# Simple Adaptive Size-Exact Testing for Full-Vector and Subvector Inference in Moment Inequality Models

## TL;DR

This paper introduces a simple, computationally efficient test for moment inequalities that maintains exact size in normal models and adapts to inequality slackness, suitable for confidence set construction and subvector inference.

## Contribution

It proposes a size-exact, tuning-parameter-free test based on a quasi-likelihood ratio statistic, adaptable for subvectors and conditional moment inequalities.

## Key findings

- Test has exact size in normal models with known variance.
- The test is computationally fast and suitable for confidence set construction.
- It adapts to the slackness of moment inequalities without tuning parameters.

## Abstract

We propose a simple test for moment inequalities that has exact size in normal models with known variance and has uniformly asymptotically exact size more generally. The test compares the quasi-likelihood ratio statistic to a chi-squared critical value, where the degree of freedom is the rank of the inequalities that are active in finite samples. The test requires no simulation and thus is computationally fast and especially suitable for constructing confidence sets for parameters by test inversion. It uses no tuning parameter for moment selection and yet still adapts to the slackness of the moment inequalities. Furthermore, we show how the test can be easily adapted for inference on subvectors for the common empirical setting of conditional moment inequalities with nuisance parameters entering linearly.