Abstract: We propose inferential results for a new integrated inequality curve, related to a new index of inequality and specifically designed for capturing significant shifts in the lower and upper tails of income distributions. In the last decades, indeed, substantial changes mainly occurred in the opposite sides of income distributions, raising serious concern to policy makers. These phenomena has been observed in countries like US, Germany, UK, and France. Properties of the index and curve have been investigated, and applications to real data disclosed a new way to look at inequality. First inferential results for the index have been published, as well. It seems natural, now, to be interested also in inferential results for the integrated curve. To fill this gap in the literature, we introduce two empirical estimators for the integrated curve, and show their asymptotical equivalence. Afterwards, we state their consistency. Finally, we prove the weak convergence in the space C[0,1] of the corresponding empirical process to a Gaussian process, which is a linear transformation of a Brownian bridge. An analysis of real data from the Bank of Italy Survey of Income and Wealth is also presented, on the base of the obtained inferential results.

Davydov, Y., Greselin, F. (2021). Inferential Results for a New Inequality Curve. MATHEMATICAL METHODS OF STATISTICS, 30(1-2), 1-15 [10.3103/S1066530721010026].

Inferential Results for a New Inequality Curve

Greselin F.
2021

Abstract

Abstract: We propose inferential results for a new integrated inequality curve, related to a new index of inequality and specifically designed for capturing significant shifts in the lower and upper tails of income distributions. In the last decades, indeed, substantial changes mainly occurred in the opposite sides of income distributions, raising serious concern to policy makers. These phenomena has been observed in countries like US, Germany, UK, and France. Properties of the index and curve have been investigated, and applications to real data disclosed a new way to look at inequality. First inferential results for the index have been published, as well. It seems natural, now, to be interested also in inferential results for the integrated curve. To fill this gap in the literature, we introduce two empirical estimators for the integrated curve, and show their asymptotical equivalence. Afterwards, we state their consistency. Finally, we prove the weak convergence in the space C[0,1] of the corresponding empirical process to a Gaussian process, which is a linear transformation of a Brownian bridge. An analysis of real data from the Bank of Italy Survey of Income and Wealth is also presented, on the base of the obtained inferential results.
Articolo in rivista - Articolo scientifico
asymptotic normality; confidence interval; consistency; economic inequality; Gini index; income inequality; Lorenz curve; nonparametric estimator;
English
1
15
15
Davydov, Y., Greselin, F. (2021). Inferential Results for a New Inequality Curve. MATHEMATICAL METHODS OF STATISTICS, 30(1-2), 1-15 [10.3103/S1066530721010026].
Davydov, Y; Greselin, F
File in questo prodotto:
File Dimensione Formato  
DG MMS2021 Inferential results for a New Inequality Curve.pdf

Solo gestori archivio

Descrizione: Article
Tipologia di allegato: Publisher’s Version (Version of Record, VoR)
Dimensione 1.09 MB
Formato Adobe PDF
1.09 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/389285
Citazioni
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
Social impact