Subvector Inference in PI Models with Many Moment Inequalities

• Activity Number: 626 - Recent Advances in High-Dimensional Statistical Inference
• Type: Invited
• Date/Time: Thursday, August 1, 2019 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Alexandre Belloni* and Federico Bugni and Victor Chernozhukov
• Companies: Duke University and Duke University and MIT
• Keywords: moment inequalities; minmax; central limit theorem; bootstrap; penalization

Abstract

This paper considers inference for a function of a parameter vector in a partially identified model with many moment inequalities. This framework allows the number of moment conditions to grow with the sample size, possibly at exponential rates. Our main motivating application is subvector inference, i.e., inference on a single component of the partially identified parameter vector associated with a treatment effect or a policy variable of interest. Our inference method compares a MinMax test statistic (minimum over parameters satisfying H_0 and maximum over moment inequalities) against critical values that are based on bootstrap approximations or analytical bounds. We show that this method controls asymptotic size uniformly over a large class of data generating processes despite the partially identified many moment inequality setting. The finite sample analysis allows us to obtain explicit rates of convergence on the size control. Our results are based on combining non-asymptotic approximations and new high-dimensional central limit theorems for the MinMax of the components of random matrices.