Advanced Econometric Theory by Chipman John;

Author:Chipman, John;
Language: eng
Format: epub
Publisher: Taylor & Francis Group

then (i’) and (iii) together imply (i), as well as the further condition that converges in distribution to N(0, σ2Mxx).13

It was pointed out by Klein (1955) that Theil’s two-stage least-squares estimator Theil (1954a, 1955) could be interpreted as one in which the instrumental variables for Z1 are the actual variables = [1, Χ2] chosen by Theil in (8.4.7) as regressors in place of Z1 = [Y1, X1], where is defined by (8.4.3). Notice that , like Z1 itself, is of order n × (m1 + k1). If X in (8.4.16) were of order n × (m1 + k1) (i.e., if m1 = k2 – the case of so-called “exact identification”), and if X′Z1 were of full rank m1 + k1 = k, then we would have the identity

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