*The asymptotic covariance matrix of the IV estimator is76 V 1 n plim n bIV...

*The asymptotic covariance matrix of the IV estimator is76 V ¼ 1 n

plim nð Þ bIV ( fl ð Þ bIV ( fl 0 * +

The IV estimator itself (Equation 9.28) can be written as bIV ¼ fl þ ðZ0 XÞ
(1 Z0 "
(Reader: Why?) Then, V ¼ 1 n plim nðZ0 XÞ
(1 Z0 ""0 ZðX0 ZÞ
(1 h i Starting with this formula, show that (repeating Equation 9.29)
VðbIVÞ ¼ σ2 ε
n SðRÞ(1 ZX SðRÞ
ZZ SðRÞ(1 XZ Caveat: This relatively simple derivation of VðbIVÞ appears, for example, in Johnston (1972, Section 9-3), but it (although not the result itself) is technically flawed (see McCallum, 1973).