Three questions concerning selection bias correction and calculation of
marginal effects. I want to run a heckman-like procedure on an export
function on a panel data set of plants. The original model is the following.
#delimit ;
heckman exportintensity wagerate spillover skill size size^2 gov forg y95
y96,
twostep select(wagerate skill outs gov forg y95 y96)
mills(mills);
#delimit cr/* y9* are the year dummies*/
But "spillover" is an endogenous variable and thus I decided to do the
following. (calculate inverse Mill's ratio from a probit equation and
substitute that in the second equation, which in this case is a 2sls
equation.
Step 1
a.probit exportdummy wagerate skill outshare gov forg y95 y96
b. calculate mills ratio
Step 2
ivreg exportintensity wagerate skill size size^2 gov mills y95 y96
(spillover = forg)
*(or ivreg2 given that disturbance is hetroscedastic)
Question 1. Is it (Steps 1 thru 2) an okay procedure?
Step 3.
Since the marginal effect (of explanatory variables included in both
equations) on dependent variable, exportintensity, is composed of the effect
on the
selection equation and the outcome equation I proceeded to adopt the formula
suggested by Scott Merryman.
"If the outcome coefficient is beta and the selection coefficient is alpha,
then dE[y| z*>0]/dx = beta - (alpha*rho*sigma*delta(alpha))
where delta(alpha) = inverse Mills' ratio *(inverse Mills' ratio * selection
prediction)"
Question 2.
In this case how do we calculate "rho" (Can I use the correlation
coefficient of the residuals of the two equations) and "sigma"?
(In the Heckman procedure these are default outputs)
Question 3.
If questions 1 and 2 can be solved, my final question would be if I could I
adopt a panel data estimation (eg.random effects).
