st: 2SLS with heckman

[tsalam@email.unc.edu]

Dear users,

I am trying to estimate expenditure functions (Y). However, I have a 
right hand side variable (wage) that is both endogenous and sample 
selected (I do not have wage for those that are not participating in 
the labor market).

Yi= alpha + alpha1 (Wage) + error

Wage =beta +beta1(Z) + errorw

 Wage=Wage* if wage*>wage0
      0        otherwise


This is what I am doing:

First running the participation equation by probit. Calculate inverse 
mills ratio for it. Then estimate Y by two stage least squares while 
including inverse mills ratio as a covariate in both Y and wage 
equation. I can also estimate by 3SLS, jointly estimate all the 
expenditure equations and wage.

Question 1. Is this a correct method if I bootstrap the errors? If not, 
what is a correct method?

Question 2. Since I am performing the probit manually, when I perform 
the 2SLS, observations for those whose wage is missing (i.e. not 
participating in the labor force) are naturally dropped. Is this 
correct? I thought 2SLS regresses the second stage with predicted 
valued from the first stage. And when you predict wage after 
regressing, shouldn't we get values for the entire sample?

Thanks in advance
SS
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