I have following question; Can I use time-invariant instrumental variable while controlling for country dummies in pooled cross-sectional dataset? Note: both instrumental variable and endogenous variables are country-specific.
Is there any alternate to solve this problem?
For instance, should I use interaction as instrument variable (for example Time Invariant Instrument * Global or Regional Average of Independent Variable).
Please also guide, does it really make sense to cluster standard errors on the country-level while including country-fixed effects?

Thanks