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st: calculating marginal effects for outcome equation in Heckman model


From   <Colin.Vance@dlr.de>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: calculating marginal effects for outcome equation in Heckman model
Date   Mon, 8 Aug 2005 10:46:29 +0200

I have estimated a Heckman model with Stata8. Now I would like to
calculate the marginal effects of variables in the outcome equation that
also appear in the selector equation. The following article presents the
formula for doing so on page 177 (equation 11):

Sigelman, L. and Zeng, L. 1999. Analyzing censored and sample-selected
data with Tobit and Heckit models. Political Analysis, Vol. 8: 167-182.

My hunch is that the formula only applies to continuous variables, but I
also need a formula for dummy variables. 

So far, here is how I have employed the formula in Stata for the case of
continuous variables. Say I estimate the following model:

heckman depvar x1 x2, select(x1 x2 x3) 

If x2 is continuous and I want to estimate its marginal effect in the
outcome equation, I have to do the following after estimating the model:

predict selxbpr, xbs  /*gets predictions from selector equation*/

gen mills = normden(selxbpr)/norm(selxbpr) /*calculate Mills ratio*/

gen Z =mills*(mills+selxbpr) /*from Sigelman and Zeng*/

gen x2marg = _b[x2]-([#2]_b[x2]*rho*sigma*Z) /*from Sigelman and Zeng;
for rho and sigma, fill in the numbers from the Stata output*/



Any insights on how to adjust the above steps to handle dummies would be
appreciated. Also, I think it is necessary to recalculate the standard
errors. Advice on how to do this would be helpful, too.

Thanks,
Colin



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