Atkinson index

The Atkinson index (also known as the Atkinson measure or Atkinson inequality measure) is a measure of income inequality developed by British economist Anthony Barnes Atkinson. The measure is useful in determining which end of the distribution contributed most to the observed inequality. The Atkinson index (also known as the Atkinson measure or Atkinson inequality measure) is a measure of income inequality developed by British economist Anthony Barnes Atkinson. The measure is useful in determining which end of the distribution contributed most to the observed inequality. The index can be turned into a normative measure by imposing a coefficient ε {displaystyle varepsilon } to weight incomes. Greater weight can be placed on changes in a given portion of the income distribution by choosing ε {displaystyle varepsilon } , the level of 'inequality aversion', appropriately. The Atkinson index becomes more sensitive to changes at the lower end of the income distribution as ε {displaystyle varepsilon } approaches 1. Conversely, as the level of inequality aversion falls (that is, as ε {displaystyle varepsilon } approaches 0) the Atkinson becomes more sensitive to changes in the upper end of the income distribution. The Atkinson ε {displaystyle varepsilon } parameter is often called the 'inequality aversion parameter', since it quantifies the amount of social utility that is assumed to be gained from complete redistribution of resources. For ε = 0 {displaystyle varepsilon =0} , (no aversion to inequality) it is assumed that no social utility is gained by complete redistribution and the Atkinson index ( A ε {displaystyle A_{varepsilon }} ) is zero. For ε = ∞ {displaystyle varepsilon =infty } (infinite aversion to inequality), it is assumed that infinite social utility is gained by complete redistribution in which case A ε = 1 {displaystyle A_{varepsilon }=1} . The Atkinson index ( A ε {displaystyle A_{varepsilon }} ) then varies between 0 and 1 and is a measure of the amount of social utility to be gained by complete redistribution of a given income distribution. Based on one's value judgement concerning the social utility of complete redistribution, as embodied in the ε {displaystyle varepsilon } parameter, different income distributions may be compared by calculating the Atkinson index at that ε {displaystyle varepsilon } value, with lower values of A ε {displaystyle A_{varepsilon }} indicating lower social utility to be gained, higher values indicating more. Lower values of A ε {displaystyle A_{varepsilon }} thus indicate a more equal distribution than higher values, given a particular degree of inequality aversion.