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.