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The hypothesis of homogeneous treatment effects is central to theinstrumental variables literature. This assumption signifies that treatmenteffects are constant across all subjects. It allows to interpret instrumentalvariable estimates as average treatment effects over the whole population ofthe study. When this assumption does not hold, the bias of instrumentalvariable estimators can be larger than that of naive estimators ignoringendogeneity. This paper develops two tests for the assumption of homogeneoustreatment effects when the treatment is endogenous and an instrumental variableis available. The tests leverage a covariable that is (jointly with the errorterms) independent of a coordinate of the instrument. This covariate does notneed to be exogenous. The first test assumes that the potential outcomes arelinear in the regressors and is computationally simple. The second test isnonparametric and relies on Tikhonov regularization. The treatment can beeither discrete or continuous. We show that the tests have asymptoticallycorrect level and asymptotic power equal to one against a range ofalternatives. Simulations demonstrate that the proposed tests attain excellentfinite sample performances. The methodology is also applied to the evaluationof returns to schooling and the effect of price on demand in a fish market.

Testing for homogeneous treatment effects in linear and nonparametric instrumental variable models