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The very last step of the Fama McBeth procedure is to aggregate the estimated regression coefficients by taking their mean. The mean is then the estimate for the "overall" regression coefficient.

The significance of this mean is derived by looking at the variation of the regression coefficients. But by doing so, don't we ignore the fact that the different regression coefficients are not fix?

If I take the mean of three regression coefficients that are not significantly different than zero, but which's values are let's say 10, 11 12. It is obvious that treating them as fixed at 10, 11 and 12 would yield to the conclusion that the mean (11) is different from zero with a high significance. However, this stands in contrast to the fact that each of the single coefficients is not significantly different from zero.

Is my thinking correct? If not - how is the fact that the estimates are not fix considered in the Fama McBeth procedure

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  • $\begingroup$ The procedure does not take them as fixed. In your example with beta values 10,11,12 the FM standard error would not be so small. However, the procedure assumes these betas are independent, which reduces the error. The rough logic is: if the standard error were large why would all the estimates be fairly close to each other? $\endgroup$ – fesman Dec 7 '20 at 11:31
  • $\begingroup$ I get that logic. However, I would imagine that this only holds asymptotically. That is, it holds when my number of coefficients over which I estimate the mean is large. Correct? Also, is there any paper or passage in a paper where the logic you mention is explicitly stated? Thanks in advance. $\endgroup$ – shenflow Dec 7 '20 at 11:48
  • $\begingroup$ Does this help: finpko.ku.edu/myssi/FIN938/…. I don't think you need asymptotics to understand that logic. $\endgroup$ – fesman Dec 7 '20 at 12:31
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    $\begingroup$ It does. Thanks a lot. However, I still don't get how it apparently does not matter wether the variable I want to calculate the SE from is based on variables that are themselves subject to SE or not. For example, take the most extreme case: I have just one coefficient with SE of 100000, estimated at 10. The average is 10 and the SE of the average is 0, since I only have 1 observation. However, the fact that the variable itself is not some observeration but an extremely unstable estimate is not considered at all. I still do not understand why this would not make a difference. $\endgroup$ – shenflow Dec 7 '20 at 13:33
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    $\begingroup$ Doesn't the issue I am describing relate to the Shanken correction procedure in some sort? With the difference that Shanken corrects the estimates when used as regressors. $\endgroup$ – shenflow Dec 7 '20 at 14:49

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