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Near/Far Matching: A Nonparametric Instrumental Variable Technique for Binary Outcomes
*Mike Baiocchi, University of Pennsylvania 
Scott Lorch, Children's Hospital of Philadelphia 
Paul Rosenbaum, University of Pennsylvania 
Dylan Small, University of Pennsylvania 

Keywords: Causal inference, instrumental variables, strength of instrument, matching, binary outcomes

Instrumental variables (IV) is a framework for making causal inferences about the effect of a treatment based on an observational study in which there are unmeasured confounding variables. The most common form of IV estimation is two-stage least squares (2SLS), which works well when the outcome of interest is continuous. However, in many policy settings the objective is to estimate the effect of a treatment on a binary outcome. We develop a nonparametric matching technique – “near/far matching” - which is capable of estimating population level treatment effects when the outcome is binary. We provide a test statistic, with standard errors, and a method for sensitivity analysis. Many researchers assume the strength of a particular instrument is fixed. It is not. A novel feature of our method is that it allows us to manipulate the strength of a particular instrument. We illustrate our method using a study of neonatal intensive care units (NICUs) treatment effect on premature babies (preemies) born in Pennsylvania.