Another set of approaches for obtaining poverty estimates in a fragile context consists of modeling consumption, or poverty, based on a set of observable covariates and then projecting estimates using cross‐survey imputation. In this manner, infrequent bulky consumption surveys can be combined with more frequent surveys that collect information on the covariates necessary for imputing poverty (for example labor force surveys as in Douidich et al., 2013; or SWIFT<sup>19</sup> ). However, this methodology is problematic in contexts where there is no consumption survey to underlie the estimation, or where there may have been deep structural change that changes the relationship between covariates and poverty across time (Beegle et al., 2016; Christiaensen et al., 2010). This is most likely the case in South Sudan, where the last full consumption survey was conducted in 2009 and which had experienced a period of rapid development leading up to independence in 2011 and until the breakout of the current conflict in 2013.

Within‐survey imputation can alleviate some of these concerns because the assumption of similar covariate distribution between the data used to estimate poverty and that used to project is more likely to hold, or the differences may not be as great. One approach consists of administering a full consumption module to a subset of respondents, generally in more secure areas where time‐constraints are not binding, and then impute consumption for less secure areas based on a smaller set of covariates (Fujii and Van der Weide 2013). However, safer areas where the full consumption module can be administered may still systematically differ from insecure areas where only the covariates are collected, thus violating the assumption of equally distributed covariates.

The HFS employed a method of within‐survey imputation, but instead of imputing the totality of consumption in certain areas based on data from other areas it imputed a randomly different fraction of consumption across all enumeration areas covered in the survey (Pape and Mistiaen, 2018, 2015). Food and non‐food consumption items were first into a core and multiple optional modules. Each household was then asked only about the core items and those items in one of the optional modules, and consumption of items in the remaining optional modules was estimated through multiple imputation. The imputation does not suffer from bias caused by different covariate distributions, since data on every one of the optional consumption modules are collected within each enumeration area. Furthermore, because a majority of consumption is accounted for by a relatively small set of items collected for each household, additional variance introduced by the imputation is minimized.

This section will describe the rapid survey consumption methodology, a more detailed treatment and simulations can be found in (Pape and Mistiaen, 2018, 2015). First, food and non‐food consumption for household _i_ are estimated by the sum of expenditures for a set of items where y�� and y�� denote the food and non‐food consumption of item _j_ in household _i_ .20 Previous consumption surveys in the same country or consumption surveys in neighboring / similar countries can be used to estimate food shares.<sup>21</sup> In South Sudan, the item assignment could draw from the NBHS 2009 survey.<sup>22</sup> The list of items was partitioned into 1 core and 4‐optional modules each with _mk_ items:

> 19 Survey of Well‐being via Instant and Frequent Tracking.

> 20 As the estimation for food and non‐food consumption follows the same principles, we neglect the upper index _f_ and _n_ in the remainder of this section.

> 21 In a case where a previous survey is not available the items can be randomly assigned to the module. This would result in larger standard errors but would not introduce bias.

> 22 With manual modifications to treat ‘other’ items correctly. Items ‘other’ are often found to capture remaining items for a food category. Using the Rapid Consumption Methodology, this creates problems as ‘other’ will include different items depending on which optional module is administered. This can lead to double‐counting after the imputation. Therefore, ‘other’ items are re‐ formulated and carefully assigned so that double counting cannot occur.

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