Uniform Validity of the Subset Anderson-Rubin Test under Heteroskedasticity and Nonlinearity

TL;DR

This paper proves that the Anderson-Rubin test remains valid across various complex data conditions, including heteroskedasticity and nonlinearity, ensuring reliable inference for nonlinear moment restrictions.

Contribution

It establishes the uniform validity of the AR test under broad conditions, introducing a novel perturbation approach for nonparametric data with complex heteroskedasticity and identification issues.

Findings

AR test maintains correct size under heteroskedasticity

Valid for both cross-sectional and time series data

Applicable without stationarity or homogeneity assumptions

Abstract

We consider the Anderson-Rubin (AR) statistic for a general set of nonlinear moment restrictions. The statistic is based on the criterion function of the continuous updating estimator (CUE) for a subset of parameters not constrained under the Null. We treat the data distribution nonparametrically with parametric moment restrictions imposed under the Null. We show that subset tests and confidence intervals based on the AR statistic are uniformly valid over a wide range of distributions that include moment restrictions with general forms of heteroskedasticity. We show that the AR based tests have correct asymptotic size when parameters are unidentified, partially identified, weakly or strongly identified. We obtain these results by constructing an upper bound that is using a novel perturbation and regularization approach applied to the first order conditions of the CUE. Our theory applies to both cross-sections and time series data and does not assume stationarity in time series settings or homogeneity in cross-sectional settings.