Empirical Methods in Economics
2014 Fall
Dr. LI Bing
SITE@CUFE
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
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 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)
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
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
Empirical Methods in Economics
2014 Fall
Dr. LI Bing
SITE@CUFE
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
SITE@CUFE
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
SITE@CUFE
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
log using example02.txt, text replace
*This file is the Second demonstration of STATA for ECONOMETRICS
course*
*by Dr. LI
Bing*
*2014.11.1
8*
use "D:\-teaching2014fall-\ME_Project\STATA_training\all.dta", clear
*regression*
reg p_gdp p_im
reg p_gdp p_im p
log using example01.txt, text replace
*This file is the first demonstration of STATA for ECONOMETRICS
course*
*by Dr. LI
Bing*
*2014.11.1
9*
insheet using "D:\-teaching2014fall-\ME_Project\STATA_training\gdp_beijing.csv",clear
describe
des
list
list p_gdp
log using example02.txt, text replace
*This file is the Third demonstration of STATA for ECONOMETRICS
course*
*by Dr. LI
Bing*
*2014.11.1
5*
*IV*
use D:\-teaching2014fall-\ME_Project\STATA_training\MROZ.DTA,clear
*Testing for Endogeneity*
reg lwage educ e
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
Econometrics
Assignment 1 (due Feb. 1, 2016)
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 g
Econometrics
Assignment 4 (due April 11, 2016)
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
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>
McGill University
Department of Economics
Economics 662D
Assignment x
John W. Galbraith
The R2 of a regression model is dened as follows:
R2 = 1
uu
(y y ) (y y )
using the standard notation in the model y = X + u, where X has column dimen2
sion k. The R
McGill University
Department of Economics
Economics 662D: Graduate Econometrics I
Assignment 1: algebra review
J. W. Galbraith
1. For a 2x2 matrix A, prove that A A = 0 i A = 0.
2. Suppose that A is a matrix of arbitrary size and x is a vector such that A
Economics 662, Part 1
Fall, 2004
R. Davidson
The principal reference for this course is the textbook Econometric Theory and Methods
(ETM), Oxford University Press, ISBN 0-19-512372-7, by James MacKinnon and me.
The bookstore tells me that it is still wait
EK2402 Macroeconomic Theory
Section 6: Back to Policy
Lecture 23: Fiscal Policy: A Summing Up
(Blanchard & Johnson Ch. 23)
Minghai Zhou1
1School
of Economics, University of Nottingham Ningbo China
Spring Semester, 2014/2015
1
Back to Policy
Fiscal Policy:
Economics Dissertation EK3500
Year: 2015/2016
DISSERTATION IDEAS FORM
This form can be used as the basis of your initial meeting with your dissertation supervisor. You
might want to use this form to work on and then e-mail an electronic version to your su
EK2402 MACROECONOMIC THEORY (Tutorials)
(2014-2015 semester 2)
Tutorial 2 Week 28, Mon. 9th March
Sketch of answers
Answer for Q1:
(a) Define IS: i.e., The short run equilibrium condition in goods market relating output to the
interest rate. Assuming a fi
EK2402 MACROECONOMIC THEORY (Tutorials)
(2014-2015 semester 2)
Tutorial 1 Week 27, Mon. 2nd March
AIM: This first tutorial will be partly devoted to organising the work you will be doing
during the semester. The questions below are meant to get you starte