Non-Asymptotic Inference in Instrumental Variables Estimation

TL;DR

This paper introduces a finite-sample inference method for IV models that is robust, non-asymptotic, and does not rely on strong assumptions about instrument strength or model linearity.

Contribution

It proposes a non-Studentized Anderson-Rubin test variant that provides finite-sample guarantees without requiring distributional or linearity assumptions.

Findings

Provides finite-sample bounds for IV inference

Applicable to nonlinear and quantile IV models

Does not require knowledge of instrument strength

Abstract

This paper presents a simple method for carrying out inference in a wide variety of possibly nonlinear IV models under weak assumptions. The method is non-asymptotic in the sense that it provides a finite sample bound on the difference between the true and nominal probabilities of rejecting a correct null hypothesis. The method is a non-Studentized version of the Anderson-Rubin test but is motivated and analyzed differently. In contrast to the conventional Anderson-Rubin test, the method proposed here does not require restrictive distributional assumptions, linearity of the estimated model, or simultaneous equations. Nor does it require knowledge of whether the instruments are strong or weak. It does not require testing or estimating the strength of the instruments. The method can be applied to quantile IV models that may be nonlinear and can be used to test a parametric IV model against a nonparametric alternative. The results presented here hold in finite samples, regardless of the strength of the instruments.