Endogenous treatment with different aggregation

[Ariel Soto-Caro]

I'm investigating the effect at the individual level of a policy applied at the county level. But this policy is potentially endogenous.
In such a case, if I decide to instrumentalize the policy (again, which varies at the county level), the instrument(s) will also vary at the county level.
Because the county indicator of the policy is binary, I was planning to use a control function approach.

My questions are:

• Is it econometrically correct to estimate the control function (e.g., a probit) at the county level and then use the predicted values as the instrument in a 2sls estimation at the individual level?
• If so, what is the standard procedure to deal with this different-levels-of-aggregation estimation because the probit should be estimated at the county level? Still, the 2sls regression will be at the individual level.

Am I too disoriented?
I appreciate any guidance.
Thanks in advance.