Household expenditure survey data cannot yield precise estimates of poverty or inequality
for small areas for which no or few observations are available. Census data are more plentiful,
but typically exclude income and expenditure data. Recent years have seen a widespread use
of small-area “poverty maps” based on census data enriched by relationships estimated from
household surveys that predict variables not covered by the census. These methods are used
to estimate putatively precise estimates of poverty and inequality for areas as small as 20,000
households. In this paper we argue that to usefully match survey and census data in this way
requires a degree of spatial homogeneity for which the method provides no basis, and which is
unlikely to be satisfied in practice. The relationships that are used to bridge the surveys and
censuses are not structural but are projections of missing variables on a subset of those variables
that happen to be common to the survey and the census supplemented by local census means
appended to the survey. As such, the coefficients of the projections will generally vary from
area to area in response to variables that are not included in the analysis. Estimates of poverty
and inequality that assume homogeneity will generally be inconsistent in the presence of spatial
heterogeneity, and error variances calculated on the assumption of homogeneity will underestimate
mean squared errors and overestimate the coverage of calculated confidence intervals.
We use data from the 2000 census of Mexico to construct synthetic “household surveys” and
to simulate the poverty mapping process. In this context, our simulations show that while the
poverty maps contain useful information, their nominal confidence intervals give a misleading
idea of precision