Proximity-sensitive individual deprivation measures

Abstract

Abstract. We propose and characterize a generalization of the classical linear index of individual deprivation based on income shortfalls. Unlike the original measure, our class allows for increases in the income of a higher-income individual to have a stronger impact on a person's deprivation the closer they occur to the income of the individual whose deprivation is being assessed. The subclass of our measures with this property is axiomatized in our second result. Journal of Economic Literature Classification No.: D63.

Relative Deprivation and School Enrolment. Evidence from Mexico

“…The motivation for concavity resides in the well‐established belief in sociological theory that individuals are more sensitive to advancements achieved by members of the reference group who are closer to their condition (Festinger, ). Other concave indices have been proposed by Paul (), Chakravarty and Chattopadhyay (); Podder (), more recently, Bossert and D'Ambrosio () characterized a generalization of individual deprivation functions based on income differences in order to account for distribution sensitivity.…”

The Impact of Social Transfers on Income Poverty and Material Deprivation

“…Income and material deprivation are complementary because they reflect related but different concepts of material wellbeing and each has its own specific measurement challenges (see Battiston et al 2013;Bossert & D'Ambrosio 2014;Cancian & Meyer 2004;Guio et al 2012, Marlier et al 2007, Nolan & Whelan 2010. Consequently, while income and material deprivation indicators often 'agree' about a person's economic wellbeing they also regularly 'disagree'.…”

“…While commonly adjusted for differences in household size (see above), income indicators are usually not adapted for differences in needs such as chronic illness or disability of household members (Sen, 1999). An implicit assumption underlying a resource-based indicator is also that needed goods and services can be purchased in well-functioning markets (Bourguignon & Chakravarty, 2003). Furthermore, in some surveys, income from the previous year is seen as the best proxy for the current income, even if this implies inconsistencies between income and the current household composition and activity status information.…”

A class of proximity-sensitive measures of relative deprivation

“…The main difference between five of these six contributions and the generalization presented in this paper is that the indices proposed by Chakravarty and Chakroborty (1984), Paul (1991), and Wang and Tsui (2000) are not derived from axioms; the perspective pursued by Esposito (2010) is not based on the income shortfall; and the index proposed by Bossert and D'Ambrosio (2007) adheres to the equal weights convention. Only the generalization offered by Bossert and D'Ambrosio (2014) derives axiomatically a class of proximity-sensitive measures of relative deprivation based on income shortfalls. Our approach follows in the steps of Bossert and D'Ambrosio (2014), yet it takes the analysis a step further.…”

“…Only the generalization offered by Bossert and D'Ambrosio (2014) derives axiomatically a class of proximity-sensitive measures of relative deprivation based on income shortfalls. Our approach follows in the steps of Bossert and D'Ambrosio (2014), yet it takes the analysis a step further. Whereas the Bossert and D'Ambrosio's (2014) index allows for only one type of proximity-sensitivity, our proposed p RD class of measures is proximitysensitive in a more general sense: right-hand side changes in income weigh differentially, depending on how distant they are in the income distribution, and this variation is exhibited by the value of the proximity-sensitive parameter p: for (0,1) p ∈ , the greater the distance, the smaller the impact of a given change in income on the relative deprivation sensed by the individual; for 1 p > , the opposite effect applies.…”