Abstract
In Multidimensional Almost First/Second Order Dominance (MAFOD and MASOD), the total number of deprived dimensions (T) is used, i.e. equal weight is given to each dimension. However, deprivation in some dimensions could be more crucial than deprivation in other dimensions. We propose the use of a weighted sum of deprived dimensions. Three different weighting techniques (MFW: most favorable weighting, FBW: frequency based weighting and NW: normative weighting) are chosen to calculate this weighted sum, hence three different weighted Multidimensional First Order Dominance (MFOD) are obtained. These three weighted MFODs and their associated MAFOD/MASODs are evaluated using: the percentage of indeterminate cells and the almost-dominance percentage. These percentages are compared with their counterparts of MFOD, MAFOD/MASOD of the T technique. In addition, the weighted MAFOD/MASODs are compared to the bootstrap dominance comparison technique of Arndt et al. (World Development, 40(11), 2290–2301, 2012) in terms of the indeterminate cells percentages. Using Egypt Demographic and Health Survey 2014, weighted MAFOD/MASOD analyses are performed to compare the Egyptian children welfare among governorates and among aggregate regions. Results provide evidence that the weighting techniques affect the dominance analysis, but barely affect the ranking of the regions or governments.
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Notes
If dimensions are substitutes, the marginal utility of one attribute decreases as the quantity of the other increases. If attributes are complements, an increase in the amount of one raises the marginal utility of the other, (Njong 2010).
Net domination is the difference between row and column average domination.
In a three dimensional scenario, if 1 denotes deprived and 0 denotes not deprived, then the outcome (0,1,1) is worse than the outcome (0,0,1).
Note if we used equal weight of 1/6 instead 1 (so that the weights would sum up to 1), the resulted ordering given to the multidimensional events would be the same as the ordering obtained by total sum; so equal weight returns same results as total sum.
The Bristol indicators were originally developed by a team at the University of Bristol and presented in the report “The Distribution of Child Poverty in the Developing World”. These indicators are based on the “deprivation approach” to poverty.
Tables 5, 6 ,7 contain only 54 deprivation events (not 64) since the percentages of deprivation in the remaining events are zero.
The static case means that the dominance analysis is used on the data set only, i.e. without bootstrap, this terminology was given by Arndt et al. (2012).
The frontier governorates poverty rates are not listed in this table, we considered the poverty rate for it above 30.
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Acknowledgements
The authors would like to show their gratitude to Alyaa Hegazy Abdelhamid for assistance with getting weights using the MFW technique and Samaa H. Hosny, Assistant Professor, FEPS, Cairo University for comments that greatly helped in the MFW weights.
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El Sayed, T., Zahran, A.R. Child Wellbeing in Egypt: a Weighted Multidimensional Almost Dominance Approach. Child Ind Res 13, 993–1022 (2020). https://doi.org/10.1007/s12187-019-09667-x
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DOI: https://doi.org/10.1007/s12187-019-09667-x