which avoids the normalization issue and provides a more direct understanding of the expected squared error of the estimates. The mean squared error in Eq. (25) is sensitive to systematic biases in the predictions. Reconsidering the biased and unbiased poverty estimates described above (i.e., _yi_<sup>_u_and</sup><sup>_y_</sup> _i_<sup>_b_),wecanwriteMSE(</sup><sup>_y_</sup> _i_<sup>_b, y_</sup> _i_<sup>_a_) = MSE(</sup><sup>_y_</sup> _i_<sup>_u_+</sup><sup>_q, y_</sup> _i_<sup>_a_) = MSE(</sup><sup>_y_</sup> _i_<sup>_u, y_</sup> _i_<sup>_a_) +</sup><sup>_q_2.Systematicbiasesin</sup> the estimates will thus be penalized by the mean squared error. Further, with multiple estimates for each entity, one can calculate entity-specific mean squared errors, which can be decomposed into parts associated with the bias and variance of the estimates. Where _yik_<sup>_p_denotesestimate</sup> _k_ = 1 _,_ 2 _, . . . , K_ for the _i_<sup>_th_</sup> entity, we have where the first term on the right-hand side of the above captures the variance of the estimates for entity _i_ and the second term captures the (squared) bias.<sup>24</sup> The primary reason for obtaining granular poverty estimates is to improve the targeting of resources. While understanding the error of the poverty estimates is useful in this regard, the ultimate concern is to understand how different methodological choices affect poverty alleviation by influencing the efficiency of targeting. Consequently, we also consider how machine-learning methods perform in terms of reducing poverty in the context of the Census created from the Mexican Intercensal Survey. Similar to Elbers et al. (2007), we propose simulating a hypothetical poverty-alleviation program that distributes resources to households according to a given set of small area estimates.<sup>25</sup> In addition to the estimates, the procedure requires true household-level incomes from a census-type dataset.

The procedure we use in our simulations is as follows:

1. Using the true household-level incomes, calculate the poverty headcount and poverty gap for the country as a whole for some chosen poverty line. Using the poverty gap measure, determine the budget required to completely eradicate poverty.<sup>26</sup> Calculate an individuallevel transfer amount by dividing the total budget by the number of people living in poverty.

2. Using a given set of small area estimates, order the municipalities according to their estimated poverty headcounts, from most to least poor. For the poorest municipality, augment the true per capita income of all households by an amount equal to the transfer (i.e., each household receives an amount equal to the transfer times the number of household members). Continue this distribution procedure for the second poorest municipality, the third poorest municipality, and so on until there are not enough resources to cover all households in a given municipality. For the marginal municipality, distribute the remaining budget equally among individuals in that municipality.

3. Using the post-transfer household incomes, calculate an updated poverty headcount to assess the effects of the distribution scheme on poverty alleviation.

> 24See Hastie et al. (2009) for derivation and detailed discussion of the bias-variance decomposition.

> 25See Yeh et al. (2020),Chi et al. (2022), and Aiken et al. (2022) for examples of other studies that have conducted targeting simulations.

> 26This requires knowing who is poor and how poor they are. The transfer is enough to bring every poor individual up to the poverty threshold.

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