DID with instrument and continuous treatment variable

[Abdelrahman Mokhtar]

Hi,
Is there a way to instrument a continuous treatment variable in DiD?
I can only think of estimating a first stage separately and predicting the instrumented treatment to be used in DiD, but I know that this doesn't give accurate standard errors in the second stage.

This is the code without instrumenting

reghdfe birthrate c.treatment##i.post treatment lpop, absorb(state post)

[George Ford]

for the interaction, control function might be best. straightforward if both continuous.