# III. Methods

This section describes the three methods that are evaluated: Direct survey estimates, the Fay-Herriot area-level model, and the household-level model. It also discusses important methodological considerations involved when estimating the household-level model, such as differences between software packages, transforming the dependent variable, the model selection procedure, and benchmarking. The final subsection considers the criteria used to evaluate the performance of different estimators.

## A. Direct survey estimates

Direct estimates obtained from the survey serve both as a benchmark against which to assess the increase in precision from incorporating satellite data, and as an input into the Fay-Herriot area-level models. We use two methods to obtain direct survey-based estimates **.** For both methods, the mean poverty estimate for each area is the weighted average, across households, of the dummy variable indicating whether each household is poor. Each household is weighted according to corresponding population weight in the survey. The two methods used to obtain direct estimates differ in how they estimate the variance of the means. The typical method of obtaining variance estimates clusters the residuals by enumeration area, which accounts for positive correlation within enumeration areas but assumes that disturbances across enumeration areas are independent. This assumption underestimates the variance of area-level poverty estimates, particularly if welfare is highly correlated across enumeration areas within target areas.

The Horvitz-Thompson (H-T) approximation offers an alternative, more conservative, approach to estimate the variance of the area poverty rates (Horvitz and Thompson, 1952). This approach is more conservative because it relaxes the standard assumption that households’ poverty statuses are independent if they live in different enumeration areas within the same target area. This comes, however, at the cost of imposing an alternative assumption, which is that the probability of one household appearing in the sample is independent of the probability of any other household appearing in the sample. This assumption is clearly violated in standard two-stage sample designs, as the probability of a household appearing in the sample is greater if a household in its same enumeration area also appears in the sample. Nonetheless, the violation of this second assumption underestimates variance by less than the standard assumption of clustered standard errors, and therefore yields less biased variance estimates than the standard approach. We include results for direct estimates based on both the Horvitz-Thompson approach and the standard approach and in results presented below in Table 9, find substantially higher coverage rates for the former.

## B. Fay-Herriot area-level model

The Fay-Herriot model was first introduced by Fay and Herriot (1979) to model incomes for small areas of fewer than 1,000 persons in the United States, and is perhaps the best-known and widely used small area estimator. It was derived as an application of the James-Stein (1961) estimator using data aggregated to the target area level, and is also the Empirical Best Linear Unbiased Predictor (EBLUP) of 10