Sopher՚s Index Measuring Disparity YouTube Lecture Handouts

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Sopher՚s Index; Modified Sopher՚s Index by Kundu & Rao - Measuring Disparity

Title: Sopher՚s Index Measuring Disparity

Sopher՚s Index

  • Developed by Sopher in 1974
  • Measures Disparity
  • Rural-Urban; Male-Female
  • 1974 by David Sopher – generally used to understand relative disparity
  • 1st applied to disparity between rural and urban literates
  • Measures disparity between 2 groups in their possession of particular property in terms of logarithm of odd ratios
  • D = 0 (perfect equality)
  • High value of D – higher extent of disparity
  • Lower value of D – lower extent of disparity
  • Where it is used: rural-urban literacy; rural-urban population; male-female literacy; male-female PCI
  • is disparity index
  • is percent of rural/female literate
  • is percent of urban/male literate
  • (if that is not done, we will have same value of disparity index but there will be negative sign)
  • Idea of taking log is to reduce the levelling of effect i.e.. , regions with higher literacy rate show lower level of disparity than regions having low literacy rate even though the gap is same for both regions.
  • If 2 numbers are big, there difference would be the same but values would be smaller however if 2
  • The natural logarithm function ln (x) is defined only for x > 0. So, the natural logarithm of a negative number is undefined.

Why we take log?

  • Sopher՚s Index modified by Kundu & Rao (1983)
  • What if the values are more than 100?
  • Additive monotonocity axiom
  • 1974 by David Sopher – generally used to understand relative disparity
  • Modified in 1983 by Kundu and Rao
  • GER: Divide the number of students enrolled in a given level of education regardless of age by the population of the age group which officially corresponds to the given level of education, and multiply the result by 100. A high GER generally indicates a high degree of participation, whether the pupils belong to the official age group or not. A GER value approaching or exceeding 100 % indicates that a country is, in principle, able to accommodate all of its school-age population, but it does not indicate the proportion already enrolled. The achievement of a GER of 100 % is therefore a necessary but not sufficient condition for enrolling all eligible children in school.
  • Sopher՚s index would have log of negative number if GER is more than 100, so present study has used modified Sopher՚s index that is modified by Kundu and Rao
  • Kundu and Rao (1986) have shown that the Sopher index fails to satisfy the additive monotonicity axiom
  • Monotonic implies if x increases, y should also increase but log of negative number is undefined so no monotonicity would exist. There 200 is used rather than 100 to have a positive value for log function.
  • The additive monotonocity axiom specifies that if a constant is added to all observations in a non-negative series, ceteris paribus (all other things remain constant) , the inequality index must report a decline. It would reduce the ratio and inequality index would decline.