Empirical Methods in Economics
2014 Fall
Dr. LI Bing
[email protected]
Lecture 02
The Simple
Regression Model
Definition of the simple linear regression model
"Explains variable
in terms of variable "
Intercept
Dependent variable,
explained variable,
response v
Assignment 4 (answers)
V.Zinde-Walsh
1. Suppose that xt ; yt ; zt are I(1) series.
(a) Show that if they are independent, then yt + zt is I(1). Can any linear
combination of independent I(1) series be anything but I(1)? Explain.
Since y; z are I(1); y; z
Economics 662.
Econometrics
Final examination
Brief answers to the problems in part B.
April 28, 2015
Examiner: V.Zinde-Walsh
Associate examiner: S. Chaudhuri
The marks for each question are given in parentheses; total for the exam
is 100.
Here is the for
Econometrics
Assignment 4 (due April 8, 2015)
V.Zinde-Walsh
1. Suppose that xt ; yt ; zt are I(1) series.
(a) Show that if they are independent, then yt + zt is I(1). Can any linear
combination of independent I(1) series be anything but I(1)? Explain.
(b)
Econometrics
Assignment 3 (due March 23, 2015)
V.Zinde-Walsh
1. Problem 4.17 from Davidson and MacKinnon "Econometric Theory and
methods", 2004, Oxford U.Press, p.175. (somewhat adjusted).
Suppose that the asymptotic distribution of a pivotal test statist
Econometrics
Assignment 1 (partial answers)
V.Zinde-Walsh
1. Some practice questions for ARMA models. You will discover a few
things for yourselves: Yule-Walker equations, equivalence of invertible and noninvertible MA.
(a) For a stationary AR(1) model gi
Econometrics 662
Winter lectures
V. Zinde-Walsh
Topic 6. Specication issues and tests of model
specication.
I. An overview of specication issues in a one-equation
model.
Model y = f (X; ) + ":
1. Error specication: heteroscedasticity, autocorrelation, non
Econometrics 662
Winter lectures
V. Zinde-Walsh
Topic 3. Maximum likelihood estimation.
Principle of maximum likelihood.
Let fx1 ; :; xg be a random sample from a distribution with density f (x; ):
Then the joint density is
f (x1 ; :xn ; ) = f (x1 ; ):f (
Econometrics 662
Winter lectures
V. Zinde-Walsh
Topic 5.Introduction to bootstrap.
1. Some concepts.
A model.
Consider an econometric model: it is a set consisting of cfw_parameters, deterministic functions, distributions that fully describes the model.
E
Econometrics 662
Winter lectures
V. Zinde-Walsh
Topic 1. Review of regression model, estimation, inference. Exact and asymptotic results.
1. Review and future topics.
Classical linear regression model
y = X + u; u
N (0;
2
I); X non-stochastic.
OLS estimat
Econometrics 662
Winter lectures
V. Zinde-Walsh
Topic 4. Classical asymptotic tests of parameter restrictions.
4.1. Intro. Parameter restrictions.
c( ) = 0:
EXAMPLES I.
I.1. Zero restrictions in a linear model.
Unrestricted model:
y = X + ";
0
= 01 : 02 (
Econometrics
Assignment 3 answers.
V.Zinde-Walsh
1. Problem 4.17 from Davidson and MacKinnon "Econometric Theory and
methods", 2004, Oxford U.Press, p.175. (somewhat adjusted).
Suppose that the asymptotic distribution of a pivotal test statistic is N (0;
April 17, 2012
Econometrics 662
Final examination
143x11mi11e1: V. Zi11cle\V 1lsh
Associate ex11111i11e1: .l.\.Cx11lhraitl'1
PLEASE \VthlIE CLEARLY IN PEN, NOT PENCIL.
DICTIONARJES, CALCULATORS NOT ALLOWED.
The 111111 ks 101 each question 1110 given; tota
Examiner: V.Zinde-\Nalsl1
Associate examiner: J .W. Galbraith
PLEASE WRITE CLEARLY IN PEN, NOT PENCIL.
DfCTIONARIES, CALCULATORS NOT ALLOWED.
'llie marks for each question are given; total for the exam is 100.
[Jere is the formula for the Wald statistic i
Empirical Methods in Economics
2014 Fall
Dr. LI Bing
[email protected]
Lecture 03
Outline for Today
What is Endogeneity Problem?
When do we have Endogeneity Problem?
The most popular method instrumental
variable (IV)
What is IV?
Why does IV work?
Tests for IV
S
Empirical Methods in Economics
2014 Fall
Dr. LI Bing
[email protected]
Lecture 04
Outline for Today
Difference in differences - DID
Propensity score matching - PSM
Endogeneity Problem
What is Endogeneity Problem?
Endogeneity:
Explanatory variables that are corr
Empirical Methods in Economics
2014 Fall
Dr. LI Bing
[email protected]
Lecture 01
Introduction
What is a PhD?
What is not a PhD?
Three stories
Why PhD?
A Graph
You tell me
Why Research?
Philadelphia Story
Outline for Today
What is this course about?
Course requ
For the question from part a) to part e)
set obs 100
Stata Code:
*gengrate 100 observations
gen e = invnormal(uniform()
gen z = (3)^(1/2)*invnormal(uniform()
gen v=0.5*e+0.5*z
* generate black, female and their interactive
gen b= rbinomial(1,.15)
gen f= r
Exercise 2.3
a) rj=dj-df. We chose to regress r1 r4 r7 and r10. The results are as follows:
gen r1= d1-rf
gen r4= d4-rf
gen r7=d7-rf
gen r10=d10-rf
regress r1 rmrf
est store m1
regress r4 rmrf
est store m2
regress r7 rmrf
est store m3
regress r10 rmrf
est
HW8 Solution
ECON662D1
November 14, 2015
When
8.5
y = X0 + u,
1
plim Q(0 , y)
n
n
the probability limit of
n1 Q(, y)
is
1
plim u> PW u
n
n
1
1 >
1 >
1 >
plim W W
plim W u . (1)
=
plim u W
n n
n n
n n
=
A standard assumption for the IV estimator to be con
aPart-time FULLtime, position age
sample size is too small?
E) female dummy+ male dummy=1
f) assumption
IF TEST R1^2 R0^2 R0^2
j) because Education level is donated only from 1 to 5.
It may be better to extend the education level from 1 to 10.
We can
HW7 Solution
ECON662D1
November 4, 2015
7.9
The question asks to show that > is equal to
1
.
.
0
0
1 + 2
.
.
0
0
0
.
.
0
0
0
0
.
.
1+
2
0
0
.
.
.
1
(1)
The rst row of times the rst column of > is equal to
(1 2 ) + 2 + 0 + + 0 = 1,
which is the upp
Econometrics 662
Winter lectures
V. Zinde-Walsh
Topic 2. Dependence, time series data and
processes. Stationary ARMA models.
0:
Independence.
x?y means that the joint distribution F (x; y) = F (x) F (y) :
x?y implies that covR (x;
R y) = 0:
R
R
Indeed, co
Econometrics 662
Assignment 3
Due March 21,2014
V.Zinde-Walsh
1. Problem 4.17 from Davidson and MacKinnon "Econometric Theory and
methods", 2004, Oxford U.Press, p.175. (somewhat adjusted).
Suppose that the asymptotic distribution of a pivotal test statis
Econometrics
Assignment 2
Due Feb. 22,2016
V.Zinde-Walsh
1. (a) For the model
yt =
+
0
1 X1t
+
2 X2t
+ ut
with ut ; t = 1; :n independent and distributed as N (0; 2 (X1t + X2t )2 ) write
the loglikelihood function and derive the rst-order conditions.
(b)
HW1 Solution
ECON662D1
September 14, 2015
1.2 Under the Cauchy distribution,
E(x) =
It is easy to see that
xdx
(1 + x2 )
(1)
d
2x
ln(1 + x2 ) =
.
dx
1 + x2
Therefore, the indenite integral in (1) is
1
ln(1 + x2 ).
2
But this quantity diverges as x and x .
HW6 Solution
ECON662D1
October 20, 2015
6.4
The SSR function is
SSR() = (y x()> (y x().
Dierentiating this with respect to , we obtain the rst-order conditions
(1)
2X > ()y + 2X > ()x() = 0,
where, as usual, X() is the matrix with typical element xt ()/t
HW2 Solution
ECON662D1
September 22, 2015
2.2 Since |x| is just a scalar, the norm of x/|x| can be computed as
|x|2
1
x> x =
= 1.
2
|x|
|x|2
The square root of 1 is 1, and so the rst result is proved.
For the next part of the question,
>
x
y
x
y
x> x
2x>