Linear Models

Course Description

This is a course in regression analysis. It has two goals. First, will learn the statistical methods needed to pursue independent large-n research projects. Second, they will develop a set of tools necessary to pursue further methods training in the social sciences. Relatively little prior knowledge of math or statistics is expected, but students are expected to work hard to develop the tools introduced in class.

Part I of the course reviews the simple linear model (as seen in Stat 220 or its equivalent) with attention to the theory of statistical inference and the derivation of estimators. Basic calculus and linear algebra will be introduced. Part II extends the linear model to the multivariate case. Emphasis will be placed on model selection and specification. Part III examines the consequences of data that is “poorly behaved” and how to cope with the problem. Part IV introduces special topics like systems of simultaneous equations, logit and probit models, time-series methods, etc. The breadth of coverage depends on time.

Required Course Materials

Griffiths, Hill, and Judge (GHJ). Learning and Practicing Econometrics

STATA 8 (software package, available in campus computer clusters)

Other Useful Texts (in order of degree of difficulty)

Allison (Al). Multiple Regression: A Primer (optional course text, available at Seminary Coop)

à A very accessible introductory text on regression analysis. I expect students to have achieved this level of competency coming into the course.

Gujarati. Basic Econometrics

à This is a very good introductory text without linear algebra or calculus.

Pindyck and Rubinfeld (PR). Econometric Models and Economic Forecasts

à This is a great text, with a very accessible presentation of econometrics within the text that presents proofs and linear algebra in chapter appendices.

Grades

Course grades will be based in equal parts on the following three criteria:

Class participation and attendance.

The course is designed as an introduction to an applied methodology, not as an opportunity to read and discuss the great works. Unlike many graduate classes, this means that you might learn something in class that you wouldn’t get from the readings. It also means that the bulk of class time will be spent in lecture. This is not to say that discussion or questions are not encouraged. I will try to reserve some time for discussion and you are always, always encouraged to ask questions. The best questions usually takes the form of something like, “huh?” or “I don’t understand that?” If you don’t understand, chances are others are in the same boat, so do not be timid about asking questions.

6 or 7 homework assignments.

In addition to the regular reading assignments, you will be expected to do a number of homework assignments designed to get you familiar with the tools for applied work.

Independent research project.

Students will be expected to write a research paper where they apply a technique that they learned in class to a research question that interests them. Miracles are not expected—a multiple regression would be more than adequate as long as you are careful.

To facilitate finishing the project, I strongly encourage each of you to pick a data set the first week of classes that you will use for the project. Then, as you work through the homework exercises, to apply the techniques from the homework to your data set. By the end of the term, all you will have to do to finish is write an introduction and conclusion and staple the results together.

Course Outline * denotes required. ** strongly recommended

Part I. Statistical Inference and Simple Regression

Week 1. Introduction and review of statistical concepts

GHJ. Chapters 1, 2, and 26*

PR. Chapter 1

Week 2. Statistical inference

GHJ. Chapters 3 and 4*

PR. Chapter 2

Degroot, Probability and Statistics. Chapters 3 and 4. Online Reserve.

Mathematics Review

GHJ. Appendix 3*

Kleppner. Quick Calculus. Chapter 2. Online Reserve**

Week 3. Simple regression

GHJ. Chapter 5 and 6*

PR. Chapters 1 and 3.

Al. Chapter 5.

Mathematics Review

GHJ. Appendix 3 and Appendix 4. *

Namboodiri. Matrix Algebra: An Introduction (reserve) **

Week 4. Hypothesis testing and model specification

GHJ. Chapters 4, 7, and 8*

PR. Chapter 3

Part II. Multiple Regression

Week 5. Multiple Regression

GHJ. Chapter 9 and 10*

PR. Chapter 4

Al. Chapters 1, 2, 4, and 6

Week 6. Model specification in multivariate models

GHJ. Chapter 11, 12, and 13*

PR. Chapter 7

Al. Chapters 3, 7, and 8

Part III. Data behaving badly

Week 7. Errors in variables and heteroscedasticity

GHJ. Chapters 14 and 15*

PR. Chapters 6 and 8.

Al. Chapter 3 and 6

Week 8. Basic time-series and pooled time-series cross section models

GHJ. Chapters 16 and 17*

PR. Chapters 6, 8, and 9.

Part IV. Advanced topics

Week 9. Simultaneous Equations

GHJ. Chapters 18 and 19*

PR. Chapter 11

Al. Chapter 9

Week 10. Logit and probit models

GHJ. Chapter 23*

PR. Chapter 10

Al. Chapter 9