## Consider regression equations

у = Za + u |
(7.3.21) |

Z = ХП + V, |
(7.3.22) |

where Ем = О, ЕУ = 0, Em’ = T*, and u and V are possibly correlated. We assume that is a known nonsingular matrix. Although the limited information model can be written in this way by assuming that certain elements of V are identically equal to 0, the reader may regard these two equations in a more abstract sense and not necessarily as arising from the limited information model considered in Section 7.3.1.

Premultiplying (7.3.21) and (7.3.22) by *P-I/2, we obtain

l/2y = 4′-i/2za + ‘F"i/2u (7.3.23)

and

^-i/2Z = ip-i/2Xn + <ir-i/2V. (7.3.24)

We define the G2SLS estimator of a as the 2SLS estimator of a applied to

(7.3.23) and (7.3.24); that is,

Ob2S = [Z’4′-1X(X,4′-1X)-,X,4′-1Z]-1Z/4′-‘X(X’4′-1X)-1X’4′-,y.

(7.3.25)

Give...

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