Timeline for LR statistics add up for nested models. What about the Wald test?
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| Apr 27 at 15:33 | history | edited | Christoph Hanck | CC BY-SA 4.0 |
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| Apr 27 at 6:56 | history | edited | Christoph Hanck | CC BY-SA 4.0 |
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| Apr 26 at 17:01 | comment | added | Richard Hardy | Got it, thank you! | |
| Apr 26 at 16:50 | comment | added | Christoph Hanck | Regarding the present question, I added some subtleties. | |
| Apr 26 at 16:50 | history | edited | Christoph Hanck | CC BY-SA 4.0 |
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| Apr 26 at 14:41 | vote | accept | Richard Hardy | ||
| Apr 26 at 14:27 | history | edited | Christoph Hanck | CC BY-SA 4.0 |
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| Apr 26 at 13:30 | history | edited | Christoph Hanck | CC BY-SA 4.0 |
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| Apr 26 at 10:38 | comment | added | Christoph Hanck | GMM theory tells us that the optimal weighting matrix is the inverse of the variance (-covariance matrix) of the moment conditions. E.g., under homoskedasticity, we get the weighting matrix $[\hat\sigma^2(Z'Z)/n]^{-1}$ (e.g. stats.stackexchange.com/questions/89378/…). If you, say, have near-multicollinearity among your instruments, this matrix would be "badly conditioned" in the terminology of the answer. | |
| Apr 26 at 6:40 | comment | added | Richard Hardy |
Thank you! I was expecting this sort of asymptotic behavior due to the asymptotic equivalence of LR and Wald (and LM) tests. In small samples the results can be quite far off, though. By the way, I got some answers to my gmm questions from Pierre Chausse. They are on point but quite brief. I could use some help deciphering this one, if/when you find some time.
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| Apr 26 at 6:39 | history | edited | Richard Hardy | CC BY-SA 4.0 |
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| Apr 26 at 6:35 | history | answered | Christoph Hanck | CC BY-SA 4.0 |