are being provided with housing by others (e.g., employer, relatives, other arrangements) are asked what they would estimate the rent for their dwelling to be. We used this self-reported value in the consumption aggregate for these households.

The consumption aggregate is computed at the household level in _per capita_ terms. We consider as household members those people in the household who share expenses. As such, we exclude domestic workers, their relatives, lodgers, and nonrelatives who do not share expenses from the calculation of the welfare aggregate.<sup>13</sup> _Temporal and spatial price adjustment._ To make the consumption aggregate and average costs per calorie comparable across households, we adjust expenditure values temporally and spatially. POF was collected throughout a full year and its reference periods go back up to 12 months. Figure 2 shows the temporal variation of prices for different Brazilian states over the reference period of the survey. On average, prices increased by 26.8 percent over the reference period – a monthly average of 1 percent. IBGE (2020) provides temporal deflators in the publicly available data, which we use to deflate prices and the consumption aggregate to express all monetary values in January 2018 values.

For Brazil, among the largest countries in the world and covering an area of over 8.5 million square kilometers, spatial differences in prices should be a concern in the estimation of the poverty line and in welfare measurement. While there is no spatial price level index available for Brazil that one could use to adjust for these differences, research suggests that these differences exist and should be taken into account. Ferreira, Lanjouw, and Neri (2003) calculate spatial price indices for Brazil and find that they matter for ranking poverty across regions. More recently, Azzoni and Almeida (2016) show that overall price-level differences in Brazilian metro areas can diverge, with levels as low as −19 percent and as high as +14 percent from the national average. We hence use the data from POF to calculate Paasche price indices that we use to spatially deflate the expenditures registered in the survey.

13 There are several differences between our consumption aggregate and other studies using POF data. In one of the most recent ones (Oliveira et al. 2016), the authors aim to measure and analyze welfare, poverty (using the administrative “poverty’’ line equivalent to half a minimum wage), inequality, and vulnerability. Thus, the differences found with our work are somewhat expected. For instance, while we exclude observations with zero food expenditures from our analysis, Oliveira et al. (2016) impute food expenditures for these households to be able to include them in the estimations. Our main objective is to estimate a poverty line and not necessarily to reproduce the population distribution of expenditures. Any imputation method chosen would potentially bias our results because it would necessarily rely on observed characteristics such as family composition and location. Instead, we want the line to rest on actual data. Other differences emerge as we apply closely the recommendations in Deaton and Zaidi (2002): Oliveira et al. (2016) include all education expenditures, without distinguishing by mode of acquisition as we do; the authors also exclude costs of mass transportation (bus, subway, train, ferryboat, alternative transportation and their connection), often used to go to and return from work and often higher for those who live far away.

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