SMU SOE Seminar Series (May 21, 2025): Evaluating Counterfactual Policies Using Instruments

TOPIC:

ABSTRACT

In settings with instrumental variables, the TSLS estimator is the most popular way of summarizing causal evidence. Yet in many settings, the instrument monotonicity assumption needed for its causal interpretation is refuted. A prominent example are designs using the (quasi-)random assignment of defendants to judges as an instrument for incarceration. But ultimately, we may not be interested in the TSLS estimand itself, but rather in the impact of some counterfactual policy intervention (e.g. an encouragement to release more defendants). In this paper, we derive tractable sharp bounds on the impact of such counterfactual policies under reasonable sets of assumptions. We show that for a variety of common policy exercises, the bounds do not depend on whether one imposes instrument monotonicity, and thus one can drop this often-tenuous assumption without loss of information. We explore other restrictions that can help to tighten the bounds, including the policy invariance assumption commonly used in applications of the marginal treatment effects framework and its relaxations. We illustrate the usefulness of this approach in an application involving the quasi-random assignment of prosecutors to defendants in Massachusetts.

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