# 2-stage Heckman instrumental variable estimation

I am working on my thesis. My main regression model is the following:

1. $$Y=x_1*{\rm Payment}+x_2*{\rm Country}+x_3*{\rm Industry}...$$

All independent variables are dummy / binary variables. In a next step I divide my sample and construct the following two regression:

2. $$Y=x_2*{\rm Country}+x_3*{\rm Industry}...$$ => Here I only consider observations which had the value "1" regarding the "Payment"-independent variable

3. $$Y=x_2*{\rm Country}+x_3*{\rm Industry}...$$ => Here I only consider observations which had the value "0" regarding the "Payment"-independent variable.

The independent variable Payment is quite important in my thesis and all remaining variables can be rather considered as control variables. Payment takes the value 1 if the M&A deal is paid in cash and 0 if it is paid in shares.

I received the following feedback from my supervisor and I am not quite sure how to incorporate it:

...Can you really split the sample into cash and stock M&A?... If you are indeed correct with your hypothesis then different companies will go for cash than for stock as a payment method...Hence your two populations are NOT the same. In other words: There is a endogeneity problem. To solve it use the 2-stage Heckman instrumental variable estimation....Pay attention to the economic justification of your IVs and to their econometric testing (valid instrument)...

When I look up the Heckman procedure (especially the female wage example) it seems that it is analysing Y. However I understand that I need to do this with my independent variable ("Payment").

Hence I am confused as I don't see the link between the female wage example and my case.