We consider a model identification problem in which an outcome variable contains nonignorable missing values. Statistical inference requires a guarantee of the model identifiability to obtain estimators enjoying theoretically reasonable properties such as consistency and asymptotic normality. Recently, instrumental or shadow variables, combined with the completeness condition in the outcome model, have been highlighted to make a model identifiable. However, the completeness condition may not hold even for simple models when the instrument is categorical. We propose a sufficient condition for model identifiability, which is applicable to cases where establishing the completeness condition is difficult. Using observed data, we demonstrate that the proposed conditions are easy to check for many practical models and outline their usefulness in numerical experiments and real data analysis.

翻译：本文考虑结果变量包含非可忽略缺失值的模型识别问题。统计推断需要保证模型可识别性，从而获得具有一致性和渐近正态性等理论合理性质的估计量。近年来，工具变量或影子变量结合结果模型中的完备性条件已被强调用于实现模型可识别。然而，当工具变量为类别型时，即使对于简单模型，完备性条件也可能不成立。本文提出模型可识别性的充分条件，该条件适用于难以建立完备性条件的情形。利用观测数据，我们证明所提条件易于在实际模型中检验，并通过数值实验和真实数据分析概述其有效性。