2017

Matthew Blackwell (Harvard University)

"Instrumental Variable Methods for Conditional Effects and Causal Interaction in Voter Mobilization Experiments"

Selection committee: Michael Peress (Stonybrook) and Brandon Stewart (Princeton)

Citation:

How can one deal with non-compliance in an experiment with a binary treatment? And how can one interpret the two-stage least squares (2SLS) estimate for an endogenous variable when that endogenous variable has a heterogeneous effect? Both of these questions are answered by Angrist, Imbens, and Rubin's (1996) landmark paper "Identification of causal effects using instrumental variables." In both cases, under a set of (arguably weak) assumptions, the 2SLS estimate yields a weighted average of treatment effects---often called a local average treatment effect (LATE). There have been numerous attempts to extend this result beyond the case of a binary instrument and binary endogenous variable, but these results are much less clear. Matt Blackwell's exceptional paper considers one particular extension that is useful for practitioners and yields concrete results---the case of two instruments and two binary treatments. Experiments with two binary treatments and noncompliance are common in applied work and practitioners have sometimes attempted to apply the Angrist et al. result to this case. Matt's paper introduces new estimands, proposes estimators, derives the properties of these estimators, and considers the implications of applying 2SLS to this case.

In the case of a binary instrument and a binary treatment, two stage least squares gives you an interpretable estimate under heterogeneous effects. In the case Matt considers, it does not. While the interaction term will give you a consistent estimate of a LATE for the interaction effect, the two base terms cannot be interpreted as LATEs without additional assumptions. In the special case where all effects are homogeneous (but potentially interacting), 2SLS will recover the correct effects. In the special case where the causal effects don't interact, 2SLS will produce correct estimates of a LATE. Otherwise, a different estimator (such as the one Matt proposes) needs to be applied.

What is a practitioner to do in light of these results? The practitioner can focus on the intent to treat effect thus bypassing issues of noncompliance. The practitioner can rely on 2SLS without an interaction term, but is assuming that there is no interaction. The practitioner can rely on the assumption that the effects are homogeneous and apply 2SLS with an interaction. Finally, the practitioner can use the alternative estimators that Matt proposes, which are interpretable as weighted averages of heterogeneous effects, invoking the additional assumption that compliance of one type does not depend on assignment to the other type of treatment. Matt's paper is a remarkably clear treatment of a very difficult problem and gives clear guidance about how to think about noncompliance in experiments with two binary treatments as well as how to think about 2SLS estimates where there are two binary instruments and two potentially interacting endogenous variables.