Page 8 - Azerbaijan State University of Economics

THE JOURNAL OF ECONOMIC SCIENCES: THEORY AND PRACTICE, V.76, # 2, 2019, pp. 4-20

where we accept α = 1/2.

Additionaly, each household can be weighed by the number of household members
(Ebert, 1967) Which is developed and as a methodology generalized by OCED as
“OECD equivalence scale” and “OECD – modified scale”.

Now we can adjust formulas for equivalent incomes for social groups (see table 3)
based on methodology mentioned above:

̅

= = √ (3)

√

̅
Where, is mean of per capita income intervals (see table 2), is equivalent

household income for income groups.

Then we can develop the mean of equivalent incomes formula for social groups:

= ∑ (4)

=1

e
Let to assume that, the vector of equivalent incomes X is ranked in ascending order:

0 ≤ ≤ ≤ ⋯ ≤ (5)

1

2

Later, to estimate mobility index in the initial period the way proposed by H. Theil
(1967) is applied:
T(X ) = (6)
e
Then, we adjust this formula for social groups (described in section 2) by changing
arithmetic average into weighted average:

T( ) = ∑ ( ln ) (7)

=1

where = 1, … , is the number of income intervals within a social group (n is
conditional and changes for each social group), µ is the mean of equivalent

incomes, and is weights of income groups according to table 2 in the initial

period.

Distribution of equivalent incomes for the last period is: = ( , , … , ), where

2
1

is ranked from lowest to highest. Thus, Theil inequality index adjusted for social
groups in the final period is:

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