I am a new user of Stata and I am trying to use Stata to estimate
Poirier(1980, Journal of Econometrics)'s bivariate probit model with
partial observability. Basically, the model is as follows:
Y1_star=X*b1+e1
Y2_star=X*b2+e2
Y1=1 if Y1_star>=0 and Y2=1 if Y2_star>=0. Let Zi=Y1i*Y2i. We have data
on Zi=0, 1. But no info about Y1* or Y2*. Prob(Zi=1)=Prob(Y1=1 and
Y2=1)=F(X*b1,X*b2,rho).
log-likelihood fn=sum[Zi*prob(Zi=1)+(1-Zi)*prob(Zi=0)].
This model is similar to a bivariate probit in spirit. The difference is
that it puts all the observations of (0 1), (1 0), and (0 0) into Zi=0.
Anyone has the code to estimate the above model? Thanks.
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