ECO 644-01: Econometric Theory
University of North Carolina Greensboro
Fall 2015
Contact Information
Instructor:
Office:
Phone:
Email:
Martijn van Hasselt
Bryan 446
(336) 334-4872
mnvanhas@uncg.edu
Lectures:
Computer lab:
Office hours:
Mondays, Wednesdays, 10:00AM – 11:15AM in Bryan 206
Thursdays, 12:30PM – 1:45PM in Bryan 211
by appointment
Graduate assistant:
Office:
Email:
Maozhao Zheng
Bryan 469
m_zheng@uncg.edu
Course description
This course provides an introduction to mathematical statistics and econometrics for students in
the Master’s program in economics. It emphasizes the theoretical underpinnings of econometrics
and is taught concurrently with ECO643 (which is a course in applied econometrics). Topics
include fundamental concepts of mathematical statistics (probability distributions, expected
value, hypothesis testing, sampling distributions, and asymptotic analysis), linear algebra, and
the linear regression model. On completion of this course, students will


have a thorough understanding of the basic concepts and tools of mathematical statistics;
and
know how to use these tools to analyze and understand the statistical properties of linear
econometric models.
Course requirements
We will meet twice a week for a 75 minute lecture. The lectures are complemented by computer
labs, which are held on Thursdays about every 3 weeks. The labs provide an introduction to the
software (SAS, see below) and will give you an opportunity to apply some of the material
covered in the lectures.
Students are required to attend and actively participate in the lectures and labs. Cell phones must
be turned off. Laptops may be used for note taking but not for surfing the web or other
distracting activities. In addition to these responsibilities, students are expected to conform to the
University’s Student Code of Conduct (http://sa.uncg.edu/handbook/student-code-of-conduct/)
and to the Bryan School’s Faculty and Student Guidelines
(http://www.uncg.edu/bae/faculty_student_guidelines.pdf).
The grade for this course is based on the following components:



Problem sets: 20%
Midterm exams: 40% (20% each)
Final exam: 40%
Problem sets will be given approximately every 2 weeks. They will receive a grade of 0 (no work
or insufficient work), 1 (substantial work but many incorrect answers) or 2 (complete work with
(mostly) correct answers). To receive credit, answers need to be turned in by the specified due
date and time. Late answers will not be accepted without prior approval of the instructor.
The problem sets will consist of a combination of theory questions and computer assignments.
The first midterm exam, scheduled for September 23, will cover all material discussed up to that
point. The second midterm exam, scheduled for November 2, will cover all material covered
after the first midterm exam. The final exam is cumulative and comprehensive: it covers all
material from the entire semester.
Software
The software package used in this course is SAS. SAS is installed in the UNCG computer labs.
SAS licenses for personal computers are available for UNCG students through ITS. To begin the
license process, connect to https://web.uncg.edu/research-access/secure/sas/sas.asp. Finally, you
can also access SAS remotely through MyCloud: https://mycloud.uncg.edu/vpn/index.html. For
more information, see http://its.uncg.edu/Virtual_Services/MyCloud/.
Academic Integrity
Students are expected to be familiar with and abide by the University’s Academic Integrity
Policy (see http://academicintegrity.uncg.edu/). Collaboration on problem sets and lab exercises
is allowed, but students must turn in their own work. Collaboration on exams is not allowed and
will be treated as a violation of the Academic Integrity Policy.
Course readings
We will use the following texts in this course (these are available at the campus bookstore).

Arthur S. Goldberger: A Course in Econometrics, Harvard University Press, 1991.

John A. Rice: Mathematical Statistics and Data Analysis (3rd edition), Cengage Learning
2007.

Rick Wicklin: Statistical Programming with SAS/IML Software, SAS Institute, 2010.
Course outline
Below is a list of topics and readings that will be covered during this course, together with a
tentative schedule. The schedule is subject to change, depending on whether more or less time is
needed to cover certain topics. However, the exam dates are fixed and are not subject to change.
Week
(1) Aug. 17, 19
(2) Aug. 24, 26
Topics
Introduction
 Experiments, sample space, events
 Probability
 Independence
Univariate random variables
 Probability mass and density function
 Cumulative distribution function
Univariate distributions: expected values
 Properties of expected value
 Variance
 Normal distributions
Lab #1 (8/27): introduction to SAS IML
(3) Aug. 31, Sep. 2
Bivariate distributions
 Joint distribution
 Marginal distribution
 Conditional distribution
(4) Sep. 9
No class on September 7 (Labor Day)
Bivariate distributions
 Expected values
 Covariance and correlation
Lab #2 (9/10): introduction to SAS IML
(cont.)
Bivariate distributions
 Conditional expectation
 Prediction
(5) Sep. 14, 16
(6) Sep. 21, 23
(7) Sep. 28, 30
Midterm exam 1: September 23
Independence
 Stochastic independence
 Mean independence
 Uncorrelatedness
The bivariate normal distribution
Sampling distributions
 Random sampling
 Statistics
 Normal, student-t and chi-square
distributions
Readings
Goldberger:
2.1-2.3, 2.5
Rice:
1.1-1.3, 1.5-1.6, 2.1,
2.1.1, 2.1.2, 2.1.5, 2.2,
2.2.1, 2.2.3, 2.3
Goldberger:
3.1-3.4, 7.1
Rice:
4.1 (skip ex. B, E, G, H),
4.1.1 (theorem A and
example A only), 4.2
Goldberger:
4.1-4.3
Rice:
3.1, 3.2, 3.3 (skip ex. C,
E, F), 3.5, 3.5.1, 3.5.2
(example A only)
Goldberger:
5.1
Rice:
4.1.2, 4.3 (skip ex. F)
Goldberger:
5.2-5.5
Rice:
4.4.1 (skip ex. B), 4.4.2
Goldberger:
6.1-6.6, 7.2-7.4
Rice:
1.6, 3.3 (example F), 3.4
Goldberger:
8.1-8.6
Rice:
6.1, 6.2, 7.3, 7.3.1
Week
(8) Oct. 5, 7
(9) Oct. 14
(10) Oct. 19, 21
(11) Oct. 26, 28
(12) Nov. 2, 4
(13) Nov. 9, 11
(14) Nov. 16, 18
Topics
Asymptotic analysis
 Modes of convergence
 Law of large numbers
 Central limit theorem
Lab #3 (10/8): statistical functions, plotting
and sampling distributions
No class on October 12 (Fall Break)
Estimation
 Analogy principle
 Bias, efficiency, consistency
 Confidence intervals
Maximum likelihood estimation
Matric algebra: basic concepts
Multiple Regression
 Population regression function
 Best Linear Prediction
 Least squares estimator: existence
and uniqueness
Lab #4 (10/29): sampling distributions and
matrix calculations
Midterm exam 2: November 2
Random vectors
 Mean and variance
 Linear transformations
The classical linear model
 Assumptions
 Properties of the LS estimator
 Gauss-Markov theorem
 Linear functions of the LS estimator
 Goodness-of-fit (R-squared)
Lab #5 (11/12): matrix calculations in the
linear model
The multivariate normal distribution
 Properties
 Functions of standard normal
variables
 Quadratic forms
The classical normal linear model
 Maximum likelihood estimation
 Sampling distributions
 Confidence intervals
Readings
Goldberger:
9.1-9.3
Rice:
5.1, 5.2, 5.3 (skip
theorem A, ex. A)
Goldberger:
11.1-11.5
Rice:
8.1-8.4
Goldberger:
12.1-12.4
Rice:
8.5, 8.5.2, 8.7
Goldberger:
14.1-14.5
Rice:
14.1
Goldberger:
15.1
Rice:
14.4.1
Goldberger:
15.2-15.5, 16.1, 16.2,
16.4
Rice:
14.2 14.2.1-14.2.3, 14.3,
14.4.2-14.4.4
Goldberger:
18.1-18.4, 19.1-19.4
Week
(15) Nov. 23
Topics
No class on November 25 (Thanksgiving
Break)
The classical normal linear model
 Hypothesis testing
(16) Nov. 30
The classical normal linear model
(continued)
 Distribution theory with unknown
variance
 Confidence intervals, hypothesis
testing
Final Exam: Wednesday, December 2, 12 Noon – 3:00PM
Readings
Goldberger:
20.1-20.3
Goldberger:
21.1-21.3