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Methodology and Application of Fuzzy and Alkire - Foster Multidimensional Poverty Indices: Case of Bosnia and Herzegovina

Unlike standard unidimensional poverty indices, based mostly on monetary poverty measure such as income or consumption, multidimensional poverty indices can include numerous nonmonetary poverty indicators. In addition to multidimensional poverty indices obtained by generalization of standard unidimensional poverty indices (Foster – Greer – Thorbecke’s indices), many authors (Ambrosio, Deutsch and Silber (2011) ; Betti, Chelli and Lemmi (2005) ; Alkire and Santos (2013)) emphasize the importance and advantages of Alkire – Foster (AF) and fuzzy multidimensional indices. This study utilized fuzzy and AF methodology to investigate poverty level in Bosnia and Herzegovina. In addition to consumption as monetary measure, we constructed AF and fuzzy indices by including the numerous nonmonetary measures that indicates dwelling quality, possession (of durable goods) and household structure (size, education and vulnerability). The usage of fuzzy sets in poverty analysis is inspired by fuzzy sets theory and motivated by artifi cial classifi cation in poor and non-poor population units. Instead of this classifi cation, fuzzy indices are based on poverty membership function that refl ects level of poverty. These indices allow the usage of all types of poverty indicators: binary, categorical and continuous. Two main approaches in determining fuzzy poverty indices are used: Totally Fuzzy (TF) and Totally Fuzzy and Relative approach (TFR). Some authors (Chelli and Lemmi (1995)) emphasize that TFR approach is less arbitrary due to defi ning poverty membership functions without predefi ned limits in the cases of categorical and continuous variables, which are required in TF approach. AF method for construction of multidimensional poverty indices uses overlapping or multiple deprivations by included poverty measures. The unit will be considered as poor if the weighted sum of its deprivations is higher than predefi ned poverty threshold. After identifi cation of poor units, information on the proportion of deprivations have to be aggregated for all units. The most commonly used and also the simplest index within the class of Alkire – Foster indices is the adjusted headcount index M0, which is the product of multidimensional headcount index and the average proportion of deprivation for the poor units (intensity of poverty). Adjusted headcount index indicates incidence and intensity of poverty. Next index, M1 indicates incidence, intensity and depth of poverty, while M2 indicates incidence, intensity and depth of poverty and also inequality in distribution of selected poverty measures within population of poor units. AF poverty indices are important because they allow decomposition by subgroups and comparisons of poverty over time. Considering these characteristics of AF poverty indices, United Nations adopted this methodology for determination global Multidimensional Poverty Index, in 2010. Fuzzy and AF multidimensional indices for Bosnia and Herzegovina are calculated based on data from Household Budget Surveys (2004, 2007 and 2011). Their advantage comparing to unidimensional poverty indices is inclusion of relevant nonmonetary poverty indicators, such as education, possession of durable goods, dwelling characteristics, household participation in the labor force etc. For certain cases, their values signifi cantly deviate from the values of corresponding unidimensional indices. Unidimensional indices indicate deterioration of poverty in 2007 comparing to 2004 and 2011 while AF adjusted headcount index indicates the permanent improvement of poverty level in B&H and its parts. Also, determined fuzzy index indicates that Brčko District suff ers from highest poverty level comparing to Federation of Bosna and Herzegovina and Republika Srpska in 2011, while unidimensional indices have the opposite direction. Authors state that, creation of more effi cient social policies and poverty reduction strategies is not suffi cient to base exclusively on unidimensional indices that address just one dimension of poverty.

multidimensional poverty indices, fuzzy poverty indices, Alkire – Foster poverty indices

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