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st: Correction for heteroscedasticity in a probit model with selection


From   "Pascal Stock" <pascalstock@freenet.de>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Correction for heteroscedasticity in a probit model with selection
Date   Wed, 12 May 2010 19:33:59 +0200

Hello STATA users,

I am trying to figure out how to solve for heteroscedasticity when the
variance of the residuals has the form Var(e_i)=sigma_e^2 * (1-(p^2)*d_i).
This is the heteroscedastic error term in a two-step selection model. In the
equation e_i is the residual of observation i in the structual equation
after estimation the equation with the inverse mills ratio from the
selection equation. P is the correlation coefficient of the residuals of the
selection and structual equation. D_i is the delta of observation i and
defined according to Greene(2003, p. 784 ? 785)). I know that I can correct
for heteroscedasticity by weighting the observations with
1/((1-(p^2)*d_i)^0.5) as the expectation of the residual then gives the
homoscedastic sigma_e^2. Unfortunately I cannot use in the ?probit? command
the weighting ?iweight=1/((1-(p^2)*d_i)^0.5)? together with the cluster
option ?vce(cluster master_deal_no)? as I have 50 copies of each observation
that differ only with respect to the values of one independent variable and
have identical values in the other independent variables. 

How do I use the ?hetprob? and have to define the variable modeling
heteroscedasticity when the variance of the residuals is biased by
(1-(p^2)*d_i) ? Trying it myself and given the description of the "hetprob"
model by James Hardin and W Gould I defined the variance variable as
variance_variable=ln((1-(p^2)*d_i)^0.5), because the heteroscedasticity
correction is (ß_0 + X * ß_i)/exp(ln((1-(p^2)*d_i)^0.5))=(ß_0 +
X*ß_i)/(1-(p^2)*d_i)^0.5 such that the expectation of the variance is
E[Var[e_i/(1-(p^2)*d_i)^0.5)]] = 1/(1-(p^2)*d_i)* E[Var(e_i)] =
1/(1-(p^2)*d_i) * sigma_e^2 * (1-(p^2)*d_i) = sigma_e^2 and thus
homoscedastic.

Do you think this manual correction for heteroscedasticity in the Heckman
selection model is correct?

Thanks for your help and kind regards

Pascal




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