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st: 2SLS with heckman

Subject   st: 2SLS with heckman
Date   Sun, 10 Feb 2008 16:31:38 -0500

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
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