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Inference on breakdown frontiers

Authors: Matthew Masten and Alexandre Poirier
Date: 15 May 2017
Type: cemmap Working Paper, CWP20/17
DOI: 10.1920/wp.cem.2017.2017


A breakdown frontier is the boundary between the set of assumptions which lead to a specifi c conclusion and those which do not. In a potential outcomes model with a binary treatment, we consider two conclusions: First, that ATE is at least a specifi c value (e.g., nonnegative) and second that the proportion of units who bene fit from treatment is at least a speci c value (e.g., at least 50%). For these conclusions, we derive the breakdown frontier for two kinds of assumptions: one which indexes deviations from random assignment of treatment, and one which indexes deviations from rank invariance. These classes of assumptions nest both the point identifying assumptions of random assignment and rank invariance and the opposite end of no constraints on treatment selection or the dependence structure between potential outcomes. This frontier provides a quantitative measure of robustness of conclusions to deviations in the point identifying assumptions. We derive √N-consistent sample analog estimators for these frontiers. We then provide an asymptotically valid bootstrap procedure for constructing lower uniform confi dence bands for the breakdown frontier. As a measure of robustness, this confi dence band can be presented alongside traditional point estimates and con fidence intervals obtained under point identifying assumptions. We illustrate this approach in an empirical application to the e ffect of child soldiering on wages. We fi nd that conclusions are fairly robust to failure of rank invariance, when random assignment holds, but conclusions are much more sensitive to both assumptions for small deviations from random assignment.

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