Application of the Kalman filter to make population estimates and projections in small geographic areas

Manuel Ordorica, El Colegio de México

In demography, it is easy to obtain good-quality population indicators for large aggregates, but it is difficult to arrive at reliable estimates for small geographic units with few inhabitants due to the high variance evidenced by population figures at those levels. The purpose of this paper is to make population estimates and projections in small geographic areas using the Kalman filter, which is comprised of two equations: an observation equation and a transition equation. The former establishes a relationship between the geographic area and the population, while in the latter, population at a given moment is linked to the population at a subsequent moment. Two sources of information are available: on the one hand, we have censuses and, on the other, there are maps. To carry out this research, we have chosen a rural area in which the population lives in one story housing. Both equations are applied recursively.