The equation can be solved for δ obtaining: The depreciation rates estimated the 2015 HFS wave were used to calculate the consumption flow in the 2016 wave. The reason being that estimating depreciation rates is much more prone to errors in a context of high and unstable inflation such as that observed in South Sudan in 2016.<sup>30</sup> Furthermore, there are few reasons to expect depreciation rates to drastically change over such a short period of time. In 2015, based on equation (10), item‐specific median depreciation rates are estimated assuming an inflation rate of 0.5 percent, a nominal interest rate of 5.5 percent and, thus, a real interest rate of 5 percent (Table 6). For all households owning a durable but that did not report the current value of the durable, the item‐specific median consumption flow is used. For households that own more than one durable, the consumption flow of the newest item is added to the item‐specific median of the consumption flow times the number of those items without counting the newest item.<sup>31</sup>

# Spatial and Temporal Price Deflators

Prices fluctuated considerably in South Sudan in 2016 (Pape and Dihel, 2017; World Bank, 2018). Prices therefore need to be adjusted to make consumption comparable across the several months of fieldwork. Furthermore, there are important differences in the cost of living between urban and rural areas. This is particularly marked in South Sudan given the sheer isolation of rural areas and state of poor market linkages across the country (African Development Bank, 2013; Pape et al., 2017). A Laspeyres deflator was chosen to calculate price differences across urban and rural areas and months of data collection, due to its relatively light data requirements. The base period for deflating prices was chosen as October 2016 in urban areas. Urban areas were chosen as a reference because the national CPI calculated by the NBS is based on prices in urban markets across some of the largest cities in South Sudan, and hence would facilitate deflating consumption across the frequent waves of data collection in the HFS.

The Laspeyres index reflects the item‐weighted relative price differences across products. Item weights are estimated as household‐weighted average consumption share across all households before imputation. Based on the democratic approach, consumption shares are calculated at the household level. Core items use total household core consumption as reference while items from optional modules use the total assigned optional module household consumption as reference. The shares are aggregated at the national level (using household weights) and then calibrated by average consumption per module to arrive at item‐weights summing to 1. The item‐weights are applied to the relative differences of median item prices for each urban/rural and month pair. Missing prices are replaced by the item‐specific median over all households. The reference strata was chosen as the urban strata for one specific month of data collection. The month with the most data points was generally chosen for the reference time period. The Laspeyres deflator can be expressed as such: The Laspeyres L�,� for strata i and month t is equal to the sum of, over all items k : w�,�,� , the national budget share of item k in optional module m , times the ratio of p�,�,�,� , the median price of item k in strata i at month t , and

> 30 One potential source of bias being that the value placed by respondents on durable goods may be inflated given high levels of uncertainty regarding the future of the currency. Another is that the volatility of inflation across time periods is problematic given the formula assuming one inflation rate prevailing across the different years.

> 31 The 2016 HFSSS questionnaire provides information on a) the year of purchase and b) the purchasing price only for the most recent durable owned by the household.

12