# 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

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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