Econometric Methods with Applications in Business and Economics by unknow

Author:unknow
Language: eng
Format: epub
Publisher: Oxford University Press, UK
Published: 2004-03-14T16:00:00+00:00

Derivation of asymptotic distribution

We will assume (in analogy with (4.6) in Section 4.1.4 (p. 196)) that

Using the notation for the last expression in (5.75), we can rewrite (5.75) as , where An has probability limit . Combining these results and using gives

In large enough finite samples, bIV is approximately normally distributed with mean β and covariance matrix . With the notation (5.73) this gives

The instrumental variable estimator is relatively more efficient if the instruments Z are more highly correlated with the explanatory variables. In practice, the exogeneity condition (5.67) is often satisfied only for variables that are relatively weakly correlated with the explanatory variables. Such weak instruments lead to relatively large variances of the IV estimator.

To use the above results in testing we need a consistent estimator of the variance σ1. Let eIV = y – XbIV be the IV residuals; then a consistent estimator is given by

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