5. Conclusions
Eric Graf and Yves Tillé
In a number of countries, national sample surveys publish extrapolated values for the Laeken indicators (Eurostat 2005), since they are key indicators that make it possible to direct decision makers with regard to political and social matters. It is therefore critical that we be able to quantify the precision of these measures, which raises the issue of the appropriateness of the precision estimates available. This article shows that a substantial improvement may be made in the precision estimates for poverty and inequality indicators by using a (local) estimate of the income density or given monetary variable.
The simulations conducted show that the Gaussian kernel density estimation method currently implemented in most cases is not recommended without at least using the logarithm as proposed in Section 3.1; otherwise, there may be significant bias in the estimated variance. The nearest neighbour method (Section 3.2), which also imposes a minimum bandwidth, may yield even better results, especially if there are agglomerations of observations with certain values in the given data. However, this method requires setting a minimum number of neighbours on the basis of the data used. If few observations are available, the use of the logarithm is preferable instead. In all cases, we hope that this work will help raise awareness of the importance of being meticulous during the implementation of calculations for the linearized variable of any indicator involving quantiles.
Acknowledgments
This work was carried out under a collaboration agreement between the Institute of Statistics at the University of Neuchâtel and the Swiss Federal Statistical Office (SFSO). We would also like to specifically thank the Income, Consumption and Living Conditions unit of the SFSO for providing us with data from the Swiss portion of the EU-SILC survey. Thanks also to Matti Langel and Anne Massiani for their support during our investigations.
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