Culling the Herd of Moments with Penalized Empirical Likelihood
针对高维矩条件模型中无效矩可能破坏估计一致性的问题，提出惩罚经验似然方法，能有效识别并剔除无效矩，同时保持估计量的渐近正态性，并通过投影方法消除偏差，提升有限样本表现。
Models defined by moment conditions are at the center of structural\neconometric estimation, but economic theory is mostly agnostic about moment\nselection. While a large pool of valid moments can potentially improve\nestimation efficiency, in the meantime a few invalid ones may undermine\nconsistency. This paper investigates the empirical likelihood estimation of\nthese moment-defined models in high-dimensional settings. We propose a\npenalized empirical likelihood (PEL) estimation and establish its oracle\nproperty with consistent detection of invalid moments. The PEL estimator is\nasymptotically normally distributed, and a projected PEL procedure further\neliminates its asymptotic bias and provides more accurate normal approximation\nto the finite sample behavior. Simulation exercises demonstrate excellent\nnumerical performance of these methods in estimation and inference.\n