st: switching regression - endogenous variable in the main equation

[Manuela Deidda <manuelad.deidda@gmail.com>]

Dear statalisters,
I would like to estimate a switching regression model with known
sample selection.
My model looks like this:

y= a+ b1*x + b2*v +e (main equation)
I=f(z)+u (selection equation)

The need to estimate a switching regression rather than simply a
sample split derives from the fact that the error term of the main
equation (e) is correlated with the error term in the selection
equation (u).


The dependent variable in the selection equation (I) is a binary
variable, assuming value 0 and 1. The main equation needs to be
estimated when I=0 and when I=1. With the command "movestay", one can
estimate simultaneously the main equation in the two regimes, together
with the selection equation.

I am interested in variable v. In particular, I want to check whether
the coefficient associated to variable v in regime 1 (I=0) is
statistically different from the coefficient associated to v in regime
0 (I=1). However, variable v in the main equation, is endogenous.
Therefore, it needs to be instrumented.

In the standard case (all regressors in the main equation are
exogenous), the movestay command works well. However, I don't know how
to deal at the same time with the endogeneity problem related to the
variable v in the main equation and the need to estimate a switching
regression model.


Thanks in advance for your help!
Manuela
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