Econ 425 - Problem Set 5
Due February 13 (Thursday) in Class
Instructions. The questions below review the identication and inference on enodgenous regression models. Do your best to make your arguments rigorous. You may discuss this problem set with
your

E (Y |X) = 0.
Cov (Y, X) = E (XY )
Cov (Y, X) = 0.
E (X) E (Y ) .
E (Y ) = E (E (Y |X) = 0
E (XY ) = E (E (XY |X) .
E (E (XY |X) = E (XE (Y |X) = E (X0) = 0.
Cov (Y, X) = 0.
E (Y |X) = a 6= 0
Cov (X, Y ) .
Cov (Y, X) = E (XY ) E (X) E (Y ) .
E (Y ) = E (E

cfw_W T, SP
2
/ cfw_W T, SP .
S
S = cfw_W T, SP, SM, F L 2cfw_W
/
T, SP
S,
S.
cfw_W T, SP , cfw_SM, F L , S,
S
S
S = cfw_W T, SP, SM, F L 2
/
cfw_, S
S
cfw_ , cfw_S
S
S = cfw_W T, SP, SM, F L 2
/ cfw_ , cfw_S .
cfw_, S
S,
cfw_W T, cfw_SP
S,
2
/ cfw_

E (Yi |Xi , Wi ) =
E (ui |Xi , Wi ) = 0
Cov (ui , Xi Wi ) = 0.
0
+
1 Xi
+
E (ui |Xi , Wi ) = 0.
E (ui ) = E (E (ui |Xi , Wi ) = 0,
Cov (ui , Xi ) = 0,
2 X i Wi ,
Cov (Yi , Xi ) =
1V
Cov (Yi , Xi Wi ) =
2
=
Cov(Yi ,Xi )
1 V ar(Xi )
Cov(Xi Wi ,Xi )
1
=
ar (

Econ 425 - Problem Set 3
Due January 29 (Thursday) in Class
Instructions. These questions review the basics of probability and regression analysis. Do your
best to make your arguments rigorous. You may discuss this problem set with your classmates and
con

Econ 425 - Problem Set 2
Due January 22 (Thursday) in Class
Instructions. These questions review the basics of probability and regression analysis. Do your
best to make your arguments rigorous. You may discuss this problem set with your classmates and
con

Econ 425 - Problem Set 4
Due February 5 (Thursday) in Class
Instructions. These questions review the basics of probability and regression analysis. Do your
best to make your arguments rigorous. You may discuss this problem set with your classmates and
con

Econ 425 - Problem Set 1
Due January 15 (Thursday) in Class
Instructions. These questions review the basics of probability and regression analysis. Do your
best to make your arguments rigorous. You may discuss this problem set with your classmates and
con

CHAPTER 10
Multiple Linear Regression Models
In this chapter, we study inference from the muliple regression model. A full exposition
of this model requires the language of linear algebra which we try to avoid using in this
course. Hence, the analysis in

Part 3
Linear Models
In this part, we study linear regression models and understand the meaning and the role
of the basic assumptions. We study how we dene the parameter of interest and interpret
the parameter, and how we come up with a systematic procedu

204
14. PANEL LINEAR REGRESSION MODELS
2.4. An Alternative Approach : First Dierencing. We saw that under Assumptions FE1-FE2, we can use within-group transforms to identify the coe cient 1 and
estimate it consistently. The within-group transform is made

CHAPTER 15
Binary Choice Models
1. Binary Dependent Variables
We have studied mainly the situation where the dependent variable Y is a continuous
variable. However, in many empirical researches, the dependent variables are discrete, or
more often, binary.

CHAPTER 13
Regression Models under Endogeneity
We have studied univariate and and multiple regression models under the assumption
that the unobserved component ui in the regression model satises that
E [ui jX1i ;
; XKi ] = 0
where X1i ; ; XKi are regresso

6. GENERAL ENDOGENOUS REGRESSION MODEL
181
6. General Endogenous Regression Model
6.1. Overidentication. As a step toward a generalization of the previous development, let us consider the situation where we have more than one instrumental variables.
The c

CHAPTER 14
Panel Linear Regression Models
1. Panel Data
Panel data consist of a set of individual observations that are observed over a period of
time. For example, the observations take the form of (Yit ; Xit ); i = 1; ; n and t = 1; ; T;
where i denotes

CHAPTER 17
Program Evaluations
1. Introduction: Program Evaluations
In this section, we study the methods of program evaluations. Suppose that a selected
set of individuals receive training or education initiated by the government with a view
to enhancing

248
17. PROGRAM EVALUATIONS
4. The Approach of Propensity Scores
The switching regression model approach uses assumptions to identify the average
treatment eect as a regression coe cient to the treatment status variable Di . Among the
assumptions is the f