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From this dicussion, the commentor said

Lastly, firm fixed effects may absorb more variation and likely reduced the size of their standard errors.

In practice, I also mainly see that the standard error for country-level mainly higher than that of firm-level variables. I am wondering if there is any mathematical or intuitive way to explain this phenomenon.

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    $\begingroup$ Consider a study of 10,000 firms over 2 countries. It should be intuitively, for such a dataset, why it's easier to estimate a slope parameter for a firm-level variable then a country-level variable. $\endgroup$ – Jase Jun 14 at 0:28
  • $\begingroup$ @Jase Thank you for your convern, could you please explain it more, thank you so much, if it can be clarified in an answer, would be much appreciated. $\endgroup$ – BeautifulMindset Jun 14 at 0:55
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    $\begingroup$ In general one has more samples by say, a few orders of magnitude, so the larger sample size will reduce the standard error, even if we account for possible correlations across samplees. $\endgroup$ – rubikscube09 Jun 14 at 13:22

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