s s 1<sup>+xx</sup> s 2<sup>+ XX</sup> 3<sup>+ uu</sup> s ss<sup>) = xx</sup> ss<sup>ββββ</sup> ss<sup>ββ</sup> ss<sup>, s=1,...,S,m=1,...,Ms; a=1,...,Asm.</sup> The state-level effect (2) G(yy is omitted because of the inclusion of a full set of state dummy variables Xs as independent variables. This mechanically causes the estimated variance of to be zero, due ss to the lack of variation across states in the residual after controlling for state dummies, which υυ ss effectively drops from the model. In other words, the state-level estimates are generated from υυ what is essentially a fixed effect estimator instead of a conditional random effect estimator. This ss is possible when generating state-level estimates, but not municipal level estimates, because the υυ survey is sufficiently large to estimate state level results precisely.<sup>8</sup> To generate the small area point estimates, the procedure simulates 100 draws from a normal distribution for both the random error term s s estimates) for each AGEB j. These estimates are then back-transformed, averaged across ss<sup>and the area effect υυ(or υυ</sup> ss<sup>for the state level</sup> simulations, and finally aggregated across AGEBs to generate municipal or state-level estimates. uu When aggregating across AGEBs, we weight using estimated population from WorldPop.<sup>9</sup> Mean squared error estimates are obtained from a parametric bootstrap procedure, as proposed by Gonzalez-Manteiga et al.(2007) and implemented in the R EMDI package (Kreutzmann et al., 2018), based on the theory developed by Butar (1997) and Butar and Lahiri (2003).

When estimating the parameters of models (1) and (2), observations are weighted using normalized inverse probability weights, using the weighting method implemented in the R nlme package (Pinheiro, et al., 2021). Because each municipality is given equal weight when evaluating the estimates, it is necessary to normalize the weights to avoid giving too much weight to more populous municipalities in the sample estimation.<sup>10</sup> We therefore normalize the weights by dividing the inverse probability of selection by the mean inverse probability of selection for the municipality, as follows: s 1 s where is the number of AGEBs contained in the sample for ∑ππ ss<sup>−1</sup> s municipality m and WW ss<sup>=</sup> NNss ss=1NNss ππ ss<sup>−1</sup> s NNss normalizes the sum of the weights in each municipality to equal the number of sample observations, ss<sup>is the probability of AGEB a being included in the sample.11 This</sup> which is one recommended method for normalizing weights when estimating conditional random ππ

> 8 The same software package was used to estimate both municipal and state level results. We experimented with omitting state-level dummies and the results were worse.

> 9 Using estimated population from WorldPop has the added benefit of being applicable to other contexts. While we have census information that would allow us to aggregate using arguably more “correct” data, this would not be possible in other contexts in which census data is missing or out of date. For this reason, we drop any AGEBs with an estimated population of zero. Only 0.6 percent of AGEBs are dropped.

> 10 For some policy contexts, it may be desirable to give greater weight to more populous municipalities when evaluating the accuracy of estimates, but in this analysis, we limit consideration to the case where each municipal estimate is given equal weight when evaluating the performance of the estimates as a whole.

11 We construct the sampling weight as the inverse of the probability of selection, using the formula for sampling with replacement, as an approximation for the actual probability of sampling based on our sampling strategy. In P s particular, the probability of selection is approximated as i = 1 −�1 − P PPt ss ~~�~~ NN , where popsma = population of AGEB a, poptotal = total national population and ππ s PP ttsstt 9 ss<sup>), the number of individuals in the sample.</sup> NN= m mm(40, P PP