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

Potential helpful textbooks:
(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
an undergraduate level.
(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
unauthorized materials or fabricated information in any academic work.” Academic
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
Quadratic forms and definite matrices
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