No change in the coefficients of my time-specific variables of interest when controlling for demographic effects

#1
Ciao Guys,
I have a balanced panel set and I study the following model:
lm(value ~ taskXjan20 + taskXfeb20 + taskXmar20 + taskXapr20 + demographic_criteria),

where value is a binary variable, being 1 if individual i has been unemployed in the previous month and 0 otherwise. It expresses therefore the probability of getting unemployed. I would like to explain this probability with the task group an individual is assigned to (which is a binary variable as well: 1 for the specific task group). This variable for a specific task group is interacted with the specific month (obviously being a binary variable as well). However, as I want to add demographic criterias as control variables (in total quite a lot ranging from AGE to Education,...) I do not see any difference for my coefficients.
Further, as I try to run a regression like that:

lm(value ~ task + taskXface_to_face + taskXremote + taskXessential + demographic_criteria),

where the interactors of my task variable are now time-independent variables, I see severe changes as I control them for my demographic effects.
My question now is, did I forget to adjust my regression for any further trends if my variables of interest directly interact with time-specific variables? And if yes, why did I not have to include them into the 2nd regression?

A model, which is similar to the first one, have been studied on page 11 and 37 of the following link.
https://www.econstor.eu/bitstream/10419/225517/1/GLO-DP-0702.pdf
Surprisingly he was able to generate different results when adding demographic control variables.


Hope somebody can help me!
Many thanks in advance, Freddy
 

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