Estimating Causal Effects of Discrete and Continuous Treatments with Binary Instruments

TL;DR

This paper introduces a new instrumental variable approach using copula invariance to identify and estimate causal effects of treatments with binary instruments, applicable to both discrete and continuous treatments.

Contribution

It develops a novel copula-based framework for causal inference with binary instruments, enabling identification of effects across populations and subpopulations.

Findings

Effective estimation of treatment effects using copula invariance

Application reveals heterogeneity in sleep's impact on well-being

Provides practical distribution regression-based inference procedures

Abstract

We propose an instrumental variable framework for identifying and estimating causal effects of discrete and continuous treatments with binary instruments. The basis of our approach is a local copula representation of the joint distribution of the potential outcomes and unobservables determining treatment assignment. This representation allows us to introduce an identifying assumption, so-called copula invariance, that restricts the local dependence of the copula with respect to the treatment propensity. We show that copula invariance identifies treatment effects for the entire population and other subpopulations such as the treated. The identification results are constructive and lead to practical estimation and inference procedures based on distribution regression. An application to estimating the effect of sleep on well-being uncovers interesting patterns of heterogeneity.