Econ 373: Time Series Econometrics. Spring 2015

Transcription

1 Econ 373: Time Series Econometrics Spring 2015 Instructor: Atsushi Inoue Phone: Lectures: Mondays and Wednesdays at 1:10pm-2:25pm in Calhoun Hall 335 Office Hours: Fridays at 9:30am-11:30am or by appointments in Calhoun Hall 208 Teaching Assistant: Carl Cheng Office Hours: Fridays at 4:30pm-5:30pm in Stevenson Center 1115 Course Descriptions This is an introductory course on time series econometrics for first-year or second-year Ph.D. students in economics. Through lectures, problem sets and readings, you will learn econometric methods for estimating structural vector autoregressive models and dynamic economic models, such as the method of maximum likelihood, Bayesian methods, and generalized method of moments. Course Goals At the end of this semester you should be able to: Understand statistical assumptions underlying the estimation and inference methods discussed in this course; Write codes for estimating time series econometric models; and Interprete and analyze empirical results provided that you: Actively participate in class (e.g., take notes, ask questions, participate in discussions); Work on every homework problem; Solve empirical and numerical exercises; and Read and digest textbooks, papers and book chapters in the reading list. Prerequisites To describe econometric methods and explain how they work, I assume that you have working knowledge of: Mathematics (especially matrix algebra and multivariate calculus) at the level of Econ 300 (or equivalent); and Statistics and econometrics at the level of Econ 307, 309 and 373 (or equivalent) To motivate econometric problems I tend to use macroeconomic examples. I expect that you are either familiar with these examples or willing to learn them if you are not. You are willing to learn and work with MATLAB codes. 1

2 Software and Computer Laboratory Sessions You are required to use MATLAB in this course. It is one of the most popular software in time series econometrics. You can purchase a MATLAB subscription valid through April 30, 2015, for $ at Vanderbilt s Software Store. Computer laboratory sessions integrate econometric theory and practice and thus are an important part for your learning econometrics. In these sessions you will work on empirical and numerical exercises and either write MATLAB codes from scratch or modify sample codes I hand out. The sessions are tentatively scheduled as follows: Dates Monday, January 26 Monday, February 9 Monday, March 9 Wednesday, March 18 Wednesday, April 1 Evaluations and Logistics Topics Estimation of Time Series Models Estimation of Structural Impulse Responses MLE of DSGE Models Bayesian Estimation of DSGE Models GMM Estimation of Macroeconomic Models Your course grade will be based on two in-class midterm exams, ten problem sets and a term paper: Due Dates/Exam Dates % of Course Grade Problem Set 1 Wednesday, January 14 2% Problem Set 2 Wednesday, January 21 2% Problem Set 3 Wednesday, January 28 2% Problem Set 4 Wednesday, February 4 2% Problem Set 5 Wednesday, February 11 2% Midterm Exam 1 Wednesday, February 18 20% Problem Set 6 Monday, February 23 2% Problem Set 7 Wednesday, March 11 2% Problem Set 8 Monday, March 23 2% Problem Set 9 Monday, March 30 2% Problem Set 10 Monday, April 6 2% Midterm Exam 2 Monday, April 13 30% Presentation April 15 and April 20 Final Deadline April 22 30% 1. I will upload pdf files of slides and problem sets to the course homepage at Blackboard. These slides are just a summary and are not a substitute for your notetaking. If you miss a class it is your responsibility to obtain a copy of notes from one of your classmates. 2. You need to submit your solution sets by the specified time on the due dates. If you hand in your solution set on the due date but after the time, I discount the mark at 10%. 3. In case you need to miss an exam, please contact me and obtain my permission in advance. Otherwise I will not give you a make-up exam. If you do not show up without notifying me in advance, you will receive a zero mark. Make-up exams can be harder than original ones. 4. You may bring one letter-size (8.5 by 11 inches) sheet of notes to the two midterm exams. 5. No individual letter grades will be given for any of the exams and problem sets. Your letter grade for the course will be based on your overall score. 2

3 6. Think about a research question that can be answered using time series econometric methods and discuss your idea with me by the end of January. Hopefull we agree on your research idea by early February. 7. Discuss your first intermediate results with me by the end of February and your second intermediate results with me by the end of March. 8. Give a 30 minute presentation on April 15 or April Submit the final version of your term paper along with your MATLAB code and data to me by the end of April 22. Your term paper should be double-spaced and be about page long. The cover page should include a title, your name and an abstract. In addition to main sections, the paper should include introductory, conclusing and reference sections. Main Topics and References Although there is no required textbook, textbooks complement original research articles and my lecture notes and I recommend: Cochrane, John (2005), Time Series for Macroeconomics and Finance, Unpublished Manuscript, University of Chicago. Hamilton, James D. (1994), Time Series Analysis, Princeton University Press: Princeton, NJ. Lütkepohl, Helmut (2005), New Introduction to Multiple Time Series Analysis, Springer: Berlin, Germany. Tsay, Ruey S. (2005), Analysis of Financial Time Series, Third Edition, John Wiley & Sons: Hoboken, NJ. Wei, William W.S. (2006), Time Series Analysis: Univariate and Multivariate Methods, Second Edition, Pearson Education: Boston, MA. Cochrane s (2005) concise monograph is not a substitute for the other four textbooks. Tentative Course Outline and Reading List Below is a preliminary and incomplete list of topics and references. Symbols References bold face Minimum required readings Textbooks and survey papers References for applications discussed in class - Classical and original references Advanced and technical references I expect that you learn and understand topics discussed in the required readings and are encouraged to ask questions about them even if I do not cover them in class. Wednesday, January 7 1. Predictive Regression Models (a) Finite-Sample Bias of OLS Estimators 3

4 (b) The Law of Large Numbers and Central Limit Theorem for Dependent Processes (c) Asymptotic Properties of OLS Estimators Hamilton (1994), Chapters 7 8. Fama, Eugene F., (1984), The Information in the Term Structure, Journal of Financial Economics, 13, Fama, E.F., and K.R. French (1988), Dividend Yields And Expected Stock Returns, Journal of Financial Economics, 22, Hall, Robert (1978), Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence, Journal of Political Economy, 86, Mankiw, Gregory N., and Matthew D. Shapiro (1986), Do We Reject Too Often? : Small Sample Properties of Tests of Rational Expectations Models, Economics Letters, 20, Mark, Nelson C. (1995), Exchange Rates and Fundamentals: Evidence on Long-Horizon Predictability, American Economic Review, 85, Meese, Richard and Kenneth Rogoff (1983), Empirical Exchange Rate Models of the 1970 s: Do They Fit Out of Sample? Journal of International Finance, 14, Zarnowitz, Victor (1985), Rational Expectations and Macroeconomic Forecasts, Journal of Business and Economic Statistics, 3, Monday, January Time Series Models (a) Autocovariances and Autocorrelations (b) Stationarity (c) Autoregressive and Moving Average Models (d) The Wald Representation Theorem (e) Vector Autoregressive (VAR) Models Hamilton (1994), Chapters 1 4, Sections 10.1 and Lütkepohl (2005), Sections 2.1 and 2.2. Cochrane (2005), Sections , , Chapter 6 and Section 7.5. Wei (2006), Chapters 2 3 and Sections Tsay (2005), Sections and Hayashi, Fumio (2000), Econometrics, Princeton University Press: Princeton, NJ, Sections Peter J. Brockwell and Richard A. Davis (1991), Time Series: Theory and Methods, Second Edition, Springer-Verlag: New York, NY, Chapters 1, 3 and 5. Wednesday, January 14 Problem Set 1 Due at 1:10pm (f) Estimation of Time Series Models 4

5 Hamilton (1994), Chapter 5 and Sections 11.1 and 11.3 Lütkepohl (2005), Sections 3.2, 3.4 and 4.3. Wei (2006), Chapters 6 and 7. Brockwell and Davis (1991), Chapter 8. Wednesday, January 21 Problem Set 2 Due at 1:10pm (g) Bayesian VAR Hamilton (1994), Section Lütkepohl (2005), Section 5.4. Gelman, Andrew, John B. Carlin, Hal S. Stern and Donald B. Rubin (2004), Bayesian Data Analysis, Second Edition, Chapman&Hall/CRC: Boca Raton, FL, Chapters 2,3 and 14. Robert, Christian P., and George Casella (2004), Monte Carlo Statistical Methods, Second Edition, Springer: New York, NY, Chapter 2. - Doan, T., R. Litterman. and C. Sims (1984), Forecasting and Conditional Pojection Using Realistic Prior Distributions, Econometric Reviews, 3, * Ingram, Beth F., and Charles H. Whiteman (1994), Supplanting the Minnesota prior: Forecasting macroeconomic time series using real business cycle model priors, Journal of Monetary Economics, 34, * Del Negro, Marco, and Frank Schorfheide (2004), Priors from General Equilibrium Models for VARs, International Economic Reviews, 45, Monday, January 26 Computer Laboratory Session 1 Wednesday, January 28 Problem Set 3 Due at 1:10pm 3. Structural VAR Models and Impulse Response Functions (a) Short-Run Restrictions (b) Long-Run Restrictions Hamilton (1994), Section Lütkepohl (2005), Sections 9.1, and Cochrane (2005), Sections and 7.4 Christiano, Lawrence J., Martin Eichenbaum and Charles L. Evans (1999), Monetary Policy Shocks: What Learned and to What End, in Michael Woodford and John Taylor eds., Handbook of Macroeconomics, Volume 1, North Holland: The Netherland, Galí, Jordi (1999), Technology, Employment and the Business Cycle: Do Technology Shocks Explain Aggregate Fluctuations? American Economic Review, 89, Sims, Christopher A. (1980), Macroeconomics and Reality, Econometrica, 48, Kilian, Lutz (2009), Not All Oil Shocks Are Alike: Disentangling Demand and Supply Shocks in the Crude Oil Market, American Economic Review, 99, Watson, Mark W. (2006), Comment on Assessing Structual VARs by L. Christiano, M. Eichenbaum, and R. Vigfusson, NBER Macroeconomics Annual. 5

6 Fernández-Villaverde, Jesús, Juan F. Rubio-Ramírez, Thomas J. Sargent and Mark W. Watson (2007), A, B, C s (and D s) for Understanding VARs, American Economic Review, 97, Monday, February 2 (c) Identification by Heteroskedasticity (d) Sign Restrictions - Rigobon, Roberto (2003), Identification Through Heteroskedasticity, Review of Economics and Statistics, 85, Blanchard, O. and D. Quah (1989), The Dynamic Effects of Aggregate Demand and Supply Disturbances, American Economic Review, 79, Fry, Renee, and Adrian Pagan, (2011) Sign Restrictions in Structural Vector Autoregressions: A Critical Review, Journal of Economic Literature, 49, Uhlig, H. (2005), What are the Effects of Monetary Policy? Results from an Agnostic Identification Procedure, Journal of Monetary Economics, 52, Faust, Jon (1998), The Robustness of Identified VAR Conclusions About Money, Carnegie-Rochester Conference Series on Public Policy, 49, Arias, J.E., J.F. Rubio-Ramirez and D.F. Waggoner (2014), Inference Based on SVARs Identified with Sign and Zero Restrictions: Theory and Applications, unpublished manuscript, Federal Reserve Board, Duke University and Federal Reserve Bank of Atlanta. Baumeister, C., and J.D. Hamilton (2014), Sign Restrictions, Structural Vector Autoregressions, and Useful Prior Information, unpublished manuscript, Bank of Canada and University of California, San Diego. Inoue, Atsushi, and Lutz Kilian (2013), Inference on Impulse Response Functions in Structural VAR Models, Journal of Econometrics, 177, Wednesday, February 4 Problem Set 4 Due at 1:10pm (e) Identification by External Shocks (f) Forecast Error Variance Decompositions, Historical Decompositions and Half Lives. (g) Confidence Intervals for Structural Impulse Responses Kilian, Lutz (2008a), Exogenous Oil Supply Shocks: How Big Are They and How Much Do They Matter for the U.S. Economy? Review of Economics and Statistics, 90, Kilian, Lutz (2008b), The Economic Effects of Energy Price Shocks, Journal of Economic Literature, 46, Ramey, Valerie A. (2011a), Identifying Government Spending Shocks: It s All in the Timing, Quarterly Journal of Economics, 126, Romer, Christina and David Romer (2004), A New Measure of Monetary Policy Shocks: Derivation and Implications, American Economic Review, 94,

7 Hamilton (1994), Sections 11.5 and Lütkepohl (2005), Sections 3.7 and 9.4. Berkowitz, Jeremy, and Lutz Kilian (2000), Recent Developments in Bootstrapping Time Series, Econometric Review, 19, Efron, Bradley, and Robert J. Tibshirani (1993), An Introduction to the Bootstrap, Chapman&Hall/CRC: Boca Raton, FL. Sims, Christopher A., and Tao Zha (1999), Error Bands for Impulse Responses, Econometrica, 67, Jorda, Oscar (2009), Simultaneous Confidence Regions for Impulse Responses, Review of Economics and Statistics, 91, Monday, February 9 Computer Laboratory Session 2 Wednesday, February 11 Problem Set 5 Due at 1:10pm (h) Examples of Nonlinear Time Series Models and Impulse Responses Tsay (2005), Section 4.1. Koop, Gary, M. Hashem Pesaran and Simon M. Potter (1996), Impulse Response Analysis in Nonlinear Multivariate Models, Journal of Econometrics, 74, Gallant, A.R., P.E. Rossi and G. Tauchen (1993), Nonlinear Dynamic Structures, Econometrica, 61, Monday, February 16 (i) Nonstationarity and Transformations of Data Hamilton (1994), Chapter 15. Cochrane (2005), Chapter 10. Wei (2006), Chapters 4 and 9 and Section Tsay (2005), Sections 2.7 and Hayashi (2000), Chapter 9. - Dickey, David A., and Wayne A. Fuller (1979), Distribution of the Estimators for Autoregressive Time Series with a Unit Root, Journal of the American Statistical Association, 74, Elliott, Graham., Rothenberg, Thomas J., and James H. Stock (1996), Efficient Tests for an Autoregressive Unit Root, Econometrica, 64, Kwiatkowski, D., P.C.B. Phillips, P. Schmidt and Y. Shin (1992), Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root, Journal of Econometrics, 54, Phillips, Peter C.B., and Pierre Perron (1988), Testing for a Unit Root in Time Series Regression, Biometrika, 75, Ohanian, Lee E. (1991), Notes on Spurious Inference in a Linearly Detrended Vector Autoregression, Review of Economics and Statistics, 73, Cogley, T., and J.M. Nason (1995), Effects of the Hodrick-Prescott Filter on Trend and Difference Stationary Time Series: Implications for Business Cycle Research, Journal of Economic Dynamics and Control, 19,

8 - Harvey, A.C., and A. Jaeger (1993), Detrending, Stylized Facts and the Business Cycles, Journal of Econometrics, 8, Wednesday, February 18 Midterm Exam 1 Monday, February 23 Problem Set 6 Due at 1:10pm 4. State Space Models (a) Examples of State Space Models (b) The Kalman Filter Hamilton (1994), Chapter 21 and Sections , and Lütkepohol (2005), Sections Tsay (2005), Sections , 3.12, , , 11.2, 11.3, and Wei (2006), Sections 15.2, 18.1, 18.2 and Woodford, Michael (2003), Interest and Prices: Foundations of a Theory of Monetary Policy, Princeton University Press: Princeton, NJ, Section 4.1 Hamilton (1994), Chapter 4 and Sections and Lütkepohl (2005), Sections 18.2 and Wei (2006), Sections 18.1, 18.2 and Tsay (2005), Chapter 11. Cochrane (2005), Sections 5.2 and 7.3. Harvey, Andrew C. (1990), Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge University Press: Cambridge, UK. Hannan, E.J., and M. Deistler (1988), The Statistical Theory of Linear Systems, Wiley: New York, NY. Wednesday, February 25 (c) The Kalman Smoother (d) Forecasting (e) Maximum Likelihood Estimation of State Space Models Hamilton (1994), Sections 13.4 and Lütkepohl (2005), Sections Tsay (2005), Sections and Harvey, Andrew C. (1990), Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge University Press: Cambridge, UK. - Canova, Fabio and Luca Sala (2010), Back to Square One: Identification Issues in DSGE Models, Journal of Monetary Economics, 56, Ireland (2007), Changes in the Federal Reserve s Inflation Target: Causes and Consequences, Journal of Money, Credit and Banking, 39, note.pdf for Ireland (2007) in 8

9 - Ruiz, Esther (1994), Quasi-Maximum Likelihood Estimation of Stochastic Volatility Models, Journal of Econometrics, 63, Monday, March 9 Computer Laboratory Session 3 Wednesday, March 11 Problem Set 7 Due at 1:10pm (f) Markov Chain Monte Carlo Methods Tsay (2005), Chapter 12. Robert, Christian P., and George Casella (2004), Monte Carlo Statistical Methods, Second Edition, Springer: New York, NY, Chapters 6, 7, 9 and 10. Gelman, Andrew, John B. Carlin, Hal S. Stern, and Donald B. Rubin (2004), Bayesian Data Analysis, Chapman& Hall/CRC: Boca Raton, FL, Chapters Chib, Siddhartha, and Edward Greenberg (1995), Understanding the Hastings-Metropolis Algorithm, The American Statistician, 49, An, Sunbae, and Frank Schorfheide (2007), Bayesian Analysis of DSGE Models, Econometric Reviews, 26, Smets, Frank, and Rafael Wouters (2007), Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach, American Economic Review, 97, pp Jacquier, Eric, Nicholas G. Polson and Peter E. Rossi (1994), Bayesian Analysis of Stochastic Volatility Models, Journal of Business & Economic Statistics, 12, Del Negro, Marco, and Frank Schorfheide (2009), Monetary Policy Analysis with Potentially Misspecified Models, American Economic Review, 99, Monday, March 16 (g) Other Commonly Used Methods in Practice (i) Marginal Likelihoods (ii) Forecasting (iii) Impulse Responses and Variance Decompositions (iv) Kalman Smoothed Estimation of Latent State Variables - Geweke, J. (1992) Evaluating the Accuracy of Sampling-Based Approaches to the Calculation of Posterior Moments, in J.M. Bernardo, J.O. Berger, A.P. Dawid and A.F.M. Smith eds., Bayesian Statistics, 4, Oxford University Press: Oxford, UK, pp Chib, Sid (1995), Marginal Likelihood from the Gibbs Output, Journal of the American Statistical Association, 90, Chib, Sid, and Ivan Jeliazhov (2001), Marginal Likelihood from the Metropolis-Hastings Output, Journal of the American Statistical Association, 96, Meng, X.-L., and W. Wong (1996), Simulating Ratios of Normalizing Constants via a Simple Identity: A Theoretical Exploration, Statistica Sinica, 6, Meng, X., and S. Schilling (2002), Warp Bridge Sampling, Journal of Computational and Graphical Statistics, 11,

10 Wednesday, March 18 Computer Laboratory Session 4 Monday, March 23 Problem Set 9 Due at 8:30am (h) Non-Gaussian State Space Models (i) Nonlinear State Space Models - Kim, Sangjoon, Neil Shephard and Siddhartha Chib (1998), Stochastic Volatility: Likelihood Inference And Comparison With ARCH Models, Review of Economic Studies, 65, Creal, Drew (2012), A Survey of Sequential Monte Carlo Methods for Economics and Finance, Econometric Reviews, 31, Fernandez-Villaverde, J., and J.F. Rubio-Ramrez (2005), Estimating dynamic equilibrium economies: linear versus nonlinear likelihood, Journal of Applied Econometrics, 20, Fernandez-Villaverde, J., and J.F. Rubio-Ramrez (2007), Estimating macroeconomic models: a likelihood approach, Review of Economic Studies, 74, Wednesday, March Extremum Estimators for Dynamic Economic Models (a) GMM Clarida, R., J. Galí and M. Gertler (2000), Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory, Quarterly Journal of Economics, 115, Hamilton (1994), Chapter 14. Hayashi (2000), Chapter 7. Hall, Alastair R. (2005), Generalized Method of Moments, Oxford University Press: Oxford, UK. Stock, James H., Jonathan H. Wright and Motohiro Yogo (2002), A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments, Journal of Business and Economic Statistics, 20, Hansen, Lars P., (1982) Large Sample Properties of Generalized Method of Moment Estimators, Econometrica, 50, Sophocles Mavroeidis (2010), Monetary Policy Rules and Macroeconomic Stability: Some New Evidence, American Economic Review, 100, Newey, W.K., and D.L. McFadden (1994), Large Sample Estimation and Hypothesis Testing, in R.F. Engle and D.L. McFadden eds., Handbook of Econometrics, Volume 4, Elsevier: Amsterdam, The Netherlands, Chapter 36, pp Gallant, A. Ronald, and Halbert White (1988), A Unified Theory of Estimation and Inference for Nonlinear Dynamic Models, Basil Blackwell: Oxford, UK. Monday, March 30 Problem Set 10 due at 1:10pm (b) HAC Covariance Matrix Estimators Hamilton (1994), Section Hayashi (2000), Section

11 Cochrane (2005), Sections 8.1, 8.2 and Andrews, Donald W.K., (1991), Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation, Econometrica, 59, Andrews, Donald W.K., and J.C. Monahan (1992), An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator, Econometrica, 60, Newey, Whitney K., and Kenneth D. West (1987), A Simple Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix, Econometrica, 55, Newey, Whitney K., and Kenneth D. West (1994), Automatic Lag Selection in Covariance Matrix Estimation, Review of Economic Studies, 61, Kiefer, Nickolas M., and Timothy J. Vogelsang (2002), Heteroskedasticity-Autocorrelation Robust Standard Errors Using the Bartlett Kernel Without Truncation, Econometrica, 70, Wednesday, April 1 Computer Laboratory Session 5, Monday, April 6 Problem Set 10 due at 1:10pm (c) Method of Simulated Moments Estimators and Indirect Inference Estimators Gourinchas, P.O., and J.A. Parker (2002) Consumption Over the Life Cycle, Econometrica, 70, Gallant, A.R., and G. Tauchen (1996), Which Moments to Match, Econometric Theory, 12, Gourieroux, C., A. Monfort and E. Renault (1993), Indirect Inference, Journal of Applied Econometrics, 8, S85 S Smith, Jr. A.A., (1993), Estimating Nonlinear Time Series Models Using Simulated Vector Autoregressions, Journal of Applied Econometrics, 8, S63 S84. - Ruge-Murcia, Francisco (2012), Estimating Nonlinear DSGE Models by the Simulated Method of Moments: With an Application to Business Cycles, Journal of Economic Dynamics and Control, 36, Dridi, Ramdan, Alain Guay, and Eric Renault (2007), Indirect Inference and Calibration of Dynamic Stochastic General Equilibrium Models,Journal of Econometrics 136, Wednesday, April 8 (d) Bayesian Approaches to Non-Likelihood-Based Extremum Estimators Chernozhukov, Victor, and Han Hong (2003), An MCMC Approach to Classical Estimation, Journal of Econometrics, 115, Gallant, A. Ronald, and Robert E. McCulloch (2009), On the Determination of General Scientific Models with Application to Asset Pricing, Journal of the American Statistical Association, 104,

12 Monday, April 13 Midterm Exam 2 Wednesday, April 15 Presentation Monday, April 20 Presentation Thurday, April 23 Deadline for your term paper Disabled Students If you need course accommodations due to a disability or if you have emergency medical information to share, please discuss this with me as soon as possible. If you have a reason to need extra time on tests or other accommodations, please provide a letter from the EAD office and then make arrangements with me. Academic Integrity/Student Conduct The Vanderbilt Honor Code applies to all work done in this course. Violations of the honor code will be prosecuted with a minimum penalty of failure for the course. The exams are closed book. To each of the midterm exams, you may bring only a writing implement and one sheet of notes. Caveat The information and course outline in this syllabus are subject to change in the event of extenuating circumstances. 12