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Eu-Silc and Echp, two longitudinal European surveys on households living condition: statistical methods to measure multidimensional poverty at “local” and time frameworks; Betti G., Lemmi A., ...

Eu-Silc and Echp, two longitudinal European surveys on households living condition: statistical methods to measure multidimensional poverty at “local” and time frameworks; Betti G., Lemmi A., Verma V.

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Ws2011 sessione5  lemmi_betti_verma Ws2011 sessione5 lemmi_betti_verma Presentation Transcript

  • Workshop on: Enhancement and Social Responsibility of Official StatisticsEu-Silc and Echp, two longitudinal European surveys on households living condition: statistical methods to measure multidimensional poverty at “local” and time frameworks Gianni Betti, Achille Lemmi, Vijay Verma Cridire “C. Dagum” - Università di Siena 1
  • Aims of the presentation• Fuzzy vs. crisp approach• Multidimensional vs. unidimensional approach• Longitudinal vs. cross-sectional (local) approach• ECHP vs. EU-SILC survey 2
  • POVERTY IS A FUZZY S TATEIT IS NOT A DISCRETE ATTRIBUTE CHARACTERISED INTERMS OF PRESENCE OR ABSENCEIT IS RATHER A VAGUE PREDICATE THAT MANIFESTSITSELF WITH DIFFERENT SHADES AND DEGREESNEVERTHELESS, TRADITIONAL METHODS OF ANALYSISTREAT POVERTY AS A DICHOTOMOUS VARIABLE POOR NON POOR 0 Z YTHIS EXCESSIVE SIMPLIFICATION WIPES OUT ALL THENUANCES THAT EXIST BETWEEN THE TWO EXTREMES: SEVERE MATERIAL HIGH HARDSHIP WELFARE 3
  • Reconsider the definition of the membership Function based on monetary variables   n    wi  µ i = (1  F ) Cheli and Lemmi (1995) = l =i n   wi     l =1  Betti and Verma (1999)    w l yl   i=i+1  µ i = FMi = (1  L ( M ),i )  =   w l yl   l=1  4
  • Membership functions used by Cheli andLemmi (1995), and Betti and Verma (1999) 5
  • Definition of the membership function based on monetary variables (diffusion) Betti, Cheli Lemmi and Verma (2005, 2006) 1  w | y > yi   w y | y > yi        µi = FM = (1 F) .[1 L(F)] =  1  .   w | y > y1   w y | y > y1  i      Where parameter  is chosen so that the mean of the m.f. is equal to head count ratio H:  + G E (FM ) = =H .( + 1) 6
  • Membership function based on supplementary variables (FS)Variables and dimensionsQuantification and putting together a large set of non- monetary indicators of living conditions involves a number of steps, models and assumptions.1. selection of indicators which are substantively meaningful and useful: mostly used ‘objective’ indicators2. identifying underlying dimensions: this is done via factor analysis and sensible considerations; grouping the indicators accordingly3. assigning numerical values to ordered categories4. weighting of measures 75. scaling of measures
  • Membership function based onsupplementary variables (FS) - diffusionHere we have adopted the methodology of theSecond European report on Poverty, Income andSocial Exclusion (Eurostat, 2002)Elementary indicators are combined to form an index describingan overall degree of deprivation. The individual’s score averagedover items (k) is written as the weighted mean: S j =  k (w k .s j,k )  k w kwhere the weights wk are defined taking into account dispersionand correlation among items. 8
  • Monetary and Supplementary Fuzzy Indexes of incidence and depthUnder the same logic, Lemmi and Panek (2010)and Panek (2010) have defined further indexesof incidence and depth both connected with theconcept of poverty gap.The indexes of incidence adopted in this workare defined as:- FMI- FSI 9
  • Fuzzy logic Table 1.1 Basic forms of fuzzy set intersections and unions Intersection a  b Union a  bStandard i(a, b) = min(a, b) = ima x u(a, b) = max(a, b) = uminAlgebraic i(a, b) = a ? b u(a, b) = a + b ? a ? bBounded i(a, b) = max(0, a + b ? 1) u(a, b) = min(1, a + b) 10
  • Fuzzy logic in the cross-sectionTable 1.2. Joint measures of deprivation according to the Betti and Verma Composite operation Non-monetary deprivation non-poor (0) poor (1) Total min(1  FM i ,1 FSi ) = Monetary deprivation non-poor max(0, FSi  FMi ) 1  FMi 1 max(FM i , FSi ) poor max(0, FMi  FSi ) min(FMi , FSi ) FMi Total 1  FSi FSi 1 11
  • Fuzzy logic in the longitudinalTa ble 1 : Applica tion of differen t types of fu zzy in tersectio ns o ver two times perio ds Fuzzy S tanda rd Algebra ic B ounded B etti-Ver ma Composite oper atorintersec tion oper ator oper ator operator Type Inte rsection Union aIb min(a,b) a*b max(0,a +b-1) Standard min(a,b) max(a,b) a I b m in(1-a ,1-b)= (1- a)*(1-b) max(0,1- a-b) Standard 1- max(a,b) 1- min( a,b) 1-m ax(a,b) a I b min(a,1-b) a *( 1- b) max(0,a-b) Bounde d m ax(0,a-b) 1- max(0,b-a ) a I b min(1-a,b) (1-a)*b max(0,b- a) Bounde d m ax(0,b-a) 1- max(0,a -b) 12
  • Implementation in the C/SIncome poverty and non-monetary deprivation in combination - 1The two measures FMj propensity to income poverty, and FSj the overall life–style deprivation propensity, may be combined to construct composite measures which indicate the extent to which the two aspects of income poverty and life-style deprivation overlap for the individual concerned. These measures are as follows.• Mj manifest deprivation, representing the propensity to both income poverty and life-style deprivation simultaneously. It represents the individual being subject to both income poverty and life-style deprivation; one may think of this as the ‘manifest’ or the ‘more intense’ degree of deprivation.• Lj latent deprivation, representing the individual being subject to at least one of the two, income poverty and/or life-style deprivation; one may think of this as the ‘latent’ or the ‘less intense’ degree of deprivation.The two concepts can be seen graphically in next slide, where Manifest deprivation can be seen as the intersection of the two fuzzy sets (Income poverty and Non- monetary deprivation), while latent deprivation can be seen as the union of the two. 13
  • Income poverty and non-monetary deprivation in combination - 2 Life-style deprivation Income poverty Manifest deprivation Latent deprivation (100) 14
  • Implementation in the longitudinalAny time povertyWe may define the anytime poverty rate of a population as the average of the individualdegrees of membership in the set ‘poor for at least one year’ = µ[1] .Continuous povertyThe continuous or ever poverty rate for a population is given by the average of theindividual joint memberships for the set intersection, estimated for example as themembership function of the set ‘poor for all the T years’ = µ[T] .These are particular cases of the propensity to be poor for at least t out of T years =µ [ t] , the tth largest value.Persistent povertyWe may define persistent poverty as the propensity to be poor over at least a majority ofthe T years. The required propensity to persistent poverty is the [int(T/2)+1]th largestvalue in the sequence ( µ1 , µ 2 ,..., µ T ). For instance, for a T= 4 or 5 year period,‘persistent’ would refer to poverty for at least 3 years; for T =6 or 7, it would refer topoverty for at least 4 years, etc. 15
  • Identification of multidimensional dimension via factor analysis1. Basic life-style – these concern the lack of ability to afford most basic requirements: Keeping the home (household’s principal accommodation) adequately warm; Paying for a week’s annual holiday away from home; Eating meat chicken or fish every second day, if the household wanted to; Ability to make ends meet.2. Financial situation – these concern the lack of ability to pay in time due to financial difficulties: Inability to cope with unexpected expenses; Arrears on mortgage or rent payments; Arrears on utility bills; Arrears on hire purchase instalments.3. Housing amenities – these concern the absence of basic housing facilities (so basic that one can presume all households would wish to have them): A bath or shower; An indoor flushing toilet; Leaking roof and lamp; Rooms to dark.4. Environmental problems – these concern problems with the neighbourhood and the environment: Pollution; Crime, violence, vandalism; Noise.5. Consumer durables - these concern enforced lack of widely desired possessions ("enforced" means that the lack of possession is because of lack of resources): A car or van; A colour TV; A pc; A washing machine; A telephone.6. Health related – these concern problems with personal health: General health; Chronic illness; Mobility restriction. 16
  • Application C/S to EU-SILC Italian Regions – NUTS2 Regions Indicator values · 100 FMI FSI FSIh=1 FSI h=2 FSI h=3 FSIh=4 FSIh=5 FSIh=6 FSI h=7Italy: 12,30 23,43 23,81 7,22 13,77 15,06 23,24 22,28 23,52Piemonte 8,17 22,53 18,01 6,63 13,43 14,24 28,50 21,66 20,80Valle d’Aosta 6,57 13,83 12,35 4,73 12,63 11,60 11,27 26,63 17,75Liguria 10,02 16,91 19,89 8,02 8,68 10,45 20,36 19,28 15,77Lombardia 7,48 17,96 14,87 5,60 10,15 12,00 24,19 23,63 18,73Trentino 6,10 15,10 14,88 3,84 10,96 8,03 16,41 23,54 17,80Alto Adi ge 5,32 13,26 13,89 3,64 12,40 6,73 15,14 23,50 17,01Veneto 8,17 19,08 19,84 3,66 13,47 11,50 21,14 24,27 21,13Friuli-Venezia Giulia 7,80 16,64 17,75 3,58 13,86 11,80 16,78 22,53 19,90Emilia Romagna 7,29 19,26 16,11 4,51 14,72 11,55 24,67 22,18 20,73Toscana 7,75 19,52 18,65 4,31 12,10 12,91 21,24 22,81 20,85Umbria 9,86 19,16 20,05 4,58 13,50 14,98 18,17 20,90 22,92Marche 9,38 19,65 21,91 4,94 14,20 13,65 18,28 24,60 23,63Lazio 11,00 25,50 23,44 6,18 12,99 15,30 29,19 18,12 24,81Abruzzo 12,43 19,89 26,12 4,40 12,14 13,87 10,13 20,36 28,63Molise 16,80 16,42 23,82 7,42 11,67 11,49 6,38 21,85 25,29Campania 22,29 35,20 36,65 12,48 18,05 21,50 34,92 22,76 26,81Puglia 17,19 29,58 35,63 12,28 13,58 19,70 18,78 24,17 28,84Basilicata 18,09 26,99 32,16 10,37 18,07 18,92 12,81 19,64 31,18Calabria 21,70 29,23 33,48 11,03 18,53 20,91 14,38 20,10 34,66Sicilia 21,95 33,79 40,59 11,99 18,12 22,82 21,55 22,11 31,02Sardegna 14,16 28,70 33,16 10,80 18,53 16,69 16,30 23,49 31,31 17
  • Application longitudinal to ECHP Italian Macro-Regions NUTS1Table 6: Longitudinal income poverty ratesM acro-Region Anytime Persistent Continuous Anytime Persistent ContinuousNorth-West 26.5 2.8 0.4 25.7 5.8 1.7North-East 26.5 3.3 0.5 24.4 6.3 2.2Center 41.1 9.1 1.3 36.1 12.6 4.0South 60.0 25.5 5.7 52.0 24.8 9.4Islands 67.1 31.8 9.5 56.9 29.1 12.7Italy 42.6 13.2 3.0 37.8 14.7 5.5 18