Top–down disaggregation of life expectancy up to municipal areas, using linear self-regressive spatial models

The paper aims to analyse a statistical procedure for the definition of territorial indicators, such as the biometric function of life expectancy of citizens of a territory e0, applying a methodology of Top–Down spatial disaggregation, using census data from 2011 in Italy. Through spatial regressions with the methodology proposed in 1971 by Chow and Lin with the use of ISTAT elaborations of annual mortality tables, which are structured from the national level to the regional level, up to the smallest details of the main level, as a dependent variable and predictors a number k of census variables plus accidents in regression models, life expectancy can also be defined at municipal levels (not elaborated by ISTAT) and even at sub-municipal levels (Census Area). The structure of the 2011 census was characterized by 152 variables, collected with CAPI and universal CAWI survey on all the survey units, throughout the national territory, divided into administrative areas of competence and 402,677 more granular areas in census sections. This structure represents a very relevant and useful information asset for applying a spatial disaggregation of indicators, based on three fundamental assumptions: 1.Structural similarity, whereby the aggregate model and the disaggregate model are structurally similar, i.e., the relationships between the variables are valid both at the aggregate (Top) and at the disaggregate (Down) level, with the consequence that the regression parameters are the same in the two models. 2.Error similarity: for spatially correlated errors they present the same structure at both aggregate (Top) and disaggregate (Down) levels, significantly testing for zero spatial correlation; 3.Reliable indicators: the variables in the regression models are efficient predictors at both aggregates (Top) and disaggregate (Down) levels, estimable from model efficiency tests. As we see in the following, compared to others, the best predictors of the census and income variables show us a good interaction in terms of active regressors on the estimation variable.