Phase transition of the monotonicity assumption in learning local average treatment effects

TL;DR

This paper investigates the sensitivity of the monotonicity assumption in LATE estimation, revealing a phase transition where small violations can drastically affect the ability to identify the sign of the treatment effect.

Contribution

It characterizes the phase transition boundary for the monotonicity assumption and proposes simple alternatives, enhancing understanding of when LATE identification is feasible.

Findings

A phase transition boundary is explicitly characterized.

Learning the sign of LATE is impossible on one side of the boundary.

Testing the monotonicity assumption is feasible in specific cases with near one-sided non-compliance.

Abstract

We consider the setting in which a strong binary instrument is available for a binary treatment. The traditional LATE approach assumes the monotonicity condition stating that there are no defiers (or compliers). Since this condition is not always obvious, we investigate the sensitivity and testability of this condition. In particular, we focus on the question: does a slight violation of monotonicity lead to a small problem or a big problem? We find a phase transition for the monotonicity condition. On one of the boundary of the phase transition, it is easy to learn the sign of LATE and on the other side of the boundary, it is impossible to learn the sign of LATE. Unfortunately, the impossible side of the phase transition includes data-generating processes under which the proportion of defiers tends to zero. This boundary of phase transition is explicitly characterized in the case of binary outcomes. Outside a special case, it is impossible to test whether the data-generating process is on the nice side of the boundary. However, in the special case that the non-compliance is almost one-sided, such a test is possible. We also provide simple alternatives to monotonicity.