A common example of the Heckman selection model involves wages, which are only observed if an individual chooses to participate in the labor force. The first stage probit model dependent variable is a labor force participation indicator. The second stage models wages (w), which are only observed conditional on working, so a correction term is added.
I’ve read a couple working papers recently that employ the Heckman model, but the selection and outcome equations seem less directly related. I’m wondering if that creates any issues. For instance, what if the second-stage here was total individual spending based on consumption data, and the first stage modeled labor force participation. Are there situations where something like this might be reasonable?
I personally haven’t worked with the Heckman model in quite some time and any clarification is much appreciated.