FINANCE Corporate financial policy and R and D Management

and its associated transform

R–1X′y⋅i= R–1X′Yiβ⋅i+ R–1X′X⋅iγ⋅i+ R–1X′u⋅i i= 1, 2,...,m (5.55)

where Ris a nonsingular matrix such that

RR′= X′X (5.56)

One of the assumptions underlying this entire estimation scheme is that

(5.57)

exists as a nonsingular matrix.
In equation (5.50), it was held that

w= Qδ+ r

Now, by definition,

(5.58)

(5.58)

and we see that if the system does not contain any lagged endogenous vari-
ables, we can argue as follows: We know that

E(u) = 0 Cov(u) = Σ⊗IT (5.59)

And thus, conditionally on X, we find

E(r) = 0 Cov(r) = F(Σ⊗IT)F′= Σ⊗R–1X′XR′–1= Σ⊗IG (5.60)

But equation (5.65) implies that even unconditionally on Fthe mean vector
and covariance matrix of rdo not depend on X. Now, if 2SLS estimation
of δis OLS estimation in the context of (5.50) and if the covariance matrix
of ris not scalar, then we are encouraged to think that Aitken methods ap-
plied to the problem will yield relatively efficient estimators.

rFu FI RX u

u

u

u

m

m

==⊗− ′ =

⋅

⋅

⋅

1

1

2

M

plim

T

XX

T

Mxx

→∞

′

=

90 AN INTRODUCTION TO STATISTICAL ANALYSIS AND SIMULTANEOUS EQUATIONS