Lahore School of Economics
MPHIL Advanced Econometrics
Winter 2010
Solutions to Problem Set 2
1.
E[yx]=
α
+
β
x where
β
= Cov(x,y)/Var(x) = 3/5 and
α
=
μ
y

βμ
x
1 – 2(3/5) = 1/5
E[yx,z]
=
α
+
γ
1
x+
γ
2
z where (
γ
1
,
γ
2
)
= [Var(x,z)]
1
Cov[(x,z),y]
=
1
5
2
3
2
6
1

÷
=
16/ 26
1/ 26
÷

and
α
=
μ
y

γ
1
μ
x

γ
2
μ
z
= 1 – 2(16/26) – 4(1/26)
2. Since log(S/Y) = log(S/N) – log(Y/N), it must be the case that log(S/Y) = 8.7851 + 1.1486log(Y/N) –
1
×
log(Y/N) etc.
But, that would mean that the coefficients in the first equation would be identical to those in the
second equation, save for that on log(Y/N) which should be exactly one less than that in the second equation.
Neither is true.
The results are wrong.
3.
The sum of squares must rise, since this is a linear restriction on
β
.
What happens to R
2
depends on how it is
computed.
Usually, packages use 1e
′
e/y
′
M
0
y, which must go down, and, in fact, can become negative.
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 Spring '10
 Cowell
 Econometrics, Regression Analysis, Lahore School of Economics, MPHIL Advanced Econometrics, 1e′ e/y′ M0y, usual multiple regression.

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