Statistics for Econometrics

Course content:
This is the first course in an econometrics sequence at the graduate level. It covers a large
number of topics fairly quickly to prepare students for subsequent econometrics courses. The
course is based directly on Appendices A–D in the Greene text and includes:
A. Matrix algebra
B. Probability and distribution theory
C. Estimation and inference
D. Large sample distribution theory

Pre-requisites:
1. MTH 253 (Infinite Series and Sequences)
2. ST 351 (Intro to Statistical Methods)
3. ST 352 (Intro to Statistical Methods) or ECON 424/524 (Intro to Econometrics)

Meeting time:
Lecture: Monday & Wednesday, 10:00-11:20, Ballard 118
Lab: Friday, 1:00-1:50, MCC 201

(1) Mathematics for Economists , by Simon and Blume. Good reference for matrix algebra,
linear independence , optimization, sequences, and other relevant topics.
(2) Introduction to the Theory and Practice of Econometrics, by Judge, Hill, Griffiths,
Lutkepohl, and Lee. Has nice summary of the topics in this course.
(3) Principles of Econometrics, by Hill, Griffiths, and Lim. Has same advantages as (2), but at
(4) Introduction to Mathematical Statistics, by Hogg and Craig. A good supplementary text for
learning the material in Greene Appendixes B-D.
(5) Statistical Inference, by Casella and Berger. An alternative to (4) for learning classical
statistics; commonly used by statistics graduate programs.
(6) Mathematical Statistics with Applications, by Wackerly, Mendenhall, and Scheaffer. At a
lower level than (4) or (5). Used in ST 521 and 522 at Oregon State.

Evaluation of student performance:
Your course grade will be based on three problem sets using SAS-IML (15% total), two
midterms (25% each), and a final exam (35%). If a SAS-IML problem set is late it may be
turned in any time until the last day of class. However, your score will be lowered by 30%.

Students with Disabilities:
Accommodations are collaborative efforts between students, faculty and Services for
Students with Disabilities (SSD). Students with accommodations approved through SSD are
responsible for contacting the faculty member in charge of the course prior to or during the
first week of the term to discuss accommodations. Students who believe they are eligible
for accommodations but who have not yet obtained approval through SSD should contact
SSD immediately at 737-4098.

Expectations for Student Conduct (cheating policies):
Oregon State University defines academic dishonesty as: “An intentional act of deception in
which a student seeks to claim credit for the work or effort of another person or uses
dishonesty includes: Cheating, Fabrication, Assisting, Tampering, Plagiarism.

Topics Covered (See the Greene text regarding the level of treatment. Depth of coverage varies.)

Greene Appendix A. Matrix Algebra
Structure of matrices and vectors
Vector and matrix operations
Identity matrix
Projection matrices
Vector spaces and basis vectors
Linear independence
Determinants
Rank
Systems of equations
Properties of inverses
Orthogonality and the least squares problem
Kronecker products
Characteristic roots and vectors
Trace
Symmetric matrices
Applications: Comparing the ‘size’ of two matrices; finding the inverse of symmetric matrix

Greene Appendix B. Probability and distribution theory
Random variables
Distribution functions
Expectations
Moments of random variables
Moment generating functions
Important probability distributions
Joint densities
Covariance and Correlation; Independence
Conditional distributions
Regression: The conditional mean
Functions of random variables
Distributions of functions of variables: Change of variable technique
Distributions of functions of variables: Moment generating technique
Multivariate distributions

Greene Appendix C. Estimation and inference
Types of non-experimental data
Sampling; definition of a random sample
Statistical inference
Descriptive Statistics
Estimators vs. estimates
Statistical models
Ways of estimating parameters
Point and interval estimates
Method of moments
Maximum likelihood
Sampling distributions, and picking the ‘best’ estimator
Least squares
Unbiasedness; how to calculate bias
Precision (variance)
Mean squared error
Efficiency: Minimum variance unbiased estimator
Information matrix
Cramér-Rao lower bound
Linearity

Greene Appendix D: Large sample distribution theory
Sequences of random variables
Limit laws
Convergence in probability
Chebyshev’s inequality
Convergence in mean square
Consistency
Khinchine’s weak law of large numbers
Convergence in distribution
Lindberg-Levy univariate central limit theorem

 Fall 2008 Schedule (Make-up exams are generally offered only for verifiable emergencies) Monday, September 29 Lecture 1 - App. A (Matrix algebra) Wednesday, October 1 Lecture 2 - App. A (Matrix algebra) Friday, October 3 No lab Monday, October 6 Lecture 3 - App. A (Matrix algebra) Wednesday, October 8 Lecture 4 - App. A (Matrix algebra) Friday, October 10 Lab lecture on SAS/IML Monday, October 13 Lecture 5 - Finish App. A, begin App. B Wednesday, October 15 Lecture 6 - App. B (Probability and distribution theory) Friday, October 17 Teaching Assistant is available in lab Monday, October 20 Exam 1 (80 minutes) Wednesday, October 22 Lecture 7 - App. B (Probability and distribution theory) Friday, October 24 HW 1 due at beginning of lab; HW 2 handed out Monday, October 27 Lecture 8 - App. B (Probability and distribution theory) Wednesday, October 29 Lecture 9 - App. B (Probability and distribution theory) Friday, October 31 Teaching Assistant is available in lab Monday, November 3 Lecture 10 - App. B (Probability and distribution theory) Wednesday, November 5 Lecture 11 - App. B (Probability and distribution theory) Friday, November 7 HW 2 due at beginning of lab; HW 3 handed out Monday, November 10 Lecture 12 - App. C (Estimation and inference) Wednesday, November 12 Exam 2 (80 minutes) Friday, November 14 Teaching Assistant is available in lab Monday, November 17 Lecture 13 - App. C (Estimation and inference) Wednesday, November 19 Lecture 14 - App. C (Estimation and inference) Friday, November 21 No lab; HW 3 due by 1:00 pm Monday, November 24 Lecture 15 - App. C (Estimation and inference) Wednesday, November 26 Lecture 16 - App. D (Large sample distribution theory) Friday, November 28 No lab Monday, December 1 Lecture 17 - App. D (Large sample distribution theory) Wednesday, December 3 Lecture 18 - App. D (Large sample distribution theory) Friday, December 5 No lab Monday, December 8, 12:00 Final exam (110 minutes)
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