food security, agricultural land use, relationship to the household head, indigenous language, occupation, economic activity, and accumulated education. The survey also includes indicators for states, municipalities, and counties.

One of the key features of the survey is its size and the fact that it includes a measure of income at the household level.<sup>23</sup> The inclusion of an income measure allows for a design-based validation of the different methods presented above. The next section describes how the survey is modified to create a census data set and how samples are then drawn from the created census data with the goal of obtaining small area estimates of poverty at the municipal level.

# **4.1 Creating a census and survey**

Because the goal of this exercise is to test how well the different methods perform under a real world scenario, the Intra Censal Survey is modified to mimic a Census in order to allow for a design-based simulation. The first step consists of randomly removing 90 percent of households that reported an income of 0. This is done to ensure that some households with an income of 0 are included in the population, but not as many as in the original data to make it more realistic.<sup>24</sup> In the second step, all municipalities with less than 500 households are removed, thus observations by municipality range from 501 to 23,513.<sup>25</sup> The final “Census” consists of 3.9 million households and 1,865 municipalities.

To draw survey samples, primary sampling units (PSU) need to be created.<sup>26</sup> Within each municipality, the original data’s PSUs are sorted<sup>27</sup> and joined until each created PSU has close to 300 households. Under the proposed approach, original PSUs are never split, just joined to others. Additionally, all original PSUs that were larger than 300 households are designated as a created PSU. The entire process yields 16,297 PSUs.

The resulting Census data is used to draw 500 survey samples to conduct a design-based simulation to establish how a method will perform over repeated sampling from a finite population (Tzavidis et al., 2018). The sampling approach reflects standard designs used in most face-toface household surveys conducted in the developing world, such as those conducted by the Living Standards Measurement Study (LSMS) program of the World Bank (Grosh and Muñoz, 1996), with some simplification for convenience. First, the 32 states that comprise Mexico are treated as the intended domains of the sample. The main indicator of interest for the survey is the welfare measure: household per capita income. The desired level of precision to be achieved in the sample is assumed to be a relative standard error ( _RSE_ ) of 7.5 percent for mean per capita income

> 23Income is defined as money received from work performed during the course of the reference week by individuals of age 12 or older within the household.

> 24Welfare values of 0 and/or missing are a common feature of household surveys.

> 25The median municipality has 1,613 households.

> 26The Intra Censal Survey has its own PSUs, however many of these have too few observations to properly work as PSUs in the created “Census” data.

> 27This assumes that the clusters’ numbering is tied to how proximate each cluster is to one and other.

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