using the Generalized Schur Form to Solve a Multivariate Linear Rational Expectations Model,” Journal of Economic Dynamics and Control, 24, pp. 1405-1423. Christopher Sims (2001), “Solving Linear Rational Expectations Models,” Journal of Computational Economics, 20(1-2), pp.1-20. F. Using the Kalman filter to estimate dynamic stochastic general