Small Area specific estimators that borrow strength across areas and across time


Time and space correlation

Cristina Rueda (University of Valladolid, Spain) (Speaker)
Esther López Vizcaíno (Instituto Galego de Estatística, Spain)
María José Lombardía Cortiña (Departamento de Matemática, Universidade da Coruña, España)

In this work a Small Area-specific estimation approach that borrows strength across areas and across time is presented to obtain Labor Force Estimators by economic activity. Several small area model-based estimators are considered, which are derived from additive regression models based on auxiliary information, with and without random effects. Often, for a given area and model, the time trend pattern is more abrupt than desired. On the other side, when time series models are considered too smoothed patterns are generated and prevent major trend changes being detected. The unequal behavior of employment in different economic activities regarding to the sample variability, the relationship with the auxiliary and the temporal evolution, give us the idea of considering different small area estimation approaches in different activities, even more after concluding, from observing the temporal patterns, that neither the direct estimators nor the standard small area model-based estimators, behave well homogeneously across activities.
We propose an approach based on obtaining the Aggregated Mixed Generalized Akaike Information Criterion statistic across time; and then using, for each area, the corresponding component. The approach selects among different estimators, including the direct estimator, and synthetic and mixed estimators, derived from different models including auxiliary information. A complete simulation study shows the good performance of the approach by comparing MSE from alternative approaches. We show the important practical advantages with the real application, which studies in each quarter the employment people by economic activity in Galicia in the period from the third quarter of 2009 to the second quarter of 2016 using data from the Labor Force Survey, and taking the economic activities (agriculture, forestry, food industry, …) as the domains.