Identification- and many moment-robust inference via invariant moment conditions
研究了当矩条件数量随样本量增长时，基于连续更新GMM的识别稳健检验的渐近性质，发现现有检验渐近保守，并提出调整方法以在大样本下达到名义水平，通过模拟和银行集中度对系统性风险影响的实证验证。
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.