A Vector Monotonicity Assumption for Multiple Instruments

TL;DR

This paper introduces the vector monotonicity assumption for multiple instruments, broadening the identification of causal effects in binary treatment models by allowing for more flexible response patterns.

Contribution

It proposes the vector monotonicity assumption, characterizes the identified causal parameters, and provides a simple estimator, extending the LATE framework for multiple instruments.

Findings

Characterizes the class of point-identified causal parameters under vector monotonicity.

Provides a constructive identification method and a simple estimator.

Revisits labor market returns to college using the new framework.

Abstract

When a researcher combines multiple instrumental variables for a single binary treatment, the monotonicity assumption of the local average treatment effects (LATE) framework can become restrictive: it requires that all units share a common direction of response even when separate instruments are shifted in opposing directions. What I call vector monotonicity, by contrast, simply assumes treatment uptake to be monotonic in all instruments. I characterize the class of causal parameters that are point identified under vector monotonicity, when the instruments are binary. This class includes, for example, the average treatment effect among units that are in any way responsive to the collection of instruments, or those that are responsive to a given subset of them. The identification results are constructive and yield a simple estimator for the identified treatment effect parameters. An empirical application revisits the labor market returns to college.