Small area estimation is receiving considerable attention due to the high demand for small area statistics. Small area estimators of means and totals have been widely studied in the literature. Moreover, in the last years also small area estimators of quantiles and poverty indicators have been studied. In contrast, small area estimators of inequality indicators, which are often used in socio-economic studies, have received less attention. In this article, we propose a robust method based on the M-quantile regression model for small area estimation of the Theil index and the Gini coefficient, two popular inequality measures. To estimate the mean squared error a non-parametric bootstrap is adopted. A robust approach is used because often inequality is measured using income or consumption data, which are often non-normal and affected by outliers. The proposed methodology is applied to income data to estimate the Theil index and the Gini coefficient for small domains in Tuscany (provinces by age groups), using survey and Census micro-data as auxiliary variables. In addition, a design-based simulation is carried out to study the behaviour of the proposed robust estimators. The performance of the bootstrap mean squared error estimator is also investigated in the simulation study.
Welfare systems can be observed according to two different perspectives. The former deals with the supply of social protection, i.e. with the funding and provision of social benefits and the production of social services and goods. The latter focuses on the demand of social protection, and particularly on the characteristics of people benefiting from social protection or asking for it. Typically, data on the supply of social benefits have an administrative nature (registers and budgets data) whereas data on beneficiaries come from sample surveys. In theory, administrative data, being census data, can be detailed by territory. On the contrary, sample surveys are usually planned to provide accurate estimates at the national level or for large sub-national areas. This chapter provides an example on the use of different data sets for the Old age and Family/children functions at the province level (LAU 1 in the EU nomenclature). Data on the supply of benefits derive from the SISSIM (Istat Survey on Interventions and Social Services of Individual and associated Municipalities) and from municipalities' budgets. Data on the demand of social protection come from EU-SILC (European Union - Statistics on Income and Living Conditions), a survey that is annually conducted by Istat in a comparable European framework. Earned benefits are estimated applying small area estimation methods, given that the sample size of the EU-SILC survey at the province level is small, so the traditional design-based estimators usually are unreliable. Results are analysed to understand whether administrative and sample survey data can be used to to compose a coherent picture of social protection delivered at the provincial level.
There has been rising interest in research on poverty mapping over the last decade, with the European Union proposing a core of statistical indicators on poverty commonly known as Laeken Indicators. They include the incidence and the intensity of poverty for a set of domains (e.g. young people, unemployed people). The EU-SILC (European Union - Statistics on Income and Living Conditions) survey represents the most important source of information to estimate these poverty indicators at national or regional level (NUTS 1-2 level). However, local policy makers also require statistics on poverty and living conditions at lower geographical/domain levels, but estimating poverty indicators directly from EU-SILC for these domains often leads to inaccurate estimates. To overcome this problem there are two main strategies: i. increasing the sample size of EU-SILC so that direct estimates become reliable and ii. resort to small area estimation techniques. In this paper we compare these two alternatives: with the availability of an oversampling of the EU-SILC survey for the province of Pisa, obtained as a side result of the SAMPLE project (Small Area Methods for Poverty and Living Conditions, http://www.sample-project.eu/), we can compute reliable direct estimates that can be compared to small area estimates computed under the M-quantile approach. Results show that the M-quantile small area estimates are comparable in terms of efficiency and precision to direct estimates using oversample data. Moreover, considering the oversample estimates as a benchmark, we show how direct estimates computed without the oversample have larger errors as well as larger estimated mean squared errors than corresponding M-quantile estimates.
"There has been rising interest in research on poverty mapping over the last decade, with the European Union proposing a core of statistical indicators on poverty commonly known as Laeken Indicators. They include the incidence and the intensity of poverty for a set of domains (e.g. young people, unemployed people). The EU-SILC (European Union - Statistics on Income and Living Conditions) survey represents the most important source of information to estimate these poverty indicators at national or regional level (NUTS 1-2 level). However, local policy makers also require statistics on poverty and living conditions at lower geographical/domain levels, but estimating poverty indicators directly from EU-SILC for these domains often leads to inaccurate estimates. To overcome this problem there are two main strategies: i. increasing the sample size of EU-SILC so that direct estimates become reliable and ii. resort to small area estimation techniques. In this paper the authors compare these two alternatives: with the availability of an oversampling of the EU-SILC survey for the province of Pisa, obtained as a side result of the SAMPLE project (Small Area Methods for Poverty and Living Conditions, http://www.sample-project.eu/ ), they can compute reliable direct estimates that can be compared to small area estimates computed under the M-quantile approach. Results show that the M-quantile small area estimates are comparable in terms of efficiency and precision to direct estimates using oversample data. Moreover, considering the oversample estimates as a benchmark, they show how direct estimates computed without the oversample have larger errors as well as larger estimated mean squared errors than corresponding M-quantile estimates." (author's abstract)
Il presente lavoro, ultimato a inizio luglio 2020, e' il frutto della collaborazione di un gruppo di docenti e ricercatori che operano nei Dipartimenti di Economia e Management, Giurisprudenza e Scienze Politiche dell'Universita' di Pisa. Nato sulla base di una richiesta della Prefettura di Pisa all'Ateneo pisano in piena emergenza sanitaria, esso si propone lo scopo di fornire un'analisi degli effetti che l'emergenza COVID-19 ha avuto sul tessuto economico e sociale della provincia di Pisa e, alla luce dei risultati ottenuti, effettuare alcune "proposte per la ripartenza" per i prossimi mesi. Il convincimento degli autori che questo contributo di analisi e proposte, ancorche' riguardante la realta' territoriale della provincia di Pisa, possa avere una qualche utilita' anche per altre realta' provinciali e regionali, nonche' per quella nazionale. La ragione di tale convinzione e' duplice. Da un lato, l'approccio utilizzato, basato sulla multidisciplinarieta' e sul coinvolgimento delle realtà socio-economiche e istituzionali del territorio, rappresenta un metodo essenziale e generale per la piena comprensione di una realta' nuova e assai complessa quale quella derivante dall'emergenza COVID-19. Gli autori, provenienti da settori scientifici diversi quali l'ambito aziendale, economico, statistico, giuridico e sociolopsicologico, sono stati i primi a rendersi conto di quanto tale metodo di "messa a sistema" delle informazioni e degli attori economici e istituzionali della provincia fosse cruciale, ancorche' inusuale rispetto al carattere tipicamente specialistico delle ricerche in ambito accademico. Dall'altro lato, le proposte contenute nel lavoro, e che sono riportate in modo sintetico val termine di questa introduzione, sono il frutto dell'analisi quantitativa e qualitativa contenuta nei primi capitoli e rappresentano un esempio di come le scienze sociali possano fornire una base informativa essenziale per processi decisionali basati sui fatti (quelli che in ambito scientifico vengono definiti "evidenze empiriche"). In altre parole, le proposte hanno valenza generale, in quanto mettono in evidenza problemi e ipotizzano soluzioni che sono comuni a tutto il territorio nazionale. Il lavoro, organizzato come segue. Il primo capitolo presenta un'analisi strutturalee dinamica dell'economia della provincia di Pisa nel periodo precedente alla crisi sanitaria. Il secondo capitolo contiene una lettura dell'impatto economico, sociale e sanitario dell'emergenza COVID-19 e delle misure di contrasto messe in campo dal governo nei mesi iniziali della crisi (marzo-giugno 2020). Il terzo capitolo contiene un approfondimento dell'analisi economico-aziendale svolta. L'impatto del COVID-19 sull'economia alcuni settori emersi come rilevanti per l'economia provinciale. Il quarto capitolo svolge riflessioni e proposte in ambito giuridico, il quinto capitolo chiude il lavoro presentando alcune proposte di policy. Gli autori desiderano ringraziare il Prefetto di Pisa, per l'attivita' di supporto istituzionale, il Rettore dell'Universita' di Pisa, e tutti gli attori istituzionali e socio-economici che hanno collaborato direttamente – mediante incontri e interviste ‒ o indirettamente – attraverso la messa a disposizione dei dati e informazioni ‒ alla stesura del lavoro.
