Econ 741 2010 Spring
Suggested answers for Exercise 1
(1)
(a) The formal proof is simple but tedious, so I skip it here.
(b) Assume AB = I and since AA1 = I we know B = A1 .
!
!
A11 A12
B1 B3
1
=
A21
Econ 741 2010 Spring
Suggested answers for Exercise 2
(1)
(a) From the restriction R1 1 + R2 2 = q, we get 1 = R11 (q R2 2 ). Then brings it back
into the regression model, we get
y = X1 1 + X2 2 + u
Econ 741 2010 Spring
Suggested answers for Exercise 3
(1) First we show
1
2 (Rg
r)0 [R(X 0 1 X)1 R0 ]1 (Rg r) is 2 (q) distributed. Under the
restriction R = r,
Rg r = Rg r (R r) = R(g ) N (0, R 2 (
\ , .,
l
x 1
,~-.,W V. \
A x
1 i M3
2 J \ i as bl
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Spring 2010 C "544 2
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#9
(1) Let A and B be two partitioned matrices as
_ A1 A2 _ Bl Ba
A<A3 A