Area-Level Time Models for Small Area Estimation of Poverty Indicators

Abstract

Small area parameters usually take the form h(y), where y is the vector containing the values of all units in the domain and h is a linear or nonlinear function. If h is not linear or the target variable is not normally distributed, then the unit-level approach has no standard procedure and each case should be treated with a specific methodology. Area-level linear mixed models can be generally applied to produce new estimates of linear and non linear parameters because direct estimates are weighted sums, so that the assumption of normality may be acceptable. In this communication we treat the problem of estimating small area non linear parameters, with special emphasis on the estimation of poverty indicators. For this sake, we borrow strength from time by using area-level linear time models. We consider two time-dependent area-level models, empirically investigate their behavior and apply them to estimate poverty indicators in the Spanish Living Conditions Survey.