Timeline for Optimal weighting matrix instrumental variables estimator
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Jun 19, 2014 at 9:29 | comment | added | Andy | That's right Kasper! Sorry it didn't come out clearly enough in the answer but I'm happy that it was eventually useful | |
| Jun 19, 2014 at 8:04 | comment | added | Kasper | Hey Andy, only now I truly get it. I did not get that you start with the covariance of the sample moments, I I read over it. Now I do. You start with the variance of the sample moments and in case of homoscedasticity you end up with the covariance matrix of the instruments. Anyway thanks again! | |
| Mar 17, 2014 at 10:49 | vote | accept | Kasper | ||
| Mar 17, 2014 at 10:49 | comment | added | Kasper | I think I get it now, thanks a lot for your time and answers!! | |
| Mar 15, 2014 at 16:40 | comment | added | Kasper | What is confusing me is the optimal weighting matrix if you have one instrument for each endogenous variable and heteroscedasticity. Is the following correct: each weighting matrix will give you the same estimates, as the system is identified. But you have to correct the variance due to heteroscedasticity (with a white correction for example). In case you have an over identified system, you should not only correct the variance, but also calculate a new weighting matrix and calculate the estimates again. The new estimates should also have a smaller variance. Thx for your help! | |
| Mar 14, 2014 at 11:42 | comment | added | Kasper | Hey Andy I am still doubting over everything, but the pieces are coming together hopefully the next days. Keep you posted! | |
| Mar 13, 2014 at 14:04 | comment | added | Andy | I guess you're still not convinced? | |
| Mar 11, 2014 at 21:33 | comment | added | Andy | I shortened the answer and (hopefully) got rid of unnecessary technicalities. The points about why the choice of the weights doesn't matter for point estimation in large samples and the motivation for giving more weight to stronger instruments in the variance estimation should be clearer now. Let me know if something requires further explanation and if be happy to edit the post again. | |
| Mar 11, 2014 at 21:31 | history | edited | Andy | CC BY-SA 3.0 |
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| Mar 11, 2014 at 21:18 | history | edited | Andy | CC BY-SA 3.0 |
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| Mar 11, 2014 at 15:51 | comment | added | Andy | I should have been more precise. In small samples the choice of the weighting matrix matters because it influences the point estimates. In large samples the GMM estimator remains consistent for any choice of $W$. In this case you choose the weight such that it minimizes the asymptotic variance. These notes explain it very nicely (google.co.uk/…) p. 21 onwards, I just found them and I'll update my answer this evening to clarify it. | |
| Mar 11, 2014 at 11:43 | comment | added | Kasper | Hey Andy, thanks for your answer. Unfortunately, after some heavy thinking, I still don't get it. Is it possible to say in three words how the weight of an instrument that is not correlated at all with the endogenous predictor gets a weight close to zero? | |
| Mar 10, 2014 at 19:14 | history | answered | Andy | CC BY-SA 3.0 |