Group Differential for Attainment and Failure Indicators

Abstract

The study revisits the properties of group differential (GD) measures and extends it to include monotonicity and policy sensitivity axioms. Imposing level sensitivity, which indicates that a given gap is worse off at higher (lower) level of attainment (failure), the study concurs that 'simple difference' and 'simple ratio' are the most basic GD measures for attainment and failure indicators, respectively. It proposes two new measures, one each for attainment and failure, which have certain advantages from a policy implication perspective. An empirical illustration has been provided by taking two indicators from Millennium Development Goals for different regions of the world. 1 There are attainment indicators such as literacy rate and immunisation rate, and failure indicators such as infant mortality rate (IMR), maternal mortality rate and death rate. An attainment indicator can be converted as failure by taking its additive inverse, like when literacy rate is replaced with illiteracy rate.

Covariates of diarrhoea among under-five children in India: Are they level dependent?

“…Temporal or cross-sectional examination of associations between development indicators tends to value a quantum of change uniformly across the entire range of values that indicators assume. However, while considering success indicators like immunization rates or antenatal care coverage rates; or failure indicators like infant or child mortality or morbidity rates; efforts needed to realise a change in the indicator at better levels need to be valued more when compared with such a change at worse levels [14]. Increasing immunization coverage in a district from 80% to 90% needs greater effort when compared to the effort needed to shift it from 40% to 50%.…”

Reckoning Level Differentials in the Measurement of Progress: An Application in the Context of Deliveries Attended by Skilled Health Personnel Across Least Developed Countries (LDCs)

“…As outlined in the introductory section, the level-sensitive behaviour assumed here is consistent with equity impacts and the notion of increasing marginal cost with higher (lower) levels of attainment (failure). The rest of this section reviews the various progress indices by invoking certain desirable axiomatic properties for an indicator of progress assessment (Kakwani, 1993;Mishra & Subramanian, 2006;Nathan & Mishra, 2013).…”

“…) and attaches a greater weight to a given Δh as desired. Similarly, two other measures of level-sensitive differentials, MS(h) and NM(h) advanced in Mishra and Subramanian (2006) and Nathan and Mishra (2013), respectively, satisfy level sensitivity and can be adapted for progress assessment. The weighting function implicit in NM(h) is f(.)…”

“…S(h) and NM(h) display policy sensitivity implying that the index values would be at least as high as the absolute gap between the two time points, that is, P(h) ≥ Δh (Subramanian, 2004;Nathan & Mishra, 2013). However, these indices do not satisfy additivity implying that progress between two time periods cannot be expressed as a sum of progress between its sub-periods.…”

“…and inter-group progress. However, an indiscriminate application of these methods is increasingly identified as an area for concern (Nathan & Mishra, 2013;Hailu & Tsukada, 2011;Fukuda-Parr et al, 2013;Easterly, 2009;Subramanian, 2008a;Osorio, 2008;Houweling et al, 2007;Mishra & Subramanian, 2006;Kakwani, 1993;Sen, 1981). It seems useful to briefly illustrate these apprehensions.…”