enough sample of comparable data, we consider improved sanitation facilities as adequate even if they might be shared between households.<sup>3</sup> Facilities such as pit latrines without a slab or platform, hanging latrines or bucket latrines are considered unimproved (JMP 2020, Annex 1).

With regards to adequate living space (3), we follow the widely used definition of over-crowding as a <mark>condition where the number of occupants exceeds the capacity of the housing unit’s space.</mark> We adhere to a rather broad operationalization of over-crowding to ensure comparability across countries and regions, where different norms on e.g., children of opposite genders occupying the same room might exist.<sup>4</sup> We consider housing units to be over-crowded if there are <mark>less than 9 square meters per person or if more than three people occupy a room (</mark> cf. Blau et al. 2019; Gove et al. 1983; UN-Habitat 2007).

Regarding durable material and good structural quality (4), we consider the type of material used to build walls, roofs, and floors. While the categorization of material varies largely by region, country, and year in HH surveys, the various materials can be harmonized into durable or nondurable materials. We categorize housing material to be adequate if durable or finished materials such as burnt bricks, tiles, shingles, iron sheets, or polished wood are used. Unfinished, rudimentary, or natural materials include cane, straw, grass, or bamboo. We assume that an HH does live in an adequate house if all three materials for wall, roof, and floor are durable.

With respect to security of tenure (5), approaches to operationalize and measure are manifold, particularly across regions. This diversity is also reflected in the various coding schemes applied across various data sources. While there have been recent calls for a globally comparable (land) tenure module to be integrated into HH surveys (e.g., Holden et al. 2016), uniform data on security of tenure are hitherto absent within most multi-purpose HH surveys. Some (more recent) HCES include detailed questions on property titles or documents that HHs hold regarding their occupation status. In some African countries, some surveys include country-specific questions on e.g., (customary) certificate of occupancy, right to occupancy, or whether HHs hold formal title deeds

> 3  For the 64 countries included in the _AHI_ , data on shared sanitation facilities were not available for the majority of countries (Albania, Angola, Argentina, Belarus, Brazil, Burkina Faso, Burundi, Chad, Côte d’Ivoire, Colombia, Costa Rica, Democratic Republic of Congo, Djibouti, Dominican Republic, Arab Republic of Egypt, Ethiopia, Guinea, Guinea-Bissau, Haiti, Indonesia, Kazakhstan, Lao PDR, Madagascar, Mexico, Mozambique, Myanmar, Nepal, Nicaragua, Pakistan, Philippines, Peru, Romania, Russian Federation, Senegal, Sierra Leone, Sri Lanka, Togo, Tunisia, Turkey, Ukraine, Uzbekistan, Vietnam, and Zambia). This means we will not be able to identify HHs that share sanitation facilities and therefore likely share a housing unit with other HHs. As comparability across countries and a uniform coding scheme of the seven adequacy dimensions is our paramount objective; therefore, we opt not to differentiate between shared and non-shared sanitation facilities.

> 4  Other agencies like Eurostat have a more nuanced classification defining an HH to be overcrowded if it does not have at least one room for the household; one room for each couple in the household; one room for each person aged 18+; one room per pair of single people of the same gender between 12-17 years or otherwise separate rooms; one room per pair of children under 12 years old (Eurostat 2014).