Econometrica: Sep 2018, Volume 86, Issue 5
Using Instrumental Variables for Inference about Policy Relevant Treatment Parameters
Magne Mogstad, Andres Santos, Alexander Torgovitsky
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 turn 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 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 treatment parameter 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 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.
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Supplement to "Using Instrumental Variables for Inference about Policy Relevant Treatment Parameters"
This supplemental appendix contains: (i) A derivation of the MTR weights for the class of linear IV estimands; (ii) a discussion of the computational advantages of the Bernstein polynomials; (iii) an analysis of consistency for the estimator developed in Section 3.2; and (iv) a discussion of how to construct the preliminary estimators used in Section 3.2.