Method to jointly estimate Logit and OLS models

Question

I am working on the following two models.

Logit: Binary outcome $y$ ($y=1$ if paid more than the item value to win the item, $y=0$ otherwise) $$ y=b_0+x_1b_1+x_2b_2+x_3b_3. $$

OLS: Continuous dependent variable $z$ (amount of overpayment) $$ z=b_0+x_1b_1+x_2b_2+x_3b_3+e. $$

My questions:

1. Do I need to estimate these two models jointly (instead of separately) since the dependent variables seem to be related?
2. If joint estimation is a must, which method (or package in Stata) should I use? Seemingly unrelated regression suest?
3. Any other thoughts in terms of methodology?

Answer 1

I think you are looking for the Heckman model (sample selection model/Heckit model). It is a two stage estimator. In Stata, you use command heckman for that.