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The Human Development Index (HDI) based on life expectancy, education and per-capita income, is one of the most used indicators of human development. However, undeniable problems in data collection limit between-countries comparisons reducing the practical applicability of the HDI in official statistics. Elvidge et al. (2012) proposed an alternative index of human development (the so called Night Light Development Index, NLDI) derived from nighttime satellite imagery and population density, with improved comparability over time and space. The NLDI assesses inequality in the spatial distribution of night light among resident inhabitants and has proven to correlate with the HDI at the country scale. However, the NLDI presents some drawbacks when applied to smaller analysis' spatial domains, since similar NLDI values may indicate very different levels of human development. A modified NLDI overcoming such a drawback is proposed in this study to assess human development at 3 spatial scales (the entire country, 5 geographical divisions and 20 administrative regions) in Italy, a country with relevant territorial disparities in various socioeconomic dimensions. The original and modified NLDI were correlated with 5 independent indicators of economic growth, sustainable development and environmental quality. The spatial distribution of the original and modified NLDI is not coherent with the level of human development in Italy being indeed associated with various indexes of environmental quality. Further investigation is required to identify in which socioeconomic context (and at which spatial scale) the NDLI approach correctly estimates the level of human development in affluent countries

The use of auxiliary variables to improve the efficiency of estimators is a well-known strategy in survey sampling. Typically, the auxiliary variables used are the totals of appropriate measurement that are exactly known from registers or administrative sources. Increasingly, however, these totals are estimated from surveys and are then used to calibrate estimators and improve their efficiency. We consider different types of survey structures and develop design-based estimators that are calibrated on known as well as estimated totals of auxiliary variables. The optimality properties of these estimators are studied. These estimators can be viewed as extensions of the Montanari generalised regression estimator adapted to the more complex situations. The paper studies interesting special cases to develop insights and guidelines to properly manage the survey-estimated auxiliary totals.

Abstract:Additive decomposability is an interesting feature of inequality indices which, however, is not always fulfilled; solutions to overcome such an issue have been given by Deutsch and Silber (2007) and by Di Maio and Landoni (2017). In this paper, we apply these methods, based on the "Shapley value" and the "balance of inequality" respectively, to the Bonferroni inequality index. We also discuss a comparison with the Gini concentration index and highlight interesting properties of the Bonferroni index.

The study of income inequality is important for predicting the wealth of a country. There is an increasing number of publications where the authors call for the use of several indices simultaneously to better account for the wealth distribution. Due to the fact that income data are usuallyinequality measures, inference, influence function | 1009 DONG et al. | INTRODUCTIONNobel Prize-winning economist, Joseph Stiglitz, stated that income inequality is an important measure for forecasting the wealth of a country (Stiglitz, 2012). The most widely used inequality measure is the Gini index (Gini, 1912(Gini, ,1914. Since Corrado Gini suggested the index, it has been the subject of numerous publications. Its use is not restricted only to the economic field. It is surprising to note that even after a century, different applications of the Gini index pop up in new fields (see, e.g. Giorgi, 2019).Recent studies encourage the use of more than one inequality index simultaneously to better catch the inequality in different parts of the income distribution and thereby to better understand the socioeconomic reality and political significance of inequality (see, e.g. Osberg, 2017;Piketty, 2015). The most suitable candidate to place side by side with the Gini index could be the Bonferroni inequality index (Bonferroni, 1933). In fact, Pundir et al. (2005) show that both can be derived from the Lorenz Curve (Lorenz, 1905). Indeed, the two indices share several properties while maintaining some very interesting peculiarities.The opposition between the Bonferroni index and the Gini index is rooted when Carlo Emilio Bonferroni proposed his index in 1930. In the beginning, the Bonferroni index was fought by Corrado Gini and his followers who were very fond of the Gini index and who tried to avoid the use of any other measures that took the Gini index down the line (Giorgi, 1998). Only in the last 40 years, the Bonferroni index has been rediscovered by Piesch (1975) and Nygård and Sandström (1981). Several extensions and interpretations proposed for the Gini index (see, e.g. Giorgi, 2005, for a comprehensive review) have then been extended to the Bonferroni index, disclosing even more similarities and differences between the two indices.