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

D.D.Deepawansa

dilhaniebg@gmail.com Department of Census and Statistics

D.D.P.M.Dunusinghe

pmdunu@yahoo.com University of Colombo

Deprivation of Well-being in Terms of Material Deprivation in Multidimensional Approach: Sri Lanka

Prepared for the 16th Conference of the

International Association of Official Statisticians (IAOS)

OECD Headquarters, Paris, France, 19-21 September 2018

ABSTRACT

In recent years, Sen’s capability approach has widely been adopted in measuring poverty although official

poverty figures in most developing countries continue to derive through monetary approach. Nevertheless,

existing analytical methods in measuring poverty multi-dimensionally continue to suffer from some

limitations. The objective of this study is two-folds; namely (a) to develop a new approach to measure poverty

multi-dimensionally and (b) to employ it for measuring poverty in the context of Sri Lanka. In order to achieve

the said objectives a new analytical approach is developed by combining fuzzy sets method and counting

method and named it as ‘Synthesis Method’. We argue that this ‘Synthesis Method’ is more preferable on the

ground of several inherited properties compared with the above two methods. This analytical approach

addresses some deficiencies in existing analytical approaches namely; (a) money metric centeredness (b)

arbitrariness of weights, and (c) inadequacy of dimensions. The empirical assessment is done by applying

Synthesis Method to a sample of survey data, collected from the Uva Province of Sri Lanka, an economically

depressed province comprising people representing various socio-economic, geographical and multi-ethnic

backgrounds. The study examines the poverty under three dimensions; namely housing facilities, consumer

durables and basic lifestyle. This study found some interesting findings which are mostly not reflected through

the official figures. The results show that on average 28 per cent of people in Uva Province is propensity to

material deprivation on Fuzzy membership measures. Nevertheless, the Synthesis Method found that the

Fuzzy intensity is 0.51 and Fuzzy head count is 20 per cent in material deprivation. More interestingly, the

highest contribution to material deprivation come from housing facilities. This reveals that the deprived people

live in houses of low quality with low facilities. The application of Synthesis method certainly will encourage

the analysis of further research on poverty in multidimensional approach.

.

Keywords: Well-being, Fuzzy sets, Multidimensional approach, Poverty, Deprivation

JEL Classification C43, I31, I32

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1. INTRODUCTION

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).

5

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.

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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

7

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

14

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.

16

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

Indicators

Average fuzzy

membership value

Fuzzy deprivation

Std.

Err.

95% Confidence

.Interval CV

Total 0.280 0.007 0.265 0.294 2.578

1 Housing facilities 0.158 0.005 0.148 0.167 3.042

1.1 Floor area 0.037 0.002 0.034 0.041 4.910

1.2 Housing satisfaction 0.032 0.001 0.030 0.034 3.167

1.3 Adequacy of the facilities of the household 0.026 0.001 0.024 0.028 4.394

1.4 Number of bed rooms 0.026 0.001 0.025 0.027 2.068

1.5 Source of drinking water 0.017 0.002 0.013 0.022 11.955

1.6 Floor 0.007 0.001 0.005 0.009 12.388

1.7 Toilet use 0.004 0.000 0.004 0.004 4.540

1.8 Wall 0.002 0.000 0.001 0.003 21.044

1.9 Ownership 0.002 0.000 0.001 0.002 12.268

1.10 Type of toilet 0.001 0.000 0.001 0.002 21.819

1.11 Electricity 0.001 0.000 0.001 0.002 21.231

1.12 Housing structure 0.001 0.000 0.001 0.001 13.472

2 Consumer Durables 0.022 0.002 0.019 0.026 7.714

2.1 Mobile phone 0.015 0.001 0.013 0.018 8.568

2.2 TV 0.007 0.001 0.006 0.009 10.325

3 Basic lifestyle 0.099 0.003 0.094 0.105 0.026

3.1 Buying new clothes 0.046 0.000 0.046 0.047 0.769

3.2 Satisfaction of clothing 0.014 0.001 0.013 0.015 3.901

3.3 Meal with fish, meat, dried fish or eggs 0.014 0.001 0.013 0.015 4.506

3.4 Adequate clothes to wear 0.013 0.002 0.010 0.016 11.660

3.5 Eat fruit 0.010 0.000 0.009 0.010 3.848

3.6 Eat green leafy vegetables 0.002 0.000 0.002 0.002 4.488

Source: Author’s calculation

Fuzzy deprivations scores depict the propensity to poverty. That is natural tendency being poor and good

indicator for understanding level of deprivation among indicators. To identify the people who need others

support to being better-off it is necessary to identify deprivation cut-off. In order to do this deprivation rates

were calculated setting the cut-off (k) as 10,20 ………..,100. Deprivation rate is the average deprivation score

of Total Fuzzy (𝜇𝐴𝑖)>= `k'/100 . Then plot the deprivation rate against the cut-offs. Considering the

dominance approach using the Figure 1 and Kendall’s Tau statistics. Figure 1 gives the deprivation for all cut-

off for five main domains.

19

Figure 1: Dominance holds in terms of deprivation for all deprivation cut-off

Source: Author’s calculation

Kendall’s Tau values for between each pairs of the cut-offs were computed (see Appendix 02) and 40 per cent

was selected as the deprivation cut-off considering to the rank correlation coefficient of the nearest cut-off

values 35 and 45. The correlation coefficient was 0.7143 at the cut-off 40, it was significant(p=0.0003). This

implied that more than 70 per cent of comparisons were concordant in each case with 35 cut-off ranking.

Table 4.2 gives the fuzzy poverty measures for material deprivation in Uva province considering the poverty

cut-off at 0.4 for fuzzy deprivation score. This analysis has produced three mean indicators. 1 ) Fuzzy

deprivation headcount ratio (FHI) that is percentage share of deprived people called incidence of fuzzy

poverty 2) Fuzzy Intensity(FI) that is average weighted deprivation experienced by poor person called

intensity of fuzzy poverty . 3) Adjusted headcount ratio(FM0). Adjusted headcount ratio is the product of

incidence and intensity. It says the share of population that is multidimensionally poor adjusted by the intensity

of the deprivation experienced by the poor. Adjusted headcount ratio index is important because the headcount

index only says the percentage of multidimensionally poor population in the region. But all of them are not

equally poor. They are not totally deprived of all indicators. Hence, Fuzzy deprivation headcount ratio is

adjusted by the intensity and called adjusted headcount ratio. It reflects the proportion of weighted deprivation

experienced by the poor in the region out of all the total potential deprivations that the region could experience.

The deprivation headcounts identify the deprived people with respect to the deprivation cut-off. But it is

unable to provide information about the depth of the deprivation. It captures by the deprivation gap index.

This gives the average gap of deprivation of poor people relative to the deprivation cut-off. That is mean

distance of deprived people from the deprivation cut-off with the non-deprived people giving zero distance.

This information is important to policy makers to allocate sources to bring up the deprived people above the

cut-off. Other important information is the inequality of the deprivation across deprived people. It captures by

the index called deprivation severity index. This index squares the deprivation gap and takes into account to

give more weight to the most deprived people capturing the inequality among deprived people. This helps the

policy makers to give priority to extremely deprived people in the region.

0.1

.2.3

.4

De

pri

vatio

n r

ate

0 20 40 60 80 100k

Badulla urban Badulla rural

Badulla estate Moneragala rural

Moneragala estate

20

Table 4.2: Fuzzy headcount, fuzzy intensity and adjusted headcount of material deprivation in Uva province

by level agriculture are, Level of education, Employment status and age group.

Fuzzy

Headcount

ratio (FH)

Fuzzy

Intensity(FI)

Adjusted

Fuzzy

Headcount

ratio (FH0)

Normalized

Deprivation Gap

ratio (FM1)

Squared

Normalized

Deprivation Gap

ratio (FM2)

Uva 0.202 0.509 0.103 0.054 0.026 Non-Plantation area 0.166 0.506 0.084 0.044 0.021 Plantation area 0.474 0.512 0.242 0.132 0.062

Level

Level of

Education

No Schooling

0.550 0.558 0.307 0.217 0.112 Up to grade 5

0.344 0.508 0.175 0.093 0.046 Grade 6 to 10 0.172 0.494 0.085 0.040 0.018 GCE(O/L) 0.073 0.448 0.033 0.009 0.002 GCE (A/L) 0.019 0.553 0.010 0.006 0.003 Employment

status

Government 0.045 0.478 0.021 0.009 0.002 Private 0.390 0.523 0.204 0.120 0.063 Own account

workers

0.168 0.494 0.083 0.040 0.189 Unpaid family

workers

0.093 0.495 0.046 0.223 0.009 Age group Below 24 yrs.

0.153 0.505 0.077 0.040 0.219 25 to 39 0.118 0.502 0.094 0.048 0.019 40 to 59

0.157 0.503 0.079 0.040 0.019 Above 60 yrs. 0.315 0.517 0.163 0.092 0.047

Source: Author’s calculation

Fuzzy headcount ratio indicates that 20 per cent of the population living in Uva province is materially

deprived. The average deprivation score(Fuzzy intensity (FI)) in which poor people are deprived is 0.51. This

reveals that the material deprivation in Uva province is very high and reflects the fact that many individuals

are deprived in approximately 51 per cent of the all the dimensions. Official poverty line indicates that 6.5 per

cent are living in consumption poverty in Uva province8.The adjusted fussy headcount ratio indicates that the

materially deprived population of Uva province experience is 10 per cent, as a share of all possible

deprivations that would be experienced if all people have been deprived in all dimensions. The people living

in plantation areas are more deprived than that of non-plantation areas. Deprivation increases with the level

of education from lower level to higher level. The data depicts that government workers are not significant

to material deprivation whereas among the private sector workers 39 percent deprived. Majority of private

sector workers in this area are agricultural workers. When we tested the deprivation by age of respondent, the

data reveals that the individual who are above 60 years of old are deprived than the other people.

What are the main indicators contributing to material deprivation? The aim of policy makers’ work is to

eradicate all form of poverty in the society. Hence, it is a necessity to show what are the main indicators of

material deprivations are? It enables to calculate contribution of each dimension and each indicator to overall

8Official Statistics declared by DCS for 2016 .

21

material deprivation. From the Table 4.4 it demonstrates the adjusted fuzzy headcount ratio and indicators’

contributions to overall deprivation.

Table 4.4: Percentage contribution of dimensions and indicators to total adjusted Fuzzy

Poverty

Dimensions/Indicators Adjusted Fuzzy

headcount ratio

95% Confidence

Interval Percentage share

Total 0.103 0.083 0.122 100.00

Housing Facilities 0.059 0.048 0.071 57.78

Floor area 0.012 0.010 0.014 11.72

Housing satisfaction 0.011 0.009 0.013 10.38

Adequacy of the facilities in the household 0.010 0.008 0.013 10.13

Number of bed rooms 0.008 0.006 0.009 7.44

Source of drinking water 0.007 0.005 0.009 6.52

Floor 0.005 0.004 0.007 5.17

Wall 0.002 0.001 0.003 1.84

Toilet use 0.001 0.001 0.001 1.09

Electricity 0.001 0.001 0.002 1.02

Type of toilet 0.001 0.000 0.002 0.98

Ownership 0.001 0.001 0.001 0.89

Housing structure 0.001 0.000 0.001 0.60

Consumer Durables 0.014 0.011 0.017 13.22

Mobile phone 0.009 0.007 0.011 8.45

TV 0.005 0.004 0.006 4.77

Basic Lifestyle 0.030 0.023 0.036 29.03

Buying new clothes 0.010 0.008 0.012 9.85

Adequate clothes to wear 0.007 0.005 0.010 7.24

Satisfaction of clothing 0.005 0.004 0.006 4.47

Meal with fish, meat, dried fish or eggs 0.004 0.003 0.005 4.17

Eat fruit 0.003 0.002 0.004 2.78

Eat green leafy vegetables 0.001 0.000 0.001 0.52

Source: Author’s calculation

The results describe that the highest contribution to fuzzy poverty to material deprivation is contributed by

housing facilities. Many poor people are deprived in floor area flowed by the deprivation of subjective feeling

of quality of the house and facilities of it, adequacy of the facilities in the household. It indicates that more

material deprived people live in very small houses with low facilities and low quality. In addition, poor people

are deprived in nutrition than the deprivation of durable goods. Unsurprisingly among the durable goods,

mobile phones and televisions have become as compulsive items of people. Deprivation of these two items

contribute to the total deprivation is 13 per cent.

22

5. CONCLUSION

This research is an empirical application to measure material deprivation in multidimensional aspects using

new method called “Synthesis Method“ combining the fuzzy set method introduced by Cerioli and Zani

(1990) and counting approach introduced by Alkire and Foster (2007) focusing the capability approached

proposed by Sen (2009). Material deprivation was measured taking the fuzziness of deprivation into account.

Addressing the lack of data, researcher conducted a new survey in Uva province covering 1200 household.

During the past two decades, Uva province in Sri Lanka has experienced dramatic decline of poverty reduction

in terms of monetary approach. Poverty headcount in Uva has been dropped from 46.7percent in 1995/96 to

6.5 per cent in 2016. On the official poverty statistics, the people who live in Uva province are not very much

poor in consumption. But on the findings of this research depicts that there are 20.2 percent people live in Uva

province are deprived in material deprivation with lack of resources and cannot afford the housing, clothing

and nutrition. Materially deprived population of Uva experience 10.3 percent, as a share of all possible

deprivations that would be experienced if all the people were deprived in all dimensions. The highest

contribution to material deprivation is experienced by people is due to the deprivation of housing facilities.

Among the housing facilities, the most important factors are floor area followed by number of bed rooms and

construction materials such as floor and wall. This reveals that the deprived people live in low quality houses

with low facilities. It was well proved from the indicators related to subjective feeling with respect to housing

about the satisfaction of housing facilities and adequacy of facilities for members living in the household.

Many of the durable goods such as washing machines, refrigerators, cookers(gas/ electric), electric fans,

telephones (fixed lines), mobile phones, laptop computers, motor cycles/scooters and three wheelers show

high level of housing condition. Consequently, it implies that the persons deprived in housing facilities are

also deprived in the above durable goods. Subsequently, two uncorrelated items, mobile phones and

televisions were selected as durable goods for the analysis. From these items deprivation of having mobile

phones was higher than that of having televisions within the person who are multidimensionally deprived

When considering the dimension of basic requirement, it indicates that the deprivation of nutrition is relatively

low in Uva. They are having adequacy of meal with fish, meat, dried fish or eggs, having meal with green

leafy vegetables and consumption of fruit. Hence, consumption and nutrition deprivation is low. However,

the deprivation of adequacy of clothing is relatively higher than the deprivation of food.

An application of individual well-being information in Uva province from the household survey conducted in

2016 by the researcher found that the individuals are more deprived in material deprivation than consumption

poverty especially in the area of housing facilities and clothing. The material deprivation is higher in plantation

areas than non-plantation areas.

Finally, it can be concluded that the Synthesis method used in this research for measuring deprivation is more

preferable and robust than the direct fuzzy set method and traditional approaches which are being employed

to measure poverty for policy implication to reduce poverty. Present study is only focused on material

deprivation. To understand the idea of deprivation in-depth in a more broader manner, it is suggested to

consider taking more dimensions into account for the analysis.

23

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25

APPENDIX

Appendix 01

Table 1: elementary indicators and deprivation dimensions

1 Housing Facilities

1.1 Principal materials of construction of wall

1.2 Principal materials of construction of floor

1.3 Principal source of lighting

1.4 Principal source of drinking water

1.5 Type of toilet

1.6 Number of bed rooms

1.7 Type of structure

1.8 Total floor area (Sq. feet)

1.9 Tenure

1.10 Toilet facilities

1.11 Satisfaction about the quality and facilities of household

1.12 The adequacy of the facilities of the household for family members

2 Consumer durables

2.1 Television

2.2 Mobile phone

3 Basic lifestyle

3.1 Meal with fish, meat, dried fish or eggs

3.2 Meal with green leafy vegetables

3.3 Eat fruit

3.4 Satisfaction of clothing

3.5 Adequate clothes to wear

3.6 Buying new clothes

26

Appendix 02 : Analytical techniques

𝐹𝑢𝑧𝑧𝑦 𝐻𝑒𝑎𝑑𝑐𝑜𝑢𝑛𝑡 𝐼𝑛𝑑𝑒𝑥 (𝐹𝐻𝐼) =1

𝑁∑ 𝜇𝐴𝑖 . 𝐼

𝑛

𝑖(2.12)

𝑤ℎ𝑒𝑟𝑒

𝐼 = 1 𝑖𝑓 𝜇𝑖 < 𝑧

𝐼 = 0 𝑖𝑓 𝜇𝑖 ≥ 𝑧

𝑧 = 𝑑𝑒𝑝𝑟𝑖𝑣𝑎𝑡𝑖𝑜𝑛 𝑐𝑢𝑡 − 𝑜𝑓𝑓

𝑁 = 𝑇𝑜𝑡𝑎𝑙 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛

𝐹𝑢𝑧𝑧𝑦 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 (𝐹𝐼) =1

𝑞∑ 𝜇𝐴𝑖

𝑛

𝑖× 𝐼 (2.13)

𝑤ℎ𝑒𝑟𝑒

𝐼 = 1 𝑖𝑓 𝜇𝐴𝑖 < 𝑧

𝐼 = 0 𝑖𝑓 𝜇𝐴𝑖 ≥ 𝑧

𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝐹𝑢𝑧𝑧𝑦 𝐷𝑒𝑝𝑟𝑖𝑣𝑎𝑡𝑖𝑜𝑛 𝐼𝑛𝑑𝑒𝑥 (𝐹𝑀0) = (𝐹𝐻𝐼) × (𝐹𝐼)(2.14)

Dimensional breakdown

𝐷𝑒𝑝𝑟𝑖𝑣𝑎𝑡𝑖𝑜𝑛 𝑠ℎ𝑎𝑟𝑒 𝑜𝑓 𝑗𝑡ℎ 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛 (𝑆𝑗) =∑ 𝜇𝐴𝑖

𝑛𝑖=1 (𝑗)

∑ ∑ 𝜇𝐴𝑖𝑘𝑗=1

𝑛𝑖=1

× 𝐼 (2.15)

𝐼 = 1 𝑖𝑓 𝜇𝐴𝑖 < 𝑧

𝐼 = 0 𝑖𝑓 𝜇𝐴𝑖 ≥ 𝑧

𝐷𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑎𝑙 𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑜𝑓 𝑗𝑡ℎ 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛 (𝐷𝐶) = (𝑆𝑗) × (𝐹𝑀0) (2.16)

𝑁𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝐷𝑒𝑝𝑟𝑖𝑣𝑎𝑡𝑖𝑜𝑛 𝐺𝑎𝑝 𝐼𝑛𝑑𝑒𝑥 (𝐷𝐺𝐼) =1

𝑁∑

𝑧 − 𝜇𝐴𝑖

z

𝑁

𝑖=1

× 𝐼 (2.17)

𝑤ℎ𝑒𝑟𝑒

𝐼 = 1 𝑖𝑓 𝜇𝐴𝑖 < 𝑧

𝐼 = 0 𝑖𝑓 𝜇𝐴𝑖 ≥ 𝑧

𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑑𝑒𝑝𝑟𝑖𝑣𝑎𝑡𝑖𝑜𝑛 𝑔𝑎𝑝𝑠 𝐼𝑛𝑑𝑒𝑥(𝐹𝑀1) = (𝐹𝐻𝐼) × (𝐹𝐼) × (𝐷𝐺𝐼) (2.18)

𝑁𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝑠𝑞𝑢𝑟𝑒𝑑 𝐷𝑒𝑝𝑟𝑖𝑣𝑎𝑡𝑖𝑜𝑛 𝐺𝑎𝑝 𝐼𝑛𝑑𝑒𝑥 (𝑆𝐷𝐺𝐼) =1

𝑁∑ (

𝑧 − 𝜇𝐴𝑖

z)

2𝑁

𝑖=1

× 𝐼 (2.19)

𝑤ℎ𝑒𝑟𝑒

𝐼 = 1 𝑖𝑓 𝜇𝐴𝑖 < 𝑧

𝐼 = 0 𝑖𝑓 𝜇𝐴𝑖 ≥ 𝑧

𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝐹𝑢𝑧𝑧𝑦 𝑆𝑞𝑢𝑎𝑟𝑒 𝐷𝑒𝑝𝑟𝑖𝑣𝑎𝑡𝑖𝑜𝑛 𝐺𝑎𝑝 𝐼𝑛𝑑𝑒𝑥(𝐹𝑀2) = (𝐹𝐻𝐼) × (𝐹𝐼) × (𝑆𝐷𝐺𝐼) (2.20)