On the instrumental variable estimation with many weak and invalid instruments
研究了线性工具变量模型中工具变量有效性未知时的识别问题，提出一种替代稀疏惩罚方法，在工具变量弱且无效时仍能一致选择有效工具变量，并应用于体质指数对舒张压影响的实证分析。
Abstract We discuss the fundamental issue of identification in linear instrumental variable (IV) models with unknown IV validity. With the assumption of the ‘sparsest rule’, which is equivalent to the plurality rule but becomes operational in computation algorithms, we investigate and prove the advantages of non-convex penalized approaches over other IV estimators based on two-step selections, in terms of selection consistency and accommodation for individually weak IVs. Furthermore, we propose a surrogate sparsest penalty that aligns with the identification condition and provides oracle sparse structure simultaneously. Desirable theoretical properties are derived for the proposed estimator with weaker IV strength conditions compared to the previous literature. Finite sample properties are demonstrated using simulations and the selection and estimation method is applied to an empirical study concerning the effect of body mass index on diastolic blood pressure.