TR 11-12:15 - ECON 5
Robert McNown Office Hours: Tuesday 3:30-5
Office: Economics 109 Friday 2:00-3:30
Tel: 492-8295 Email Address: mcnownr@colorado.edu
Class Content
The primary objective of this course is to offer exposure to several modern topics in macro-econometrics. These include, primarily, time series analysis and simultaneous equations models. Although these models are often applied to aggregate time series data, they may also be appropriate for some microeconometric applications. For example, empirical work in labor economics with microdata sets pays considerable attention to issues of simultaneous equations identification and estimation. Also the analysis of individual markets with time series data should employ appropriate time series methods. In addition, it is recognized that panel data analysis involves a temporal dimension, and as a result some time series topics are beginning to appear in these models.
The first section of the course will cover topics in time series, with particular emphasis on problems of inference when variables are nonstationary. Traditionally, regressions with time series have ignored the issue of nonstationarity, proceeding as though the well-established properties of standard estimators hold even in the nonstationary environment. This complacency was upset by simulation studies by Granger and Newbold (1974) and analytical work by Phillips establishing that regression estimators and test statistics do not have standard distributions in models with nonstationary or integrated variables. At the same time Engle and Granger (1987) provided the framework of cointegration for modeling relations among integrated time series, and established the connection between cointegration and the dynamic error correction models that Hendry and his disciples had pioneered. Following the seminal work by Engle and Granger, published twenty years ago, there has been a flowering of research extending their ideas and applying these methods to a variety of estimation problems. During this section of the course you will be introduced to the statistical foundations, tests, and estimation procedures appropriate for work with integrated time series.
The second section of the course will cover simultaneous equations identification and estimation, extending coverage of these topics from ECON 7828. In particular, theorems of model identification will be proven, and procedures for checking identification in more general contexts will be developed. We will also consider the problem of weak instruments through a student presentation.
Evaluation and Administration
There will be one examination in this course at midterm, counting towards 30% of your course grade. There will also be some problem sets and computer exercises counting another 20% of the final grade. There will be no final exam, but we will reserve the final exam period for some student presentations. The remaining 50% of your grade will be based on your individual project (30%) and a class presentation of an article on econometric methodology (20%), both described below.
If you qualify for accommodations because of a disability, please submit to me a letter from Disability Services (DS) early in the semester so that your needs may be addressed. DS determines accommodations based on documented disabilities (303-492-8671, Willard 322, www.colorado.edu/sacs/disabilityservices)
I shall make every effort to accommodate all students who, because of religious obligations, have conflicts with scheduled exams, assignments, or other required attendance, provided I am notified well in advance of the scheduled conflict. Please notify me at least two weeks in advance of the conflict to request special accommodation. The campus policy concerning religious observances can be viewed at http://www.colorado.edu/policies/index.html.
The new Student Honor Code system has now been implemented in all schools and colleges. Please see http://www.colorado.edu/academics/honorcode/. If you have any specific questions about what constitutes plagiarism with respect to the assignments in this course, please raise them with me.
Individual Projects
You will each be responsible for an individual term project on an econometrics topic of interest to you. Your choice of topic should be related to the general areas described above (simultaneous equations problems or time series methods). Ideally your project should have both a theoretical or analytical component and an application, and the project should encompass a topic in econometrics that goes beyond what we cover in class. To make this assignment more concrete, an example of an appropriate project could involve allowing for structural breaks in tests of nonstationarity (unit roots). Although we will cover unit root testing in some depth, we will probably not cover this particular extension. There is a theoretical literature in which these tests are developed, and the analytical component of the project would present the statistical foundations behind these tests. Then the tests could be applied to one or more time series of interest as the applied component.
To assure that your project is appropriate, you should prepare a proposal describing (1) the econometric procedure you will investigate, (2) some key references to the relevant econometric theory, (3) the data set or model to which you plan to apply the procedure, and (4) the data sources. One or two pages should suffice for this proposal, and it should be submitted to me by February 10. Your final project is due on Thursday, April 29.
Computer Projects and Problem Sets
To get some practical experience with some of the econometric methods discussed in the course, you will complete several computer projects using EViews, which is available on our Economics Network. These projects are designed to give you some experience applying the procedures that are discussed in class. You will be asked to submit relevant output and answers to exercises requiring some interpretation of the output.
I will design several problem sets that require you to extend the mathematical presentation from class into new areas. Collaboration on the computer exercises and problem sets is acceptable, as long as you inform me about this in advance.
Article Presentation
In keeping with the seminar format, each student will be responsible for a presentation to the class of an article on econometric methodology. I have listed below a number of articles that would be appropriate for student presentations. Each of these is related to the major topics of the course, and presentations will be scheduled to fit with the course sequence. I am open to suggestions for other articles for presentation, as long as these fit within the major themes of the course. During the first two weeks of the class, you are urged to look over the titles below, examine any articles that sound interesting to you, and begin to sign up with me to reserve a presentation topic. I have copies of these papers that I can lend out for your examination. I will match presenters with articles during the first week of February, and give you a schedule of presentations. The tentative order of the presentations is given in the topical outline below.
Given the weight attached to this assignment (20%), you can see that considerable effort is expected to go into this presentation. You are encouraged to read a few related papers and/or the complementary pages in Maddala and Kim or Greene, to help put the article in a broader context. It should be possible to combine the topic for presentation with your individual project for some obvious complementarities. Your presentation will be based on the clarity of presentation, the use of visual aids, your ability to respond to questions from the class, and how well you motivate the topic in terms of its relation to this course or practical lessons for future research. If some articles are too long to present in one class period, we can discuss strategies for limiting the scope of the presentation.
Prior to the presentation all students are urged to read the either article or the corresponding pages from the text by Maddala and Kim. You can obtain the articles from me, or some can be printed from JSTOR accessible through the library's Webcat. In the past students have found it particularly useful if handouts presenting the main points of the presentation (e.g., copies of the slides or overheads) were made available for the group.
Articles for Student Presentations
Campbell, John and Pierre Perron, "Pitfalls and Opportunities: What Macroeconomists Should Know About Unit Roots," NBER Macroeconomics Annual 1991. Cambridge: MIT Press (1991). A survey of the implications of nonstationarity for traditional econometric practice, with critical comments by Cochrane and Miron.
Engle, Rob, David Hendry, and J. Richard, "Exogeneity," Econometrica 51 (1983) 277-304. This paper establishes the modern concept of exogeneity and related terms.
Engle, Rob, D. Lilien, and R. Robins, "Estimating Time-Varying Risk Premia in the Term Structure: The ARCH-M Model. Econometrica 55 (1987) 391-407. Extends the ARCH model to allow the conditional variance to enter the regression equation.
Freedman, David A., and Stephen C. Peters, "Bootstrapping a Regression Equation: Some Empirical Results," Journal of the American Statistical Association, vol. 79 (March 1984), 97-106. A very accessible presentation and application of the bootstrap procedure in a multiple equation regression model. See also MacKinnon (2002) in Additional Readings for a survey of more recent developments with this technique.
Granger, C.W.J. and P. Newbold, "Spurious Regressions in Econometrics," Journal of Econometrics 2 (1974), 111-120. A cautionary tale about regressions with integrated series, this is the first of several papers that have shown how spurious regressions can arise in a variety of situations.
Hahn, J. and Jerry Hausman, "A New Specification Test for the Validity of Instrumental Variables," Econometrica 70 (January 2002) 163-189. This paper deals with the problem of weak instruments which results in poor small sample properties of two-stage least squares estimators. See also Hahn and Hausman (2003) in the Additional Readings for a brief survey of work on this problem.
Hausman, J. A., "Specification Tests in Econometrics," Econometrica 46 (November 1978) 1251-1271. A single principle is applied to a variety of tests for model misspecification, including applications to simultaneous equations models.
Hylleberg, S., R.F. Engle, C.W.J. Granger, and B. S. Yoo, "Seasonal Integration and Cointegration," Journal of Econometrics 44 (1990) 215-28. Presents tests for integration and cointegration at the seasonal frequency.
Inder, Brett, "Estimating Long-Run Relationships in Economics," Journal of Econometrics
57 (1993) 53-68. This Monte Carlo study compares several least-squares approaches to the estimation of cointegrating relations.
Johansen, Soren, and Katarina Juselius "Identification of the Long-Run and the Short-Run Structure: An Application to the ISLM Model," Journal of Econometrics 63 (1994) 7-36. This article presents an approach to identification that combines both statistical and theoretical considerations. The rules for identification are applied specifically to cointegration equations.
King, R.G., C.I. Plosser, J.H. Stock, and M.W. Watson, "Stochastic Trends and Economic Fluctuations," American Economic Review 81 (September 1991) 819-840. Application of cointegration and common trends analysis to real business cycle model.
Kwiatkowski, Denis, et al. (KPSS) "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root," Journal of Econometrics 54 (1992) 159-178. Presents a test that reverses the null and alternative hypotheses from those of the Dickey-Fuller approach.
Maddala, G. S. and Shaowen Wu, "A Comparative Study of Unit Root Tests with Panel Data and a New Simple Test," Oxford Bulletin of Economics and Statistics Special Issue, 61 (1999) 631-652. One strategy for increasing the power of unit root tests is to combine several related time series into a pooled regression. A number of strategies for testing unit roots in panel data sets have been developed in recent years, and this paper provides a lucid review of the issues involved.
Mroz, Thomas A. "The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions," Econometrica 55 (July 1987) 765-800. This is an prominent example of a meta-analysis, analyzing the properties of alternative tests and estimators in a simultaneous equations context. The Mroz data set is available and often used for investigation of new tests or estimation procedures.
Nelson, Charles R., and Heejoon Kang, "Pitfalls in the Use of Time as an Explanatory Variable in Regression," Journal of Business and Economic Statistics 2 (1984) 73-82. The traditional practice in regression analysis with trended variables is to control for deterministic trends. This article shows what happens under such treatment if the variables actually have stochastic trends.
Pantula, S.G., G. Gonzalez-Farias, and W.A. Fuller, "A Comparison of Unit-Root Test Criteria," Journal of Business and Economic Statistics 12 (October 1994) 449-459. Presents several extensions of the Dickey-Fuller test and evaluates these in a Monte Carlo study.
Perron, P. "The Great Crash, the Oil Shock, and the Unit Root Hypothesis," Econometrica 57 (1989) 1361-1402. The seminal paper in a growing literature that considers tests for unit roots in the context of possible structural breaks.
Schwert, G.W., "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business and Economic Statistics 7 (1989) 147-59. One of the first Monte Carlo investigations of the comparative properties of several unit root tests. This paper is also an good introduction to the Monte Carlo method.
Sims, Christopher, "Macroeconomics and Reality," Econometrica 48 (January 1980) 1-49. The classic presentation of Sims' VAR methodology and critique of traditional structural econometric methods.
Stock, J.H., and M.W. Watson,"A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica 61 (1993) 783-820. Consistent with the title, the authors present a least-squares based approach to estimating cointegrating relations that can be used with systems involving I(1), I(2), or higher orders of integration.
Texts
Maddala, G. S., and In-Moo Kim, Unit Roots, Cointegration, and Structural Change Cambridge: Cambridge University Press (1998)
Greene, William H., Econometric Analysis fifth edition, Upper Saddle River, New Jersey: Prentice-Hall (2003).
Topics, Reading Assignments, and Student Article Presentations
I. Statistical Inference with Integrated Variables.
A. Basic concepts and statistical foundations.
Maddala and Kim, chapters 1, 2 and 3.1-3.2.
Greene, Sections 18.1-18.3
B. Unit root tests.
Maddala and Kim, chapters 3, 4.
Student presentations:
Pantula, et al. (1994); Maddala and Kim, 4.2 and 4.3
Kwiatkowski, et al. (1992); Maddala and Kim, 4.5
Maddala and Wu (1999); Maddala and Kim, 4.9
Schwert (1989); Maddala and Kim, 4.2
Computer exercise: unit root testing
Computer exercise: programming Eviews for a Monte Carlo experiment
C. Testing and Estimation of Cointegrating Relations.
Maddala and Kim, chapters 5, 6.
Student Presentations:
Phillips and Loretan (1991); Maddala and Kim, 5.4
King, et al. (1991)
Computer exercise: cointegration testing and estimation
Midterm Examination
D. Properties of regression estimators and test statistics in models with integrated variables.
Student Presentations:
Campbell and Perron (1991); Maddala and Kim, chapter 7
Nelson and Kang (1984)
Granger and Newbold (1974)
E. Extensions; Student presentations
ARCH models: Engle, Lilien, Robins (1987); Greene, 17.4
Seasonal unit roots: Hylleberg, et al. (1990); Maddala and Kim, 12.1-12.3
Unit roots and structural breaks: Perron (1989); Maddala and Kim, 13.1-13.7
Higher order systems: Stock and Watson (1993) Maddala and Kim, chapter 11.
Computer exercise: ARCH testing and modeling.
II. Simultaneous Equations Models
A. Identification
Greene, Sections 16.1-16.3
Student presentation:
Johansen and Juselius (1994); Maddala and Kim, 5.6
C. Estimation.
Greene, Sections 16.4-16.7
Student Presentation:
Engle, Hendry and Richard (1983)
Mroz (1987)
D. Specification tests;
Student Presentation:
Hausman (1978); Greene, Section 16.8
E. The Bootstrap: Freedman and Peters (1984); Maddala and Kim, chapter 10
(Final Exam Period - reserved for student presentations: Monday, May 3, 4:30-7:00 p.m.
Our texts contain numerous references to additional literature. In addition to these, the following references are included for further reading, with an emphasis on time series econometrics.
Banerjee, Anindya, Juan Dolado, John Galbraith, and David Hendry, Cointegration, Error Correction and the Econometric Analysis of Non-Stationary Data. Oxford: Oxford University Press (1993. A textbook covering both theoretical and practical issues in unit root testing and cointegration. This text is a level above Enders' text in theoretical rigor, but not as demanding and Hamilton's text.
Campbell, John and Pierre Perron, "Pitfalls and Opportunities: What Macroeconomists Should Know About Unit Roots," NBER Macroeconomics Annual 1991. Cambridge: MIT Press (1991). A survey of the implications of nonstationarity for traditional econometric practice, with critical comments by Cochrane and Miron.
DeJong, D.N. et al. "Integration vs. Trend Stationarity in Macroeconomic Time series," Econometrica 60 (1992) 423-434.
DeJong, D.N., and C. H. Whiteman, "Reconsidering Trends and Random Walks in Macroeconomic Time Series," Journal of Monetary Economics, 28 (1991) 221-254. A pair of articles that presents a forceful critique of unit root testing and the conclusion that most macroeconomic time series are I(1).
Dickey, David, William Bell and R. Miller, "Unit Roots in Time Series Models: Tests and Implications," American Statistician 40 (1986) 12-26. A readable presentation, with empirical examples, of the Dickey-Fuller tests for unit roots.
Doldado, Juan, Tim Jenkinson, and Simon Sosvilla-Rivero, "Cointegration and Unit Roots," Journal of Economic Surveys 4 (1990) 249-73. A survey of this literature up to 1990.
Enders, Walter, Applied Econometric Time Series New York: Wiley (1995). A practical text on various time series topics including ARIMA modeling, unit root tests, ARCH models, vector autoregressions, and cointegration.
Engle, Rob, and C.W.J. Granger, "Cointegration and Error-Correction: Representation, Estimation and Testing," Econometrica 55 (March 1987) 251-76. The original presentation of the concept of cointegration and its connection to error correction models.
Engle, Rob, and C.W.J. Granger, (eds.) Long-Run Economic Relationships: Readings in Cointegration Oxford: Oxford University Press (1991). A collection of readings on cointegration.
Hahn, Jinyong, and Jerry Hausman, "Weak Instruments: Diagnosis and Cures in empirical Econometrics," American Economic Review 93 (May 2003) 118-125. This is a brief survey of the problem of weak instruments in two-stage least squares estimation.
Hamilton, James, Time Series Analysis Princeton: Princeton University Press (1994). A comprehensive and often advanced presentation of time series analysis. Includes statistical distribution theory relevant to nonstationary processes.
Handbook of Econometrics, volumes 1-4, Amsterdam: North Holland. Of particular relevance to our topics on time series are two chapters in volume 4: Chapter 46 by James Stock, "Unit Roots, Structural Breaks, and Trends" and Chapter 47 by Mark Watson, "Vector Autoregression and Cointegration." These chapters update earlier surveys of these topics with numerous references to theoretical and applied papers.
Harris, Richard, Using Cointegration Analysis in Econometric Modelling London: Prentice Hall (1995). This is a hands-on text with examples demonstrating how to do empirical analysis with nonstationary data.
Harvey, Andrew, Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge: Cambridge University Press (1989). Harvey promotes the use of state space models, estimated by the Kalman filter, as an approach to capturing stochastic trends and short term fluctuations characteristic of economic time series. This is an alternative to the Box-Jenkins and Dickey-Fuller approaches emphasized in the class.
Johansen, Soren, Likelihood-Based Inference in Cointegrated Vector Autoregressive Models, Oxford: Oxford University Press (1995). This is a comprehensive presentation of Johansen's maximum likelihood approach to modeling, estimating, and testing systems of cointegrating relations.
Johansen, Soren, and K. Juselius, "Maximum Likelihood Estimation and Inference on Cointegration: with Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, vol. 52 (1990) 169-210. This is a fairly accessible presentation of Johansen's maximum likelihood approach to cointegration modeling with a useful empirical example.
Journal of Business and Economic Statistics 10 (June 1992). A special issue devoted to tests of unit roots and structural change. Tests with unknown break points are presented by Perron and Vogelsang, and by Zivot and Andrews.
Journal of Econometrics volume 80, No. 2 (1997) is a special issue on cointegration and dynamics in econometrics. Especially recommended are Li and Maddala's article on bootstrapping of cointegrating regressions, and Entorf's paper on spurious regressions in a panel data model.
Journal of Economic Dynamics and Control volume 12 (June-Sept. 1988) is a special issue containing some early and important papers on unit roots and cointegration.
Journal of Economic Surveys volume 12, no. 5 (December 1998) A special issue of surveys on practical issues in unit root testing and cointegration. The article by Haldrup is a fairly intelligible paper on I(2) modeling.
Journal of Policy Modeling volume 14 (August 1992) is a special issue on Cointegration, Exogeneity, and Policy Analysis.
MacKinnon, James G. "Bootstrap Inference in Econometrics," Canadian Journal of Economics 35 (November 2002) 615-645. this Presidential Address surveys some recent developments in bootstrap simulation techniques with particular insights into when this technique is likely to perform well.
Nelson, Charles, and Charles Plosser, "Trends and Random Walks in Macroeconomic Time Series: Some Evidence and Implications," J. of Monetary Economics 10 (1982) 130-62. An early application of unit root tests to economic time series. They find most of the series studied to be integrated, a result contested by later researchers using different methods. Their data set is available for further investigations.
Ng. Serena, and Peirre Perron, "Unit Root Tests in ARMA Models with Data-Dependent Methods for the Selection of the Truncation Lag," J. of the American Statistical Association 90 (March 1995) 268-281. This paper studies alternative methods for selecting the lag length in the Dicky-Fuller equation and presents simulation evidence that supports the search procedure advocated in this course.
Oxford Bulletin of Economics and Statistics volume 48 no. 3 (1986) is a special issue containing early papers on cointegration and error correction models.
Oxford Bulletin of Economics and Statistics Volume 54, No. 3 (August 1992) is another special issue on Testing Integration and Cointegration.
Oxford Bulletin of Economics and Statistics Volume 61, No. 4 (Supplement 1999) is a special issue on panel unit root and cointegration. The article my Maddala and Wu is a particularly useful review of the various unit root tests that have been proposed.
Perron, Pierre, "Testing for a Unit Root in a Time Series with a Changing Mean," Journal of Business and Economic Statistics 8 (1990) 153-62.
Perron, Pierre, "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica 60 (January 1992) 119-43.
The first of this pair or articles presents the test of a unit root against the stationary alternative with change in mean or change in trend slope. The second applies the test to the Nelson-Plosser data.
Phillips, Peter, and Mico Loretan, " Estimating Long Run Economic Equilibria," Review of Economic Studies 58 (1991) 407-36. They review several procedures for estimating cointegrating equations, including a quite straightforward, single-equation procedure that is efficient and yields asymptotically valid test statistics.
Zellner, Arnold, and Franz Palm, "Time Series Analysis and Simultaneous Equation Econometric Models," Journal of Econometrics, vol 2 (1974), 17-54. Shows the correspondence between structural econometric models (SEM) and various time series models, and employs this correspondence to design tests of the underlying SEM.