The core module was designed to maximize its consumption share based on NBHS 2009 consumption, and therefore contains all the most commonly consumed items. This includes staple foods such as dura, maize, onions, okra, common types of flour (e.g. millet, maize, cassava, and groundnut flour), common types of meat (e.g. goat, sheep, poultry, beef), and some fruits. The nonfood core module similarly captures common expenditures including fees for education, common types of transportation, common medicines and health related expenditures, and clothing. Optional modules were constructed using an algorithm to assign items iteratively to optional modules so that items are orthogonal within modules and correlated between modules.<sup>23</sup> This step is followed by the actual data collection. Conceptual division into core and optional items is not reflected in the layout of the questionnaire. Rather, all items per household are grouped into categories of consumption items (like cereals, meats, etc.). Using CAPI, it is straight‐forward to hide the modular structure from the enumerator. For ��� ��<sup>∗</sup> � each household, only the core module y� and one additional optional module y� are collected. In each enumeration area, 12 households were interviewed with an ideal partition of three households per optional module.<sup>24</sup> The assignment of optional modules was stratified per EA to ensure that an equal number of households are assigned to each optional module. This served to minimize potential EA effects during the imputation process. Household consumption was then estimated using the core module, the assigned module and estimates for the remaining optional modules: where K<sup>∗</sup> ∶��1, ... , k<sup>∗</sup> �1, k<sup>∗</sup> �1, ... , M� denotes the set of non‐assigned optional modules. Consumption of non‐ assigned optional modules is estimated using multiple imputation techniques taking into account the variation absorbed in the residual term.

Multiple imputation was implemented using multi‐variate normal regression based on an EM‐like algorithm to iteratively estimate model parameters and missing data. This technique is guaranteed to converge in distribution to the optimal values. An EM algorithm draws missing data from a prior (often non‐informative) distribution and runs an OLS to estimate the coefficients.<sup>25</sup> Iteratively, the coefficients are updated based on re‐estimation using imputed values for missing data drawn from the posterior distribution of the model. The implemented technique employs a Data‐Augmentation (DA) algorithm, which is similar to an EM algorithm but updates parameters in a non‐

> 23 In each step, an unassigned item with the highest consumption share was selected. For each module, total per capita consumption was regressed on household size, the consumption of all assigned items to this module as well as the new unassigned item. The item in questions was then assigned to the module with the highest increase in the R2 relative to the regression excluding the new unassigned item. The sequenced assignment of items based on their consumption share can lead to considerable differences in the captured consumption share across optional modules. Therefore, a parameter is introduced ensuring that in each step of the assignment procedure the difference in the number of assigned items per module does not exceed _d_ . Using _d=1_ assigns items to modules (almost) maximizing equal consumption share across modules. Increasing _d_ puts increasing weight on orthogonality within and correlation between modules. The parameter was set to _d=3_ balancing the two objectives.

24 Field work implementation aimed to achieve a balanced partition among optional modules but due to challenges in following the protocol exactly some enumeration areas are not completely balanced.

25 The model employed in the HFS was constructed using the following indicators: demographics variables including household size, the fraction of children, the fraction of elderly persons, the sex of the household head, and the employment status of the household head; indicators of access to amenities including the water source, whether the household had electricity to power its lighting, the number of sleeping rooms, and whether the household had access to a toilet; geographic indicators including an urban‐rural dummy and state fixed effects; finally, the model included dummies for each quartile of consumption of food and non‐food per capita. One hundred imputations were run for the consumption imputation process to maximize the accuracy of results.

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