Endogenous Selection/Treatment Models

Hi, all

I am estimating an endogenous selection models. The model is estimated using Stata command " etreg", which I believe implements a two-stage Heckman procedure. I understand that a Heckman approach does not require any excluded variable in the first stage, as the nonlinear nature of the first stage allows the second stage to be identified. However, the question is that we get substantively different results in a model with excluded instrumental variables in the first stage and one without (except the two excluded variables in the first stage, the two models are exactly the same). The sign of the selection variable changes. The two excluded variables are tested using ivreg2 and found to be excellent (highest explanatory power in the first stage) and valid (satisfy the two conditions) instrumental variables. I understand the Heckman procedure assumes joint normality but don't know the consequences if it is violated.

My question is how to explain the different results of the two estimations( with and without excluded instrumental variables) and which model we should trust.

Thank you very much.

Best

Gao