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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, 10:0011:20, Ballard 118
Lab: Friday, 1:001:50, 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 BD.
(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 SASIML (15% total),
two
midterms (25% each), and a final exam (35%). If a SASIML 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 7374098.
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 nonexperimental 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
CramérRao 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
LindbergLevy univariate central limit theorem
Fall 2008 Schedule  (Makeup 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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