Simultaneous Confidence Intervals for Partially Identified Parameters

Abstract

This article extends the Imbens and Manski (2004) and Stoye (2009) confidence interval for a partially identified scalar parameter to a vector-valued parameter. The proposed method produces uniformly valid simultaneous confidence intervals for each dimension, or, equivalently, a rectangular confidence region that covers points in the identified set with a specified probability. The method applies when asymptotically normal estimates of upper and lower bounds for each dimension are available. The intervals are computationally simple and fast relative to methods based on test inversion or bootstrapped calibration, and do not suffer from the conservativity of projection-based approaches.

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