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st: limited dependent variable & cross equation restrictions
I'd like to understand how to deal with the 2 issues below and would
welcome any references/feedback you may be able to suggest.
I run the regression (coefficients omitted):
Fijt = constant + Nijt + Djt + Djt*Nijt + control variables + error
where Fijt = share of foreigners of skill group i in region j at time t
Nijt = corresponding share amongst natives
Djt = dummy indicating whether region j is abundant in skill i relative to
all regions at time t. Djt = 1 is Nijt > average share of skill i amongst
natives across all regions at time t. Dji = 0 otherwise.
I estimate that regression using fixed-effects.
1. Fijt is a limited dependent variable whose value ranges between 0
and 1. Do I really need to transform my variable so that its value
2. I have 3 skill groups and hence have an add-up constraint (i.e. the
sum of Fijt across the i is 1). Is it legitimate to estimate separately the
above regression for the 3 skill groups on the understanding that the
non-linearity given by the dummy and the interaction term makes it
virtually impossible to impose an add-up constraint across the Djt and
Dij*Nijt ? In other words, can i simply estimate the regression above for
the 3 groups on the assumption that any add-up restriction is picked up
by the error term (hence I should only worry about heteroskedasticity)?
Many thanks for your help,
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