Small Area Estimation of Entropy Inequality Measures: a Comparison Between Alternative Distribution Models

Small area statistics on economic inequality are becoming important for better planning public regional policies. We focus on the estimation of entropy inequality measures in Italian provinces by using data taken from the EU-SILC sample survey for Italy. In EUSILC survey the number of units sampled at provincial level is generally too small to obtain reliable estimates, and the use of small area estimation models is advisable. We consider small area models specified at area level that include the “direct” survey weighted estimators. In these models “direct” estimators are usually assumed to be unbiased and normally distributed. Nevertheless, in the case of inequality measures, design based estimators are known to be biased for small sample sizes. To solve this problem, we search for a correction that can produce approximately unbiased direct estimators. Moreover, due to the range of values that these estimators can assume and to the possible asymmetry of their distribution, the normality assumption could be inadequate in small area estimation models. In this regard we propose a small area model based on more flexible distributions as alternative to the normal one.