I am struggling with possible sample selection bias at the moment, and I was wondering whether someone has a methodological tip or possibly knows of fancy statistical/econometric tools I could use to solve this issue.
The context is as follows: I am studying the effects of cultural risk attitudes on the engagement in some risky behaviour. To do so, I am developing a logistic regression model using various socioeconomic characteristics of immigrants in a country and their countries of origin. The focus on immigrants in the same country is needed to isolate purely cultural effects from institutional and economic factors (which is why we do not simply employ a panel-data analysis of different countries). However, (economic) immigrants are known to be less risk averse than their cultural counterparts in their motherland. Leading to a self-selection into our sample. This could bias the estimated cultural effect upwards when naively applying logistic regression.
The main problem I have is the following. Suppose we had data on both the immigrants as well as the people who decided to not emigrate, then we could employ a tobit like regression model to take this self-selection effect into account. Sadly we have no observations about the people who stay home so this is no option. We also have no data on reasons of migration, so we are unable to filter economic migrants out of our sample.
Any help or tips would be greatly appreciated!