Justification of the small area estimation Small area estimation (SAE) is usually a useful theory to provide results for domains “for which direct estimates of adequate precision cannot be produced.” This theory involves using data from an entire sample for small domains (like a NUTS-2) estimation, according to auxiliary variables for each domain. The major interest of SAE is to have a larger sample size for each NUTS-2 and thus, to provide more stable and accurate results. In our case, SAE is accurate to provide poverty indicator at NUTS-2 in Belgium. Indeed, the SILC survey was planned to provide results at national level, and some NUTS-2 sampling sample are very small (for example, around 300 in the province of Luxembourg). As result, the AROP poverty indicator can have some high variations year per year (figure 1 next page). These results are unrealistic and cannot be published. We need to stabilize them. Because of the low sampling size, the sample can have some different characteristics from the entire population. We have access to administrative data for the population, so we can check the difference between the sample and the population. We highlight 5 explanatory variables provided by administrative data: Fiscal Income: we collect the fiscal income (N-2) for all households in Belgium. For each individual, we affect the fiscal income of his household Non-work income : we collect all the allocations (N-2) perceived by a household for a weak workforce (pension, unemployment, sickness) Age Gender Household size : we use four categories : 1,2,3 or 4 and more members in the household Figure 1 : AROP indicator at NUTS-2 level for SILC 2011 to 2016 Table 1 (next page) shows the differences between the sample and the population, for Belgium and for each NUTS-2. There is no difference at national level, but some high differences at NUTS-2 level for the two fiscal variables. In the table, we highlight the variable when the ratio Sample/Population is higher than 5%. In order to use these auxiliary variables, we need to prove that a model of our poverty indicators is relevant (otherwise, the estimator would be biased). We test four successive hypotheses for each poverty indicators:
Oost Vlaanderen (BE23), West Vlaanderen (BE25), Vlaams Brabant (BE24), with an AROP rate around 9%. The EBLUP estimation for these provinces is very stable over the time too. Figure 6 : AROP direct estimation by NUTS-2, SILC 2011 - 2016 Figure 7 : AROP EBLUP estimation by NUTS-2, SILC 2011 - 2016 The analysis for the indicator is similar. For 2016, the direct and the EBLUP estimation of AROPE is quite the same, except for few NUTS-2 (see table 14). The regional correction is weak and the indicator is stable over the time. The gap between the two estimators can be explained by the difference of the auxiliary variables between the sample and the entire population. Figure 8 and 9 illustrate the effect of the EBLUP estimation from 2011 to 2016 for AROPE. The four clusters defined for AROP are quite similar for AROPE. Table 12 : AROPE direct and EBLUP estimation by NUTS-2, SILC 2016 Direct estimation EBLUP Corrected EBLUP BE10 (Brussels) 38.30% 42.86% 38.30% BE21 (Antwerpen) 16.19% 18.19% 17.06% BE22 (Limburg) 15.32% 18.21% 17.08% BE23 (Oost Vlaanderen) 12.94% 14.55% 13.65% BE24 (Vlaams Brabant) 12.74% 12.68% 11.89% BE25 (West Vlaanderen) 14.94% 13.00% 12.20% BE31 (Brabant Wallon) 19.22% 19.06% 18.02% BE32 (Hainaut) 29.42% 32.08% 30.34% BE33 (Liège) 26.66% 29.34% 27.75% BE34 (Luxembourg) 16.47% 16.30% 15.42% BE35 (Namur) 27.54% 25.51% 24.12% Figure 8 : AROPE direct estimation by NUTS-2, SILC 2011 - 2016 Figure 9 : AROPE EBLUP estimation by NUTS-2, SILC 2011 - 2016