Instrument Validity for Heterogeneous Causal Effects

TL;DR

This paper introduces a flexible nonparametric test for instrument validity in models with heterogeneous causal effects, applicable to multivalued treatments, and demonstrates its effectiveness through simulations and empirical application.

Contribution

It develops a general, asymptotically size-controlled test for instrument validity that extends to multivalued treatments and improves upon existing methods.

Findings

Test is asymptotically size controlled and consistent.

Performs well in finite sample simulations.

Successfully applied to return to schooling study.

Abstract

This paper provides a general framework for testing instrument validity in heterogeneous causal effect models. The generalization includes the cases where the treatment can be multivalued ordered or unordered. Based on a series of testable implications, we propose a nonparametric test which is proved to be asymptotically size controlled and consistent. Compared to the tests in the literature, our test can be applied in more general settings and may achieve power improvement. Refutation of instrument validity by the test helps detect invalid instruments that may yield implausible results on causal effects. Evidence that the test performs well on finite samples is provided via simulations. We revisit the empirical study on return to schooling to demonstrate application of the proposed test in practice. An extended continuous mapping theorem and an extended delta method, which may be of independent interest, are provided to establish the asymptotic distribution of the test statistic under null.