Dear S.J.,

there's a step-by-step procedure with an example on the FAO website (Food and Agriculture Organization of the United Stations): http://www.fao.org/home/en/

Bellù, L.G., Liberati, P. (2006): Policy Impacts on Inequality: Welfare Based Measures of Inequality - The Atkinson Index. Modul No. 50.see the link: http://www.fao.org/docs/up/easypol/451/welfare_measures_inequa_atkinson_050en.pdf

Abstract: This tool illustrates one of the most popular welfare-based measures of inequality, the Atkinson Index . In particular, it discusses the foundations of this Index, in terms of social welfare specifications, and the concept of equally distributed equivalent income on which the measure is based. The use of this measure is then exemplified in a step-by-step procedure and in a numerical example.

Perhaps you are interested in: Fernando G De Maio (2007): Income inequality measures. Journal of Epidemiology and Community Health, 2007, 61(10), pp.: 849-852.  see: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2652960/ (free download)

Abstract: The Gini coefficient has been the most popular method for operationalising income inequality in the public health literature. However, a number of alternative methods exist, and they offer researchers the means to develop a more nuanced understanding of the distribution of income. Income inequality measures such as the generalised entropy index and the Atkinson index offer the ability to examine the effects of inequalities in different areas of the income spectrum, enabling more meaningful quantitative assessments of qualitatively different inequalities. This glossary provides a conceptual introduction to these and other income inequality measures.

Finally try the following link unter the HDR Website (United Nations Development Programme. Human Development Reports): http://hdr.undp.org/en/content/gini-coefficient-not-sufficient-measure-inequality-what-difference-between-gini-and-atkinson

Good luck and kind regards, Detlef

http://www.fao.org/home/en/

http://www.fao.org/docs/up/easypol/451/welfare_measures_inequa_atkinson_050en.pdf

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2652960/

http://hdr.undp.org/en/content/gini-coefficient-not-sufficient-measure-inequality-what-difference-between-gini-and-atkinson

Thanks Detlef.

Hi Detlef,

In Atkinson's Index, i read that higher the value of the inequality aversion parameter (epsilon), higher are the weights given to the poor.  I also read that the theoretical range of the epsilon is zero to infinity.  Then the question would be what value of the epsilon will be more appropriate for a given income distribution.  Is the value entirely depends on some value judgments? (The common values preferred are 0,1,2).

Thanks.

Dear S.J.,

the parameter (epsilon) is a parameter in order to integrate Rawl's concept of social justice (see the annex of my first contribution: de Maio, 2007, p. 850). So, the choice of the parameter (epsilon) is based on a normative/ethical judgement/assessment. From this point of view, the value "social justice" determines the action in this process of judgement / assessment. (Background: Atkinson Index is a parameter for welfare and welfare can't be measured without definining the normative frame)

So the choice of parameter (epsilon) depends on the weight, you want to give to the value "social justice". The parameter (epsilon) was designed in order to estimate the dimension of "inequality aversion". So, based on the following - sorry German-speaking - publication:

Unger et al (2013): Verteilungsbericht 2013. Trendwende noch nicht erreicht. WSI Report (10). Download: http://www.boeckler.de/pdf/p_wsi_report_10_2013,

you can define, related to chapter 3.1, pp. 19-21:

parameter (epsilon) = 0,5: little inequality aversion

parameter (epsilon) = 1,0: medium inequality aversion

parameter (epsilon) = 2,0: great inequality aversion

All reports, that I know, emphases that's important to choose a great inequality aversion (parameter (epsilon) = 2,0) in order to consider very low income levels. Personally, I assume, it could be valuable, to calculate the Atkinson Index with the three dimensions (see the diagrams on pp. 19-21, chapter 3.1) in order to illustrate the differences. Based on this, you can demonstrate the utility of a great inequality aversion.

Perhaps, you find a classification of parameter (epsilon) in the following original publications of Atkinson:

Atkinson Anthony (1970): On the Measurement of Inequality. Journal of Economic Theory, 2, S.244-263, 1970.

Atkinson Anthony (2007): Measuring Top Incomes: Methodological Issues. Top Incomes over the Twentieth Century. A contrast between European and English-Speaking Countries, Oxford University Press.

So finally, I would like to state, that the choice of parameter (epsilon) doesn't depend on a given income distribution (your question above), because it depends on the normative definition of the parameter (epsilon).

Kind regards, Detlef

http://www.boeckler.de/pdf/p_wsi_report_10_2013

Thanx Detlef.  I used all three values for comparison and referred with Gini.  But Gini seems overestimating inequality than Atkinson's Index.  You can refer the attached file.

Dear S.J.,

related to your conservative conclusion "Gini seems overestimating inequality than Atkinson's Index" De Maio (2007, p. 850) discusses, that

"The Gini coefficient’s main weakness as a measure of income distribution is that it is incapable of differentiating different kinds of inequalities."

and:

"Along with this limitation, researchers working with the Gini coefficient need to be aware that it is most sensitive to inequalities in the middle part of the income spectrum."

and finally:

"Atkinson argued that this index was a way to incorporate Rawls’ conception of social justice into the measurement of income inequality. In practice, paramater (epsilon) values of 0.5, 1, 1.5 or 2 are used; the higher the value, the more sensitive the Atkinson index becomes to inequalities at the bottom of the income distribution. 

So, the question is to me, where are the inequalities within the range of the income distribution to be found. (In my opinion, both cases are possible). So, there are two more hints in order for further analyses (and in order to get more clarity):

Related to De Maio (2007, p. 850f.), calculate the decile ratios, and compare these results with the GINI coefficient. (Perhaps you'll get knew and enlarged findings. I assume, you perhaps can recognize certain inter-connections / interdependences and certain changes between the three indexes - just have a try.)

Related to Unger et al (2013, pp. 19ff.), calculate Atkinson index, GINI coefficient and decile ratios over a period of 10 or 20 years (depends on the available data). (Perhaps you'll get knew and enlarged findings over the analysed timeline. - just have a try, too.)

Kind regards, Detlef

Thanks Detlef, for the detailed information.