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st: Command or user-written program for Probit switching model
Dear STATA users,
I am trying to estimate a "Probit switching model" as follows.
y1* = a1 + b1 x + u1 if d* > 0 --> treatment group
y2* = a2 + b2 x + u2 if d* < 0 --> control group
d* = p + qz + w --> selection equation
where y1*, y2*, and d* are all latent variables.
y1 = 1 if y1* > 0, otherwise y1 = 0
y2 = 1 if y2* > 0, otherwise y2 = 0
d = 1 if d* > 0, otherwise d = 0.
The error terms (i.e. u1, u2, and w) in the three equations have joint normal distribution. In particular, these three error terms are all correlated in the following way.
Var (u1) = 1
Var (u2) = 1
Var (w) = 1
Cov(u1, u2) = sigma u1 u2
Cov(u1, w) = sigma u1 w
Cov(u2, w) = sigman u2 w
The parameters to be estimated are a1, b1, a2, b2, p and q.
As far as I know, STATA does not have any official command to estimate the above probit switching model. I only find two user-written codes for CONTINOUS switching model namely "movestay" and "switchr". Please do suggest me if you know of any user-written code for probit switching.
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