Appraisal and vulnerability in 3 spoonfuls: change the denominator, change the map

Most countries tax immovable property, and most of them argue about it badly. The argument usually skips the part that decides the answer: before any map is coloured, someone has to choose what is added up, what it is divided by, over which territory it is aggregated, and which cases are left out. Change any of those and the map can change while the underlying data stay identical. This post works through that problem with Chilean data, because Chile happens to publish the pieces needed to do it honestly: a national cadastre of every taxable property, and an official index that ranks small civic territories by socio-territorial vulnerability. The mechanics, though, are not Chilean. Any jurisdiction that assesses property for tax and then maps the result against a deprivation measure faces exactly the same four choices. The question fits in one small fraction: territorial indicatorthe unit you compare it againstthe total you want to describe​ Adding up the assessed value inside a territory answers how much administrative value was allocated there. Dividing that same total by households, by residents or by square metres answers different questions. None of them is «the correct one» by nature; the error appears when one is presented under another's name. The arithmetic is usually innocent. The narrative is not always. Reading contract I cross two Chilean administrative registers: the real-estate cadastre of the Servicio de Impuestos Internos (SII) —Chile's tax authority, roughly the counterpart of the IRS or HMRC— and the Índice Global de Vulnerabilidad Socioterritorial (IGVUST), a socio-territorial vulnerability index published by the Ministry of Social Development and Family. The unit of analysis is the neighbourhood unit, not the parcel, the household or the person. A word on that unit, because it has no clean equivalent elsewhere and it drives half of what follows. A Chilean unidad vecinal (UV) is a civic territory drawn for neighbourhood organisation and local participation — closer to a British ward or an American neighbourhood association boundary than to a census tract. Crucially, it was never designed to tile the country. Large stretches of rural Chile belong to no UV at all. A census geography would cover everything by construction; this one does not, and pretending otherwise is the first way to get the map wrong. Concept What it means here What it does not mean SII cadastre Administrative register of real estate and its characteristics. A population census or a register of residents. Parcel Cadastral unit identified by municipality, block and parcel number. A dwelling, a household, an owner or a person. Fiscal appraisal Administrative valuation used as the base of the property tax. Sale price, income, or the wealth of whoever lives there. IGVUST A ranking of neighbourhood units by socio-territorial vulnerability. An individual diagnosis or a causal mechanism. RSH Chile's Registro Social de Hogares, the means-testing registry that supplies the households and people used as denominators. In this processing it sums 15,978,644 people, close to 85% of the country's population. A complete census, or a universe with even coverage across municipalities. Neighbourhood unit (UV) Territory defined for neighbourhood organisation and participation. An exhaustive mesh covering all of Chile parcel by parcel. Denominator The magnitude the allocated appraisal is divided by. Small print added afterwards: it defines the question. The RSH matters because it is the source of the households and people I use as denominators. Nationally it is broad —around 85% of the population— but it does not cover every municipality equally. In municipalities with low relative RSH enrolment, as can happen in the wealthiest districts of Santiago, an indicator «per RSH household» can inflate because the denominator is narrow, not because there is more appraised value. That is a coverage artefact, not a finding. Fiscal appraisal is also not market price: the S