Transcript Document
2006 Conference of the European Panel User Network (EPUNet) May 8-9, Barcelona - Spain
On the overlap of multidimensional and income poverty
Alessio Fusco IMPALLA – CEPS/INSTEAD [email protected]
Direct vs indirect approaches (Sen, 1979; Ringen, 1987)
Indirect approaches Lack or resources Means to satisfy the needs Potential satisfaction of the needs Income approach of poverty is an indirect approach => unidimensional approach Direct approaches Failure to achieve basic functionings Ends or results Factual satisfaction of the needs Sen’s capability approach or Townsend’s relative deprivation => multidimensional approaches
Direct vs income approach: which one to choose?
Theoretical point of view: direct approach more satisfying than income approach; Main critique to the income/indirect approaches: Social justice theory (see Sen’s work) Not only lack of money but also « multifaceted combination of deprivations and unmet needs that prevent from participating in the society in the same way that others do. » Income method is at most a second best (Sen, 1979)
Direct vs income approach: which one to choose?
However, multidimensional approaches face many difficulties in their operationalisation (choice of dimensions and elementary indicators, aggregation, etc.) What is their practical utility/validity?
Important question as the measurement of multidimensional poverty implies a high cost in terms of time, resources and data (Klasen, 2000; Kuklys, 2005) => study of the overlap
Study of the overlap
Several methods to study the overlap: econometrics (Dekkers, 2003), correlation, or comparison of the population identified as poor by the two approaches (Lollivier and Verger, 1997; Layte et alii , 2001; Perry, 2002) First Step: determine a threshold on each measure Income approach: 60% of the median of the distribution of equivalent income Multidimensional approaches: no consensus on where to place the threshold. Common practices: to use the same arbitrary proportion of poor on the two measures (Lollivier et Verger, 1997) to set the deprivation threshold in order to obtain the same proportion of multidimensional and income poor (Layte et alii , 2001; Perry, 2002)
Aim of the paper
Main conclusion: mismatch between the income and the multidimensional approaches of poverty (Perry, 2002); non monetary indicators are related to monetary measures but not enough to consider them as equivalent Drawback: the result is each measure conditional to the thresholds chosen for Propose an extension of this method using an innovative methodology: the Receiver Operating Characteristics => assess of the overlap independently of the threshold on the multidimensional index
Receiver Operating Characteristic (ROC)
Graphic and non parametric way of portraying accuracy of a diagnosis test in a binary outcome for different cut points Medical decision making: to detect presence/absence of a disease we need a diagnosis test T i =0..T
max
cut-off Z => presence/absence of the disease For each Z=0..T
max
diagnosis error are likely to occur
Presence of disease Absence of disease Test positive (T > Z) Fraction of True Positive (TP) (Sensibility) Fraction of False Positives (FP) Test negative (T < Z) Fraction of False Negative (FN) Fraction of True Negatives (TN) (Specificity) TP + FN = 1 FP + TN = 1
Analogy with the concept of consistent poverty (Nolan and Whelan, 1996)
Income poverty: «disease» - binary outcome Multidimensional index S i : «diagnosis test» hyp: the income threshold of 60% of the median is a good threshold of poverty
Deprived (S > Z) Non deprived (S < Z) Income poverty Non income poverty Consistent Poverty
Fraction of True Positive (TP) (Sensibility)
Deprivation only
Fraction of False Positives (FP)
Income poverty only
Fraction of False Negative (FN)
Consistent non poverty
Fraction of True Negatives (TN) (Specificity)
TP + FN = 1 FP + TN = 1
ROC curve - France
France - poverty line: 60% - index Si Z=0 TP= 1 TN=0 FP= 1 – TN =1 Z=S max TP=0 TN=1 0.00
0.25
0.50
0.75
Fraction False Positive - (1 - Specificity) FP= 1 - TP =0 Area under ROC curve = 0.6838
Figure 1: Curve of the Receiver Operating Characteristic for France Source: ECHP-UDB version December 2003, year 1995, author's computation 1.00
Area under the ROC Curve
Criterion of the quality of the overlap Area = probability that the index of deprivation of an income poor chosen randomly be higher than the index of deprivation of a non income poor chosen randomly. Area=1 => perfect overlap Area=0,5 => no discriminating power Area<0,5 => measures inversely correlated Reference values: Area ]0.9 , 1] ]0.8 , 0.9] ]0.7 , 0.8] ]0.6 , 0.7] ]0.5 , 0.6] association Excellent Good Medium Poor insufficient
Application to the ECHP
Wave 2 - 1995
13 countries
Unit of observation: individuals of more than 16 years old
Match the income of wave 3 with household characteristics from wave 2
Income poverty threshold=60% of the median of the distribution of equivalent income
Austria Belgium Country Denmark France Germany (ECHP) Greece Ireland Italy Luxembourg (ECHP) Netherlands Portugal Spain UK (ECHP) Total frequency* 6 316 5 212 4 513 11 297 7 973 10 659 6 165 16 227 1 795 8 119 10 594 13 648 6 362 108 880
Multidimensional index: dimension and items
Several criteria to choose the items (frequency, social consensus, interrelation, Cronbach alpha) 6 dimensions (q=1..6) and 26 items (j=1..26): A. Inability to afford most basic requirements B. Inability to meet payment schedules C. Absence of basic housing facilities D. Problems with accommodation E. Problems with environment F. Enforced lack of widely desired possessions
Table 4: List of items Inability to afford most basic requirements (basic needs):
hf003 … keeping its home adequately warm hf004 hf005 … paying for a week's annual holiday away from home … replacing any worn-out furniture hf006 … buying new, rather than second-hand, clothes hf007 hf008 … eating meat, chicken or fish every second day, if wanted … having friends or family for drink or meal at least once a month
Inability to meet payment schedules (arrears):
hflog … rent for the accommodation (hf009) or mortgage payments (hf010) hf011 hf012 … utility bills, such as electricity, water, gas … hire purchase instalments or other loan repayments
Absence of basic housing facilities:
ha009 ... a bath or shower ha010 ha011 ha012 ... an indoor flushing toilet … hot running water … heating or electric storage heaters
Problems with accommodation:
ha014 … shortage of space ha016 ha017 ha018 ha019 ha020 ... too dark/not enough light … lack of adequate heating facilities … leaky roof … damp walls, floors, foundations, etc.
… rot in window frames or floors
Problems with the environment:
ha015 ha021 … noise from neighbors or outside … pollution, grime or other environmental problems caused by traffic or industry ha022 … crime or vandalism in the area
Enforced lack of widely desired possessions (durable goods):
hb001 … a car or van (available for private use) hb002 hb003 hb006 … a colour TV … a video recorder … a telephone
Deprivation by dimension
ξ j D All items are dichotomous: x ij x ij = 1 deprivation on item j=1..26
= 0 absence of disadvantage Weighted index by dimension: S iq
with
m q j 1 w j 1 and w j ln w j m q 1 ln 0 j ξ 1 j D ξ 1 j D avec ssi ξ J D 0 ξ D j 1 ou ξ D j 0 m j q 1 w j ξ D j (i)
is the proportion of people deprived on item j
Overall index of multidimensional poverty
Two axiomatic indexes Pe et P α (Chakravarty et alii, 1998) P e (X; z) P α (X; z) 1 n 1 n q k q 1 1 i D k i q D q a q a q 1 1 x iq z q x iq z q e α where aq=1/q=1/6; xiq = 1 - Siq ; and e=0,5 and α=2 Composite index S i q 1 i q 1 S iq
Multidimensional measure
Autriche Belgique Pays Danemark France Allemagne Grèce Irlande Italie Luxembourg Pays-Bas Portugal Espagne Royaume-Uni moyenne pondérée* Pα (α=2) 0.69% 1.40% 0.39% 1.23% 0.64% 3.94% 1.08% 2.30% 0.84% 0.53% 4.62% 1.55% 1.27% 1.43% Pe (e=0,5) 0.81% 1.57% 0.47% 1.41% 0.72% 4.18% 1.24% 2.48% 0.96% 0.64% 4.91% 1.70% 1.46% 1.59% Si 0.065
0.080
0.043
0.086
0.060
0.171
0.073
0.104
0.051
0.062
0.177
0.105
0.092
0.089
Table 8: Indexes of multidimensional poverty Source: ECHP-UDB version December 2003, computation from the author *weighted by the population of more than 16 years old of the different countries
Results – 60% of the median
country_nom Austria Belgium Denmark France Germany (ECHP) Greece Ireland Italy Luxembourg (ECHP) Netherlands Portugal Spain UK (ECHP) Pα (α=2) 0,562 0,585 0,542 0,584 0,569 0,655 0,575 0,607 0,633 0,565 0,650 0,546 0,575 Pe (e=0,5) 0,562 0,585 0,542 0,584 0,569 0,655 0,575 0,607 0,633 0,565 0,651 0,546 0,575 Si 0,650 0,655 0,568 0,684 0,655 0,707 0,681 0,703 0,738 0,683 0,708 0,651 0,670
Table 9: Area under the ROC curve for a threshold of 60% of the median Source: ECHP-UDB version December 2003, computation from the author
0.00
0.25
0.50
0.75
1.00
Fraction False Positive - (1 - Specificity) Area under ROC curve = 0.6548
0.00
0.25
0.50
0.75
1.00
Fraction False Positive - (1 - Specificity) Area under ROC curve = 0.5678
0.00
0.25
0.50
0.75
1.00
Fraction False Positive - (1 - Specificity) Area under ROC curve = 0.6829
0.00
0.25
0.50
0.75
1.00
Fraction False Positive - (1 - Specificity) Area under ROC curve = 0.6555
UK (ECHP) - poverty line: 60% - index Si Ireland - poverty line: 60% - index Si 0.00
0.25
0.50
0.75
1.00
Fraction False Positive - (1 - Specificity) Area under ROC curve = 0.7380
0.00
0.25
0.50
0.75
1.00
Fraction False Positive - (1 - Specificity) Area under ROC curve = 0.6838
0.00
0.25
0.50
0.75
1.00
Fraction False Positive - (1 - Specificity) Area under ROC curve = 0.6697
0.00
0.25
0.50
0.75
1.00
Fraction False Positive - (1 - Specificity) Area under ROC curve = 0.6810
Italy - poverty line: 60% - index Si Greece - poverty line: 60% - index Si Spain - poverty line: 60% - index Si Portugal - poverty line: 60% - index Si 0.00
0.25
0.50
0.75
1.00
Fraction False Positive - (1 - Specificity) Area under ROC curve = 0.7033
Austria - poverty line: 60% - index Si 0.00
0.25
0.50
0.75
1.00
Fraction False Positive - (1 - Specificity) Area under ROC curve = 0.7071
0.00
0.25
0.50
0.75
1.00
Fraction False Positive - (1 - Specificity) Area under ROC curve = 0.6508
0.00
0.25
0.50
0.75
1.00
Fraction False Positive - (1 - Specificity) Area under ROC curve = 0.7077
0.00
0.25
0.50
0.75
1.00
Fraction False Positive - (1 - Specificity) Area under ROC curve = 0.6502
Threshold of 50% and 70%
Pays Autriche Belgique Danemark France Allemagne Grèce Irlande Italie Luxembourg Pays-Bas Portugal Espagne Royaume-Uni Pα (α=2) 0,5623 0,5962 0,5497 0,6053 0,5907 0,6640 0,5688 0,6163 0,5999 0,5606 0,6630 0,5614 0,5775 seuil 50% Pe (e=0,5) 0,5622 0,5963 0,5498 0,6062 0,5907 0,6646 0,5688 0,6164 0,5998 0,5607 0,6638 0,5615 0,5775 0,5938 Si 0,6555 0,6595 0,6148 0,7067 0,6660 0,7140 0,6509 0,7185 0,7045 0,6744 0,7154 0,6646 0,6628 0,6823 Pα (α=2) 0,5582 0,5713 0,5316 0,5750 0,5590 0,6432 0,5773 0,5921 0,5795 0,5516 0,6381 0,5343 0,5771 0,5716 seuil 70% Pe (e=0,5) 0,5583 0,5714 0,5317 0,5755 0,5590 0,6437 0,5775 0,5922 0,5794 0,5516 0,6391 0,5344 0,5773 0,5718
Tableau 4.17: ROC à différents seuils Source: ECHP-UDB version décembre 2003, année 1995, calculs de l'auteur *pondération par la population de plus de 16 ans des différents pays
Si 0,6299 0,6591 0,5850 0,6771 0,6514 0,7033 0,6889 0,6918 0,6647 0,6789 0,7015 0,6416 0,6752 0,6681
Conclusion