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Required Text

Amazon logo Hamilton, James D. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994. ISBN: 9780691042893.

Recommended Texts

Amazon logo Brockwell, Peter, and Richard Davis. Time Series: Theory and Methods. New York, NY: Springer-Verlag, 1998. ISBN: 9780387974293.

Amazon logo Canova, Fabio. Methods for Applied Macroeconomic Research. Princeton, NJ: Princeton University Press, 2007. ISBN: 9780691115047.

Amazon logo DeJong, David, and Chetan Dave. Structural Macroeconometrics. Princeton, NJ: Princeton University Press, 2007. ISBN: 9780691126487.

Amazon logo Hall, Peter, and C. C. Heyde. Martingale Limit Theory and Its Application. New York, NY: Academic Press, 1980. ISBN: 9780123193506.

Amazon logo Griliches, Zvi, and Michael Intriligator, eds. Handbook of Econometrics. Vol. 3. Amsterdam, The Netherlands: Elsevier Science Publishing Company, 1986. ISBN: 9780444861870.

Amazon logo Lütkepohl, Helmut. Introduction to Multiple Time Series Analysis. New York, NY: Springer-Verlag, 1993. ISBN: 9780387569406.

Course Outline

The following is a tentative list of topics that will be covered in this course. I reserve the right to add (hardly possible) or delete (very likely) topics as the course progresses. The asterisked references are more important to the course.

The following acronyms appear below:

ARMA – Autoregression moving average

DSGE – Dynamic stochastic general equilibrium

FAVAR – Factor-augmented vector autoregressive approach

GMM – Generalized method of moments

HAC – Heteroscedasticity autocorrelation-consistent

IV – Instrumental variables

MCMC – Markov Chain Monte Carlo

ML – Maximum likelihood

NBER – National Bureau of Economic Research

OLS – Ordinary least squares

VAR – Vector autoregression

I. Introduction to stationary time series
Introduction to stationary time series: ARMA, limit theory for stationary time series, causal relationships, HAC

*Hamilton. Chapters 1-5, 7, and 8.

*Hall and Heyde. Chapter 3.

Brockwell and Davis. Chapters 1, 3, section 5.7.

*Newey, W. K., and K. D. West. "A Simple Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix." Econometrica 55 (1987): 703-708.

*Andrews, D. W. K. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation." Econometrica 59 (1991): 817-858.

Beveridge, S., and C. R. Nelson. "A New Approach to Decomposition of Economic Time Series into Permanent and Transitory Components with Particular Attention to Measurement of the 'Business Cycle.'" Journal of Monetary Economics 7 (1981): 151-174.

Andrews, D. W. K., and J. C. Monahan. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator." Econometrica 60 (1992): 953-966.

Amazon logo den Haan, W. J., and A. Levin. "A Practitioner's Guide to Robust Covariance Matrix Estimation." In Handbook of Statistics. Edited by G. S. Maddala and C. R. Rao. Amsterdam, The Netherlands: Elsevier, 1997. ISBN: 9780444821720.

Kiefer, N., and T. Vogelsang. "Heteroskedasticity-Autocorrelation Robust Testing Using Bandwidth Equal to Sample Size." Econometric Theory 18 (2002): 1350-1366.

Frequency domain analysis: spectra, filters, transforms, nonparametric estimation

*Hamilton. Chapter 6.

Brockwell and Davis. Chapters 4 and 10.

*Baxter, M., and R. King. "Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series." Review of Economics and Statistics 81 (1999): 575-593.

Berk, K. N. "Consistent Autoregressive Spectral Estimates." Annals of Statistics 2 (1974): 489-502.

Hodrick, R., and E. Prescott. "Post-War U.S. Business Cycles: An Empirical Investigation." Journal of Money Banking and Credit 29 (1997): 1-16.

Christiano, L. J., and T. J. Fitzgerald. "The Band Pass Filter." NBER Working Paper 7257, 1999.

Model selection and information criteria: consistent estimation of number of lags, discussion of non-uniformity and post-selection inferences

*Geweke, J., and R. Meese. "Estimating Regression Models of Finite But Unknown Order." International Economic Review (1981): 55-70.

Ng, S., and P. Perron. "A Note on the Selection of Time Series Models." Oxford Bulletin of Economics and Statistics 67, no. 1 (2005): 115-134.

Leeb, H., and B. M. Potscher. "Model Selection and Inference: Facts and Fiction." Econometric Theory 21 (2005): 21-59.

———. "The Finite-Sample Distribution of Post-Model-Selection Estimators and Uniform versus Nonuniform Approximations." Econometric Theory 19 (2003): 100-142.

Hansen, B. "Challenges for Econometric Model Selection." Econometric Theory 21 (2005): 60-68.

Kuersteiner, G. M. "Automatic Inference for Infinite Order Vector Autoregressions." Econometric Theory 21 (2005): 85-115.

II. Multivariate stationary analysis
VAR: definition, estimation: OLS, ML, Granger causality, impulse response functions and variance decompositions

*Hamilton. Chapters 10 and 11.

*Lütkepohl. Chapters 2 and 3.

Canova. Chapter 4.

Lütkepohl and Kratzig. Chapter 4.

Amazon logo Watson, M. "Vector Autoregression and Cointegration." In Handbook of Econometrics. Vol. 4. Edited by Robert Engle and Daniel McFadden. Amsterdam, Netherlands: Elsevier Science, 1999. ISBN: 9780444887665.

Stock, J. H., and M. W. Watson. "Vector Autoregressions." Journal of Economic Perspectives 15, no. 4 (2001): 101-116.

Wright, J. H. "Confidence Intervals for Univariate Impulse Responses with a Near Unit Root." Journal of Business and Economic Statistics 18 (2000): 368-373.

Killian, L. "Small Sample Confidence Intervals for Impulse Response Functions." Review of Economics and Statistics (1998): 218-230.

Structural VARs: identification, short-term restrictions, long-term restrictions

*Sims, C. A. "Macroeconomics and Reality." Econometrica 48 (1980): 1-48.

*Blanchard, O. J., and D. Quah. "Dynamic Effects of Aggregate Demand and Supply Disturbances." American Economic Review 79 (1989): 655-673.

Blanchard, O. J. "A Traditional Interpretation of Economic Fluctuations." American Economic Review 79 (1989): 1146-1164.

King, R. G., C. I. Plosser, J. H. Stock, and M. W. Watson. "Stochastic Trends and Economic Fluctuations." American Economic Review 81 (1991): 819-840.

Cooley, T., and S. LeRoy. "A Theoretical Macroeconomics: A Critique." Journal of Monetary Economics 16 (1985): 283-308.

Braun, P., and S. Mittnik. "Misspecification in VAR and Their Effects on Impulse Responses and Variance Decompositions." Journal of Econometrics 59 (1993): 319-341.

Cooley, T., and M. Dwyer. "Business Cycle Analysis Without Much Theory: A Look at Structural VARs." Journal of Econometrics 83 (1998): 57-88.

VAR and DSGE models: world decomposition, fundamentality of shocks, do long-run restrictions identify anything?

Chari, V., P. Kehoe, and E. McGrattan. "A Critique of Structural VARs Using Business Cycle Theory." Federal Reserve Bank of Minneapolis, Research Department Staff Report 364, 2005.

*Christiano, L., M. Eichenbaum, and R. Vigfusson. "Assessing Structural VARs." Northwestern University, manuscript, 2005.

*Fernandez Villaverde, J., J. Rubio Ramirez, and T. Sargent. "The ABC and (D's) to Understand VARs." NYU, manuscript, 2005.

Erceg, C., L. Guerrieri, and C. Gust. "Can Long Run Restrictions Identify Technology Shocks?" Board of Governors of the Federal Reserve, International Finance discussion paper 792, 2005.

Lippi, M., and L. Reichlin. "VAR Analysis, Non-Fundamental Representation, Blaschke Matrices." Journal of Econometrics 63 (1994): 307-325.

Faust, J., and E. Leeper. "Do Long Run Restrictions Really Identify Anything?" Journal of Business and Economic Statistics 15 (1997): 345-353.

Factor model and FAVAR: motivation, principal components, choosing number of static and dynamic factors, structural FAVAR, IV regression with factors

*Stock, J. H., and M. W. Watson. "Implications of Dynamic Factor Models for VAR Analysis." NBER Working Paper 11467, 2005.

Bernanke, B. S., and J. Boivin. "Monetary Policy in a Data-Rich Environment." Journal of Monetary Economics 50 (2003): 525-546.

*Bernanke, B. S., J. Bovian, and P. Eliasz. "Measuring the Effects of Monetary Policy: A Factor-augmented Vector Autoregressive (FAVAR) Approach." Quarterly Journal of Economics 120 (2005): 384-387.

*Forni, M., D. Giannoni, M. Lippi, and L. Reichlin. "Opening the Black Box: Structural Factor Models with Large Cross-Sections." European Central Bank, Working Paper 712, 2007.

Chamberlain, G., and M. Rothschild. "Arbitrage, Factor Structure and Mean-Variance Analysis of Large Asset Markets." Econometrica 51 (1983): 1281-1304.

Favero, C. A., M. Marcellino, and F. Neglia. "Principal Components at Work: The Empirical Analysis of Monetary Policy with Large Datasets." Journal of Applied Econometrics 20 (2005): 603-620.

Forni, M., M. Hallin, M. Lippi, and L. Reichlin. "The Generalized Factor Model: Identification and Estimation." Review of Economics and Statistics 82 (2000): 540-554.

Bai, J., and S. Ng. "Determining the Number of Factors in Approximate Factor Models." Econometrica 70 (2002): 191-221.

———. "Determining the Number of Primitive Shocks in Factor Models." Journal of Business & Economic Statistics 25 (2007): 52-60.

*———. "Instrumental Variable Estimation in a Data Rich Environment." Manuscript, 2006.

III. Univariate non-stationary processes
Asymptotic theory of empirical processes

*Hamilton. Sections 17.1-17.3.

Hall and Heyde. Chapters 3, 4, 5, and the appendix.

Univariate unit roots and near unit root problem: unit root testing, confidence sets for persistence, tests for stationarity

*Hamilton. Chapter 17.

Amazon logo *Stock, J. H. "Unit Roots, Structure Breaks and Trends." In Handbook of Econometrics. Vol. 5. Edited by J. J. Heckman and E. E. Leamer. Amsterdam, Netherlands: Elsevier, 2001. ISBN: 9780444823403.

Dickey, D. A., and W. A. Fuller. "Distribution of the Estimators for Autoregressive Time Series with a Unit Root." Journal of the American Statistical Association 74 (1979): 427-431.

Campbell, J. Y., and P. Perron. "Pitfalls and Opportunities: What Macroeconomists Should Know about Unit Roots." NBER Technical Working Paper 100, 1991.

Andrews, D. W. K. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models." Econometrica 61, no. 1 (1993): 139-165.

Hansen, B. E. "The Grid Bootstrap and the Autoregressive Model." Review of Economics and Statistics 81, no. 4 (1999): 594-607.

*Phillips, P. C. B. "Toward a Unified Asymptotic Theory for Autoregression." Biometrika 74, no. 3 (1987): 535-547.

Stock, J. "Confidence Intervals for the Largest Autoregressive Root in U.S. Macroeconomic Time Series." Journal of Monetary Economics 28 (1991): 435-459.

Mikusheva, A. "Uniform Inference in Autoregressive Models." Econometrica 75, no. 5 (2007): 1411-1452.

Structural breaks and non-linearity: testing for breaks with known and unknown dates, multiple breaks, estimating number of breaks

*Hamilton. Chapter 22.

*Andrews, D. W. K. "Tests for Parameter Instability and Structural Change with Unknown Change-Point." Econometrica 61 (1993): 821-856.

*Hansen, B. E. "The New Econometrics of Structural Change: Dating Breaks in U.S. Labor Productivity." Journal of Economic Perspectives 15 (2001): 117-128.

*Perron, P. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis." Econometrica 57 (1989): 1361-1401.

Andrews, D. W. K., and W. Ploberger. "Optimal Tests When a Nuisance Parameter is Present Only Under the Alternative." Econometrica 62 (1994): 1383-1414.

Bai, J. S. "Estimating Multiple Breaks One at a Time." Econometric Theory 13 (1997): 315-352.

Bai, J., and P. Perron. "Estimating and Testing Linear Models with Multiple Structural Changes." Econometrica 66 (1998): 47-78.

Bai, J., R. L. Lumsdaine, and J. H. Stock. "Testing for and Dating Common Breaks in Multivariate Time Series." Review of Economic Studies 65 (1998): 395-432.

Zivot, E., and D. W. K. Andrews. "Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis." Journal of Business and Economic Statistics 10 (1992): 251-270.

IV. Multivariate non-stationary
Multivariate unit roots and co-integration: estimating co-integration relations, canonical form

Stock, J. H. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors." Econometrica 55 (1987): 1035-1056.

Stock, J. H., and M. W. Watson. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems." Econometrica 61 (1993): 783-820.

*Amazon logo Watson, M. "Vector Autoregression and Cointegration." In Handbook of Econometrics. Vol. 4. Edited by Robert Engle and Daniel McFadden. Amsterdam, Netherlands: Elsevier Science, 1999, sections 1-2. ISBN: 9780444887665.

Persistent regressors (prediction regression) limit theory, Stambaugh correction, nuisance parameter problem, conservative procedures, conditional procedures

Bekaert, G., and R. J. Hodrick. "Expectations Hypotheses Test." Journal of Finance 56 (2001): 1357-1394.

Campbell, J. Y., and M. Yogo. "Efficient Tests of Stock Return Predictability." Journal of Financial Economics 81 (2006): 27-60.

*Cavanagh, C. L., G. Elliott, and J. H. Stock. "Inference in Models with Nearly Integrated Regressors." Econometric Theory 11 (1995): 1131-1147.

Lewellen, J. "Predicting Returns with Financial Ratios." Journal of Financial Economics 74 (2004): 209-235.

*Stambaugh, R. F. "Predictive Regressions." Journal of Financial Economics 54 (1999): 375-421.

Torous, W., R. Valkanov, and S. Yan. "On Predicting Stock Returns with Nearly Integrated Explanatory Variables." Journal of Business 77 (2004): 937-966.

Jansson, M., and M. J. Moreira. "Optimal Inference in Regression Models with Nearly Integrated Regressors." Econometrica 74, no. 3 (2006): 681-715.

V. Simulated GMM
GMM and simulated GMM: GMM estimation and asymptotic theory, testing in GMM setting, simulated method of moments and time series specifics: estimation of covariance structure, initial condition problem, indirect inference

*Hamilton. Chapter 14.

*DeJong and Dave. Chapter 7.

Canova. Chapter 5.

*Hansen, L. P. "Large Sample Properties of GMM Estimators." Econometrica 50 (1982): 1029-1054.

*Hansen, L. P., and K. Singleton. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models." Econometrica 50 (1982): 1269-1286.

McFadden, D. "A Method of Simulated Moments of Estimation for Discrete Response Models Without Numerical Integration." Econometrica 57 (1989): 995-1026.

Pakes, A., and D. Pollard. "Simulation and the Asymptotics of Optimization Estimators." Econometrica 57 (1989): 1027-1057.

*Lee, B., and B. Ingram. "Simulation Estimation of Time Series Models." Journal of Econometrics 47 (1991): 197-205.

Duffie, D., and K. Singleton. "Simulated Moments Estimation of Markov Models of Asset Prices." Econometrica 61 (1993): 929-952.

*Smith, A. "Estimation of Nonlinear Time Series Models Using Simulated VARs." Journal of Applied Econometrics 8 (1993): s63-s84.

Estimating DSGE with GMM6

Rotemberg, J., and M. Woodford. "An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy." NBER Technical Working Paper 233, 1998.

Christiano, L., M. Eichenbaum, and C. Evans. "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy." Journal of Political Economy 113, no. 1 (2005): 1-45.

Altig, D., L. Christiano, M. Eichenbaum, and J. Linde. "Firm-Specific Capital, Nominal Rigidities and the Business Cycle." Northwestern University, manuscript, 2004.

Jordà, O., and S. Kozichi. "An Efficient IRF Matching Estimator for Rational Expectations Models." University of California at Davis, manuscript, 2005.

Hall, A., A. Inoue, J. M. Nason, and B. Rossi. "Information Criteria for Impulse Response Function Matching Estimation of DSGE Models." Manuscript, 2007.

VI. Likelihood methods
Kalman filter and its applications: state-space models, time varying coefficients

*Hamilton. Chapter 13.

Canova. Chapter 6.

*Hamilton. J. D. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle." Econometrica 57 (1989): 357-384.

ML estimation of DSGE: stochastic singularities problem, misspecification and quasi-ML, identification

DeJong and Dave. Chapter 8.

Canova. Chapter 6.

Sargent, T. "Two Models of Measurements and the Investment Accelerator." Journal of Political Economy 97, no. 2 (1989): 251-287.

Ingram, Beth, Narayana Kocherlakota, and N. E. Savin. "Explaining Business Cycles: a Multiple-Shock Approach." Journal of Monetary Economics 34 (1994): 415-428.

Hansen, Lars, and Thomas Sargent. "Recursive Linear Models of Dynamic Economies." NBER Working Paper 3479, 1990.

Ireland, P. "A Method for Taking Models to Data." Journal of Economic Dynamics and Control 28 (2004): 1205-1226.

———. "Sticky Price Models and the Business Cycle: Specification and Stability." Journal of Monetary Economics 47 (2000): 3-18.

Watson, M. "Recursive Solution Methods for Dynamic Linear Rational Expectations Models." Journal of Econometrics 41 (1989): 65-89.

White, H. "Maximum Likelihood Estimation of Misspecified Models." Econometrica 50 (1982): 1-25.

VII. Bayesian methods
Bayesian concepts *Hamilton. Section 12.3.
Markov Chain Monte Carlo (MCMC): Metropolis-Hastings, Gibbs sampler, data augmentation

*Chib, S., and E. Greenberg. "Understanding the Metropolist-Hastings Algorithm." American Statistician 49, no. 4 (1995): 327-335.

*———. "Markov Chain Monte Carlo Simulation Methods in Econometrics." Econometric Theory 12 (1996): 409-431.

*Amazon logo Chib, S. "Markov Chain Monte Carlo Methods: Computation and Inference." In Handbook of Econometrics. Vol. 5. Edited by J. J. Heckman and E. Leamer. Amsterdam, Netherlands: Elsevier Science, 2001, pp. 3564-3634. ISBN: 9780444823403.

Chib, S., F. Nardari, and N. Shephard. "Markov Chain Monte Carlo Methods for Stochastic Volatility Models." Journal of Econometrics 108 (2002): 281-316.

Estimation of DSGE models using Bayesian methods

Del Negro, M., and F. Schorfheide. "Priors from General Equilibrium Models for VARs." International Economic Review 45 (2004): 643-673.

Del Negro, M., F. Schorfheide, F. Smets, and R. Wouters. "On the Fit and Forecasting Performance of New Keynesian Models." Journal of Business and Economic Statistics (2007).

Rabanal, P., and J. Rubio-Ramirez. "Comparing New Keynesian Models of the Business Cycle: A Bayesian Approach." Journal of Monetary Economics 52 (2005): 1151-1166.

Fernandez-Villaverde, J., and J. Rubio-Ramirez. "Estimating Dynamic Equilibrium Economies: Linear Versus Nonlinear Likelihood." Journal of Applied Econometrics 20 (2005): 891-910.

Boivin, J., and M. P. Giannoni. "DSGE Models in a Data-Rich Environment." Columbia University, manuscript, 2005.