Introductory Econometrics
ECON3121
What is Econometrics?
Econometrics is about measuring economic relations.
What is the quantitative effect of reducing class size on
student achievement?
How does another year of education change earnings?
What is the pri
CHAPTER 18
SOLUTIONS TO PROBLEMS
18.1 With zt1 and zt2 now in the model, we should use one lag each as instrumental variables, zt- 1,1
and zt- 1,2. This gives one overidentifying restriction that can be tested.
18.3 For , yt zt = yt zt + ( )zt, which is a
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 17
SOLUTIONS TO PROBLEMS
17.1 (i) Let m0 denote the number (not the percent) correctly predicted when yi = 0 (so the
prediction is also zero) and let m1 be the number correctly predicted when yi = 1. Then the
proportion correctly predicted is (m0
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
CHAPTER 16
SOLUTIONS TO PROBLEMS
16.1 (i) If 1 = 0 then y1 = 1z1 + u1, and so the right-hand-side depends only on the exogenous
variable z1 and the error term u1. This then is the reduced form for y1. If 1 = 0, the reduced
form for y1 is y1 = 2z2 + u2. (N
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 15
SOLUTIONS TO PROBLEMS
15.1 (i) It has been fairly well established that socioeconomic status affects student performance.
The error term u contains, among other things, family income, which has a positive effect on
GPA and is also very likely t
CHAPTER 15
TEACHING NOTES
When I wrote the first edition, I took the novel approach of introducing instrumental variables as
a way of solving the omitted variable (or unobserved heterogeneity) problem. Traditionally, a
students first exposure to IV method
CHAPTER 14
SOLUTIONS TO PROBLEMS
2
14.1 First, for each t > 1, Var( uit) = Var(uit ui,t- 1) = Var(uit) + Var(ui,t- 1) = 2 u , where we use
the assumptions of no serial correlation in cfw_ut and constant variance. Next, we find the
covariance between uit a
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 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
Simple Linear Regression Model
y = 0 + 1x + u
Issues: Causality and Ceteris Paribus?
y = 1 x
if u=0
E(u) = 0
- Meaning:
In the population,
the average value of u, the error term, is 0.
- Assumption? Not a restrictive assumption,
since we can always use 0
Multiple Regression Analysis
y = 0 + 1x1 + 2x2 + . . . kxk + u
-allows us to explicitly control for many other
factors, and so allows ceteris paribus analysis
- allows to generalize functional relationship
ceteris paribus
y = 0 + 1x1 + 2x2 + . . . kxk +
ECON3121 Miscellaneous Material (Not for the Examination)
A. Sampling Variances of the OLS estimator,
Interceptin SLR
n
P
21
V ar( ^ 0 ) =
n i=1
n
P
(xi
x2
i
(1)
x)2
i=1
(Proof) Conditioning on x,
V ar( ^ 0 ) = E [ ^ 0
2
0]
^x
1
= E [y
= E[
(2)
0
+
1x
2
ECON3121, Understanding STATA
The aim of this lecture is to introduce very basic STATA commands and to give opportunities
for you to practice econometrics with actual data. You are supposed to learn the following
commands:
1) clear, help, log using/close,
Real basic mathematical/statistical knowledge:
This material is based on Professor Chong previous lecture note for this class. You may
s
also want to study the appendix of the Wooldridge book. Whenever you think that you
s
are suering from your lack of kn
Fixed Effects Estimation
FE or FD?
Assumptions for Pooled OLS using FE
Dummy Variable Regression
Unobserved Heterogeneity
Pooled OLS with
Quasi-demeaned Data
Even in the case that unobserved heterogeneity is
uncorrelated with explanatory variables, we wa
Panel Data Analysis
Types of data
Cross-sectional data:
obtained by random sampling at a given point in time
Time series data:
have a separate observation for each time period
Cross-sectional data + Time-Series Dimension
Pooled cross section data
obtaine
Heteroskedasticity
Homoskedasticity - Var(u|x) = 2
Heteroskedastic Case
Heteroskedasticity with a single regressor
= + ( xi x ) ui
1
1
(xi x )2
(xi x )2 i2
Var (1 ) =
2
( ( xi x ) ) 2
Heteroskedasticity with a single regressor
When i2 2
(xi x )2ui2
)=
Binary (Dummy) Variable
A Single Dummy Independent Variable
y = 0 + 0D + 1x + u
e.g. wage= 0 + 0female + 1educ + u
Comparison-of-means
Simple regression on a constant and a dummy variable is a
straightforward way to compare the means of two groups
When th
Multiple Regression Analysis: Further Issues
1. Data Scaling
2. Functional Form - Logarithmic/Quadratic/Interaction
terms
(Nonlinear functions of x and y,
but still linear in the parameters)
3. Goodness-of-Fit (R-squared)
4. Prediction and Residual Analys
Multiple Regression Analysis:
OLS Asymptotics
Small Sample/ Large Sample
Issues:
(1) Consistency
(2) Asymptotic Normality
(3) Asymptotic Efficiency
Consistency
Under the Gauss-Markov assumptions OLS is BLUE, but not
all useful estimators are unbiased
=
CHAPTER 13
SOLUTIONS TO PROBLEMS
13.1 Without changes in the averages of any explanatory variables, the average fertility rate fell
by .545 between 1972 and 1984; this is simply the coefficient on y84. To account for the
increase in average education leve
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 6
TEACHING NOTES
I cover most of Chapter 6, but not all of the material in great detail. I use the example in Table
6.1 to quickly run through the effects of data scaling on the important OLS statistics. (Students
should already have a feel for th
CHAPTER 5
SOLUTIONS TO PROBLEMS
5.1 Write y = 0 + 1 x1 + u, and take the expected value: E(y) = 0 + 1 E(x1) + E(u), or y =
0 + 1 x since E(u) = 0, where y = E(y) and x = E(x1). We can rewrite this as 0 = y - 1
x. Now, = y x1 . Taking the plim of this we
CHAPTER 5
TEACHING NOTES
Chapter 5 is short, but it is conceptually more difficult than the earlier chapters, primarily
because it requires some knowledge of asymptotic properties of estimators. In class, I give a
brief, heuristic description of consisten
CHAPTER 4
SOLUTIONS TO PROBLEMS
4.1 (i) and (iii) generally cause the t statistics not to have a t distribution under H0.
Homoskedasticity is one of the CLM assumptions. An important omitted variable violates
Assumption MLR.3. The CLM assumptions contain