Econometrica: Jul, 2019, Volume 87, Issue 4
Confidence Intervals for Projections of Partially Identified Parameters
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.
Supplement to "Confidence Intervals for Projections of Partially Identified Parameters"
This zip file contains the replication files for the manuscript and a supplemental appendix containing material not found within the manuscript.