There is a panel dataset with daily observations over two years and a control variable that changes on a monthly level and is the same for all units, so for all units within a month it takes the same value. Is it problematic to include the control and a month fixed effect in a regression, since they change simultaneously? Under what circumstances should one choose one or the other?
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$\begingroup$ It sounds problematic, but can you clarify? Do you want month as a fixed effect as in each unique month is different (i.e. Jan 2023 and Jan 2024 are different levels?) Or do you want month identity as the fixed effect? The second might be possible, but it's likely still problematic since you only have 2 years. $\endgroup$– Jacob WeverkaCommented Sep 10 at 16:21
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$\begingroup$ @JacobWeverka What’s “month identity” mean? I’m just curious. $\endgroup$– Thomas BilachCommented Sep 10 at 17:04
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$\begingroup$ As in all measurements from January of any year being grouped vs Jan 2023 vs Jan 2024 as different groups. $\endgroup$– Jacob WeverkaCommented Sep 10 at 18:18
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$\begingroup$ @JacobWeverka thanks for the answer! My initial idea was month identity (so any January is the same, be it 2023 or 2024) but now I am thinking of including a fixed effects for each unique month (so same month in different years is different) and removing the control variable with monthly frequency. I just wonder if that is a good idea, since I am basically ignoring some information that I have available. If I choose the unique month effects, does that control for the omitted variable, given that it is has the same frequency? $\endgroup$– jacob2881Commented Sep 11 at 8:47
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