Abstract

Policy-makers desire high-quality expenditure estimates for small geographic areas (districts) but the traditional survey samples utilised in official statistics have sample sizes that are too small for reliable direct estimates. Therefore, national statistical institutes turn to auxiliary information and model-based small area estimation techniques to bridge the gap. However, that auxiliary information can itself be unavailable unless we can utilise data from other surveys, while models make assumptions relating to the distribution of our outcome. Therefore, in this paper we combine two established extensions of the Fay–Herriot small area model. To broaden the available auxiliary information, we allow for error in a covariate taken from another survey, while we model on the log scale for skewed outcomes to improve model performance. As a case study, we estimate mean per capita expenditure for 514 Indonesian districts, combining data from the 2022 national socio-economic survey with covariates from the 2020 village census (no error) and the 2020 Census Long Form survey (error). We compare models that explicitly adjust for error in the covariates with a simpler approach that makes no adjustment when fitting the model but explicitly adjusts the variance. In this study, the two approaches lead to similar estimates. However, modelling on the log scale brings large precision gains for the back-transformed estimates.