Economic models based on weak but credible assumptions in some cases only deliver set identification, or bounds, on quantities of interest. Many such models quite naturally result in intersection bounds, where the model delivers a number of upper and lower bounds. In such cases, the tightest bounds available are then the lowest upper bound and the highest lower bound. Typical estimators of such bounds are biased. Moreover, standard inferential methods for the measurement of statistical variation do not apply. This work develops a novel and practical method for estimation of and inference on such bounds, applicable in both parametric and non-parametric contexts.

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