Detecting Grouped Local Average Treatment Effects and Selecting True Instruments

TL;DR

This paper introduces a two-step data-driven method to identify true instruments and homogeneous local average treatment effects in models with multiple, potentially invalid instruments, improving causal inference accuracy.

Contribution

It proposes a novel clustering-based procedure to distinguish valid instruments from invalid ones and consistently estimate homogeneous treatment effects despite instrument heterogeneity.

Findings

The method accurately identifies true instruments in simulations.

It provides consistent and asymptotically normal LATE estimators.

Empirical application shows effectiveness in real-world data.

Abstract

Under an endogenous binary treatment with heterogeneous effects and multiple instruments, we propose a two-step procedure for identifying complier groups with identical local average treatment effects (LATE) despite relying on distinct instruments, even if several instruments violate the identifying assumptions. We use the fact that the LATE is homogeneous for instruments which (i) satisfy the LATE assumptions (instrument validity and treatment monotonicity in the instrument) and (ii) generate identical complier groups in terms of treatment propensities given the respective instruments. We propose a two-step procedure, where we first cluster the propensity scores in the first step and find groups of IVs with the same reduced form parameters in the second step. Under the plurality assumption that within each set of instruments with identical treatment propensities, instruments truly satisfying the LATE assumptions are the largest group, our procedure permits identifying these true instruments in a data driven way. We show that our procedure is consistent and provides consistent and asymptotically normal estimators of underlying LATEs. We also provide a simulation study investigating the finite sample properties of our approach and an empirical application investigating the effect of incarceration on recidivism in the US with judge assignments serving as instruments.