Using Instrumental Variables for Inference About Policy Relevant Treatment Parameters

Abstract

We propose a method for using instrumental variables (IV) to draw inference about causal effects for individuals other than those affected by the instrument at hand. Policy relevance and external validity turns on the ability to do this reliably. Our method exploits the insight that both the IV estimand and many treatment parameters can be expressed as weighted averages of the same underlying marginal treatment effects. Since the weights are known or identified, knowledge of the IV estimand generally places some restrictions on the unknown marginal treatment effects, and hence on the values of the treatment parameters of interest. We show how to extract information about the average effect of interest from the IV estimand, and, more generally, from a class of IV-like estimands that includes the two stage least squares and ordinary least squares estimands, among many others. Our method has several applications. First, it can be used to construct nonparametric bounds on the average causal effect of a hypothetical policy change. Second, our method allows the researcher to flexibly incorporate shape restrictions and parametric assumptions, thereby enabling extrapolation of the average effects for compliers to the average effects for different or larger populations. Third, our method can be used to test model specification and hypotheses about behavior, such as no selection bias and/or no selection on gain. To accommodate these diverse applications, we devise a novel inference procedure that is designed to exploit the convexity of our setting. We develop uniformly valid tests that allow for an infinite number of IV--like estimands and a general convex parameter space. We apply our method to analyze the effects of price subsidies on the adoption and usage of an antimalarial bed net in Kenya.