Understanding Instrumental Variables in Models with Essential Heterogeneity

TLDR

The paper investigates how instrumental variables perform in models where treatment responses are heterogeneous and agents choose interventions based on partial knowledge of their own responses. The study aims to extend prior work by creating weighted treatment effect estimators for general instruments and proposing a simple test for essential heterogeneity. The authors analyze two‑ and multiple‑outcome choice models, permitting both transition‑specific and general instruments, and develop weighted estimators and a test for essential heterogeneity. The analysis reveals that essential heterogeneity is asymmetric—outcomes vary while choices do not—and that IV estimation fails when both choices and outcomes are symmetrically heterogeneous.

Abstract

This paper examines the properties of instrumental variables (IV) applied to models with essential heterogeneity, that is, models where responses to interventions are heterogeneous and agents adopt treatments (participate in programs) with at least partial knowledge of their idiosyncratic response. We analyze two-outcome and multiple-outcome models, including ordered and unordered choice models. We allow for transition-specific and general instruments. We generalize previous analyses by developing weights for treatment effects for general instruments. We develop a simple test for the presence of essential heterogeneity. We note the asymmetry of the model of essential heterogeneity: outcomes of choices are heterogeneous in a general way; choices are not. When both choices and outcomes are permitted to be symmetrically heterogeneous, the method of IV breaks down for estimating treatment parameters.