Sensitivity Analysis for Instrumental Variables Under Joint Relaxations of Monotonicity and Independence

TL;DR

This paper introduces a breakdown frontier method to evaluate how sensitive Local Average Treatment Effect estimates are to violations of key assumptions like monotonicity and independence, providing new bounds and inference tools.

Contribution

It develops a novel sensitivity analysis framework using breakdown frontiers for LATE and ATE under joint relaxations of assumptions, with estimators and bootstrap inference.

Findings

Breakdown frontiers quantify the robustness of causal conclusions.

Monte Carlo simulations confirm finite-sample reliability of estimators.

Empirical application shows conclusions are sensitive to assumption violations.

Abstract

In this paper I develop a breakdown frontier approach to assess the sensitivity of Local Average Treatment Effects (LATE) estimates to violations of monotonicity and independence of the instrument. I parametrize violations of independence using the concept of $c$-dependence from Masten & Poirier (2018) and allow for the share of defiers to be greater than zero but smaller than the share of compliers. I derive identified sets for the LATE and the Average Treatment Effect (ATE) in which the bounds are functions of these two sensitivity parameters. Using these bounds, I derive the breakdown frontier for the LATE, which is the weakest set of assumptions such that a conclusion regarding the LATE holds. I derive consistent sample analogue estimators for the breakdown frontiers and provide a valid bootstrap procedure for inference. Monte Carlo simulations show the desirable finite-sample properties of the estimators and an empirical application shows that the conclusions regarding the effect of family size on unemployment from Angrist & Evans (1998) are highly sensitive to violations of independence and monotonicity.