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Gorkhmaz Imanov, Asif Aliyev : Fuzzy Linguistic Forecasting of Social Mobility

In addition, when the No.8 index adopts the equal weight, it is accordant with No.3.
Furthermore, if the value of p is 1, then No.8 takes the form of No.1; if the value of
p is 2, then No.8 takes the form of No.4. If we consider the welfare factor or ordinal
ranks, the No.8 can take the form of No.2 and No.5. As for what is optimal p, it
depends on the researcher’s point of view about the income mobility since the
mobility is multi-facet. In all, the index No.8 is similar to the formula proposed by
Van Kerm (2006), and it is a generalized form for many other indices.

In this study, we use mobility estimation mothodology used by J.P.Rodriguez and et
al. (2010) and apply it in a country level.

Let X = ( , … , ) be the initial income distribution for N households. Then
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equivalent income vector X e is defined through dividing money income by
equivalence (e) scale. Thus, for household i the equivalent income is defined:

= ( ) (1)

where Ni is the number of household members, and e is the equivalence scale,
where 1 ≤ e ≤ Ni . It means that, the needs of a household grow with each additional
member but − due to economies of scale in consumption – not in a proportional
way. Needs for housing space, electricity, etc. will not be three times as high for a
household with three members than for a single person. With the help of equivalence
scales each household type in the population is assigned a value in proportion to its
needs. The factors commonly taken into account to assign these values are the size
of household and the age of its members (whether they are adults or children). A
wide range of equivalence scales exist, but we consider only common methodology
developed by OECD . In the 2008 and 2011 publications of the Organization for
Economic Co-operation and Development, the comparison of income distribution
and poverty comparisons across countries is calculated by dividing household
income by the square root of the number of households.
(http://www.oecd.org/eco/growth/OECD-Note-EquivalenceScales.pdf)

It implies that, four-person houshold has needs twice as large as one composed of a
single person.

Thus, we consider the parametric scale proposed by Buhmann et al. (1988) and
apply OECD 2011 methodology of “square root scale”:

e( ) = , 1 ≥ ≥ 0 , (2)

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