QualificaProfessore Ordinario
Settore Scientifico DisciplinareSECS-S/01
Cellulare aziendale86935
IndirizzoVia Silvio D'Amico 77
  • Dipartimento di Economia
Altre informazioniSito web personale
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Profilo INSEGNAMENTI Prodotti della ricerca Avvisi Ricevimento e materiale didattico


Titoli e cariche

Professore ordinario di Statistica


Titolare del corso di Statistica - corso di laurea in Economia

Titolare del corso di Analisi statistiche per le scienze sociali -  corso di Laurea Magistrale in Mercato del Lavoro e sistemi di Welfare e corso di Laurea Magistrale in Ambiente e Sviluppo


Key-words: composite indicators; concordance; local concordance; inequality; concentration.


Main recent research issues

The most recent research issue stems from the study of composite indicators. First of all how to build composite indicators: endogenously or exogenously derived weights? For composite indicators based on latent multidimensional variables – such as Human Development or Competitiveness – structural equations models such as PLS – path models provide the most flexible framework. On this issue see papers

A second issue is concerned with inequality: how to account for horizontal inequality when aggregating different dimensions of a composite indicator? When designing composite indicators attention is often focused on its multidimensionality and on aggregation across different dimensions. However, two other aspects need consideration: the distribution of each indicator within its dimension (inequality) and the joint distribution of individual achievements or—viceversa—of deprivations. The suggestion is to correct the composite indicator by means of indicators that take into account joint distribution of the single components across dimensions. This line of research has led to the suggestion of a corrected Human Development Index (paper How to Integrate Macro and Micro Perspectives: An Example on Human Development and Multidimensional Poverty) and of a corrected indicator of infrastructural endowment (Terzi – Pierini Rivista di Statistica Ufficiale 2015).


Along this line a more committing issue concerns association among the different components. This line of research has lead to the definition of a local concordance function. Loosely speaking d variables are concordant if for a unit i (i =1,…,n) large  values on some variables are associated with large values on all the others and conversely for another unit i’ small values for some variables are associated with small values on all the others. Perhaps the most widely used coefficient of concordance between 3 or more distributions is Kendall’s W designed to assess the agreement between d raters.

For d variables and n units we take moves from a similar concept of concordance/agreement and rank all the observations.  We then divide each of the d distributions in slices of s[1] consecutive ordered observations and assess local agreement by counting how many times one observation in the r-th slice of any of the d distributions also belongs to r-th slice of any of the others. The greater the number of overlaps between corresponding slices, the higher the local concordance between the d distributions. Vice-versa maximum disagreement is when the units belonging to the r-th slice  of the h-th distribution do not belong to the same r-th slice of any of the other d-1 distributions. Thus if we count the number of units belonging to the union of the r-th slices we reach a minimum (s) in case of maximum concordance and a maximum (sd ) in case of maximum disagreement. We define and plot a concordance curve by computing local concordance for each sliding window of s consecutive ranks/integers.

The concordance curve can have many uses. Apart from measuring concordance among different variables or different components of a  composite indicator it can also be used to compare different rankings derived from different composite indicators, and this leads us once again to the first of these issues.

But it could also – when computed for the head or for the tail of a multivariate distribution – be used to measure concentration or inequality.

As for the areas of applications they have been mainly well- being and/or quality of life indicators.



[1] For the sake of simplicity we assume sn/d.