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

TL;DR

This paper introduces two novel tests for assessing the assumption of homogeneous treatment effects in instrumental variable models, applicable to both linear and nonparametric settings, with proven asymptotic properties and demonstrated effectiveness.

Contribution

It develops two new tests for homogeneous treatment effects in IV models, one linear and one nonparametric, that do not require the covariate to be exogenous.

Findings

Tests have correct asymptotic level

Tests achieve power of one against alternatives

Simulations show excellent finite sample performance

Abstract

The hypothesis of homogeneous treatment effects is central to the instrumental variables literature. This assumption signifies that treatment effects are constant across all subjects. It allows to interpret instrumental variable estimates as average treatment effects over the whole population of the study. When this assumption does not hold, the bias of instrumental variable estimators can be larger than that of naive estimators ignoring endogeneity. This paper develops two tests for the assumption of homogeneous treatment effects when the treatment is endogenous and an instrumental variable is available. The tests leverage a covariable that is (jointly with the error terms) independent of a coordinate of the instrument. This covariate does not need to be exogenous. The first test assumes that the potential outcomes are linear in the regressors and is computationally simple. The second test is nonparametric and relies on Tikhonov regularization. The treatment can be either discrete or continuous. We show that the tests have asymptotically correct level and asymptotic power equal to one against a range of alternatives. Simulations demonstrate that the proposed tests attain excellent finite sample performances. The methodology is also applied to the evaluation of returns to schooling and the effect of price on demand in a fish market.