Econ 616: Macroeconometrics – Spring 2025

Instructor

Course Time and Location

Class will meet once a week Tuesdays from 6:30p-9:00 for lecture. (That’s a long time; we’ll take a 5-10 minute break midway through!) The classroom is ICC-223A.

Course Description

The course is an introduction to univariate and multivariate time series models. Time domain methods, including VAR’s, structural VAR’s, Bayesian VAR’s for linear models and GMM for non-linear stationary models are covered. An introduction to non-stationary time series models is given. Frequency domain methods and their applications to business cycle inference are also covered. The course starts by introducing basic concepts and progresses to more complicated models. The course intends to meet two goals. It provides tools for empirical work with time series data, mostly for macroeconomic applications and provides a heuristic introduction into the theoretical foundation of time series models.

Webpage

Course documents and information are available via canvas.

Course Requirements

Prerequisites: Econ 613 and 614.

Assessment. Your grade will be equally weighted based on problems sets and a final exam.

Problem Sets: [50%] There will be approximately 5 problem sets assigned during the semester. The problem sets are designed to give the students the opportunity to review, enhance, and extend the material learned in class. Students are encouraged to form small study groups, however, each student has to submit his or her own write-up of the solution. These solutions must be submitted on the specified due dates.
Final Exam: [50%] (take home)

Programming and Computation. Macroeconometrics is an intensely computational field. It is important to be proficient in at least one interpeted programming language popular in economics. The assignments will require (some) light programming. I’ll say more about this on the first day of class.

Course Text

There is no one textbook that exactly matches the material covered in class. I will make my lecture notes available on the internet. You should get a copy of Hamilton (1994), which broadly covers classical approach to time series analysis (and some Bayesian analysis).

Course Outline

Note: This course outline is subject to change during the semester!

Part 1: Fundamentals of Time Series

Time Series Models

Topics: Estimation and Serial Dependence, Empirical Measures of Dependency; Covariance Stationarity, Stationarity and Ergodicity; Martingales and Martingale Difference Sequences Theoretical Properties: Moving Average Processes Theoretical Properties: Autoregressive Models.

Readings: Hamilton: chapters 1-3; Brockwell and Davis: chapters 2 and 3; Cochrane chapters 1-4.

Literature: Slutzky (1937); Orcutt and Irwin (1948)

Analysis of Difference Stationary Time Series

Topics: Analysis of the Deterministic Trend Model: Rates of Convergence, OLS; Autoregressive Models with a Unit Root; Wiener processes; Testing for Unit Roots; Unit Roots from the Frequentist and the Bayesian Perspective; Cointegration and Error Correction Models;

Readings: Hamilton: chapters 15-16. More technical details in Davidson and MacKinnon.

Literature: Dickey and Fuller (1979); Phillips (1986); Phillips (1987)

Spectral Analysis and Extremum Estimation

Topics: Spectrum; fourier transformation; spectral representation; linear filters; GMM.

Readings: Hamilton: chapter 6; Brockwell and Davis: chapter 4; Prandoni and Vetterli (2008).

Literature: Granger (1966)

Bayesian Analysis of Linear Time Series Models

Topics: Introduction to Bayesian Statistics: Point Estimation, Testing Theory;Bayesian Analysis of AR Models;Bayesian Model Selection: Determining the Order of an AR process; Markov-Chain Monte Carlo Methods;

Readings:Del Negro and Schorfheide (2011); Robert (1994); Geweke (2005);

Literature:Sims and Uhlig (1991); Sims and Zha (1998)

Part 2: Empirical Application of Linear Time Series Models

Vector Autoregressions

Topics: VAR extension of AR(p) model; Estimation of VARs; Forecasting with VARs;

Readings: Stock and Watson (2001); Del Negro and Schorfheide (2011); Ramey (2016).

Literature: Sims (1980); Blanchard and Quah (1989); Faust (1998); Uhlig (2005); Gertler and Karadi (2015); Baumeister and Hamilton (2015); Antolín-Díaz and Rubio-Ramírez (2018); Arias, Rubio-Ram ;irez, and Waggoner (2018);

Local Projections

Topics: iterated vs. direct forecasting; bias-variance trade off; impulse response estimation; small sample analysis;

Literature: Schorfheide (2005);Marcellino, Stock, and Watson (2006); Jorda (2005); Plagborg-Møller and Wolf (2021); Herbst and Johannsen (2024); Kolesár and Plagborg-Møller (2024)

Linear State Space Models and Factor Models

Topics: Kalman filter

Linear (and Nonlinear) Rational Expectations (LRE) Models

Linear LRE Models

Topics: LRE models as approximations to dynamic stochastic equilibrium (DSGE) models; Moment-based Estimation of linear and nonlinear rational expectations models; Likelihood-based Estimation of LRE models; state space vs. sequence space solutions

Nonlinear LRE Models

Topics: conditionally linear models, sequential Monte Carlo for static parameters;Particle Filtering;Advanced MCMC

References

Antolín-Díaz, J., and J. F. Rubio-Ramírez. (2018): “Narrative sign restrictions for svars,” American Economic Review, 108, 2802–29.

Arias, J. E., J. F. Rubio-Ram ;irez, and D. F. Waggoner. (2018): “Inference based on structural vector autoregressions identified with sign and zero restrictions: Theory and applications,” Econometrica, 86, 685 720.

Baumeister, C., and J. D. Hamilton. (2015): “Sign restrictions, structural vector autoregressions, and useful prior information,” Econometrica, 83, 1963–99.

Blanchard, O. J., and D. Quah. (1989): “The dynamic effects of aggregate demand and supply disturbances,” American Economic Review, 79, 655–73.

Bollerslev, T. (1986): “Generalized autoregressive conditional heteroskedasticity,” Journal of Econometrics, 31, 307 327.

Brockwell, P. J., and R. A. Davis. (1987): “Time series: Theory and methods,” Springer Series in Statistics, .

Cochrane, J. (2005): “Time series analysis for macroeconomics and finance,” Mimeo, .

Davidson, R., and J. G. MacKinnon. (2003): Econometric Theory and Methods, Oxford University Press.

Del Negro, M., and F. Schorfheide. (2011): “Bayesian Macroeconometrics,” in Handbook of Bayesian Econometrics, ed. by Dijk, H. van, G. Koop, and J. Geweke. Oxford University Press, 293-389.

Dickey, D. A., and W. A. Fuller. (1979): “Distribution of the estimators for autoregressive time series with a unit root,” Journal of the American Statistical Association, 74, 427–31.

Engle, R. F. (1982): “Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation,” Econometrica, 50, 987.

Faust, J. (1998): “The robustness of identified var conclusions about money,” Carnegie Rochester Conference Series on Public Policy, 49, 207–44.

Ferguson, T. S. (1973): “A bayesian analysis of some nonparametric problems,” The Annals of Statistics, 1, 209 230.

Gertler, M., and P. Karadi. (2015): “Monetary policy surprises, credit costs, and economic activity,” American Economic Journal: Macroeconomics, 7, 44 76.

Geweke, J. (2005): Contemporary Bayesian Econometrics and Statistics, John Wiley & Sons, Inc.

Granger, C. W. J. (1966): “The typical spectral shape of an economic variable,” Econometrica, 34, 150–61.

Hamilton, J. (1994): Time Series Analysis, Princeton, New Jersey: Princeton University Press.

Herbst, E. P., and B. K. Johannsen. (2024): “Bias in local projections,” Journal of Econometrics, 240, 105655.

Jorda, Ò. (2005): “Estimation and inference of impulse responses by local projections,” American Economic Review, 95, 161 182.

Kim, C.-J., and C. Nelson. (1999): State-Space Models with Regime Switching, MIT Press, Cambridge.

Kolesár, M., and M. Plagborg-Møller. (2024): “Dynamic Causal Effects in a Nonlinear World: The Good, the Bad, and the Ugly,”.

Marcellino, M., J. H. Stock, and M. W. Watson. (2006): “A comparison of direct and iterated multistep ar methods for forecasting macroeconomic time series,” Journal of Econometrics, 135, 499 526.

Orcutt, G. H., and J. O. Irwin. (1948): “A study of the autoregressive nature of the time series used for tinbergen’s model of the economic system of the united states, 1919-1932,” Journal of the Royal Statistical Society: Series B (Methodological), 10, 1–53.

Phillips, P. (1986): “Understanding spurious regressions in econometrics,” Journal of Econometrics, 33, 311–40.

Phillips, P. C. B. (1987): “Time series regression with a unit root,” Econometrica, 55, 277–301.

Plagborg-Møller, M., and C. K. Wolf. (2021): “Local projections and vars estimate the same impulse responses,” Econometrica, 89, 955–80.

Prandoni, P., and M. Vetterli. (2008): Signal Processing for Communications, Lausanne, Switzerland: EPFL Press.

Ramey, V. (2016): “Macroeconomic shocks and their propagation,”.

Robert, C. P. (1994): The Bayesian Choice, New York: Springer-Verlag.

Schorfheide, F. (2005): “Var forecasting under misspecification,” Journal of Econometrics, 128, 99–136.

Sims, C. A. (1980): “Macroeconomics and reality,” Econometrica, 48, 1–48.

Sims, C. A., and H. Uhlig. (1991): “Understanding unit rooters: A helicopter tour,” Econometrica, 59, 1591–99.

Sims, C. A., and T. Zha. (1998): “Bayesian methods for dynamic multivariate models,” International Economic Review, 39, 949–68.

Slutzky, E. (1937): “The summation of random causes as the source of cyclic processes,” Econometrica, 5, 105–46.

Stock, J. H., and M. W. Watson. (2001): “Vector autoregressions,” Journal of Economic Perspectives, 15, 101–15.

Stock, J. H., and M. W. Watson. (2007): “Why has u.s. inflation become harder to forecast?,” Journal of Money, Credit and Banking, 39, 3 33.

Uhlig, H. (2005): “What are the effects of monetary policy on output? results from an agnostic identification procedure,” Journal of Monetary Economics, 52, 381–419.