CHAPTER
14
Advanced Panel Data Methods
I
n this chapter, we cover two methods for estimating unobserved effects panel data models
that are at least as common as first differencing. Although these methods are somewhat
harder to describe and implement, seve
CHAPTER
4
Multiple Regression Analysis:
Inference
T
his chapter continues our treatment of multiple regression analysis. We now turn
to the problem of testing hypotheses about the parameters in the population regression model. We begin by finding the dist
CHAPTER
2
The Simple Regression Model
T
he simple regression model can be used to study the relationship between two
variables. For reasons we will see, the simple regression model has limitations as a
general tool for empirical analysis. Nevertheless, it
CHAPTER
3
Multiple Regression Analysis:
Estimation
I
n Chapter 2, we learned how to use simple regression analysis to explain a dependent
variable, y, as a function of a single independent variable, x. The primary drawback in
using simple regression analy
CHAPTER
13
Pooling Cross Sections
across Time: Simple Panel
Data Methods
U
ntil now, we have covered multiple regression analysis using pure cross-sectional
or pure time series data. Although these two cases arise often in applications, data
sets that hav
CHAPTER
7
Multiple Regression Analysis
with Qualitative Information:
Binary (or Dummy) Variables
I
n previous chapters, the dependent and independent variables in our multiple regression
models have had quantitative meaning. Just a few examples include ho
CHAPTER
8
Heteroskedasticity
T
he homoskedasticity assumption, introduced in Chapter 3 for multiple regression,
states that the variance of the unobservable error, u, conditional on the explanatory
variables, is constant. Homoskedasticity fails whenever t
CHAPTER
6
Multiple Regression Analysis:
Further Issues
T
his chapter brings together several issues in multiple regression analysis that we
could not conveniently cover in earlier chapters. These topics are not as fundamental
as the material in Chapters 3
CHAPTER 2
TEACHING NOTES This is the chapter where I expect students to follow most, if not all, of the algebraic derivations. In class I like to derive at least the unbiasedness of the OLS slope coefficient, and usually I derive the variance. At a minimu
CHAPTER 4
TEACHING NOTES At the start of this chapter is good time to remind students that a specific error distribution played no role in the results of Chapter 3. That is because only the first two moments were derived under the full set of Gauss-Markov
CHAPTER 3
TEACHING NOTES For undergraduates, I do not work through most of the derivations in this chapter, at least not in detail. Rather, I focus on interpreting the assumptions, which mostly concern the population. Other than random sampling, the only
CHAPTER
5
Multiple Regression Analysis:
OLS Asymptotics
I
n Chapters 3 and 4, we covered what are called finite sample, small sample, or exact
properties of the OLS estimators in the population model
y 0 1x1 2 x2 . k xk u.
5.1
For example, the unbiasednes
CHAPTER
9
More on Specification
and Data Issues
I
n Chapter 8, we dealt with one failure of the Gauss-Markov assumptions. While heteroskedasticity in the errors can be viewed as a problem with a model, it is a relatively
minor one. The presence of heteros
CHAPTER
12
Serial Correlation
and Heteroskedasticity
in Time Series Regressions
I
n this chapter, we discuss the critical problem of serial correlation in the error terms
of a multiple regression model. We saw in Chapter 11 that when, in an appropriate
se
CHAPTER
15
Instrumental Variables Estimation
and Two Stage Least Squares
I
n this chapter, we further study the problem of endogenous explanatory variables in
multiple regression models. In Chapter 3, we derived the bias in the OLS estimators
when an impo
CHAPTER
1
The Nature of Econometrics
and Economic Data
C
hapter 1 discusses the scope of econometrics and raises general issues that arise in
the application of econometric methods. Section 1.3 examines the kinds of data sets
that are used in business, ec
CHAPTER
10
Basic Regression Analysis with
Time Series Data
I
n this chapter, we begin to study the properties of OLS for estimating linear regression
models using time series data. In Section 10.1, we discuss some conceptual differences
between time serie
CHAPTER
16
Simultaneous Equations Models
I
n the previous chapter, we showed how the method of instrumental variables can
solve two kinds of endogeneity problems: omitted variables and measurement error.
Conceptually, these problems are straightforward. I
Nikhil Patel
September 21 ,2016
HCAD 8517
South End Community Health Center
Vision Statement: Reaching out with Heart in Hand championing the needs of the
underserved and providing healthcare for all, regardless of their ability to pay, as we eliminate
di
CHAPTER 16
TEACHING NOTES I spend some time in Section 16.1 trying to distinguish between good and inappropriate uses of SEMs. Naturally, this is partly determined by my taste, and many applications fall into a gray area. But students who are going to lea
CHAPTER 17
TEACHING NOTES I emphasize to the students that, first and foremost, the reason we use the probit and logit models is to obtain more reasonable functional forms for the response probability. Once we move to a nonlinear model with a fully specif
CONTENTS
PREFACE
iii
SUGGESTED COURSE OUTLINES
iv
Chapter 1
The Nature of Econometrics and Economic Data
1
Chapter 2
The Simple Regression Model
5
Chapter 3
Multiple Regression Analysis: Estimation
15
Chapter 4
Multiple Regression Analysis: Inference
28
C
CHAPTER 19
TEACHING NOTES
Students should read this chapter if you have assigned them a term paper. I used to allow
students to choose their own topics, but this is difficult in a first-semester course, and places a
heavy burden on instructors or teaching
CHAPTER 18
TEACHING NOTES
Several of the topics in this chapter, including testing for unit roots and cointegration, are now
staples of applied time series analysis. Instructors who like their course to be more time series
oriented might cover this chapte
CHAPTER 14
TEACHING NOTES
My preference is to view the fixed and random effects methods of estimation as applying to the
same underlying unobserved effects model. The name unobserved effect is neutral to the issue
of whether the time-constant effects shou
CHAPTER 13
TEACHING NOTES
While this chapter falls under Advanced Topics, most of this chapter requires no more
sophistication than the previous chapters. (In fact, I would argue that, with the possible
exception of Section 13.5, this material is easier t
CHAPTER 12
TEACHING NOTES
Most of this chapter deals with serial correlation, but it also explicitly considers
heteroskedasticity in time series regressions. The first section allows a review of what
assumptions were needed to obtain both finite sample an
CHAPTER 10
TEACHING NOTES
Because of its realism and its care in stating assumptions, this chapter puts a somewhat heavier
burden on the instructor and student than traditional treatments of time series regression.
Nevertheless, I think it is worth it. It
CHAPTER 11
TEACHING NOTES
Much of the material in this chapter is usually postponed, or not covered at all, in an introductory
course. However, as Chapter 10 indicates, the set of time series applications that satisfy all of
the classical linear model ass
APPENDIX D
SOLUTIONS TO PROBLEMS
0 1 6
2 1 7
20
D.1 (i) AB =
1 8 0 =
4 5 0
5
3 0 0
6
12
36 24
(ii) BA does not exist because B is 3 3 and A is 2 3.
D.2 This result is easy to visualize. If A and B are n n diagonal matrices, then AB is an n n