st: Why Heckprob's estimate of rho is off?

 From Rachel To statalist Subject st: Why Heckprob's estimate of rho is off? Date Mon, 13 Aug 2007 14:34:57 -0400

```I am trying to simulate data for a censored probit model and then use
heckprob to check how close its estimates are to the true values.  It
turns out the estimates of the coefficients are very close and highly
significant, but the estimates of rho (whose true value is -0.5) is
off and highly insignificant.  Here is my code:

matrix Csample = (1, -.5\-0.5, 1)
drop eps11 eps22
drawnorm eps11 eps22, n(2000) corr(Csample)

drawnorm x1 x2 x3, means(10 -9 11) sd (1 1 1)

//defined all beta parameters here--will not list this part//

replace yselectstar=beta00+beta11*x1+beta22*x2+eps11
regress yselectstar x1 x2
gen yselect=0
replace yselect=1 if ystar>0

gen yhat=alpha+beta33*x3
gen ystar=yhat+eps22
gen y=0
replace y=1 if ystar>0

heckprob y x3, sel(yselect=x1 x2)

I get estimates for the parameters that are very close to the true
values, with p-values of 0.000.  But the estimated rho value is
-.2056815 with a
p value of 0.69.

Can anyone spot the problem with the way I am simulating the data for
the censored probit?   (I realize that I have values of y for all
observations, regardless of the value of yselect, but this doesn't
seem to make a difference in Heckprob's estimates.) Or is the problem
with heckprob?  I understand that heckprob estimates atanhrho and then
transforms the parameter and estimates the standard errors using the
delta method. But I don't understand why it would land at a value that
is so far off.

Thanks,
Rachel
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