Covariate-assisted bounds on causal effects with instrumental variables

TL;DR

This paper develops new methods to estimate bounds on causal effects using instrumental variables, accommodating covariates and continuous outcomes, with a focus on influence function-based estimators and their finite sample performance.

Contribution

It introduces influence function-based estimators for covariate-adjusted bounds on causal effects with IVs, applicable to continuous outcomes and observational data.

Findings

Proposed estimators attain parametric rates under a margin condition.

Extensions to continuous outcomes are developed.

Simulation studies demonstrate finite sample performance.

Abstract

When an exposure of interest is confounded by unmeasured factors, an instrumental variable (IV) can be used to identify and estimate certain causal contrasts. Identification of the marginal average treatment effect (ATE) from IVs relies on strong untestable structural assumptions. When one is unwilling to assert such structure, IVs can nonetheless be used to construct bounds on the ATE. Famously, Balke and Pearl (1997) proved tight bounds on the ATE for a binary outcome, in a randomized trial with noncompliance and no covariate information. We demonstrate how these bounds remain useful in observational settings with baseline confounders of the IV, as well as randomized trials with measured baseline covariates. The resulting bounds on the ATE are non-smooth functionals, and thus standard nonparametric efficiency theory is not immediately applicable. To remedy this, we propose (1) under a novel margin condition, influence function-based estimators of the bounds that can attain parametric convergence rates when the nuisance functions are modeled flexibly, and (2) estimators of smooth approximations of these bounds. We propose extensions to continuous outcomes, explore finite sample properties in simulations, and illustrate the proposed estimators in an observational study targeting the effect of higher education on wages.