The Width of Partial-Identification Bounds as a Function of Dependence Among Selection Mechanisms

When individuals are excluded by all relevant selection mechanisms, no outcome observations arise about them. This note records an elementary but useful comparative statics: the width of the Manski bound for a population mean of a [0,1]-bounded outcome equals the mass of the jointly unobserved region, and — holding each mechanism’s marginal rejection rate fixed — this mass is non-decreasing in the supermodular order of the rejection indicators. More closely aligned exclusions widen the bound even when no single mechanism rejects more. The results are direct compositions of established tools (Manski bounds; Fréchet–Hoeffding inequalities; stochastic orders); the contribution is the separation of the dependence effect from the volume effect, not technical novelty. The bridge from ‘similar models’ to dependent rejections is stated as an empirical hypothesis, not a theorem.