Poverty Mapping (Small-Area Estimation)

Both are small-area estimation methods, but they operate at different levels. The ELL method is a unit-level approach: it estimates a model of household consumption and imputes it into individual census households, then aggregates. The Fay-Herriot model is an area-level approach: it combines direct survey estimates for each area with area-level auxiliary covariates through a mixed model, without needing unit-level census records. ELL is used when a matching census exists and consumption can be modeled at the household level; Fay-Herriot is used when only aggregated area-level data are available.

Plugging the regression's point predictions into the census would ignore two sources of uncertainty — the sampling error in the estimated coefficients and the unexplained household and cluster variation — and would systematically distort poverty estimates, which are nonlinear functions of the consumption distribution. By drawing parameters and error components repeatedly and recomputing poverty in each draw, ELL reconstructs the full distribution of consumption and of the poverty estimate, yielding both an unbiased point estimate and a valid standard error for each small area.

Ideally they should be contemporaneous or only a year or two apart. The method assumes the relationship between household characteristics and consumption estimated in the survey still holds in the census; the larger the gap, the more economic conditions, prices, and that relationship can change, biasing the imputed welfare. A common rule of thumb is to keep the gap to a few years and to be cautious about interpreting maps built from a census and survey separated by a long interval.