intuition/explanation for "Hausman's result"?

Question

Greene (econometric analysis p. 235 7th ed) discusses the Hausman test (test for whether the OLS is consistent). Greene states:

Probably, Greene believes that Hausman's technical statement of this result is too difficult for his readers. I nevertheless would like an intuition of why the covariance term would be zero, because it is not at all intuitive to me, especially that the efficiency has anything to do with it.

score 2 · Answer 1 · answered Jan 09 '18 at 18:48

2

Intuitively, if it was not zero, the efficient estimator could be made more efficient by exploiting that non-zero correlation.

answered Jan 09 '18 at 18:48

dimitriy

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How could it be exploited? – user56834 Jan 09 '18 at 19:54
@Programmer2134 By making the variance smaller. – dimitriy Jan 09 '18 at 20:10
By definition of inefficiency we can make the variance smaller, but I meant how could we do that. – user56834 Jan 10 '18 at 04:20
@Programmer2134 By combining it with an estimator that is unbiased estimator of zero. There's a nice proof with some intuition [here](https://stats.stackexchange.com/a/196996/7071). – dimitriy Jan 10 '18 at 04:46

intuition/explanation for "Hausman's result"?

1 Answers1