A Cautionary Tale on Instrumental Calibration for the Treatment of Nonignorable Unit Nonresponse in Surveys

Response rates have been steadily declining over the last decades, making survey estimates vulnerable to nonresponse bias. To reduce the potential bias, two weighting approaches are commonly used in National Statistical Offices: the one-step and the two-step approaches. In this article, we focus on the one-step approach, whereby the design weights are modified in a single step with two simultaneous goals in mind: reduce the nonresponse bias and ensure the consistency between survey estimates and known population totals. In particular, we examine the properties of instrumental calibration, a special case of the one-step approach that has received a lot of attention in the literature in recent years. Despite the rich literature on the topic, there remain some important gaps that this article aims to fill. First, we give a set of sufficient conditions required for establishing the consistency of instrumental calibration estimators. Also, we show that the latter may suffer from a large bias when some of these conditions are violated. Results from a simulation study support our findings. Supplementary materials for this article are available online.近数十年来，调查应答率持续下滑，导致调查估计结果极易受到无应答偏倚（nonresponse bias）的影响。为降低此类潜在偏倚，各国国家统计局通常采用两种加权方法：一步法与两步法。本文聚焦于一步法，该方法通过单一步骤对设计权重（design weights）进行修正，同时达成两大目标：降低无应答偏倚，同时确保调查估计结果与已知总体总量的一致性。具体而言，本文探讨了工具校准法（instrumental calibration）的性质——该方法是一步法的一种特殊情形，近年来在相关文献中受到广泛关注。尽管该主题已有大量研究文献，但仍存在若干重要研究空白，本文旨在填补这些空白。首先，本文给出了证明工具校准估计量（instrumental calibration estimators）一致性所需的一组充分条件。此外，本文还证明，当上述部分条件不满足时，工具校准估计量可能会出现较大偏倚。一项模拟研究的结果验证了本文的结论。本文的补充材料可在线获取。