This course will provide fundamental econometric tools for Ph. D. or advanced Master students. It is designed to prepare the student for doing thesis or dissertation and understanding the track of Econometrics. Knowledge of basic Statistics and Econometrics is required for this course. The course is divided into two parts. The first half we will study the mathematical (statistical) foundation for Econometrics. The second half is the advanced tools of asymptotic analysis for Econometrics. After being familiar with these material, students can understand what the content of most formidable papers. This is a course of theoretical Econometrics not an application one. However, the programming software can help students to understand the theory behind. Some programming software can be used in this course are Gauss, Matlab or Sas IML. Students should be able to operate one after this course.

· Course requirements: Lectures, readings, midterm and final exams, several home works. A short term paper is optional.

· Textbooks

1. Ramanathan, Ramu, (1993), Statistical Methods in Econometrics, Academic Press.

2. White, Halbert, (2000), Asymptotic Theory for Econometricians: Revised Edition, Academic Press.

· Reference Textbooks

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

2. Greene, W.H. (2002), Econometrics Analysis, 5th edition, Prentice-Hall.

3. Hamilton, (1994), Time Series Analysis, University of Princeton Press.

4. Johnston, J. and J. Dinardo (1998), Econometric methods, 4th Edition, McGraw-Hill.

5. Kennedy, P. (2003), A Guide to Econometrics, 5th edition, the MIT Press.

6. Mittelhammer, Ron C., George G. Judge, and Douglas J. Miller. (2000), Econometric Foundations, Cambridge University Press, New York.

7. Wooldridge, J.M. (2002), Introductory Econometrics: A Modern Approach, 2nd edition, South Western College Publishing.

· Lecture notes

1. Hansen, B. (2005), Econometrics, University of Wisconsin,

http://www.ssc.wisc.edu/~bhansen/notes/notes.htm

2. Weber, A. (2003), Lecture Notes: Econometrics I, Institute for Advanced Studies, Austria, http://elaine.ihs.ac.at/~webera/rlecture.pdf

Topics

Basic Probability

Random Variables and Distributions.

Some Special Distributions

Multivariate Distributions.

Sampling Theory

Asymptotic Distribution Theory.

Estimation.

Tests of Hypothesis.

Multiple Regression.

Functional Forms and Dummy Variables

Nonspherical Disturbances.

Midterm

The Linear Model and Instrumental Variables Estimators

Consistency

Laws of Large Numbers

Asymptotic Normality

Central Limit Theory

Estimating Asymptotic Covariance Matrices

Functional Central Limit Theory and Applications

Directions for Further Study

Final

Software: I recommend to students who want to carry out research in Econometrics or Applied Finance/Economics to use Gauss or Matlab (or Octave, its freeware version) or S-Plus (or R, its freeware version). The rest can use E-views or any other statistical package.

LeSage, J.P. (1999) Applied Econometrics using MATLAB. (Available at

http://www.spatial-conometrics.com/html/mbook.pdf).

GAUSS Source Code Archive at American University. (Available at

http://www.american.edu/academic.depts/cas/econ/gaussres/GAUSSIDX.HTM)

MATLAB Tutorials.

http://www.cyclismo.org/tutorial/matlab/

http://www.math.siu.edu/matlab/tutorials.html

http://www.engin.umich.edu/group/ctm/basic/basic.html

Gauss

http://www.wws.princeton.edu/~mwatson/ec518/gauss_tutorial.html

http://www.arec.umd.edu/gauss/gauss.htm

www.aae.wisc.edu/aae636/gausscode/nerlove/Basics.doc

Others: Tex, Latex, Scientific wordplace, Word2tex, Tex2word

Textbook:

Ramanathan, Ramu, (1993), Statistical Methods in Econometrics, Academic Press.

Book Description

This book is appropriate for beginning graduate courses in mathematical statistics and econometrics in which the foundations of probability and statistical theory are developed for application to econometric methodology. Because econometrics generally requires the study of several unknown parameters, emphasis is placed on estimation and hypothesis testing involving several parameters. Accordingly, special attention is paid to the multivariate normal and the distribution of quadratic forms. Lagrange multiplier tests are discussed in considerable detail, along with the traditional likelihood ration and Wald tests. Characteristic functions and their properties are fully exploited. Also asymptotic distribution theory, usually given only cursory treatment, is discussed in detail.
The book assumes a working knowledge of advanced calculus (including integral calculus) basic probability and statistics, and linear algebra. Important properties from matrix algebra are summarized in the appendix. Numerous examples, exercises, and practice problems are included.

White, Halbert, (2000), Asymptotic Theory for Econometricians: Revised Edition, Academic Press.

Book Description
This book provides the tools and concepts necessary to study the behavior of econometric estimators and test statistics in large samples. An econometric estimator is a solution to an optimization problem; that is, a problem that requires a body of techniques to determine a specific solution in a defined set of possible alternatives that best satisfies a selected object function or set of constraints. Thus, this highly mathematical book investigates situations concerning large numbers, in which the assumptions of the classical linear model fail. Economists, of course, face these situations often.

Key Features
* Completely revised Chapter Seven on functional central limit theory and its applications, specifically unit root regression, spurious regression, and regression with cointegrated processes
* Updated material on:
* Central limit theory
* Asymptotically efficient instrumental variables estimation
* Estimation of asymptotic covariance matrices
* Efficient estimation with estimated error covariance matrices
* Efficient IV estimation

Lecture Progress

09/18 Ramanathan Chapter 1,2,3

09/25 Ramanathan Chapter 4,5

10/2 Ramanathan Chapter 6,7

10/9 Ramanathan Chapter 8

10/16 Ramanathan Chapter 9

10/23 出國開會No class

10/30 Ramanathan Chapter 10,11

11/6 Ramanathan Chapter 12 White 1

11/13 期中考

11/20 White Chapter 2,3

11/27 White Chapter 4

12/4 White Chapter 5

12/11 White Chapter 6

12/18 White Chapter 7

12/25 White Chapter 7

1/1 No class

1/8 White Chapter 8

1/15 期末考

Class Presentation

09/18 Econometric methodology

09/25 Bayesian

10/2 Application of log-normal distribution or exponential family

10/9 Application of extreme value distribution to VaR

10/16 Numerical Optimization procedure

10/23 出國開會No class

10/30 Misspecification test

11/6 Model selection criteria

11/13 期中考 Multicollnearity

11/20 Application of IV & GMM

11/27 Bootstrapping, MCMC, Gibbs Sampler

12/4 Nonparametric (Kernel) estimation

12/11 Q-MLE

12/18 Var-cov estimation

12/25 Unit root test

1/1 No class

1/8 Panel unit root

1/15 期末考