USING INSTRUMENTAL VARIABLES FOR INFERENCE ABOUT POLICY RELEVANT TREATMENT PARAMETERS
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. The question of policy relevance and external validity turns on our 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 logically permissible values of the treatment parameters of interest. We show how to extract the information about the average effect of interest from the IV estimand, and more generally, from a class of IV like estimands which includes the TSLS and OLS estimands, among many others. Our method has several applications. First, it can be used to construct nonparametric bounds on the average causal effects of an actual or 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 provides specification tests. In addition to testing the null of correctly specified model, we can use our method to test null hypotheses of no selection bias, no selection on gains and instrument validity. Importantly, specification tests using our method do not require the treatment effect to be constant over individuals with the same observables. To illustrate the applicability of our method, we use Norwegian administrative data to draw inference about the causal effects of family size on children's outcomes. *We thank the audience at the 2016 Cowles Foundation Summer Econometrics Conference. Bradley Setzler provided excellent research assistant. +Department of Economics, University of Chicago; Statistics Norway; NBER. +Department of Economics, University of California at San Diego. Research supported in part by National Science Foundation grant SES 1426882. SSDepartment of Economics, Northwestern University. Research supported in part by National Science Foundation grant SES 1530538. The hospitality of the Department of Economics at the University of Chicago is gratefully acknowledged.