Labor Seminars Amsterdam

Magne Mogstad (University of Chicago, United States)
Tuesday, 13 December 2016

We propose a method for using instrumental variables (IV) to draw inference about causal e ffects for individuals other than those aff ected 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 e ffects. Since the weights are known or identi fied, knowledge of the IV estimand generally places some restrictions on the unknown marginal treatment eff ects, and hence on the logically permissible values of the treatment parameters of interest. We show how to extract the information about the average eff ect 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 eff ects 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 eff ects for compliers to the average e ffects for di fferent or larger populations. Third, our method provides speci fication tests. In addition to testing the null of correctly specifi ed model, we can use our method to test null hypotheses of no selection bias, no selection on gains and instrument validity. Importantly, specication tests using our method do not require the treatment e ffect 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 eff ects of family size on children’s outcomes. Joint with A. Santos and A. Torgovitsky.