It is worth noting that many countries only adjust for food prices with spatial deflators, neglecting housing costs. However, this approach can lead to a significant underestimation (overestimation) of poverty in urban (rural) areas, as housing costs tend to be higher in urban areas compared to rural areas.<sup>24</sup> To address this, we incorporate housing prices into the spatial deflators. While capturing accurate spatial variations in non-housing non-food prices can be challenging due to limited information on product specifications and unit values in market price surveys, housing characteristics and price information are typically available in the HBS data. Therefore, we estimate a housing price index using the HBS data and incorporate it into the spatial deflators.<sup>25</sup> The updated spatial deflators for 16 SSA countries clearly demonstrate that the cost of living is higher in urban areas, particularly in dense urban areas, compared to rural areas (Figure 2).

Figure 2: Cost of living index across urban versus rural areas in 16 SSA countries <!-- Start of picture text --> (A) Official definition (B) DOU (C) DB<br>1.4 1.4 1.4<br>1.2 1.2 1.2<br>1 1 1<br>.8 .8 .8<br>Urban Rural Urban center Rural Core Town<br>Urban cluster Suburb Other rural<br><!-- End of picture text --> Source: International Urban Poverty Database.

Note: DOU: Degree of urbanization. DB: Dartboard. The cost-of-living index is prepared as a spatial deflator for each country. It is normalized to 1 for each country overall. WorldPop 250m is used for both the DOU and DB methods.

# **4.3 Analysis with the new global dataset**

To examine the relationship between household welfare and population density, we conduct regression analysis using household consumption expenditures as a proxy measure of household welfare. It is important to consider that the association between welfare and location may be influenced by household characteristics. For example, if more educated households tend to reside in urban rather than in rural areas, urban areas may have lower poverty rates simply due to the composition of more educated households (that is, “sorting”). Therefore, we investigate the extent to which household welfare is determined by location characteristics after controlling for household characteristics. Our main specifications are as follows: and rural areas for six regions). In the case of the DOU classification, we reclassify them into urban centers, urban clusters, and rural areas for six regions. Then, the ratio of the regional poverty lines is calculated as a new spatial price deflator that is applied to the consumption aggregate when measuring poverty with international poverty lines.

> 24However, compared to richer countries, households in poor countries tend to allocate less budget to housing (see Figure A3 in Appendix A).

> 25The housing price index is calculated by estimating the following hedonic regression model with HBS data:

ln ( _RENT ij_ ) = _α_ + _β_ 1 _Xij_ + _β_ 2 _LOCATION j_ (1) + _εij_

> where _RENT ij_ is either observed or imputed rents for household _i_ in location _j_ , _Xij_ is a vector of housing characteristics, and _LOCATION j_ (1) is the geographic domain to distinguish prices relative to the base location _j_ =1. _β_<sup>�</sup> 2 is the log of a housing price index. Distinguishing housing prices between urban and rural areas is challenging if rent observations are limited in the latter.

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