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

Transcription

1 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, September 2018 Session 1.B., Day 01, 19/09, 11.00: Poverty and well-being

2 D.D.Deepawansa Department of Census and Statistics D.D.P.M.Dunusinghe University of Colombo Deprivation of Well-being in Terms of Material Deprivation in Multidimensional Approach: Sri Lanka Prepared for the 16 th Conference of the International Association of Official Statisticians (IAOS) OECD Headquarters, Paris, France, September 2018

3 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

4 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 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 Lanka 1. 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 However, this province is still the fourth poorest province among the other nine provinces /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). 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 poverty 2. 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. 5

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 crisis 3. 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, Unidimensional 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 context 4. 3 The 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 6

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 multidimensional 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 onedimensional monetary approach in country context. 7

8 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 respondents 5 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 nonpoor 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. 8

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, μ A (q)} (3.1) Whereμ A (q): is the membership function (m.f) is a mapping from Q [0,1]. The value of μ A is the degree of membership in the incident of q in A. When μ A = 1 then q completely belongs to A. If μ A = 0 then q does not belong to A. Whereas the elements q which is0 < μ A (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 μ A (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; μ Ai i= 1,2.n (3.2) 9

10 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 μ Ai for 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 (μ A ) 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 (FM 0) as a product of Fuzzy Headcount Index (FHI) and Fussy intensity (FI). FM 0 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 FM 0 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 FM 1 (Adjusted weighted deprivation gaps Index) as a product of three indices: FM 1= FHI FI DGI; that is the sum of the weighted deprivation gaps that deprived people experience, divided by the total population. 10

11 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 FM 2 (Adjusted weighted squared deprivation gaps Index) as a product of three indices: FM 2= 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 (FM 0, FM 1,FM 2) 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(μ Ai ) ; If μ Ai = 0 ; i th individual is not definitely belong to poor If μ Ai = 1; i th individual is completely poor (3.3) If 0 < μ Ai < 1 then i th 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 j th number of indicators and then the membership function for i th individual is μ Aj (i). They suggested fixing the two thresholds for minimum(j mim ) and maximum(j max ) value to continuous variables in a reasonable manner 6. If membership value is less than j mim then the individual is considered as poor and if greater than j max 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 level 7. The value of the membership function is given by the following equation. Consider q ji is the value of i th individual in j th indicator where (i=1,2 n) and (j=1,2 k) in the poor set μ A. Then the membership faction for each individual is; μ Ai (j) = 1 if 0 q ij < j min q μ Ai (j) j,max q ij = ifj q j,max q min< q ij < j max (3.4) j,mim μ Ai (j) = 0 ifq ij j max 6 The 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) 11

12 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. μ Ai (j) = 1 if q ij = 0 (not success with the condition) μ Ai (j) = 0 if q ij = 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 i th individual by the following equation. k μ Ai (i) = 1 k μ Ai(j) j=1 Cerioli and Zani (1990) suggested a frequency based weight phenomenon. The weight ω j of each indicator can be computed by using following equation. (3.6) ln 1 f j ω j = k ln 1 j=1 f j. ( 3.7) In this equation, the term f j denotes the number of individuals who are completely deprived in j th indicator. The natural logarithm of the inverse of frequency was applied so that a greater weight is not assigned for a low value of f j. Using equations 3.6 and 3.7 the total value of individual membership in multidimensional weighted fuzzy deprivation was calculated using following equation: μ Ai = k j=1 ω j μ Ai (j) k j=1 ω j. (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 nonpoor. The average weighted fuzzy membership value of fuzzy deprivation in multidimensional approach is; n FM = μ A = 1 N μ Ai i=1 where, N = Total population. (3.9) 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 12

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 r n set of subgroups where n=1 n. then (x 1, y 1 ), (x 2, y 2 ),. (x n, y n ) be the joint observation of two random variables X and Y with unique values of x i and y i. Any pair of observation (x i, y i ), (x t, y t ) said to be concordant if the ranking of both pair of elements x i > x t and y i > y t or x i < x t and y i < y t. The pairs are said to be discordant if x i > x t and y i < y t or x i < x t and y i > y t. If x i = x t and y i = y t 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 = x i < x t and y i < y t D = x i < x t and y i > y t T = x i = x t U = y i = y t Then the Kendall τ coefficient is defined by τ = C D 1 n(n 1) (3.10) 2 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 τ b is use for computation. τ b = C D 1 2 n(n 1) T 1 2 n(n 1) U (3.11) Where: T- number of ties in X U- number of ties in Y 13

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 (μ Ai ) < 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 μ Ai ). 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(FM 1). Squared the deprivation gap and normalized by dividing z to the calculated Squared Normalized Gap Index (FM 2). 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 (FM 2) 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 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 14

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 (w j) 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; w j=log(1/f j ); f j>0 j=1,2, k ; ( 3.12) Where f j 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 f j=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. 15

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 cutoff 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 16

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 ), 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 17