An Analysis of Poverty in Italy through a fuzzy regression model Paola Perchinunno, Francesco Campobasso, Annarita Fanizzi, Silvestro Montrone - Department of Statistical Science, University of Bari

1. AN ANALYSIS OF POVERTY IN ITALY THROUGH A FUZZY REGRESSION MODEL S. Montrone, F. Campobasso, P. Perchinunno, A. Fanizzi Università degli Studi di Bari - Dipartimento di Scienze Statistiche ICCSSA 2011 GEOG-AN-MOD 11 Santander, 20-23 June 2011

2. Over recent years, and related in particular to the significant contemporary international economic crisis, an increasingly worrying rise in poverty levels has been observed both in Italy, as well as in other countries. INTRODUCTION The present work elaborates data revealed by the EU-SILC survey (2006) regarding the perception of poverty by Italian families, through a fuzzy regression model .

3. 1. Different approaches to the poverty (absolute, relative, subjective) INDEX 2. Techniques of the Fuzzy Set ( A Fuzzy Regression Model ) 3. The application of the Fuzzy Approach: construction of Eu-Silc indicators and definition of fuzzy numbers 4. Results of the Fuzzy Regression Model

5. 2. A FUZZY REGRESSION MODEL Fuzzy regression techniques can be used to fit fuzzy data into a regression model. Diamond (1988) treated the simple Fuzzy regression model introducing a metrics into the space of triangular fuzzy numbers . In this work we explicit the expression of the parameters of the model with fuzzy asymmetric intercept in the multiple case, starting from the simple model handled by Diamond.

6. A FUZZY NUMBERS Modalities of quantitative variables are commonly given as exact single values, although sometimes they cannot be precise (the imprecision of measuring instruments and the continuous nature of some observations). On the other hand qualitative variables are commonly expressed using common linguistic terms (which also represent verbal labels of sets with uncertain borders). The appropriate way to manage such an uncertainty of observations is provided by fuzzy numbers.

13. In the present study data are elaborated arising from EU-SILC survey regarding the perception of the Italian families in “getting through to the end of the month”. 3. THE APPLICATION OF THE FUZZY APPROACH It emerges, in particular, that the majority of households surveyed declared themselves to be in a state of hardship (either in great hardship 13.4%, in hardship 19.4% or in some degree of hardship, 40.2%). There are, however, few families (6.0%) declaring that they get through to the end of the month with absolute confidence.

14. 3. THE APPLICATION OF A FUZZY REGRESSION MODEL

15. The present work aims to identify the relationship between several independent variable X i (expenses for rent or mortgage payments, for the running of the household and for other debts) and a single dependent variable Y (the difficulty of “getting through to the end of month”). 3. DEFINITION OF FUZZY NUMBERS Furthermore, in order to normalize the data collected, the explanatory variables have been quantified with the same criteria.

16. In particular, the response categories in terms of mortgage payments, rent and household costs are centred on 1, 3 and 5, whilst the response categories in terms of expenses for other debts are centred on 0, 1, 3 and 5. 3. DEFINITION OF FUZZY NUMBERS

18. The estimated regression coefficients for families in rented houses are reported below: The most relevant expenses (in terms of difficulty in getting through to the end of month) results those relative to rental payments in all geographic area. The “expenses for other debt” are relevant only in the North area. 4.RESULTS OF THE REGRESSION MODEL

19. The estimated regression coefficients for families with mortgage rates are reported below: The most relevant expenses results those relative to the payment of mortgage rates and differently from the previous model, above all in the south of Italy. Besides, as we can see by the spread values, the variability is higher in this case. 4.RESULTS OF THE REGRESSION MODEL

20. In this work we propose a Fuzzy Regression Model in order to identify the factors that most influence the perception of poverty by Italian families . 5. CONCLUDING REMARKS A subjective approach to poverty suggests the adoption of a fuzzy regression model, made possible by an initial transformation of data into triangular fuzzy numbers The results of the analysis of poverty levels has showed at what degree the most relevant expenses (in terms of getting through to the end of the month), for Italian families, are those for rent and mortgage in the different geographical areas.