Mapping poverty when household data cannot be joined

The missing piece is overlap

Poverty can involve several disadvantages at once: limited education, inadequate sanitation, or living far from essential services. Measuring their combination requires knowing which disadvantages affect the same households.

That information is often missing locally. Census tables may report separate totals for education and housing, while maps show distances to schools and hospitals. Without linked household records, identical totals can describe very different situations: disadvantages concentrated in the same homes, or spread across different ones.

In an arXiv preprint, Maja Gerovska Mitev and Viktor Stojkoski examine what can still be learned under these conditions. Their study covers North Macedonia’s 80 municipalities, combining information for 598,632 households across 1,575 settlements. The findings should be read as preprint results, not established conclusions from peer review.

Building a measure from separate sources

The researchers combine two groups of indicators. Six describe geographic access: road distance to kindergartens, primary and secondary schools, primary health care, hospitals, and parks or green spaces. Seven census indicators describe education, youth employment, sanitation, housing, heating, and water.

Each group receives half the index’s weight, divided equally among its indicators. A household counts as multidimensionally poor when its weighted deprivation score strictly exceeds one third. The distinction matters: exactly one third does not qualify under the baseline definition.

The study reports both the share of households classified as poor and an MPI that also reflects how extensively those households are deprived.

All six access indicators are measured together for each settlement, so their overlap is known. But the census tables provide only separate municipal totals for the socio-economic indicators. Their overlap with one another—and with geographic disadvantages—is unknown.

The authors first calculate a point estimate by assuming that these unobserved relationships are independent within each municipality. They preserve the geographic overlaps actually observed rather than treating every indicator as independent.

They then use linear programming to find the smallest and largest poverty rates compatible with the same observed information. These are “sharp bounds”: each endpoint can be achieved by some arrangement of household disadvantages consistent with the inputs.

Uncertain levels, clearer local contrasts

Under independence, the national poverty headcount is 5.01 percent. But the compatible range extends from 2.01 to 17.44 percent. That wide interval shows how much the missing household overlap matters.

These bounds are not confidence intervals. They describe uncertainty about how disadvantages combine, not sampling uncertainty, and they do not account for measurement errors in the inputs.

Municipal contrasts can nevertheless be decisive. Staro Nagorichane has a headcount point estimate of 65.67 percent. More importantly, its lower bound of 31.13 percent exceeds Aerodrom’s upper bound of 3.43 percent. Under this index and the observed inputs, no permitted rearrangement of disadvantages reverses that comparison.

Across municipalities, 517 ordered comparisons remain valid regardless of the missing overlap. Regional bounds, however, all overlap, preventing an assumption-free ranking of the eight regions.

A point estimate rounding to zero also does not establish an absence of poverty. Independence can make multiple socio-economic disadvantages rarely coincide, even when each is present locally.

What the map measures—and misses

Distance to a kindergarten is the most common measured deprivation, affecting 41.13 percent of households. Low adult education and distance to secondary school follow. These individual rates are observed without assumptions about household overlap.

External comparisons offer qualified support. The socio-economic component aligns more closely with relevant official statistics and a fieldwork deprivation index than the geographic component does. Agreement with the Global MPI’s regional ranking is weak. Different indicators, years, and populations mean the new estimate is not a correction of that existing measure.

The access indicators also have limits. They assign every household its settlement’s status, including school-access disadvantages to households without children. Road distance from a settlement point does not measure transport availability, travel time, facility capacity, or service quality. Some education and employment indicators are proxies rather than standard definitions.

Municipal rankings remain similar across 20 alternative specifications of weights, distances, and indicator selection, but poverty levels change. Changing the poverty cutoff can shift levels beyond the baseline bounds.

This is a descriptive measurement study, not evidence that remoteness causes poverty or that a particular intervention will reduce it. Its practical contribution is narrower: identifying some places that warrant attention while showing why local maps cannot replace household assessment. Publishing cross-tabulations of overlapping disadvantages could narrow the uncertainty without requiring a fully linked database.