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

The examining of welfar e, social inequality, and poverty has concluded that these
indicators are not always sufficient to comprehend. In order to gain a complete
picture, it is necessary to study income mobility or change of population income
over time (Fields and Ok, 1996a). Van Kerm (2004) classifies income mobility as
follows: growth, dispersion, and exchange mobility. The first of these comprise an
increase in mean income of the distribution produced by economic growth. The
dispersion component evaluates the degree to which income convergence occurs,
studying the variation in the inequality of distribution without income being
reranked. Lastly, the exchange component shows the magnitude of the rerankings
among incomes.

In the article growth, dispersion, and exchange mobility are estimated in the time
intervals of 2009–2017. In particular, mobility indices are estimated as proposed by
H. Theil, and G. S. Fields and E. A. Ok which calculates mobility based on total
income per capita, then the data are forecasted for the next period based on fuzzy
linguistic Markov chain.

Section II of the article provides a theoretical framework for measuring social
mobility; Section III presents the estimation of social mobility indices on social
groups; Section IV presents social mobility forecasting.

II.Theoretical basis for assessment of social mobility
In order to highlight the advantage of the mobility index that will be applied, there is
necessity to compare it with existing ones. Some mobility indices that are well
constructed and widely accepted have been classified by M.Peng and et al (2010).

When justifying an index, there are some properties that must be taken into
consideration to make comparisons: homogeneity (H), translation invariant (TI),
decomposability (D), population consistency (PC), monotonicity (M), growth
sensitivity (GS), and distance dimension (DD).

The comparison results are listed in Table 1, and we can see that:

(i) Each index obey variance axioms (properties), but all of them differ
mainly in the distance functions.
(ii) No.7 and No.8 generalize the form of the distance function.
(iii) No.7 and No.8 are in accordance with each other, and their only
difference lies in whether the distance function f is continuous or
discrete.

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