INTERMEDIATE ECONOMETRICS
(ECONOMETRICS III)
http://www.nes.ru/~sanatoly/Econometrics3/Econometrics3.htm

5th Module, 2002/2003

Instructor: Stanislav Anatolyev

The course serves as an introduction to principles of contemporary art of econometric estimation and inference, when applied in both cross-sectional and time-series setting. Motivated by dissatisfaction with exact inference, we consider competing alternatives: asymptotic approximation and bootstrap. Then, after having reviewed certain important econometric notions, we will focus on estimation and inference in a linear environment. At the end, however, we will study some simple nonlinear models and methods. Emphasis will be put on conceptual content rather than mathematical sophistication, although the latter is sometimes unavoidable. The assigned exercises will include regular problems as well as computer tasks based on GAUSS. Home assignments serve as an important ingredient of the learning process.

ORGANIZATION

There will be six weekly homework assignments that account for 20% of the final grade. The assignment will contain both analytical problems and computer exercises. Solutions for computer exercises can be submitted one for a group of 2 or 3 students. The groups should be determined at the beginning and should not change during the module. Suggested solutions will be distributed. The Problems and Solutions manual contains additional problems for independent work and discussion in sections. The final exam, which accounts for 80% of the grade, will have an open-book format.

MAIN TEXTS AND MANUALS

· Анатольев, С. (2002) Курс лекций по эконометрике для продолжающих, Российская Экономическая Школа

· Anatolyev, S. (2002) Intermediate and Advanced Econometrics: Problems and Solutions, Sections 1–5, New Economic School

ADDITIONAL LITERATURE

· Hayashi, F. (2000) Econometrics, Princeton University Press

· Goldberger, A. (1991) A Course in Econometrics, Harvard University Press

· Greene, W. (2000) Econometric Analysis, 4^th edition, Prentice Hall

SYLLABUS

I. Approximate Inference

1.       Three approaches to inference

·         Three approaches to inference: exact, asymptotic, bootstrap.

·         Problems with exact inference.

2.       Asymptotic approach: independent data

·         Modes of convergence of sequences of random variables.

·         Laws of Large Numbers (LLN).

·         Rates of convergence. Central Limit Theorems (CLT).

·         Continuous mapping theorems. Delta-method.

·         Asymptotic confidence intervals and large sample hypothesis testing.

3.       Asymptotic approach: time series data

·         Measures of dependence. Stationarity and ergodicity. Martingale difference sequence.

·         Ergodic Theorem.

·         CLT for martingale difference sequences. CLT for general stationary sequences.

·         Heteroskedasticity and autocorrelation consistent estimators: Hansen–Hodrick, Newey–West, Andrews.

·         Introduction to asymptotic inference in models with nonstationary data.

4.       Bootstrap approach: independent data

·         Data and empirical distribution function.

·         Approximation by bootstrapping and approximation by simulation.

·         Nonparametric bootstrap in linear mean regression model. Parametric bootstrap.

·         Bootstrap bias correction.

·         Bootstrap confidence interval and hypothesis testing.

·         Why does bootstrap work? Asymptotic refinement and asymptotic expansions.

5.       Bootstrap approach: time series data

·         Residual bootstrap.

·         Overlapping and non-overlapping block bootstrap.

·         Stationary bootstrap.

II. Econometric Concepts

1.       Conditional expectations and best linear predictors

·         Conditional expectation function.

·         Linear predictors and best linear predictors.

·         Multivariate normal distribution.

2.       The analogy principle

·         Identification vs. estimation.

·         Population values and sample analogs.

·         Analogy principle.

3.       Regression concepts

·         Notion of regression. Mean, median and quantile regressions.

·         Sample. Random sampling.

·         Parametric, semiparametric and nonparametric estimation.

III. Parametric Estimation of Linear Models

1.       Estimation of a linear mean regression

·         OLS estimator in linear mean regression model.

·         Asymptotic inference in linear mean regression model.

·         Efficiency and GLS estimator in linear mean regression model.

·         Skedastic regression. Feasible GLS estimation and its asymptotics.

·         Linear regression with generated regressors: estimation and inference.

·         Time series linear regression.

2.       Instrumental variables in a linear model

·         Endogeneity and simultaneity. Errors in variables.

·         Instrumental variables. Validity and relevance of instruments.

·         Just identified model and IV estimator.

·         Overidentified model and 2SLS estimator.

·         Asymptotic inference in instrumental variables regression.

·         Instrumental variables in time series models.

IV. Introduction to Parametric Estimation of Non-Linear Models

1.       Non-linear mean regression

·         Nonlinear LS estimator in non-linear mean regression model.

·         Computation of NLLS estimate: concentration method and linearized regression.

·         Asymptotic inference in non-linear mean regression model.

·         Efficiency and Weighted NLLS estimator.

·         Example: binary choice model.

·         Inference when nuisance parameters are not identified under null hypothesis.

2.       Non-linear regression with instrumental variables

·         Nonlinear instrumental variables estimation.

·         Nonlinear 2SLS estimation.