estimation model is to improve upon sample estimates.<sup>21</sup> However, the low R<sup>2</sup> does raise concerns about biased estimates at the tails of the distribution, especially when estimating unemployment rates using the simple random sample. We expect that the combination of low marginal and conditional R<sup>2</sup> may lead to particularly inaccurate estimates for male and female unemployment rates when using the simple random sample. Model predictions for labor force participation using the simple random sample look significantly better for LFP than for unemployment, however, especially for women where the marginal and conditional R<sup>2</sup> values are 0.132 and 0.293 (as opposed to men where the same R<sup>2</sup> values are 0.071 and 0.17). The ratio of the estimated variance of the area effect to total variance is 0.19 for female participation and 0.11 for male participation, while the corresponding ratio for unemployment is about 0.1 for women and about 0.05 for men.

Using the full enumeration sample, not surprisingly, dramatically improves the prediction models. Marginal R<sup>2</sup> rises to about 0.27 for female LFP and 0.22 for men, and to approximately 0.16 for unemployment rates. The ratio of the variance of the estimated area effect to total variance ranges from 30 to 44 percent, depending on the indicator. Compared with the models developed using the simple random sample, more weight is given to the sample, which more accurately reflects municipal outcomes when sample AGEBs are fully enumerated. The higher R<sup>2</sup> s of the models reflects the elimination of the considerable noise in the sample data, which drove down the R<sup>2</sup> s of the models estimated using the simple random sample.

Finally, Appendix Figure A1 shows quantile-quantile plots for both components of the residuals, which is useful to check whether they appear to be normally distributed as assumed. The residuals are highly non-normal in most cases, except for the random area effect for male and female LFP. The non-normal random effects for unemployment, as well as non-normality in the household error terms may contribute to biased estimates of outcomes and uncertainty, which we will assess by comparing the small area estimates with the census. Future research can explore alternative transformations, such as the rank transformation used in Masaki et al.(2020), that might help achieve a more normal distribution.

# **B. State-Level Results**

We first consider estimates at the state level, the level at which the survey is considered to be representative. We present the seven statistics listed in section 2.e, separately for direct and small area estimates, in Table 3 .

The results are striking: Even though the direct estimates are considered to be reliable at the state level, we see large improvements in all seven statistics, across all four indicators, when incorporating geospatial data. The estimated mean squared error is smaller, the estimated correlation with the full-census benchmark increases, and the estimated absolute deviation from the benchmark decreases. Median relative bias declines for all outcomes. Coverage rates improve, sometimes dramatically. The estimates of unemployment rates improve on the direct estimates on most dimensions, even though the R<sup>2</sup> of some models is low. Because the outcomes measured in

> 21 For example, suppose as in this case that the sample covers 15 percent of the enumeration areas. Even a model that explains 10 percent of the variation in the remaining 85 percent of the population contributes at least the additional 8.5 percent of the total variation in the population not captured by the sample, in addition to any improvement in the estimates for sampled areas due to averaging samples with model predictions.

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