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I suppose I want to run the following regression:

$$y_{ist} = \beta_0 + \beta_1 \tau_{st} + \beta_2 T_t + \beta_3 \tau_{st} T_t + \epsilon_{ist} $$

$\tau_{st}$ is my continuous treatment variable. It depends only on a sector $s$ and time $t$, being constant across firms $i$ from the same sector in the same time period. There are only two time periods.

I am worried about the precision of my estimators, since the number of sectors is much smaller than of firms. Should that matter? Or only the whole sample size matters? What about variability? Do I depend on variability on both my dependent and independent variables? Does the same logic applies if I include industry-by-year effects, where subsets of sectors belong to the same industry?

Thank you

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  • $\begingroup$ How are you doing the standard errors? Clustering on sector? $\endgroup$
    – dimitriy
    Commented Jun 6, 2020 at 18:29
  • $\begingroup$ I haven't run regressions yet. But I guess I would cluster at the s level $\endgroup$
    – Arthur Carvalho Brito
    Commented Jun 6, 2020 at 18:30
  • $\begingroup$ Precision is about standard errors, which depend on how you do the clustering, since that influences cluster size, within cluster error correlation, and etc. How many sectors do you have, roughly? $\endgroup$
    – dimitriy
    Commented Jun 6, 2020 at 18:40
  • $\begingroup$ There are about 80 sectors, and i is above 10000 $\endgroup$
    – Arthur Carvalho Brito
    Commented Jun 6, 2020 at 18:58
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    $\begingroup$ Take a look this question, my answer, and the Cameron and Miller JHR paper that the OP cited. You treatment is at sector level, so you should cluster at that level. The $\rho_x$ parameter is going to be 1, so the main precision concern is about within-sector error correlation and how the number of firms varies accross clusters. 80 sectors is probably high enough that you don't run into problems. This is also discussed on that paper. $\endgroup$
    – dimitriy
    Commented Jun 7, 2020 at 2:35

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