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CORNELL UNIVERSITY
Economics 321:
Applied Econometrics, Spring 2007, G. Jakubson
PRELIMINARY EXAM #2 ANSWER KEY
1.
(10 points)
30% poor and 40%of the poor are program, so P(program) = P(program  poor)P(poor) = (.4)(.3) = 12% in program.
Wealthy
Poor, not in
Poor, participate
Prob
.7
.18
.12
mean income
800
450
x
E(income) = 700 = (.7)(800) + (.18)(450) + (.12)(x) => x = 491.67
2.
(15 points)
a. V(income) = E(income  E(income))
2
= (.7)(800700)
2
+ (.18)(450700)
2
+ (.12)(491.67700)
2
b. E(income  poor) = (450)(.18/.3) + (491.67)(.12/.3) = 466.67
(use conditional distribution  probability weights must add to one)
c.
V(income  poor) = E[income  E(income  poor)  poor]
2
= (.6)(450466.67)
2
+ (.4)(491.67466.67)
2
(For parts a and c could also use V(x) = E(x
2
)  (E(x))
2
form)
3.
(35 points)
a. No.
Harleyson says to compare the mean incomes for nonparticipants vs. participants without regard to whether a
country is wealthy or poor.
The mean income for nonparticipating counties is (800)(.7/.88) + (450)(.18/.88) =
728.41> the mean income for participating counties (all poor) = 491.67.
Most nonparticipators are not poor.
b.
y = per capita income.
y =
ββ
;
β
01
++
Du
0
= mean of nonparticipating;
β
0
+
β
1
= mean for participating;
β
1
= mean of participating minus mean of nonparticipating < 0 ;
c.
y =
;
β
β
2
+++
DC
u
0
= mean for nonpoor nonprogram;
β
0
+
β
2
= mean for poor nonprogram; (
β
0
+
β
1
+
β
2
)= mean for poor program, so
β
1
= mean for poor program minus mean for poor nonprogram, while
β
2
= mean
for poor nonprogram minus mean for nonpoor nonprogram.
4.
(20 points)
a. Using the above calculations and parameter interpretations, we want
β
1
from the simple regression = mean of
participating minus mean of nonparticipating
= 491.67728.41 = 236.74
b. Again using the above information, we want
β
1
from the multiple regression = mean for poor program minus
mean for poor nonprogram 491.67 450 = 41.67.
When we control for whether or not a nation is poor, we see that
the program is effective.
5. (40 points)
a.
Simple regression:
y =
α
0
+
α
1
D + u
1
Multiple regression:
y =
β
0
+
β
1
D +
β
2
A + u
2
Auxiliary regression:
A =
δ
0
+
δ
1
D + u
3
The relationship between simple and multiple regression says:
α
1
=
β
1
+ (
β
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This note was uploaded on 05/26/2008 for the course ECON 3210 taught by Professor Molinari during the Spring '07 term at Cornell University (Engineering School).
 Spring '07
 MOLINARI
 Econometrics

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