Dilation bootstrap

TL;DR

This paper introduces a dilation bootstrap method for constructing confidence regions in partially identified models, leveraging a novel approach to handle sampling uncertainty without relying on the economic structure.

Contribution

It develops a dilation bootstrap technique that generalizes the bootstrap of the quantile process to higher dimensions for better confidence region construction.

Findings

Provides a new bootstrap-based method for confidence regions in complex models

Allows for distribution-free inference in partially identified models

Enables practical implementation using empirical data

Abstract

We propose a methodology for constructing confidence regions with partially identified models of general form. The region is obtained by inverting a test of internal consistency of the econometric structure. We develop a dilation bootstrap methodology to deal with sampling uncertainty without reference to the hypothesized economic structure. It requires bootstrapping the quantile process for univariate data and a novel generalization of the latter to higher dimensions. Once the dilation is chosen to control the confidence level, the unknown true distribution of the observed data can be replaced by the known empirical distribution and confidence regions can then be obtained as in Galichon and Henry (2011) and Beresteanu, Molchanov and Molinari (2011).