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：我们考虑结果变量包含不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被广泛用于实现模型可识别。然而当工具变量为分类变量时，即使对于简单模型，完备性条件也可能不成立。我们提出了一个适用于难以建立完备性条件情形的模型可识别充分条件。基于观测数据，我们证明所提条件易于在诸多实用模型中验证，并通过数值实验和真实数据分析展示了其有效性。