🤖 AI Summary
This paper addresses the failure of conventional generalized method of moments (GMM) tests under high-dimensional moment conditions—where the number of moments grows at the same rate as the sample size. Under such settings, standard weighted GMM tests become asymptotically conservative and fail to control Type I error when the null-implied moment conditions satisfy reflection invariance. We propose a robust inference framework grounded in reflection invariance. First, we establish a novel theoretical link between the structure of the weighting matrix and reflection invariance, demonstrating that conventional weighting induces size distortion. Building on this insight, we construct an asymptotically exact invariant test. Our theory guarantees consistent size control, and simulations confirm accurate finite-sample significance levels after correction. Empirically, applying the method to banking data reveals that greater concentration in financial activities exacerbates systemic risk.
📝 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 is reflection invariant. 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 asymptotically nominal size. We illustrate our findings through simulations for various (non-)linear models, and an empirical application on the effect of the concentration of financial activities in banks on systemic risk.
