Sample selection bias and logistic regression 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!
 A: Welcome, Pokemonfan! 
Are you able to make your conclusions conditional on the self-selection bias implied by emigration and acknowledge that generalization beyond that context is speculative, but not wholly without merit? If so, then there is nothing to worry about. 
If you require the ability to generalize beyond the immigrant subgroup of a country, then you certainly would need data from non-emigrants. If you can't get the most relevant data, you might try to correlated behaviors through some intermediate variables that couple "cultural risk attitudes" to observables like fraction of assets in stocks vs. riskless investments or mean-time in a job or entrepreneurial rates (new business account openings per 1000), but then you would need to have that data from the home country. Likewise, if you could correlate through immigrants from another country whose non-emigree data is available, then that could be a pathway from observables here to observables there. If the correlations are weak as often happens in the social science, and if you need a chain of such weak correlations, then you are probably better off by amending your analysis with the dependent clause given that they came to America.
How is a limiting conditional statement still worthwhile? Conditional statements are better received by reviewers than unconditional ones, and that speculative generalizations of conditional statements are perfectly employable as Bayesian priors . . . conditional on the assumption that no better priors exist, naturally.
