The low unemployment rates in the population lead to two issues. First, the estimated R<sup>2</sup> of the model is very low, meaning that the linear model predicts little of the variation in unemployment rates in the sample. This is not surprising, given the large amount of sampling error in the AGEBlevel unemployment rates in the simple random sample. This does not rule out the possibility that the small area estimates improve on the direct estimates.<sup>18</sup> In this case, however, the large share of sample municipalities with zero unemployment also downwardly biases the variance estimate of the municipal conditional random effect. This in turn leads the predictions to give too much weight to inaccurate predictions from the model, relative to the sample, which in turn generates inaccurate estimates.

The most direct approach to this problem would be to implement a non-linear model such as a two-part model (Belotti et al., 2015), although doing so in an empirical best framework with existing software is not straightforward. However, increasing the size of the second stage of the sample may mitigate this issue by reducing the number of municipalities with zero unemployment in the sample.<sup>19</sup> As a robustness check, we calculate small area estimates using a hypothetical full enumeration of sampled AGEBs. In other words, we use the actual census value of the labor market outcomes in each selected AGEB to estimate the model. In many developing countries, it is not uncommon to perform a full listing of all households in selected enumeration areas before drawing the second stage sample. It may therefore be feasible to collect data on low-probability events like unemployment from all adults in selected enumeration areas, as part of a listing exercise.

# **3. Results**

# **A. Model diagnostics**

Before comparing results against the full census, we check the characteristics of the models themselves. Table 2 shows the number variables selected, the R<sup>2</sup> values of the regression, and a variety of other model diagnostics for the lasso and post-lasso results for all four outcome variables. The first panel presents the results for the state-level estimates, while the second and third panels present results for the municipality-level results. Marginal R<sup>2</sup> represents the variance explained by the auxiliary variables, while conditional R<sup>2</sup> represents the variance explained by both the auxiliary variables and the conditional random effect. The R<sup>2</sup> values for the simple random sample that generates municipal level estimates are generally lower than individual level models, particularly for modeling unemployment.<sup>20</sup> However, the conditional R<sup>2</sup> of the female LFP model is significantly higher, at approximately 0.3, and EBP models can perform well even in cases when the available covariates are not strong predictors (Marhuenda et al, 2017).

> 18 This is counterintuitive but follows from Stein’s paradox. Stein’s paradox implies that a shrinkage estimator that takes a weighted average of direct survey estimates for subpopulations and the grand mean, when there are three or more subpopulations, can substantially improve predictions for the subpopulations (Stein, 1964, Efron and Morris, 1977). This is also consistent with Marhuendra et al.(2017), who note that EB estimates can perform well even in cases where the available covariates are not strong.

> 19 The problem can also be fixed by using a non-linear estimator such as a two-part model (Belotti et al., 2015).

> 20 R2s may increase after adjusting for sampling error (Li and Lahiri, 2018).

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