bias.<sup>20</sup> This misspecification is manifested as failure of the linearity assumption and the magnitude of this bias depends on the form of the covariates (see Figure 5 and appendix). Additionally, it will vary for each type of indicator. For example, when estimating mean income in a model without log transformation, linearity is preserved when aggregating and thus the approach is expected to perform well.<sup>21</sup> However, the empirical MSEs for the unit-context models in most areas outperform those from ELL (see Table 1 for average results). In fact, under scenario 1 (Figure 2) in some areas the MSE for the unit-context models are only slightly worse than those of the _CEBa_ and _CEBac_ . Under scenario 2, where the area effects have a higher variance relative to that of the cluster effect, which is likely the case in real world scenarios, the empirical MSE for the unit-context models show considerable variability for both fitting models. The results suggest the method could outperform direct estimates as well as misspecified models with random effects for the area level only, in terms of MSE, and may be an alternative under scenarios where census and survey data are not aligned. However, bias in these unit-context models may be a considerable concern. As one can see in the results from Table 1 the unit context method yields FGT0 estimators with an average absolute bias that is 56 times larger than the bias of the CensusEB estimators, and almost 5 times larger than ELL’s average absolute bias.<sup>22</sup> In the sections that follow this is further explored.

# **4 Design-based simulation**

In this section we present a design-based simulation experiment based on the Mexican Intra Censal Survey of 2015 (Encuesta Intracensal). The purpose of the simulation is to observe performance of the different methods under more realistic scenarios. The survey is carried out by the Mexican National Institute of Statistics and Geography (Instituto Nacional de Estadistica y Geografia - INEGI). The survey has a sample of 5.9 million households and is representative at the national, state (32 states) and municipal or delegation level (2,457 municipalities), as well as for localities with a population of 50,000 or more inhabitants.

The 2015 Intra Censal Survey questionnaire includes the following topics related to the housing unit: dwelling features, size and use of the dwelling, conditions for cooking, ownership and access conditions, access to water, sanitation facilities and sanitation, electric power, solid waste, equipment, appliances and automobile; and information and communication technologies (ICT). It also includes the following demographic information: total population and structure, birth registration, marital status, health services, ethnicity, education, economic characteristics, nonpaid work, migration, daily mobility, fertility and mortality, household composition, non-labor household income,

> 20  ̄ The correlation is also present between _x_ 5 _ac_ and other omitted deviations, _zach_ .

> 21The empirical average relative root MSE of the mean for the UC approach is slightly higher than that of the CensusEB.

> 22The unit context method also yields mean welfare estimators that are 38 times more biased than Census EB variants (not shown).

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