Testing Inequalities Linear in Nuisance Parameters

TL;DR

This paper introduces a new, practical test for inequalities linear in nuisance parameters, applicable in various econometric models, with proven asymptotic validity and demonstrated effectiveness in simulations and an empirical case study.

Contribution

It develops a simple, tuning-parameter-free test for inequalities linear in nuisance parameters, with a novel data-dependent chi-squared critical value and proven uniform asymptotic validity.

Findings

Test has correct size in finite samples.

Test demonstrates high power in simulations.

Empirical application shows practical usefulness.

Abstract

This paper proposes a new test for inequalities that are linear in possibly partially identified nuisance parameters. This type of hypothesis arises in a broad set of problems, including subvector inference for linear unconditional moment (in)equality models, specification testing of such models, and inference for parameters bounded by linear programs. The new test uses a two-step test statistic and a chi-squared critical value with data-dependent degrees of freedom that can be calculated by an elementary formula. Its simple structure and tuning-parameter-free implementation make it attractive for practical use. We establish uniform asymptotic validity of the test, demonstrate its finite-sample size and power in simulations, and illustrate its use in an empirical application that analyzes women's labor supply in response to a welfare policy reform.