Deprivation of Well-being in Terms of Material Deprivation in Multidimensional Approach: Sri Lanka D.D.Deepawansa and D.D.P.M.Dunusinghe Paper prepared for the 16 th Conference of IAOS OECD Headquarters, Paris, France, 19-21 September 2018 Session 1.B., Day 01, 19/09, 11.00: Poverty and well-being
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Deprivation of Well-being in Terms of Material Deprivation
in Multidimensional Approach: Sri Lanka
D.D.Deepawansa and D.D.P.M.Dunusinghe
Paper prepared for the 16th Conference of IAOS
OECD Headquarters, Paris, France, 19-21 September 2018
Session 1.B., Day 01, 19/09, 11.00: Poverty and well-being
In the twentieth century, there have been a number of theoretical challenges for welfare measurements
resulting many theoretical approaches to measure poverty. In the recent past, there was a growing interest
among researchers and policymakers to measure poverty in multidimensional approach using Alkire and
Foster (AF) (2007) counting methodology. This method has now risen to prominence among policymakers
and researchers. AF family of measures satisfy many of the desirable properties of poverty measures stated
by Sen (1976). The Sustainable Development Goals (SDGs) also have been flagged the multidimensionality
of poverty in using Alkire and Foster (2007) counting methodology. In Sri Lankan context, poverty is
measured officially in consumption approach. According to the official poverty line, overall incidence of
poverty has declined dramatically from 1995/1996 survey year to 2016 from 28.8 percent to 4.1 percent.
Similarly during the same corresponding period, the poverty headcount index has declined from 46.7 per cent
to 6.5 percent in Uva Province.
The objective of this study is to measure poverty in multidimensional aspects based on Sen’s Capability
Approach in Sri Lankan context in terms of material deprivation using a new method called “Synthesis
Method” to understand deprivation of well-being in Uva province. This study enables to make comparison
of real achievement of non-monetary measures of poverty with monetary measures of poverty on consumption
based to understand poverty in Sri Lanka. In particular, this study attempts to achieve;
a. To what extent does poverty exist in terms of material deprivation?
b. What are the main indicators contributing to material deprivation?
To achieve the research objectives a survey was conducted to collect primary data in Uva province in Sri
Lanka.
1.1 Rationale for the study
Uva province has been one of the highly affected provinces in terms of poverty among the nine provinces in
Sri Lanka for a long period. However, this province has shown a considerable progress in combating against
poverty in 2016. Sri Lanka has achieved successive progress reducing poverty and improving some socio
economic and human development indicators during the last few decades. Conversely, socio economic
development disparities have been problematic issues throughout the history of the country. Hence, some
regions called “provinces” are still having concerns in terms of economic development. In this respect,
according to the Household Income and Expenditure Survey Uva has been reported as one of the
economically backward provinces in Sri Lanka1. According to the official Statistics declared by Department
of Census and Statistics (DCS) using Small Area Estimates made in 2012/13 , the poorest ten District
Secretariat (DS) divisions are located in this province. However, in 2016, Uva province has shown a steady
progress in combating against poverty resulting the decline of poverty headcount index from 15.4 in 2012/13
to 6.5 in 2016. However, this province is still the fourth poorest province among the other nine provinces.
1 1990/91, 1995/96, 2002 and 2006/7 survey periods recorded the highest poverty head count in this province (Poverty
head Indices in 1990/91, 1995/96, 2002 and 2006/7 were 31.9, 46.7, 37.2 and 24.2 respectively). In 2009/10, the Uva
province recorded the second highest poverty incidence (13.7 per cent) and again in 2012/13 Uva reported the highest
HCI(15.4).
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Uva province is a suitable laboratory to investigate poverty in multidimensional when compared with the other
provinces in Sri Lanka. Uva has been an economically backward province throughout in the past but recently
showed some progress combating against poverty. Uva consists of different geographical areas and represents
multi ethnic and multi religious backgrounds as well as it represents all three sectors called urban, rural and
estate. Estate sector is a special sub-economic sector in Sri Lanka and somewhat unique in its characteristics
in all forms, ranging from composition of household units to organization of political establishments. This
province represents 6.2 per cent from the total population of Sri Lanka (DCS, 2012). It comprises various
socioeconomic, geographical and multi-ethnic backgrounds. The main livelihood in Uva is based on
agriculture. There are many large reservoirs and waterways to support agrarian products. In addition, many
cash crops such as tea, rubber, coconut, sugar cane, and tobacco have been introduced which contributes to
the province’s economy. Out of the total employed workforce 54.3 percent work in the agriculture industries.
Uva province is an ideal selection to understand poverty in a more realistic nature and can be considered as a
cross section to gain accurate picture of poverty in Sri Lanka. The numerous poverty alleviation programs
have been launched within the province on the basis of poverty measures based on monetary indicators.
Nevertheless, poverty is still a considerable issue to be addressed despite of many poverty alleviation programs
which have been implemented by both the government and non-governmental agencies (Samaraweera,
2010).Therefore, Uva province can be considered as one of the most conducive provinces to research on
poverty in multidimensional approach when compared with other provinces in terms of economic
development, social infrastructure facilities, socio economic and human development indicators. On the basis
of these factors, this research can be used as a pilot attempt to measure poverty in new multidimensional
approach in Sri Lanka.
A comprehensive new survey is essentially a prerequisite and needed to be conducted to capture the real nature
of poverty in multidimensional approach in Sri Lanka. The main micro data sources are used to measure
poverty in Sri Lanka are; Household Income and Expenditure Survey (HIES) and Demography and Health
Survey (DHS) conducted by the Department of Census and Statistics. HIES is generally performed once in
three years and DHS is once in five years. Both HIES and DHS consists limited dimensions which are easy
to address and related to poverty2. Common dimensions which are more important for poverty analysis such
as; nutrition, security, social relationship, adequacy of consumption materials, empowerment are not collected
in a single data source. There is no single data source in existence in Sri Lanka containing representative
sample for at least to represent a geographical area drawn in a scientific way including above information to
measure poverty in multidimensional approach. Hence, it impedes the potential to accomplish analysis joining
the dimensions to make high-impact policies for interventions. Therefore, in order to capture the real nature
of poverty, it is needed to collect data on qualitative and quantitative aspects in multidimensional approach as
such information is unavailable. The SDG goal for poverty is “End poverty in all its forms everywhere”.
Therefore, it is paramount to consider more dimensions for measuring poverty. In view of this circumstances,
it led the researcher to conduct a new survey to capture the information covering nineteen dimensions
including the missing dimensions in HIES and DHS.
2 HIES collects information on household achievements such as consumption, possession of durable goods and
indebtedness. DHS collects mainly nutrition related data from eligible women those who are ever married between 15
and 49 years old and from 0 to 5 years old children and housing facilities.
6
The new survey which has been conducted by the researcher covering 1200 housing units was enriched with
poverty related information and has fulfilled the data gap for poverty analysis. The unit identification was the
respondent (an adult person) above eighteen years old in the household and the other household members’
information was also collected to get an overview of the household. This allowed the researcher to analyze
poverty measures by individual characteristics such as; age, gender, occupation and other characteristics.
Further, it paved the way to identify high-impact policy sequence targeting reduction of poverty in Sri Lanka.
When measuring poverty, consumption poverty is important but it is incomplete. It provides rough measures
of the quality of life because they are unable to describe fully what people can really achieve with resources
and capabilities (Sen, 2009).Sri Lanka’s official poverty statistics has been measured adapting a very narrow
definition in terms of consumption using Cost of basic Need method developed by Ravallion and Bidani
(Ravallion & Bidani, 1994). Although in Sri Lanka, poverty has declined from 28.8 % in 1995/96 to 4.1 in
2016 in consumption approach, the majorities of better- off people who are just above the poverty line and
are very much subject to vulnerability and associated with the effect of “shocks” such as natural disasters and
financial crisis3. Although poverty has dropped in consumption approach significantly, country is still
suffering in deprivation of well-being. Nevertheless, one-dimensional consumption is the best approach to
measure deprivation by monetary aspects yet it partially describes the poverty and does not fully explore the
nature of existing poverty in other dimensions such as; lack of security, material deprivation , access to basic
facilities and assets. Because of conventional limitations of unidirectional measures of poverty, most of
poverty target policy strategies have not been directly aimed at accurate targets. Hence, those are inappropriate
for long term success. Since independence, all successive Sri Lankan governments have introduced various
poverty reduction programs; Janasaviya, School Midday Meal Program and Samurdhi. Nevertheless, many of
these programs have not been able to achieve their intended targets (Samaraweera, 2010). Therefore, Uni-
dimensional consumption poverty is inadequate to capture the real nature of poverty in Sri Lanka.
In view of the limitations of existing poverty measures, it is indispensable to measure poverty in extensive
aspects in multidimensional approach to understand the real nature and magnitude of poverty. There have
been some previous attempts trying to measure poverty in multidimensional approach in Sri Lanka;
Siddhisena and Jayatilaka (2003) , Weerahewa and Wickremasigha (2005), Semasinghe (2011),
Kariyawasam, et al. (Kariyawasam, et al., 2012) and Nanayakkara (2012). However, these approaches were
plugged with several coverage, methodological and conceptual issues. When considering the coverage, most
studies have been limited to a few dimensions such as health, education and living standard which are used in
global multidimensional poverty index(MPI) implemented to compare poverty across countries (Alkire &
Santos, 2010). But this method is not sufficiently adequate to understand real nature of poverty in Sri Lanka.
The weight assigned in Global MPI analysis is equal to all three dimensions. This method facilitates each
person to assign a deprivation score according to the household’s deprivation for 10 indicators for three
dimensions. This threshold and weights have been set normative way for cross country comparison for global
Multidimensional Poverty Index (MPI). Applying this threshold and weights to measure poverty in Sri Lankan
context, makes it difficult to measure poverty precisely. Hence, it is important to assign weight scientifically
which paves the way to capture the real picture of poverty in relevant dimensions in Sri Lankan context4.
3The value of poverty line is increased by 10 percent (from Rs. 4,166 to Rs. 4,582.6) then the poverty head count index
increases up to 6.1 percent. That means number of people who are in poverty increases from 843,913 to 1,255,702 (DCS,
2016). 4 It is evident that using the same HIE survey data in 2009/10 multidimensional poverty index (4.7) was lower than the
one- dimensional consumption poverty headcount ratio (8.9). When taking into account both survey results on poverty
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This study uses fuzzy set method of Cerioli and Zani, (1990) and Alkire and Foster (2007) counting method
to develop a new method called “Synthesis Method’’ to measure poverty in Sri Lanka in multidimensional
approach. Section 2 illustrates why this method is particularly appropriate pragmatically than Alkire and
Foster method and Fuzzy method to measure poverty. This paper is structured as follows. Section 2 presents
a brief description of the data and methodology. Section 3 provides the analytical techniques used in Synthesis
method to calculate families of poverty indicators on multidimensional approach and describe the facts that
how Synthesis method defers from Fuzzy and Alkire and Foster methods. Section 4 presents the finding of
poverty indices and Section 5 is the conclusion.
2. DATA AND METHODOLOGY
This chapter presents the practical procedure and its application to answer the research questions in this study
contributing towards to survey instrumentation, sampling method, data collection methods and analytical
method. The main objective of this study is to understand deprivation of well-being in Uva province in multi-
dimensional approach. This is achieved by recognizing the dimensions of poverty on Capability Approach
and analyzing data through the Synthesis Method developed by the researcher combining fuzzy set theory and
Alkire and Foster counting method.
2.1 Survey Instrument
In this study, survey schedule is used as an instrument to collect the data by conducting face to face interview.
The schedule was designed systematically to elicit the responses from the respondent by dividing it into
nineteen sections. The questions in the schedule are structured and some control and guidance have been given
to the answers. The interviewer poses the oral questions to elicit the oral answers from interviewee and records
the answers in the schedule.
2.2 Survey Sampling
The dataset used in this study is drawn from the primary survey of households conducted by the researcher
from November 2016 to December 2016 in the two districts called Badulla and Moneragala in Uva Province,
Sri Lanka. The survey sample is a representative of the province. Sample design of the survey is two stage
stratified and Primary Sampling Units (PSUs) are the census blocks, which consist with average 80 building
units. In the Census of Population and Housing, the entire country is divided into the smallest geographical
units as census enumeration areas called census blocks. The secondary sampling units are housing units which
are in the selected blocks. The three sectors; urban, rural and estate in each districts are the main selection
domains. Badulla has three sectors while Moneragala has only the rural and urban sectors. Five stratums were
considered as selection domains. The sample size was decided in a systematic way to represent the entire
population of Uva province (UN, 2008, p. 44). The sample size of the survey was 1200 housing units. This
sample was allocated to each stratum proportionate to the population. According to the sampling design,
housing units were selected by two stages. At the first stage, the Primary Sampling Units (PSUs) were selected
from each stratum systemically with a selection probability given to each census block proportionately to the
number of housing units available in the census blocks within the selection domains called systematic
measurement. It appears that this multidimensional approach had not captured poverty even accurately as one-
dimensional monetary approach in country context.
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probability proportionate to size (PPS). Accordingly, a hundred and twenty PSUs were selected from the
sampling frame for the survey in Uva Province. Out of 120 PSUs, 78 from Badulla district and 42 from
Moneragala district. At the second stage, final sampling units, which are also called the housing units were
selected from each and every selected PSUs at the first stage. These sampling units were the Secondary
Sampling Units (SSUs). Ten housing units from each census block was selected systematically for the survey.
A total of 10 housing units (SSUs) were selected for the survey from each PSU. In this way, the entire sample
sizes of 1200 housing units were selected from Uva Province for the survey. All the households within the
selected housing units have been enumerated.
The survey included schedules which obtained information on general characteristics of individuals and
households. It was administered through face to face interviews. The respondent of the survey was the person
usually lives in the household who is over 18 years of age. The questions in the schedule were structured and
the closed options provided ensured control and guidance. The interviewer posed oral questions to elicit the
oral answers from the interviewee and recorded the answers in the schedule. In order to compute the material
deprivation index, the researcher used the information on demographic characteristics, ownership of durable
goods, housing information and food and clothing related information collected from this survey.
The reference population in this study was all the people living in Uva Province and the unit of analysis is the
individual who responded to the enumerator at the interview. There was no specific method to select the
respondent in the household. By chance, males and females over 18 years of age were enumerated at the
survey. Data was collected from 1,193 respondents of whom 730 were females and 463 males. However, in
this analysis all the required information for material deprivation was available only from 848 respondents5
which are above 18 years old.
2.3 Synthesis Method
This study goes beyond the traditional way of measuring poverty dividing the population into poor and non-
poor using a yardstick called poverty line. In order to understand the realistic nature of poverty, it increased
the complexity of both conceptual and analytical context. Such complexity required an adequate data and
analytical tool to make it more realistic. It is impractical to draw a line to any society to divide the population
into poor and non-poor. Hence, there is no sharp borderline to identify a person being poor or non-poor. It is
just like many philosophical descriptions of pretty and happiness. Instead of that, this study measures poverty
in multidimensional phenomenon to understand poverty as degree of deprivation indicating between zero
(totally non- deprived) and one (totally deprived). It gives the varying degree of deprivation for the entire
individual in the population in the form of membership function in fuzzy set theory. In addition to that, this
study uses the special household survey data gathered by the researcher to collect the information which was
not available by any other sources of data in Sri Lankan context. In analytical context, it has been used a new
method called “Synthesis Method” combining the fuzzy set and Alkire-Foster Counting Methodology to
identify the individual deprivation in well-being in multidimensional setup. This conveys the fact that with
more complete and realistic view of poverty in multidimensional increases the complexity at both the
analytical and conceptual intensity.
Many concepts in social science such as deprivation, empowerment, and autonomy are essentially vague in
sense. It is improbable to fix a boundary to separate into two groups. This concept was mathematically applied
5 In this study the sample size of respondents is 891 individuals and among them 542 females and 349 males.
9
using fuzzy set theory ,Cerioli and Zani, in (1990) and followed by Cheli and Lemmi (1995) and Betti et al
(2005a, 2005b). Thereafter, it has rapidly expanded to analyze poverty in uni-dimensional and
multidimensional approach based on capability approach theoretically and empirically (Chakravarty (2006) ;
Betti& Verma (2008); Betti et al. (1999,2002,2004); Belhadj (2012); Verma, et al. (2017).
(Alkire & Santos, 2010) Counting method is an axiomatic approach which is empirically implemented in
larger scale throughout the world to calculate Multidimensional Index (MPI). Counting approach identifies
the poor person in two main steps using two cut-offs called indicator cut-off and poverty cut-off. Alkiare and
Foster (AF) uses different indicators, weights and cut-offs on normative judgments to create MPI for different
situations at global and national context. It provides more flexible framework to produce MPI measures.
3. ANALYTICAL TECHNIQUES
3.1 Driving indicators
In this study, in order to minimize correlation across the variables correlation analysis was carried out.
Selection of appropriate variables for each dimension was carried out statistically using the data redundancy
test, the Pearson Correlation test and the Point Biserial correlation. First, the data redundancy test was done
for dichotomous variables, and Pearson Correlation test was applied for continuous variables. Finally Point
Biserial correlation was applied to select the variables among the selected dichotomous and continuous
variables from the above two methods.
3.2 Analytical techniques of Synthesis method
In analytical techniques of Synthesis method, there are two main challenges i) identification of deprived
people and ii) aggregation of deprivations. Prior to providing the detail description, the following gives the
steps how calculation is done to identify the multidimensionally poor persons and how to aggregate
deprivation scores to measure poverty in multidimensional approach using Synthesis Method. For
identification of poor, use the Fuzzy membership function introduced by Cerioli and Zani (1990) as described
in section 2.3.
The calculation method of membership function has been explained bellow;
If 𝑄 be the set of elements 𝑞 ∈ 𝑄 then the fuzzy sub set 𝐴 𝑜𝑓 𝑄 can be describe as;
𝐴 = {𝑞, 𝜇𝐴(𝑞)} (3.1)
Where𝜇𝐴(𝑞): is the membership function (m.f) is a mapping from 𝑄 → [0,1]. The value of 𝜇𝐴 is the degree
of membership in the incident of 𝑞 𝑖𝑛 𝐴. When 𝜇𝐴 = 1 then 𝑞 completely belongs to 𝐴 . If 𝜇𝐴 = 0 then
𝑞 does not belong to 𝐴. Whereas the elements q which is0 < 𝜇𝐴(𝑞) < 1 then 𝑞 partially belongs to 𝐴
and the degree of it’s membership in the fuzzy set increases when nearer the propensity to 𝜇𝐴(𝑞) to 1.
Let’s n of individuals (n; i=1 …….n) in a sub set 𝐴 and then poor can be described as follow in fuzzy set
approach;
𝜇𝐴𝑖 i= 1,2…………….n (3.2)
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Identification
1. Define the set of indicators which will be available for all the individuals considered in material deprivation
2. Calculate the degree of deprivation 𝜇𝐴𝑖for each indicator in terms of fuzzy membership function for the
entire individual as a real value in between zero (totally non-deprived) and one (totally deprived).
3. Calculate the frequency weight for each indicator in terms of totally deprived individuals.
4. Compute the weighted deprivation score for each indicator for all individuals and create sum of weighted
deprivation score (𝜇𝐴) for each individual in all dimensions.
5. Determine the deprivation cut-off (z) based on Kendall rank correlation (tau_b) coefficients .tau_b were
calculated for different cut-off points and based on robustness test poverty cut-off was decided to identify the
multidimensional poor persons.
6. A person considered to be multidimensionally poor or not with respect to the selected cut-off for and
aggregated weighted deprivation score.
Aggregation
The steps and the methods used to aggregate the fuzzy deprivation score follows the methods introduced by
Alkire et al. (2015). Aggregation method is an extension of Foster-Greer-Thorbeck (1984). For this study, five
poverty indices are produced using the fuzzy deprivation scores of individuals; i) Fuzzy Headcount Index
(FHI) ii) Fussy Intensity (FI) , iii) Adjusted Fuzzy Deprivation Index (FM0), iv) Normalized Deprivation Gap
Index (FM1) V) Squared Normalized Deprivation Gap Index (FM2)
7. Compute the proportion of individuals identified as in multidimensional poor and create the Fuzzy
Headcount Index (FHI) to measure the incidence of Fuzzy poverty in multidimensional approach.
8. Calculate average per capita fuzzy deprivation in other ward propensity to poverty for the individual who
are multidimensionally poor. This is the Fussy intensity (FI) of multidimensional deprivation.
9. Compute the Adjusted Fuzzy Deprivation Index (FM0) as a product of Fuzzy Headcount Index (FHI) and
Fussy intensity (FI). FM0 can be calculated dividing the sum of aggregated Fuzzy Deprivations by total
population.
10. Compute the contribution of each indicator and dimensions to average Adjusted Fuzzy Deprivation Index
multiplying the FM0 by average share of deprivation scores for each indicator and dimensions scores to total
average deprivation scores.
11. Calculated the normalized Deprivation Gap Index (DGI). DGI is computed getting a sum of aggregated
deprivation difference to poverty cut-off of multidimensional people and divided it by the deprivation cut-off.
It gives a good indication of the depth of Deprivation (individual who are not deprived are censored. Hence,
normalized gap for them are zero)
12. Compute the FM1 (Adjusted weighted deprivation gaps Index) as a product of three indices: FM1= FHI×
FI× DGI; that is the sum of the weighted deprivation gaps that deprived people experience, divided by the
total population.
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13. Calculate the Squared Deprivation Gap Index (SDGI) that measures the severity of deprivation. This index
measures the inequality among the deprived people by weighting the normalized DGI itself. So, it gives the
more weight to the most deprived people.
14. Compute the FM2 (Adjusted weighted squared deprivation gaps Index) as a product of three indices:
FM2= FHI× FI× SDGI; that is, the sum of the weighted squared deprivation gaps that multidimensionally poor
people experience, divided by the total population.
Note: These three indices (FM0, FM1,FM2) were calculated considering the concord distribution of
multidimensionally poor people that is the individual whose deprivation score is above the cut-off are
censored. As the other poverty indices like Foster-Greer-Throbeck (1984) and Alkire et al. (2015) these three
indices satisfy the key axioms in poverty measures introduced by Sen (1976) ; monotonicity and transfer
axiom .
Denote each individual a grade of membership in the sub set poor(𝜇𝐴𝑖) ;
If 𝜇𝐴𝑖 = 0 ; ith individual is not definitely belong to poor
If 𝜇𝐴𝑖 = 1; ith individual is completely poor (3.3)
If 0 < 𝜇𝐴𝑖 < 1 then ith individual is partially belong to poor sub set.
This membership function has been applied to the value of continuous variables and the orderly categorized
variables. Let’s jth number of indicators and then the membership function for ith individual is 𝜇𝐴𝑗(𝑖). They
suggested fixing the two thresholds for minimum(𝑗𝑚𝑖𝑚) and maximum(𝑗𝑚𝑎𝑥) value to continuous variables
in a reasonable manner6. If membership value is less than 𝑗𝑚𝑖𝑚 then the individual is considered as poor and
if greater than 𝑗𝑚𝑎𝑥 then the individual is completely considered as non- poor.
This logic can be applied to the categorical variables and the corresponding minimum and maximum values
can be determined by ordering the level of variables appropriately. As an example, the degree of satisfaction
of the neighbor or outside environment can be categorized at five levels as “Highly interrupt” to “peaceful”.
When ordered these categories the minimum value should give to the most poor condition and maximum
otherwise. Hence, in this case one applied to the highly interrupt level and five should be peaceful level7.
The value of the membership function is given by the following equation.
Consider 𝑞𝑗𝑖 is the value of ith individual in jth indicator where (i=1,2……n) and (j=1,2……k) in the poor set
𝜇𝐴.
Then the membership faction for each individual is;
𝜇𝐴𝑖(𝑗) = 1 if 0 ≤ 𝑞𝑖𝑗 < 𝑗𝑚𝑖𝑛
𝜇𝐴𝑖(𝑗) = 𝑞𝑗,𝑚𝑎𝑥−𝑞𝑖𝑗
𝑞𝑗,𝑚𝑎𝑥− 𝑞𝑗,𝑚𝑖𝑚if𝑗𝑚𝑖𝑛<𝑞𝑖𝑗 < 𝑗𝑚𝑎𝑥 (3.4)
𝜇𝐴𝑖(𝑗) = 0 if𝑞𝑖𝑗 ≥ 𝑗𝑚𝑎𝑥
6The relative deprivation concept use 60% of median income as poverty threshold in Europe for social policy criterions. 7 The ordering scale of categorical variables, it is important to give underline interval with equal distance between
midpoints of successive categories (Cerioli,A Zani,S, 1990)
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For dichotomous variables, this logic can be applied very easily because of only having two possible values.
The individual belongs to fuzzy set if the person does not success with the condition and otherwise not belongs
to fuzzy set. Hence, For instance, the membership value of a person having a car is zero and not having a car
is one.
𝜇𝐴𝑖(𝑗) = 1 if 𝑞𝑖𝑗 = 0 (not success with the condition)
𝜇𝐴𝑖(𝑗) = 0 if 𝑞𝑖𝑗 = 1 ( success with the condition) (3.5)
The averages of membership scores of all indicators give a fundamental product of fuzzy set of poor of the ith
individual by the following equation.
𝜇𝐴𝑖(𝑖) =1
𝑘∑ 𝜇𝐴𝑖(𝑗)
𝑘
𝑗=1
(3.6)
Cerioli and Zani (1990) suggested a frequency based weight phenomenon. The weight 𝜔𝑗of each indicator
can be computed by using following equation.
𝜔𝑗 =𝑙𝑛
1
𝑓𝑗
∑ 𝑙𝑛1
𝑓𝑗
𝑘𝑗=1
. ( 3.7)
In this equation, the term 𝑓𝑗 denotes the number of individuals who are completely deprived in jth indicator.
The natural logarithm of the inverse of frequency was applied so that a greater weight is not assigned for a
low value of 𝑓𝑗. Using equations 3.6 and 3.7 the total value of individual membership in multidimensional
weighted fuzzy deprivation was calculated using following equation:
𝜇𝐴𝑖 =∑ 𝜔𝑗 × 𝜇𝐴𝑖(𝑗)𝑘
𝑗=1
∑ 𝜔𝑗𝑘𝑗=1
. (3.8)
Getting average of overall individual membership scores exhibit more realistic figures of deprivation than the
headcount obtaining from conventional method by dividing the population dichotomously as poor and non-
poor. The average weighted fuzzy membership value of fuzzy deprivation in multidimensional approach is;
𝐹𝑀 = 𝜇𝐴 =1
𝑁∑ 𝜇𝐴𝑖
𝑛
𝑖=1
(3.9)
𝑤ℎ𝑒𝑟𝑒, 𝑁 = 𝑇𝑜𝑡𝑎𝑙 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛.
3.3 Determining the poverty cut-off
To identify the poverty cut-off (z), Kendall rank correlation (tau-b) coefficients were calculated for different
cut-off points for sub groups of population in the province. There are various methods to test the robustness
of ranking. The commonly use methods are Spearman rank correlation coefficient (𝜌) and Kendall rank
correlation coefficient (𝜏). In this study, Kendall rank correlation is used because of small number of
subgroups are considered for ranking and Kendall rank correlation coefficient is smaller Gross Error
13
Sensitivity (GES) for and smaller asymptotic variance. Hence, Kendall correlation measure is more robust
and slightly more efficient than Spearman rank correlation (Croux & Dehon, 2010).
3.4 Kendall correlation measure
Let consider 𝑟𝑛 set of subgroups where n=1………n. then (𝑥1, 𝑦1), (𝑥2, 𝑦2) , … … … . (𝑥𝑛,𝑦𝑛) be the joint
observation of two random variables X and Y with unique values of 𝑥𝑖and 𝑦𝑖. Any pair of observation
(𝑥𝑖, 𝑦𝑖), (𝑥𝑡, 𝑦𝑡) said to be concordant if the ranking of both pair of elements 𝑥𝑖 > 𝑥𝑡 𝑎𝑛𝑑 𝑦𝑖 > 𝑦𝑡 𝑜𝑟 𝑥𝑖 <
𝑥𝑡 𝑎𝑛𝑑 𝑦𝑖 < 𝑦𝑡 . The pairs are said to be discordant if 𝑥𝑖 > 𝑥𝑡 𝑎𝑛𝑑 𝑦𝑖 < 𝑦𝑡 𝑜𝑟 𝑥𝑖 < 𝑥𝑡 𝑎𝑛𝑑 𝑦𝑖 > 𝑦𝑡 . If
𝑥𝑖 = 𝑥𝑡 𝑎𝑛𝑑 𝑦𝑖 = 𝑦𝑡 those pair are neither concordant or discordant. For the n observations number of
concordant (C) , number of discordant (D) , tied pairs (T) in X and (U) in Y. That is;
𝐶 = 𝑥𝑖 < 𝑥𝑡 𝑎𝑛𝑑 𝑦𝑖 < 𝑦𝑡
𝐷 = 𝑥𝑖 < 𝑥𝑡 𝑎𝑛𝑑 𝑦𝑖 > 𝑦𝑡
𝑇 = 𝑥𝑖 = 𝑥𝑡
𝑈 = 𝑦𝑖 = 𝑦𝑡
Then the Kendall τ coefficient is defined by
𝜏 =𝐶 − 𝐷
1
2𝑛(𝑛 − 1)
(3.10)
Where n - number of observation
𝐶 – number of concordant pair
𝐷 – number of discordant pair
Kendall coefficient|𝜏| ≤ 1
If all pairs are concordant that is perfect agreement between two ranking and 𝜏 = 1. If all pairs are discordant
that is perfect disagreement between two rankings and 𝜏 = −1. All other arrangement 𝜏 is in between 1 to -
1. 𝜏 value close to 1 implies the increasing agreement and 𝜏 value close to -1 implies the increasing
disagreement. If 𝜏 = 0 indicate the complete independent ranking. If two values of X or two values of Y has
same ranking the 𝜏𝑏 is use for computation.
𝜏𝑏 =𝐶 − 𝐷
√1
2𝑛(𝑛 − 1) − 𝑇√
1
2𝑛(𝑛 − 1) − 𝑈
(3.11)
Where: T- number of ties in X
U- number of ties in Y
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Correct choice of poverty cut-off (z) is decided on the Kendall coefficients for different cut-offs in terms of
stochastic dominance by sub groups. A person considered as multidimensionally poor if he/she deprivation
score (𝜇𝐴𝑖) < 𝑧.
3.5 Class of Fuzzy poverty measures
Fuzzy Headcount Index (FHI) is the percentage of multidimensionally poor person with respect to total
population, Fuzzy intensity (FI) was calculated dividing the sum of deprivation of deprived people by total
number of deprived people. Adjusted Fuzzy Deprivation Index (FM0) as a product of Fuzzy Headcount Index
(FHI) and Fussy Intensity (FI). Deprivation Gap was the difference of deprivation score of deprived person
to deprivation cut-off (𝑧 − 𝜇𝐴𝑖). It was normalized by (z). Dividing sum of normalized gap of all deprived
people by total number of population produced the Normalized Deprivation Gap Index(FM1). Squared the
deprivation gap and normalized by dividing z to the calculated Squared Normalized Gap Index (FM2). This
measures the inequality among the deprived people by weighting the normalized gap itself. So it gives a higher
weight to more deprived people. Compute the Squared Normalized Deprivation Gap Index (FM2) that is the
sum of the weighted squared deprivation gaps that deprived people’s experience, divided by the total
population. All the related equation to compute all the above poverty measures are given I Appendix 01.
3.6 How Synthesis method defers from Fuzzy and AF methods?
AF counting approach based on rigid dichotomization of population as deprived and non-deprived by each
and every indicator uses to create MPI. Deprivation of well-being is continuum situation and by dividing it
into two discrete states tends to oversimplify which causes the loss of information. In order to avoid such a
rigid situation, fuzzy approach can be used which is coherent with intrinsic nature to identify the propensity
to deprivation not by a cut-off but by defining a degree of membership with the states definitely deprived and
definitely non - deprived
Alkire and Foster use equal weights for each dimension and within each dimension the indicators are also
equally weighted for compiling the global MPI. When compiling national MPI, weights are assigned in
normative way giving priority to policy relevance. These are normative unequal weights giving higher weight
to the most important indicators decided by policy makers or researchers. Conversely, there is a debate for
giving equal weights and arbitrariness.
It is important to consider uncorrelated indicators within the dimensions and independence among the
dimensions when measuring poverty in multidimensional aspect for construction of more influential indicators
for arriving at precise policy formulation to target the poor. Without considering the correlation among
indicators, clear ranking is impossible (Ferreira & Lugo, 2013, p. 223). Duclos et al. (2006) pointed that it is
important to consider correlation among indicators when measuring poverty in multidimensional approach.
Nonetheless, Global MPI is incapable of capturing such kind of correlation among the indicators as it has been
set to compare poverty across countries and the indicators have been selected in normative manner giving
more priority to policy requirement. But it is obvious that, from country to country, the correlation among the
indicators are different.
One of the key components of poverty measures is assigning weight to poverty indicators. It is important to
assign a priority to more disadvantage indicators when determine overall deprivation of individual and it
should be transparent. Cerioli and Zani (1990) proposed a method to calculate weight based on frequency of
15
relative deprivation that people are poor if they fail to meet the living standards which are customary in the
society. The weight is sensitive enough to the frequency of deprived people. The weight (wj) was produced as
the log of invers function of the number of individuals who show the poverty symptoms in the reference
population. It is given by;
wj=log(1/fj ); fj>0 j=1,2,……k ; ( 3.12)
Where fj denotes the deprivation rate of individuals in the reference population who show the poverty
symptoms of variable j. Here, it does not provide an excessive important to extremely rare deprivation because
logarithm does not defined weigh when fj=0. However, it gives higher weight to the variables which have very
low proportion of people with poverty symptoms and very low weight for high proportion of people with
poverty symptoms. This concept of weight is not defined for the variables deprived by all or the variables
successive by all. Hence, Desai and Shah (1988, p. 512) interpreted this method as “objective measure of
subjective feelings of deprivation”.
In Sri Lankan context, to reduce or eradicate poverty achieving Sustainable Development Goals (SDG) “End
poverty in all its forms everywhere” it is more practical to make intervention at macro level targeting high
proportion of deprived people in all forms of poverty symptoms. Consequently, higher weight should be
assigned to the poverty indicators which show the poverty symptoms by high proportion of people. The weight
generated by this study has achieved this successfully by using the frequency weight applied by Cerioli &
Zani (1990) instead of logarithmic value of inverse of rate or average of poverty symptoms, here applied the
logarithmic value of inverse of frequency of totally deprived individuals in the reference population. It is
important to give more weight to high frequent poverty indicators to create opportunity to target more people
who are deprived in poverty indicators. For instant, safe drinking water is considered as an improved living
condition. There are a few households which use unsafe water in region A and more households use unsafe
water in region B. If a higher weight is assigned to a low frequency and less weight to a higher frequency,
policy making will be targeting region “A” in intervention and as a result a few households will benefit and
macro level issue of poverty symptom will remain intact. If weight is assigned vice -versa, targeting the region
“B” more deprived people will be benefited.
In the analysis of this paper, selection of variables have been statistically achieved using the data redundancy
test, Pearson correlation test and point Biserial correlation test as mentioned in methodology chapter for the
dichotomous variables, continuous variables and dichotomous and continuous variables respectively to get
uncorrelated set of variables for the analysis.
The main method of identifying people who live in multidimensional poverty is accomplished using poverty
cut-off called “poverty line”. The identification of poverty is the acknowledgement of deprivation. The
poverty is defined as failure of basic capabilities to reach certain minimally acceptable level (Sen, 1992, p.
109). This leads policy recommendation to eliminate poverty. In fuzzy set approach, it enables computing
intensity of poverty by membership function and it provides an average of deprivation that is propensity
poverty. It is the best indicator to understand the intensity of poverty and give a more complete picture of
poverty on capability approach. Nonetheless, knowing only this figure, it is hard to identify people who need
external assistance to overcome from poverty. Consequently, it is essential to derive a poverty cut-off to
identify the people who need assistance to become better-off people and make policies to support them.
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In multidimensional poverty analysis, the most common method of identifying deprived people are “union
approach” that is a person considered as multidimensionally poor if he/she is deprived at least in one
dimension. The other common way of identification is “intersection approach” in which a person is considered
as multidimensionally poor if he/she is deprived in all dimensions. However, both these approaches are more
imprecise for policy making as union approach identifies a larger number of people as deprived and
intersection approach identifies a very small number of people as deprived. Therefore, it is required to identify
intermediate approach to identify deprived people. Alkire, et al. (2015) provides a range of intermediate
possibilities to identify a person as deprived including the union and intersection approaches as special cases
considering the set of weights on the dimension. It should be required to get any level by applying robustness
tests to explore the transparency and good justification. According to the Alkire-Foster counting approach
when computing global Multidimensional Poverty Index(MPI) introduced by Alkire and Santos (2010) a
person is identified as deprived if his/her deprivation score is equal or higher than 1/3. This cut-off point aims
to capture the acute deprived people. Alkire and Santos (2010, p. 61) have shown that the 94.5 percent of
comparisons to change the cut-off between 20 to 40. The cut-off 1/3 is a normative decision within the
reasonable range of 20 to 40.The analysis of the study done by the researcher is based on Uva province survey
applied the technical method which was used by Alkire, et al. (2015) considering the changes in the range of
cut-off points from zero to hundreds of the deprivation score with dominance approach and fix a robust cut-
off without affecting to the ranking by level of sub group regions. The robustness of ranking was assessed by
the using the Kendall rank correlation coefficient.
In this research, deprivation of each individual was computed on the fuzzy set theory and weight was defined
for each dimension changing the frequency weight appropriate to design macro level policies targeting to
identify the areas with high proportion of deprived people. The weighted deprivation was calculated and
indictor cut-offs were unavailable. Thereafter, the average weighted deprivation was calculated for each
individual. Poverty cut-off was calculated based on Alkire, et al. (2015). Hence, the technique used in this
research is a combination of fuzzy set approach and Alkire and Foster approach of measuring poverty in
multidimensional approach. Consequently, this method can be introduced /proposed as the Synthesis Method
of Alkier and Foster and Fuzzy set theory (MAFF).
The AF method satisfies a number of typical axioms; symmetry, replication invariance, scale invariance,
poverty, focus, deprivation focus, monotonicity, transfer, rearrangement, decomposability and dimensional
breakdown. Fuzzy measures of poverty also fulfill many of the above axioms. Despite the fact that, the fuzzy
measures capture the vagueness inherent in the concept of poverty it lacks a borderline to identify poor and
non-poor. This is the main disadvantage of the fuzzy measures of poverty when it comes to practical
application.
Alkire and Foster MPI constitutes arguments regarding the use of equal and arbitrary setting of weights and
indicator and poverty cut-offs in normative way. Fuzzy set approach has challenges in identification of
deprived people. The Synthesis method enables to address the aforementioned weakness of MPI. Similarly,
the Synthesis method enables to accomplish the strengthening of two methods when analyzing poverty in
multidimensional approach. The poverty measures computed by Synthesis method applied unequal weights
giving priority to the high frequent poverty symptoms according to the recognized living standards in the
region. This method sets a poverty cut-off based on robustness test to identify the poor and non-poor. In
addition, the data used in this research enriches with more information than the other survey exists in the
context of poverty analysis in Sri Lanka. Therefore, the poverty measures computed by the Synthesis Method
17
generate well-informed evidence for policy making to eradicate poverty in the context of Uva province in Sri
Lanka. Hence, the Synthesis method is more realistic than AF methods and fuzzy method to measure poverty
in Sri Lankan context. The calculation method of Synthesis method is described below.
The study makes an attempt to identify more realistic picture on poverty by considering three dimensions on
capability approach in material deprivation. In this process assigning weights to every dimension scientifically
to obtain precise measurements on poverty based on fuzzy set theory. The study incorporates several variables
that affect the well-being of people. Hence, this study enables to measure poverty in multidimensional
approach beyond traditional approaches to overcome the deficiencies ;(a) measuring poverty in one-dimension
(b) arbitrariness set of weights in country context (c) inadequacy of dimensions. Hence, Synthesis method
produced more realistic picture of poverty than conventional monetary approaches.
4. THE RESULTS : MULTIDIMENSIONAL POVERTY IN UVA
Low income is a key characteristic of poverty as it impacts on what people can do and cannot do. But while
income enables capability or functioning (Sen - 2009), income alone can convey little about the well-being of
an individual. Shortfalls in well-being can also arise from shortfalls in access to other resources. As Sen
(2009) argues that, a person’s well-being does not adequately describe by means such as income or wealth
but for the actual ability to do the different things that she/he values doing. It should be analyzed using a set
of opportunities people have namely their combinations of functioning. Functions are a set of capabilities a
person can do and being with their substantive freedom that she/he has reason to value. This provides a strong
direction to shift the unidirectional measure of poverty to multidimensional measure of poverty. Deprivation
of well-being can be described in a material deprivation or from social point of views. Material deprivation is
relatively lack of resources such as housing, goods and / or services.
The methodology requires the selection of variables that can be used as indicators of material deprivation.
Selection of appropriate variables was carried out using the data redundancy test, the Pearson Correlation test
and the Point Biserial correlation for dichotomous variables, continuous variables and dichotomous and
continuous variables respectively. Firstly, out of 23 dichotomous variables 10 were selected. Secondly, 12
variables were also selected from the categorical variables which were transformed as continuous variables
from the membership function. Finally, 20 were selected for the analysis. The selected variables were regarded
as indictors for material deprivation and categorized into three dimensions ;housing facilities, consumer
durables and basic lifestyle as given in the Table 1 In Appendix 01 . Under the housing facilities 12 indicators
were considered. Out of them 10 indicators describes the quality housing and housing facilities. Other two
indicators describe the subjective feeling of the respondent about the housing satisfaction and quality and
facilities and the adequacy of the facilities of the household for family members. Only two indicators were
selected under the dimension of consumer durables goods. This result is not surprising because many of the
durable goods are highly correlated with housing qualities and facilities. Under the dimension of lifestyle six
indicators were considered in terms of clothing and nourishment.
4.2 Fuzzy Poverty in Uva Province
To what extent poverty exists in terms of material deprivation in Uva Province? The results are presented in
Table 4.2. The results show that on average 28.0% of population in Uva province is propensity to material
deprivation on Fuzzy membership measures. Moreover, the results indicate that 15.8 per cent of population
18
is deprived in housing facilities, 2.2 per cent deprived in durable goods and 9.9 per cent are deprived in basic
lifestyle. Among the indicators under the housing facilities, the most important indicator for considering
poverty is floor area of the household. It shows that 3.7 per cent of households are deprived in floor area.
According to the housing satisfaction is considered, 3.2 per cent are declared as dissatisfaction of their housing
quality and facilities. In addition, 2.6 per cent of population is deprived inadequacy of the facilities of the
household for family members. The average deprivation is 2.2 per cent when considering the possession of
durable goods such as TVs and mobile phones. According to the survey, 10 per cent are deprived in basic
lifestyle.
Table 4.1: Weighted fuzzy deprivation score by indicator