When I want to estimate educational return, I run a regression like:
ln(wage)=beta1+beta2*education+other control variables+u
In order to tackle the endogenous problems induced by potential individual abilities, I use education level of spouse as instrumental variable for own education level. Because on the one hand, spouse's education is usually correlated correlated with own education, and on the other hand spouse's education can only affect my wage earnings through my own education.
However, this is not valid for unmarried people. So can anyone tell me how to tackle such endogeneities with "truncated" data structure?
You would need a model allowing for selection and an additional IV.
Follow this advice of Wooldridge:
https://www.statalist.org/forums/forum/general-stata-discussion/general/1295287-heckman-sample-selection-and-instrumental-variable-iv-or-simultaneous-equations-model
You would need an instrument for education (wife's education) and also an instrument for being married or not (for the first equation).
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