On the instrumental variable estimation with many weak and invalid instruments

被引:3
|
作者
Lin, Yiqi [1 ]
Windmeijer, Frank [2 ,3 ]
Song, Xinyuan [1 ]
Fan, Qingliang [4 ,5 ]
机构
[1] Chinese Univ Hong Kong, Dept Stat, Hong Kong, Peoples R China
[2] Univ Oxford, Dept Stat, Oxford OX1 1NF, England
[3] Univ Oxford, Nuffield Coll, Oxford, England
[4] Chinese Univ Hong Kong, Dept Econ, Hong Kong, Peoples R China
[5] Chinese Univ Hong Kong, Dept Econ, Shatin, 903 Esther Lee Bldg, Hong Kong, Peoples R China
关键词
invalid instruments; model identification; non-convex penalty; treatment effect; weak instruments; MENDELIAN RANDOMIZATION; LASSO; REGRESSION; SELECTION;
D O I
10.1093/jrsssb/qkae025
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
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.
引用
收藏
页码:1068 / 1088
页数:21
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