Unified Inference on Moment Restrictions with Nuisance Parameters

TL;DR

This paper introduces a unified inference method for moment restrictions that avoids nuisance parameter estimation, applicable to various models, and demonstrates strong theoretical and empirical performance.

Contribution

It presents a novel test characterization that simplifies inference with nuisance parameters, applicable across diverse settings, and improves upon existing methods.

Findings

Asymptotically size controlled and consistent test

Performs well in finite samples

Outperforms existing approaches in weak instrument scenarios

Abstract

This paper proposes a simple unified inference approach on moment restrictions in the presence of nuisance parameters. The proposed test is constructed based on a new characterization that avoids the estimation of nuisance parameters and can be broadly applied across diverse settings. Under suitable conditions, the test is shown to be asymptotically size controlled and consistent for both independent and dependent samples. Monte Carlo simulations show that the test performs well in finite samples. Numerical results from the application to conditional moment restriction models with weak instruments demonstrate that the proposed method may improve upon existing approaches in the literature.