# st: 2SLS with sample selected variable

 From tsalam@email.unc.edu To statalist@hsphsun2.harvard.edu Subject st: 2SLS with sample selected variable Date Thu, 07 Feb 2008 14:41:14 -0500

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?

SS
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