Module 3, 2000/2001
January 15, 2001

Instructors:

Dr. Pavel Katyshev pkatish@nes.ru, room 908,
Dr. Anatoly Peresetsky, perstsky@cemi.rssi.ru, room 908,

TAs:

Sergei Golovan sgolovan@nes.ru,
Dmitry Shapiro dmshapir@nes.ru

General Information. This course is designed to be a first course in econometric theory. The students are assumed to have sufficient background in statistics and mathematics (matrix alge-bra).

This course meets Mondays 14:30, Wednesdays 12:00, Sections meets Wednesdays 14:30. 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. 3-е издание, Дело, Москва, 2000.

Project. A project will be suggested to students. Students can work on projects in teams (no more than four students in a team). Project reports are due February 28.

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:

Project deadline February 28, 2001
Final exam March 6, 2001 (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 homeworks, the project, final exam will have the following weights:

Homework 0.15
Project 0.25
Final exam 0.60

The final grade will be based on the final score, which is a weighted average of the homeworks, the project and the final exam. But less than 25% on the final means failed.

Bonus points. Students, who will be firsts to find misprints in the main textbook, may gain extra points to their scores.

Tentative topic sequence

Lecture 1. Introduction.

Models, why we need them, time series models, regression models, cross sections and time series. The 2-variable regression model, curve fitting, loss functions (sum-of-squares, Huber's, sum-abs-values), deviations. Ordinary Least Squares, First Order Conditions (derived from min loss function), geometric interpretation of OLS (in Rⁿ). Analysis of variance, goodness of fit: ESS, TSS, RSS, R², geometric interpretation of R². R² as sample correlation between y and , R² if constant not included.

Lecture 2. 2-variable Linear Regression.

Classical Linear Regression Model. Source of stochasticity in error term. Basic assumptions, homoscedasticity, heteroscedasticity, serial correlation. Normally distributed errors. Statistical properties of OLS estimations. Gauss-Markov Theorem, discussion of basic assumptions, proof.

Lecture 3. 2-variable Linear Regression (continued).

Distributions of , covariance, independence of and with . Errors and residuals. Testing hypothesis , critical values, significance level, P-value, confidence intervals. Testing regression equation, discussion on R² and t-, F-statistics. Maximum likelihood estimation,

Lecture 4. k -variable Linear Regression.

The multiple regression model, matrix algebra, random vectors, n-dimensional normal distribution, OLS estimator, unbiasedness of , Gauss-Markov theorem (proof). Geometric interpretation. Estimation of . Residuals and their properties, independence of and . R² and adjusted R².

Lecture 5. k-variable Linear Regression (continued) confidence intervals and hypothesis testing.

Confidence intervals and confidence regions for the coefficients. t-statistics for . F-test for general linear restriction , and particular cases. Test Chow.

Two versions of F-test, proof of their equality.

Lecture 6. k-variable Linear Regression (continued).

Multicollinearity (geometrical interpretation, examples), non-stability of estimates, interpretation of regression coefficients. Partial correlation, stepwise regression. Dummy variables (examples, testing for significance of dummies). Dummy variables and test Chow.

Lecture 7. k-variable Linear Regression (continued).

Model specification error, omitted variables, irrelevant variables, short and long regression.

Lecture 8. k-variable Linear Regression (continued).

GLS estimator. Properties of OLS estimates in the violation of homoscedasticity. Aitken theorem. Feasible GLS. Some examples when error covariance matrix depends on few number of parameters. Weighted least squares.

Lecture 9. GLS and Heteroscedasticity.

Estimation in the presence of heteroscedasticity and tests for heteroscedasticity: Goldfeld-Quandt test, Breusch-Pagan test, White test. Two-step procedure.

Lecture 10. Serial correlation.

Autoregressive errors. Estimation, Cochran-Orcutt procedure, Hildtreth-Lu procedure. Tests for serial correlation: Durbin-Watson (DW), Durbin's h-statistic. Underestimations of standard errors of coefficients if serial correlation is present.

Lecture 11. Stochastic regressors and exogeneity problem.

Stochastic regressors. Two cases: regressors uncorrelated and correlated with errors. Biasedness and inconsistency of OLS in the second case. Measurement errors.

Lecture 12. Instrumental variables.

Example of endogenous regressors: supply-demand equation. Instrumental variables. Geometric interpretation of IV. The problem of IV selection. Hausmann test.

Lecture 13. Forecasting.

Forecasting in regression models. Point and interval forecasting. Unconditional and conditional forecasting. Forecasting with serially correlated errors.

Supplementary reading.

1. R.S. Pindyck & D.L. Rubinfeld, Econometric Models and Economic Forecasts, 3^rd edition, McGraw Hill, 1991.
2. W.H.Greene, Econometric Analysis, 3^rd edition, Prentice Hall, 1997.
3. J.Johnston, J.DiNardo, Econometrics Methods, 4^th edition, McGraw-Hill, 1997.
4. П.К.Катышев, А.А.Пересецкий, Сборник задач к начальному курсу эконометрики. Дело, Москва, 1999.