I am interested in incorporating time-invariant variables to a fixed-effects panel data model. As we know, the coefficient corresponding to the time-invariant variable will be dropped, because of the fixed-effects specification. Regarding this, I am aware that we can overcome this problem by using the interaction of a year dummy (time fixed effect) and the time-invariant variable (please see How to keep time invariant variables in a fixed effects model). My question is that if it would be correct to include only the interacted term(s) without the time (year) dummy? Many thanks in advance!
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