A ten-hour course introduces students to the analysis, modelling and estimation of stationary time series processes.
Topic 1
Basic Time Series concepts: Recap on difference equations, Stationarity, Ergodicity, ARMA processes. Hamilton (Chapters 1, 3), Lecture notes.
Topic 2
Maximum Likelihood Estimation: Estimation of ARMA models using MLE. Statistical Inference. Likelihood Ratio test. Model selection criteria. Hamilton (Chapter 5), Lecture notes.
Topic 3
Multivariate VAR Models: Stationarity, Conditional likelihood and OLS estimation, Granger Causality, Impulse responses, error bands, recursive VARs. Hamilton (Chapter 11), Lecture notes.
Topic 4
State-Space Representation and the Kalman Filter : Representation, a recursive algorithm. Hamilton (Chapter 13), Lecture notes. Exercise classes There will be 3-4 exercise classes Teaching material • Hamilton, J. H. (1994), Time Series Analysis, Princeton University Press • Slides notes by the instructor. Final exam and Grading There will be problems sets graded by TAs in classes (20%) and a final exam (80%).
 

This ten-hour course focuses on simulation based estimators. This will include simulated method of moments, indirect inference and the Generalized Method of Moments approach. The course is built around the book by Adda and Cooper. The lectures will be applications based, drawing on dynamic optimization problems for households, firms and the stochastic growth model. Here are key papers by topic. The full reading list is more substantial. All courses include Topics 1 and 2. Some years include the consumption component, Topic 3, while others include firm dynamics, Topic 4.
Topic 1
Tools
• Jerome, Adda and Russell Cooper, Dynamic Economics: Quantitative Methods and Applications, MIT Press, 2003. (AC), Chpt. 2-4 • Cooper, R “An Overview of Applied Dynamic Programming” February 2020
Topic 2
Stochastic Growth Model
• AC, Chpt. 5
• Altug, Sumru. “Time-to-build and aggregate fluctuations: some new evidence.” International Economic Review (1989): 889-920.
• Ingram, B. F., Kocherlakota, N. R., and Savin, N. E. (1994). Explaining business cycles: A multiple-shock approach. Journal of Monetary Economics, 34(3), 415- 428.
• (E) Jord`a, O. (2005). Estimation and inference of impulse responses by local ` projections. American economic review, 95(1), 161-182.
• King, Robert G., Charles I. Plosser, and Sergio T. Rebelo. “Production, growth and business cycles.” Journal of monetary Economics 21, no. 2/3 (1988): 196-232.
• Kydland, Finn E., and Edward C. Prescott. “Time to build and aggregate fluctuations.” Econometrica, (1982): 1345-1370.
• Krusell, Per, and Anthony A. Smith, Jr. “Income and wealth heterogeneity in the macroeconomy.” Journal of Political Economy 106.5 (1998): 867-896.
• (E) Smith, Anthony A. “Estimating nonlinear time-series models using simulated vector autoregressions.” Journal of Applied Econometrics 8.S1 (1993): S63-S84.
Topic 3a
Consumption
• AC, Chpt. 6
• Bonaparte, Yosef, Russell Cooper, and Guozhong Zhu. “Consumption smoothing and portfolio rebalancing: The effects of adjustment costs.” Journal of Monetary Economics 59, no. 8 (2012): 751-768. 10
• Carroll, Christopher D., Robert E. Hall, and Stephen P. Zeldes. “The buffer-stock theory of saving: Some macroeconomic evidence.” Brookings papers on economic activity 1992, no. 2 (1992): 61-156.
• Carroll, C. “Death to the Log-Linearized Consumption Euler Equation,” NBER Working Paper 6298, 1997.
• Cooper, Russell, and Guozhong Zhu. “Household finance over the life-cycle: What does education contribute?.” Review of Economic Dynamics 20 (2016): 63-89.
• Deaton, A. “Savings and Liquidity Constraints,” Econometrica, 59 (1991), 1121- 42.
• Eichenbaum, M., Hansen, L. and K. Singleton, “A Time Series Analysis of Representative Agent Models of Consumption and Leisure Choice under Uncertainty,” Quarterly Journal of Economics, 103 (1988), 51-78.
• Gourinchas, P. and J. Parker, “Consumption over the Life Cycle”, Econometrica, 70 (2002), 47-89.
• Hall, R. “Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence,” Journal of Political Economy, 86 (1978), 971-87.
• Hansen, L. “Proofs for Large Sample Properties of Generalized Method of Moments Estimators.” University of Chicago, March 2012. (M).
• Hansen, L. and K. Singleton, “Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models,” Econometrica, 50 (1982), 1269-86.
• Newey, K. Whitney, “Generalized Method of Moments.” MIT October 2007 (M).
• Zeldes, S. “Consumption and Liquidity Constraints: An Empirical Investigation,” Journal of Political Economy, 97 (1989), 305-46.
Topic 3b
Durable Consumption
• AC, Chpt. 7
• Adda, J. and R. Cooper, “Balladurette and Juppette: A Discrete Approach,” Journal of Political Economy, August, 2000.
• Mankiw, N.G. “Hall’s Consumption Hypothesis and Durable Goods,” Journal of Monetary Economics, 10 (1982), 417-25.
Topic 4
Firm Dynamics
• AC, Chpt. 8 • Abel, A. and J. Eberly, “A Unified Model of Investment Under Uncertainty,” American Economic Review, 94 (1994), 1369-84. 
• Bloom, N. “The Impact of Uncertainty Shocks,” Econometrica, 2009. • Bloom, Nicholas, Max Floetotto, Nir Jaimovich, Itay Saporta-Eksten, and Stephen J. Terry. “Really uncertain business cycles.” Econometrica 86, no. 3 (2018): 1031-1065. 11
• Caballero, R. and E. Engel, “Explaining Investment Dynamics in U.S. Manufacturing: A Generalized (S,s) Approach," Econometrica, 67 (1999), 783-826.
• Caballero, R., E. Engel and J. Haltiwanger, “Plant Level Adjustment and Aggregate Investment Dynamics,” Brookings Papers on Economic Activity, 2 (1995b), 1-39.
• Cooper, R. and J. Ejarque, “Financial Frictions and Investment: A Requiem in Q,” Review of Economic Dynamics, 6 (2003), 710-28.
• Cooper, R. and J. Haltiwanger, “On the Nature of Capital Adjustment Costs,” Review of Economic Studies, 73 (2006), 611-33.
• Khan, Aubhik, and Julia K. Thomas. “Idiosyncratic shocks and the role of nonconvexities in plant and aggregate investment dynamics.”Econometrica 76, no. 2 (2008): 395-436.
• Rust, John. “Optimal replacement of GMC bus engines: An empirical model of Harold Zurcher. ”Econometrica: Journal of the Econometric Society (1987): 999-1033.
• Thomas, J. “Is Lumpy Investment Relevant for the Business Cycle? ”Journal of Political Economy 110, no. 3 (2002): 508-534.
Homework, exams and grading
Over this course there wil be three homework assignments. The way to learn this material is by using it, both in the homework assignments and beyond. The homework will be evaluated on a pass/fail basis. You are encouraged to work in a group, but you should submit answers independently. Your grade will be based entirely upon the exam.