Econometrica: Jul 2019, Volume 87, Issue 4

Confidence Intervals for Projections of Partially Identified Parameters

https://doi.org/10.3982/ECTA14075
p. 1397-1432

Hiroaki Kaido, Francesca Molinari, Jörg Stoye

We propose a bootstrap‐based calibrated projection procedure to build confidence intervals for single components and for smooth functions of a partially identified parameter vector in moment (in)equality models. The method controls asymptotic coverage uniformly over a large class of data generating processes. The extreme points of the calibrated projection confidence interval are obtained by extremizing the value of the function of interest subject to a proper relaxation of studentized sample analogs of the moment (in)equality conditions. The degree of relaxation, or critical level, is calibrated so that the function of θ, not θ itself, is uniformly asymptotically covered with prespecified probability. This calibration is based on repeatedly checking feasibility of linear programming problems, rendering it computationally attractive.



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