The Proximal Bootstrap for Constrained Estimators

• Econometrics

Date and Location

Monday, November 8, 2021, 3:40 PM - 5:00 PM
ARE Library Conference Room, 4101 Social Sciences and Humanities

Abstract

We demonstrate how to use the proximal bootstrap to pointwise consistently estimate the limiting distribution of \sqrt{n}-consistent estimators defined as the solution to a constrained optimization problem with a possibly nonsmooth and nonconvex sample objective function and a constraint set defined by smooth equalities and/or inequalities that can be either fixed or estimated from the data at the \sqrt{n} rate. The proximal bootstrap estimator is typically much faster to compute than the standard bootstrap because it can be written as the solution to a quadratic programming problem. Monte Carlo simulations illustrate the valid coverage of the proximal bootstrap in a boundary constrained nonsmooth GMM model, a conditional logit model with estimated capacity constraints, and a Mathematical programming with equilibrium constraints (MPEC) formulation of the Rust (1987) Bus Engine Replacement model proposed in Su and Judd (2012).