I have the following PANEL model:
Regime 1 (observed if z1 = 0): y = y(t-1) + exog
Regime 2 (observed if z1 > 0): y = y(t-1) + exog + z1 + z2 + endog
At t=0, all observations are in regime 1; changing from 1 to 2 depends on y(t-1) and exog; changing from 2 to 1 not possible.
y is a count variable, y(t-1) is past y (I am uncertain about using lagged y or a depreciated stock up to t-1; in regime 2, alternatively, I can use a "years-since regime 2" time counter), z1 and z2 are proportions (endogenous; my key independent variables), endog are additional endogenous variables, exog are exogenous. To put it differently, in regime 1 all endogenous are 0, while in regime 2 z1 is not 0 (and remaining endogenous may be 0 or not).
All endogenous variables are almost time-invariant (e.g. 0/0/0/0/0/0/0/0/50/50/50/50/50/50/50; 0/0/0/0/0/0/0/0/0/0/0/0/0/0/0; 0/0/0/0/0/0/0/0/0/0/0/0/25/25/50; etc...).
I have thought about xtivreg y (z1 z2 endog y(t-1) = exog).
Do you have any suggestion or better idea?
Nicola
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