Marginal Interventional Effects

Abstract: Conventional causal estimands, such as the average treatment effect (ATE), reflect how the mean outcome in a population or subpopulation would change if all units received treatment versus control. Real-world policy changes, however, are often incremental, changing the treatment status for only a small segment of the population who are at or near "the margin of participation." To capture this notion, two parallel lines of inquiry have developed in economics and in statistics and epidemiology that define, identify, and estimate what we call interventional effects. In this article, we bridge these two strands of literature by defining interventional effect (IE) as the per capita effect of a treatment intervention on an outcome of interest, and marginal interventional effect (MIE) as its limit when the size of the intervention approaches zero. The IE and MIE can be viewed as the unconditional counterparts of the policy-relevant treatment effect (PRTE) and marginal PRTE (MPRTE) proposed in the economics literature. However, different from PRTE and MPRTE, IE and MIE are defined without reference to a latent index model, and, as we show, can be identified either under unconfoundedness or through the use of instrumental variables. For both scenarios, we show that MIEs are typically identified without the strong positivity assumption required of the ATE, highlight several "stylized interventions" that may be of particular interest in policy analysis, discuss several parametric and semiparametric estimation strategies, and illustrate the proposed methods with an empirical example.