I am asking this because I know there are IA's for cross sectional estimators and D-in-D estimators, but am unsure if there are any for IV estimation. Does anyone know if there is or isn't, and if there is - what would it be?
The instrumental variable $Z$ must be:
There is also a third assumption that has to do with what parameter you are trying to estimate. It only applies if there's heterogeneity in the effect of X on Y. Simply put, IV measures the average effect of X on Y caused by wiggling X through Z. If there are 2 types of people who respond differently when X changes, and our instrument only wiggles X for the first type, IV will give you the effect of X on Y for only those folks. OLS would give you a weighted average of the two (assuming you solved the endogeneity problem somehow). If everyone is the same (no heterogeneity), you don't need to worry about this.