ECONOMETRICS-2

4th Module, 2002/2003

Professor: Dr. Pavel Katyshev, pkatish@nes.ru,  room 908,

TAs:

• Sergei Golovan, sgolovan@nes.ru,
• Vitaliy Kazakov, vkazakov@nes.ru,
• Kanat Khusainov, khusaino@nes.ru,
• Dmitry Shakin, dshakin@nes.ru.

General Information: This course is a continuation of the course "Econometrics-1". This course meets Mondays and Wednesdays, Sections meets Wednesdays. Office hours are Mondays, Wednesdays room 908, from 17:45-18:45. If you have any questions come and ask.

Texts:

The main textbook for this course is:

• П.К.Катышев, Я.Р.Магнус, А.А.Пересецкий. Эконометрика. Начальный курс. 5-е издание, Дело, Москва, 2001.

Supplementary reading.

1)       С.А.Айвазян, В.С.Мхитарян, Прикладная статистика и основы эконометрики, ЮНИТИ, Москва, 1998.

2)       R.S. Pindyck & D.L. Rubinfeld, Econometric Models and Economic Forecasts, 3^rd edition, McGraw Hill, 1991.

3)       J.Johnston, J.DiNardo, Econometrics Methods, 4^th edition, McGraw-Hill, 1997.

4)       J.D.Hamilton, Time Series Analysis, Princeton University Press, 1994.

5)       П.К.Катышев, А.А.Пересецкий, Сборник задач к начальному курсу эконометрики. Дело, Москва, 3-е издание, 2001.

Project. Two projects will be suggested to students. Students can work on projects in teams (no more than four students in a team). First project reports are due April 2, second project reports are due April 23.

Homework and Exams. Homework will be assigned and will be due each Wednesday. Homework will be graded. There will be only final exam. Tentative dates are:

Projects deadline            April 2 and April 23, 2003
Final exam                April 28, 2003 (the date could be revised).

Policy on examination.  A4 - format paper with your own notes. Xerox copies, printed outputs, books are not allowed.

Grading. The homework, the project, final exam will have the following weights:

            Homework            0.15
            Projects            0.25
            Final exam            0.60

The final grade will be based on the final score, which is a weighted average of the homework, the projects and the final exam.

Bonus points. Students, who will be active during classes, may gain extra points to their scores.

COURSE OUTLINE

I. MAXIMUM LIKELIHOOD ESTIMATION

Two lectures

1.       Maximum likelihood estimation (MLE): examples and formal treatment.

2.       Properties of ML estimators.

3.       Three general criteria for testing hypothesis: likelihood ratio test, Wald test, Lagrange multipliers test.

4.       MLE for linear regression model.

5.       Likelihood ratio, Wald, Lagrange multipliers tests in classical regression model for testing general linear restriction.

II. MODELS WITH LIMITED DEPENDENT VARIABLES

Four lectures

1.       Discrete dependent variables: qualitative (nominal), ranking, counted dependent variables.

2.       Binary choice models. Linear probability model. Probit and Logit models. Interpretation of the coefficients in binary choice models. Maximum likelihood estimates in Probit and Logit models.

3.       Specification errors in binary choice models. Multi-choice models.

4.       Models with truncated and censored dependent variables. Tobit model. Biasedness and inconsistency of OLS estimates. ML estimates.

5.       Sample selection. Tobit-2 (Heckman) model.

6.       Duration models.

III. MODELS WITH LAGGED VARIABLES AND TIME SERIES

Six lectures

1.  Models with lagged variables.
Distributed lags models.
Estimation of the distributed lags models. Polynomial lags (method Almon). Geometric lags (Koyck model).

2.  Dynamic models.
Autoregressive model with autocorrelated errors. Estimation. Tests for error autocorrelation (Durbin and Lagrange multiplier tests).
Examples of the models with lagged variables. (Partial adjustment model, adaptive expectation model, error correction model). Granger causality test.

3.  Unit roots and cointegration.
Stationarity. Random walk. AR(p) process. Unit roots. Dickey-Fuller statistic. Augmented Dickey-Fuller test. Spurious regression. Cointegration. Engel and Granger approach. MakKinnon statistic. Cointegration vector. Long-run dynamic equilibrium.

4.  Box-Jenkins model (ARIMA).
Trend, seasonality, differenciing. Tests for stationarity. ACF and PACF. Yule-Walker equations. MA models. Invertibility. Properties of ARMA models.
Box-Jenkins methodology. Model identification. Estimation and diagnostic checking. Ljung-Box test. Akaike and Schwarz criteria. Forecasting with an ARIMA models. Seasonal ARIMA models.

6.       GARCH models.
ARCH, GARCH, ARCH-M, E-GARCH models. Lagrange multiplier test for ARCH. Estimation methods.

III. SYSTEMS OF REGRESSION EQUATIONS

Two lectures

1.       Seemingly unrelated regression (SUR).

2.       Simultaneous equations (SE). Structure and reduced form of the system. Identification. Order and rank conditions.

3.       Estimation of SE: indirect least squares, two-step least squares.