On Semiparametric Instrumental Variable Estimation of Average Treatment Effects through Data Fusion

TL;DR

This paper develops new methods for estimating average treatment effects using data fusion from two sources with instrumental variables, providing identification conditions, efficiency bounds, and robust inference techniques.

Contribution

It introduces a general framework for nonparametric identification and efficient estimation of causal effects from fused data with heterogeneous populations and instrumental variables.

Findings

Proposed multiply robust, locally efficient estimator.

Derived the efficiency bound for the causal parameter.

Validated methods through simulations and real data application.

Abstract

Suppose one is interested in estimating causal effects in the presence of potentially unmeasured confounding with the aid of a valid instrumental variable. This paper investigates the problem of making inferences about the average treatment effect when data are fused from two separate sources, one of which contains information on the treatment and the other contains information on the outcome, while values for the instrument and a vector of baseline covariates are recorded in both. We provide a general set of sufficient conditions under which the average treatment effect is nonparametrically identified from the observed data law induced by data fusion, even when the data are from two heterogeneous populations, and derive the efficiency bound for estimating this causal parameter. For inference, we develop both parametric and semiparametric methods, including a multiply robust and locally efficient estimator that is consistent even under partial misspecification of the observed data model. We illustrate the methods through simulations and an application on public housing projects.