Universal Inference for Incomplete Models

Abstract

This paper develops a robust inference method with finite-sample validity for general discrete choice models. The procedure’s appeal is its simplicity and versatility; it compares a novel likelihood-ratio statistic to a fixed critical value and can be used in models with set-valued predictions and nuisance parameters. It does not require moment selection tuning parameters or resampling. The key is to construct a likelihood that captures the worst-case scenario for controlling the test’s size. We show that the proposed test is valid even if unknown selection mechanisms are incidental parameters that may vary arbitrarily across units.