Testing Partial Instrument Monotonicity

TL;DR

This paper introduces a nonparametric test for partial instrument monotonicity in multi-instrument causal inference, demonstrating its effectiveness through simulations and an application to HIV status knowledge.

Contribution

It proposes a simple nonparametric test for partial monotonicity in multi-instrument settings, extending the validity of 2SLS estimands under weaker assumptions.

Findings

The test has good finite sample properties in simulations.

The test applied to real data on HIV status instruments.

Partial monotonicity can be reliably tested in practice.

Abstract

When multi-dimensional instruments are used to identify and estimate causal effects, the monotonicity condition may not hold due to heterogeneity in the population. Under a partial monotonicity condition, which only requires the monotonicity to hold for each instrument separately holding all the other instruments fixed, the 2SLS estimand can still be a positively weighted average of LATEs. In this paper, we provide a simple nonparametric test for partial instrument monotonicity. We demonstrate the good finite sample properties of the test through Monte Carlo simulations. We then apply the test to monetary incentives and distance from results centers as instruments for the knowledge of HIV status.