Abstract

The pressure on National Statistical Institutes to produce highly disaggregated data on indicators that are typically available only from household surveys is increasing; driven within a country by policy-makers and externally through international commitments such as UN's SDGs. However, this presents an issue as the required level of dis-aggregation is beyond what surveys can support through direct estimation. Therefore, NSIs are turning increasingly to small-area approaches that seek to borrow strength for dis-aggregated estimates via a statistical model. However, that is not without its issues, as often the auxiliary variables that might be used in statistical models for small area estimation are themselves estimated from surveys, introducing the additional complication of measurement errors. Within small area estimation, there are two basic approaches: those based on an area-level model and those based on a unit-level model. The unit-level model is ideal when you have auxiliary information within the same survey as the variable of interest, while the area-level model is ideal when you have auxiliary information external to the survey. We apply the approach of Ybarra and Lohr (2008) to correct for measurement error in the Fay-Herriot area-level model, and Torabi, Datta, and Rao (2009) to correct for measurement error in the unit-level model. We use a comprehensive simulation study to explore the impact of measurement error on a single auxiliary variable, and the situation where there are two auxiliary variables, one with and one without measurement error. The results demonstrate the robustness of the standard approaches when ignoring measurement error, but show there are specific scenarios where correct adjustment for measurement errors is beneficial. We apply the approach to a case-study example utilising Indonesian household survey data, estimating at the sub-district level. In the case study, we estimate per capita household expenditure from the National Socio-Economic Survey (SUSENAS) as variable of interest and use village potential data (PODES) for auxiliary variables as well as survey-based auxiliary information.