Page 6 - Azerbaijan State University of Economics

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

There are a few points to further explain: both No.1 and No.2 are proposed by G. S.
Fields et al., but only No.1 satisfies homogeneity (H) or translation invariant (TI).
Moreover, No.2 formula is not a pure absolute income mobility index. Such an
interesting phenomenon implicates that even the same person is in dilemma in how
to characterize the income mobility due to its diversity. Secondly, No.5 is a general
index when compared to No.2. When the function g has a determined form, | −

|, No.5 satisfies homogeneity (H) and translation invariance (TI). Finally, all

indices from No.1 to No.6 are equal-weighted, that is, every individual make an
equal contribution to the total mobility. No.6 and No.7 have considered the effect of
different weights

Table1. The comparison of absolute income mobility indices

№ Formula H TI D PC M GS Papers

DD(p)
Fields and

1 ∑ | − | √ √ √ √ √ √ 1 | − | Ok (1996a),

=1 (1996b)
Fields and
|log
1

2 c( ∑ |log − log |) √ √ √ √ √ √ 1 Ok (1999),

=1 − log | Fields(2006)

, (2007)
1 Matra and
3 (∑ | − | ) √ √ √ √ √ √ p
| − |

=1 Ok (1998)
Dardanoni
(1993),
DAgostino
1 1
4 ( ∑ ( ) ) 2 √ √ √ √ √ √ 2 and
2
( − )

=1 − Dardanoni
(2006),(2009
a)
DAgostino
and
1 Dardanoni
( ( ∑ ( ( ) ( ( ) (2009b),

5 =1 √ √ √ √ √ √ 2

1 − ( )) Checchi and

− ( )) )) 2 Dardanoni
2

(2002),
(2006)
′ Ding and
∫ | ( ) − ( − ∆ )| | ( ) − (

6 ∑ √ √ √ √ √ √ 1 Wang

− ∆ )|
′
=1 ( − ) (2006)
Van Kerm
( , , )
7 ∬ ( , , ) ( , ) √ √ √ √ √ √ p (2004),
(2006)
1 Peng and et
8 (∑ ( ) ) √ √ √ √ √ √ p ( )

=1 al (2010)

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