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I would like to know from you some advise on how to deal with this issue: I want to explore in a multivariate OLS framework the association between my X and Y. I suspect that my cases are selected in X by their education, and then I need to account for this potential bias in estimating the association btw X and Y (the core focus of my research).

Hence: what procedure should I apply to deal with this situation? I would like to know if it exists a 'gold standard' or different techniques, both to verify if actually education (or whatever other variable) select people within X, and, if so, how to 'purify' the association between X and Y from this selection.

Hope that I was clear enough.

Thanks in advance for you support.

Best, G

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It's hard to tell from the way you describe your problem, but it seems you're dealing with a truncated sample (both $x$ and $y$ values missing in a systematic way). In this case, Heckman's model would be your "gold standard." Keep in mind, however, that the whole technique hinges on your ability to (more or less) correctly model the selection mechanism (i.e., the process that included some $x$ and $y$ in your sample, but excluded others).

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