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Today, when asking for some suggestions about adding the interaction variables, a commentor ask me that I should include all elements of this interaction variable to this equation:

For example:

My original equation is:

Y= X + pt + fixed effects + error term (1)

My dummy variable is developed receiving 1 if this observation belonging to firm in developed countries, my estimated equation is:

Y= X + pt + pt*developed + fixed effects + error term (2)

However, the commentator told that the proper equation should include all elements of the interactive variable:

Y= X + pt + pt*developed + developed + fixed effects + error term (3)

Is the commentator correct in pointing this?

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Normally your commentator would be correct, but in your case you are using fixed effects and in a standard fixed effects within estimator you show in your question you will not be able to include developed dummy (unless some countries happen to switch development status in the sample). Thus if you would include developed dummy you would have problem with perfect multicollinearity and the coefficient for developed dummy cannot be estimated.

However, since you have already fixed effects any effect that development dummy would have is already controlled for by the fixed effect.

If you want to include development dummy you have to move from simple within estimator fixed effects model and do something different. For example, you could run random effects model. Random effects model has a bit more stringent assumption on the distribution of unobservable, but if you don't mind that and you want to have development dummy there then it is an option.

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  • $\begingroup$ so do you mean the developed dummy will be perfectly multicollinear with firm fixed effect? (I had two way fixed effect in my case: firm and year) $\endgroup$
    – Louise
    Jul 26 at 4:46
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    $\begingroup$ @BeautifulMindset 1. yes it will. 2. With within estimator you can’t include any time invariant variables as they drop off $\endgroup$
    – 1muflon1
    Jul 26 at 9:27

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