In fieldwork, a sufficient number of households must be assigned each optional module to obtain a reliable total consumption estimate. In wave 2 of the SHFS, this was ensured by interviewing 12 households per EA allowing for the ideal partition of three items per optional module.

# Consumption estimation

Household consumption was then estimated using the core module, the assigned optional 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 was estimated using multiple imputation techniques taking into account the variation absorbed in the residual term (Pape and Mistiaen, 2018). Multiple imputation was implemented using multivariate normal regression based on an EM‐akin algorithm to iteratively estimate model parameters and missing data.<sup>9</sup> The standard errors capture the error distribution of the multiple imputation process. The underlying model is a welfare model relating consumption to key household characteristics thus explaining 71 percent of variation in food consumption and 64 percent in nonfood consumption. The model parameters were household size, share of children in household, share of seniors in household; household head gender, employment, and education; dwelling type, dwelling drinking water access, dwelling floor, and dwelling ownership status; household experience of hunger; receipt of remittances; population type (urban, rural, IDP, nomadic) and a region‐ population type interaction, as well as each household’s core consumption quartile.<sup>10</sup> Pape and Mistiaen (2018) demonstrate that the Rapid Consumption Methodology yields reliable estimates of poverty using an ex‐post assessment with household budget data from Hargeisa and mimicking the Rapid Consumption methodology by masking consumption of items that were not administered to households.<sup>11</sup>

# _Durable consumption flow_

The consumption aggregate includes the consumption flow of durables calculated based on the user‐cost approach. The consumption flow distributes the consumption value of the durable over multiple years.

9 Pape and Mistiaen (2018) test various other techniques for imputing total consumption, including OLS and tobit module‐wise regression and multiple imputation chained equations, concluding that multivariate normal regression is the preferred technique.

10 Negative imputed values are corrected by scaling all associated imputed values to an average of zero without affecting the variance.

11 Pape and Mistiaen (2018) compare the imputation results with consumption estimates from the full consumption modules of the 2013 Somaliland Household Survey. The authors present the performance of the estimation techniques in terms of the relative bias (mean of the error distribution) and the relative standard error. The methodology generally does not perform well at the household level (HH) but improves considerably already at the enumeration area level (EA) where the average of 12 households is estimated. At the national aggregation level, the Rapid Consumption methodology slightly over‐estimates consumption by 0.3 percent. Assessing the three standard poverty measures (Foster et al., 1984) including poverty headcount (FGT0), poverty depth (FGT1) and poverty severity (FGT2), the simulation results show that the Rapid Consumption methodology retrieves estimates within 1.5 percent of the reference measure (Figure A.5). Generally, the estimates are robust as suggested by the low standard errors (Figure A.6). Simulations were also run for the complete data set from the Somaliland 2012 household budget survey producing comparable results.

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