## IV and causality

We like to tell the IV story in two iterations, first in a restricted model with constant effects, then in a framework with unrestricted heterogeneous potential outcomes, in which case causal effects must also be heterogeneous. The introduction of heterogeneous effects enriches the interpretation of IV estimands, without changing the mechanics of the core statistical methods we are most likely to use in practice (typically, two – stage least squares). An initial focus on constant effects allows us to explain the mechanics of IV with a minimum of fuss.

To motivate the constant-effects setup as a framework for the causal link between schooling and wages, suppose, as before, that potential outcomes can be written

Y si = fi (s) ;

and that

fi (s) = ^0 + KlS + Vi, (4.1.1)

as in the introduction ...

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