JAVADEKAR, Sayli; Krishnakumar, Jaya (2017). 'Decomposition of Multidimensional Well-being inequality' Paper presented at the annual conference of the HDCA, Cape Town 2017.


In this paper we address the question of decomposition of wellbeing inequalities into aspects beyond individual responsibility (i.e. circumstances) and aspects within individual responsibility (i.e. effort) in a multidimensional framework. Among all the theories that critique utilitarianism and provide an alternative solution to achieve equality with social justice, the most dominant ones have been Sen’s Capability Approach (CA) and Roemer’s Equality of Opportunity (EOp) theory. These theories have been contrasted and compared by many recent studies (Chiappero-Martinetti (CM) 2009; Nogales and Krishnakumar (NK) 2015). On one hand CM 2009 points out major differences arguing that CA is much richer in scope and upholds a multidimensional notion of well-being albeit being much less concrete in policy suggestions. On the other hand, NK 2015 have argued that certain elements of CA could be incorporated in the EOp setting for obtaining concrete policy suggestions. With respect to Inequality of Opportunity measurement, both parametric and nonparametric approaches have been proposed along with many empirical applications.  Checchi and Peragine 2010 put forth the non-parametric approach where the population is partitioned into types based on circumstances and then further each type is partitioned into tranches (quantile of the type specific outcome distribution). IOp is computed as the inequality of measured outcomes within tranches between different types called ex-post or inequality between types of mean outcomes called ex-ante.  In the parametric regression based approach by Bourguignon et al, the outcome is considered a linear function of circumstances, effort and a random error. They have argued that the coefficient on circumstances would capture the direct effect of circumstances on outcome as well as the indirect effect through effort. According to Roemer's more recent view (2002, p458), if individuals belonging to different types face different incentives and constraints in exerting effort, this must be considered as a characteristic of that type and so must be outside the realm of individual responsibility. Roemer's distinction between `level of effort' and `degree of effort' has been used by Bjorklund et al (2011) to estimate separately the effects on outcome due to circumstances and effort. The error term from the regression of income on circumstances is regressed on circumstances to get the fitted values and the sterilised residual. The fitted values capture the `level of effort' and the sterilised residuals capture the 'degree of effort'. The IOp is then estimated using these newly estimated variables. In both settings- parametric and nonparametric, outcome is unidimensional. In this paper we will use the regression based approach for a multidimensional vector of outcome indicators rather than a unidimensional measure of well-being, as advocated by the capability approach. In addition, we would like to estimate the contribution of aspects beyond and within individual responsibility to the inequality in multidimensional well-being. This will be done in the modelling framework of Simultaneous Equation Models with latent variables that has been shown to be suitable for deriving the capability scores using multiple indicators.  As efforts could themselves be influenced by circumstances, we would explicitly introduce this relationship into our model by splitting the effort into a part influenced by circumstances (level of effort) and another part that is purely within individual responsibility (degree of effort). The measurement equations would link latent well-being to multiple outcome indicators. The structural model would associate well-being to circumstances and efforts. In addition, we introduce another equation that will take into account the influence of circumstances on observed effort indicators. We assume that certain effort variables are observable while the unobservable part of effort is incorporated in the residual of the structural model along with random shocks. Estimation of this model will lead to multidimensional well-being scores, which would be used to calculate a multidimensional inequality measure. This inequality will then be decomposed into shares of different circumstances based on the decomposition methodology of Shorrocks (1982) and Biggota, Krishnakumar and Rani (2012). This methodology will be applied to the National Sample Survey Organisation (NSSO) data of India covering representative samples of individual household for a period from 1983-2012.

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