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This paper proposes a novel tool to nonparametrically identify models with adiscrete endogenous variable or treatment: semi-instrumental variables(semi-IVs). A semi-IV is a variable that is relevant but only partiallyexcluded from the potential outcomes, i.e., excluded from at least one, but notnecessarily all, potential outcome equations. It follows that standardinstrumental variables (IVs), which are fully excluded from all the potentialoutcomes, are a special (extreme) case of semi-IVs. I show that full exclusionis stronger than necessary because the same objects that are usually identifiedwith an IV (Imbens and Angrist, 1994; Heckman and Vytlacil, 2005; Chernozhukovand Hansen, 2005) can be identified with several semi-IVs instead, providedthere is (at least) one semi-IV excluded from each potential outcome. Forapplied work, tackling endogeneity with semi-IVs instead of IVs should be anattractive alternative, since semi-IVs are easier to find: mostselection-specific costs or benefits can be valid semi-IVs, for example. Thepaper also provides a simple semi-IV GMM estimator for models with homogenoustreatment effects and uses it to estimate the returns to education.

Don't (fully) exclude me, it's not necessary! Identification with semi-IVs