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I am running an international regression, the number of observations and adjusted R-squared is as below

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In Column 1, we only consider the effect of a leniency law without any additional controls, and, in Column 2, we add firm-specific variables and several other variables to capture macroeconomic conditions, in Column 3, we add some industry-level variables, In Column 4, I excluded the industry-level variable and add industry * year fixed effects, In column 5, I added region * year fixed effect. And In the last column, I exclude US out of my sample.

I follow Dong, 2019 and his result is like below, and he did not concern the number of observations

enter image description here

I am wondering if I should concern the change in the number of observations and normally when we should concern the change in the number of observations?

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The number of observation changes likely because there are missing observations for some controls. Unless you suspect that statistics might systematically not collect data for some firms (e.g. maybe data on some control was recorded only for big firms) this is not concerning. You could consider investigating if there are any systematic reasons for missing data.

Additionally you should also be concerned if too many observations are dropped if you have small sample as parametric models require certain quantity of observations so you can reasonably justly their asymptotic properties. For standard regression a typically a sufficient sample size to justify its asymptotic properties is 30 observations per independent regressors (see Verbeek A Guide to Modern Econometrics pp 36). However, in your case you have more than 300k observations even in the most general model so this is not an issue.

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  • $\begingroup$ Thanks 1muflon1, regarding "Unless you suspect that statistics might systematically not collect data for some firms (e.g. maybe data on some control was recorded only for big firms) this is not concerning", what if I exclude some financial services and utility firsm as extant literature, whether I need to concern about that point? $\endgroup$
    – Louise
    Jun 30 at 4:05
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    $\begingroup$ @BeautifulMindset depends on reasons you exclude them financial services are routinely excluded on purpose from many papers because they behave differently from rest of the economy $\endgroup$
    – 1muflon1
    Jun 30 at 9:03
  • $\begingroup$ I understand, 1muflon1, I mean, if I exclude financial services based on this reason, whether I need to concern the part "Unless you suspect that statistics might systematically not collect data for some firms" ? Thank you $\endgroup$
    – Louise
    Jun 30 at 10:32
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    $\begingroup$ @BeautifulMindset I am not sure if I understand the comment, if you on purpose exclude something then of course it is not of concern but then that also means that results are not applicable to the category you excluded. That is its completely fine to exclude financial system from your research, but then you cannot claim that the results you find can say anything about financial system at all, if you are fine with that then you can exclude to your hearts desire. You could also exclude all retail but then the results do not apply there etc. $\endgroup$
    – 1muflon1
    Jun 30 at 14:46
  • $\begingroup$ awesome, it is exactly what I want to ask $\endgroup$
    – Louise
    Jun 30 at 20:48

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