Identification- and many moment-robust inference via invariant moment conditions

TL;DR

This paper develops new asymptotic inference methods for high-dimensional GMM models under reflection invariance, improving test accuracy when the number of moments grows with sample size.

Contribution

It introduces an alternative asymptotic approach leveraging reflection invariance, providing adjustments for conservative tests in high-dimensional settings.

Findings

Existing tests are asymptotically conservative under high-dimensional conditions.

Proposed adjustments achieve correct nominal size in large samples.

Simulation and empirical results demonstrate improved inference accuracy.

Abstract

Identification-robust hypothesis tests are commonly based on the continuous updating GMM objective function. When the number of moment conditions grows proportionally with the sample size, the large-dimensional weighting matrix prohibits the use of conventional asymptotic approximations and the behavior of these tests remains unknown. We show that the structure of the weighting matrix opens up an alternative route to asymptotic results when, under the null hypothesis, the distribution of the moment conditions satisfies a symmetry condition known as reflection invariance. We provide several examples in which the invariance follows from standard assumptions. Our results show that existing tests will be asymptotically conservative, and we propose an adjustment to attain nominal size in large samples. We illustrate our findings through simulations for various linear and nonlinear models, and an empirical application on the effect of the concentration of financial activities in banks on systemic risk.