January 12, 2012
LECTURE 1
REVIEW OF GMM FOR LINEAR MODELS
Denition and asymptotic properties
Suppose that an econometrician observes the data cfw_(Yi , Xi , Zi ) : i = 1, . . . , n, and the model is given by
Yi
= Xi + Ui , and
E (Zi Ui )
=
0,
(1)
where R
APRIL 19, 2007
LECTURE 13
SPURIOUS REGRESSION, TESTING FOR UNIT ROOT
Spurious regression
In this section, we consider the situation when is one unit root process, say Yt ; is regressed against another
unit root process, say Xt ; while the two processes ar
MARCH 29, 2006
LECTURE 12
UNIT ROOT, WEAK CONVERGENCE, FUNCTIONAL CLT
(Davidson (2000), Chapter 14; Phillips Lectures on Unit Roots, Cointegration and Nonstationarity;
White (1999), Chapter 7)
Unit root processes
Denition 1 (Random walk) The process fXt g
APRIL 17, 2009
LECTURE 11
LINEAR PROCESSES III: ASYMPTOTIC RESULTS
(Phillips and Solo (1992) and PhillipsLecture Notes on Stationary and Nonstationary Time Series)
In this lecture, we discuss the LLN and CLT for a linear process fXt g generated as
Xt
=
1
MAY 2, 2011
LECTURE 10
LINEAR PROCESSES II: SPECTRAL DENSITY, LAG OPERATOR, ARMA
In this lecture, we continue to discuss covariance stationary processes.
Spectral density
(Gourieroux and Monfort (1990), Ch. 5; Hamilton (1994), Ch. 6)
A convenient way to r
APRIL 17, 2009
LECTURE 9
LINEAR PROCESSES I: WOLD DECOMPOSITION
In this lecture, we focus on covariance stationary processes.
Denition 1 (White noise) A process f"t g is called a white noise (WN) if E"t = 0; E"2 =
t
E"t "t j = 0 for all t and j 6= 0:
2
<
MAY 2, 2011
LECTURE 8
LINEAR REGRESSION WITH WEAKLY DEPENDENT DATA
Consider the usual regression model Yt = Xt +Ut , where Rk is unknown vector of parameters and the
1
n
n
data consists of weakly dependent observations. The LS estimator of is n = ( t=1 Xt
MAY 2, 2011
LECTURE 7
STATIONARITY, ERGODICITY, WEAK DEPENDENCE
The material is adapted from Peter Phillips Lecture Notes on Stationary and Nonstationary Time Series
and White (1999).
Often econometricians have to deal with data sets that come in the form
April 30, 2009
LECTURE 6
WEAK INSTRUMENTS
In this lecture, we discuss the IV regression model with weak instruments. The discussion follows Staiger
and Stock 1997 paper in Econometrica.
s
Model
Consider the following regression model with a single endogen
JANUARY 21, 2009
LECTURE 5
SIMULTANEOUS EQUATIONS IV: LIMITED INFORMATION ML (LIML)
In this lecture, we consider ML estimation of a single equation which is a part of the system of simultaneous
equations. Without loss of generality, we can focus on the rs
March 3, 2010
LECTURE 4
SIMULTANEOUS EQUATIONS III: FULL INFORMATION ML (FIML)
Denition
Consider again the model dened in Lecture 2,
0 Yi
EZi Ui0
= B0 Zi + Ui ;
= 0;
where subscript 0 is used to denote the true values of the coe cients. We assume that all
JANUARY 31, 2012
LECTURE 3
SIMULTANEOUS EQUATIONS II: MULTIPLE-EQUATION GMM, 3SLS.
In this lecture, we consider joint GMM estimation of more than one simultaneous equation. As we will
see, joint estimation can lead to eciency gains.
Multiple-equation GMM
JANUARY 18, 2011
LECTURE 2
SIMULTANEOUS EQUATIONS I: DEFINITION, IDENTIFICATION, INDIRECT LS,
SINGLE-EQUATION GMM
Denition
We consider the following system of equations :
Yi
= BZi + Ui ,
(1)
=
EZi Ui
(2)
0,
where Yi is an m-vector of endogenous variables:
APRIL 17, 2008
NONPARAMETRIC KERNEL METHODS
In this lecture, we discuss kernel estimation of probability density functions (PDF). Nonparametric density
estimation is one of the central problems in statistics. In economics, nonparametric density estimation