We discuss the fundamental issue of identification in linear instrumental variable (IV) models with unknown IV validity. We revisit the popular majority and plurality rules and show that no identification condition can be "if and only if" in general. 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 trade on economic growth.

翻译：我们讨论了线性工具变量(IV)模型中的识别基本问题,其有效性不明。我们重新审视了流行的多数和多元规则,并表明,一般而言,任何识别条件都不能是“如果而且只有在”的情况下。假设“最区别规则”,这相当于多元规则,但在计算算法中开始起作用。我们调查并证明,在选择选择一致和容纳个别弱小的IV的两步基础上,非混杂处罚方法优于其他四类估计方法的优势。此外,我们提议了一种与识别条件相一致的最稀疏的替代处罚,同时提供稀疏结构。与以前的文献相比,提议的四类强度条件较弱的估算者,其理想的理论属性是产生;使用模拟来证明非精度抽样特性,选择和估计方法用于关于贸易对经济增长影响的经验研究。