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st: Simulatenous equation system with probit
I am trying to estimate a simultaneous equation system in a panel data
context. The model is the following:
Y1= a1 + b*Y2 + c*Y3 + d*X1 + u1
Y2= a2 + f*Y3 + g*X2 + u2
Y3= a3 + k*X3 + u3
Where Y1, Y2 and Y3 are the endogenous dependant variables and X1, X2 and X3
the exogenous variables.
Y1 and Y2 are continuous endogenous variables.
Besides Y3 is an endogenous binary (0-1) variable.
Is a recursive model but the var-cov matrix is not diagonal (I expect that
u2 and u3 are contemporanoeus correlated (so it is not diagonal).
I have seen different ways to treat the last two equation: the Wooldridge
procedure or the treatreg command.
Besides the cdsimeq of Omar Keshk is for a coefficient different of zero for
Y2 in the Y3 equation.
In the case of the system estimation the reg3 procedure it will imply a
linear estimation for the Y3 variable.
What do you think about this?? There is a way to transform the reg3
procedure in order to take into account a binary endogenous variable??
Or because only the last two equation have the endogeneity problem can I use
a kind of Wooldridge´s procedure (first: run a probit of Y3 on all the
exogenous variables of the system, including the exogenous in the first
equation and run a linear regressions of Y2 on all the exogenous variables
of the system including the exogenous of the first equation). And lastly run
an xtivreg of Y2 on X2 and Y3hat)and a xtivreg of Y1 on Y2hat, Y3hat and X1.
Any assitance will be appreciated.
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