Welfare metrics for gender asset gaps

Abstract

It is now well established that welfare outcomes for women are impacted by their ownership and control of household assets. In recent years, household asset surveys that enumerate individual asset ownership patterns rather than treat the household as one unitary entity are beginning to take root. One of the key objective of these surveys is the measurement of gender asset gaps (GAP) – the gendered difference in ownership patterns of household assets. Extant GAP measures are positive in nature. These metrics (both as incidence measures or ad valorem measures) quantify the gendered gaps in asset ownership but cannot directly shed light on welfare consequences of womens’ lack of control or ownership of household assets. However, there is evidence to show that gendered difference in asset ownership can impact life outcomes for women by influencing their bargaining power within the household. In this paper, we develop a general theoretical framework that allows development of a class of GAP metrics for directly measuring welfare loss from inequality in intrahousehold asset distribution. Our framework allows measuring welfare at both the household level, as well as aggregate societal welfare. The general framework developed here is agnostic to particular assumptions about inequality and its welfare consequences. Our framework only requires that there exists a real-valued household social welfare function, W (·) that is defined on the household asset matrix, Y i . The household asset matrix Y i records for every household i ∈ {1, 2, 3 . . . n} the self-reported value of m ∈ Z+ different assets, owned by k ∈ Z+ people in the household. For assets that are collectively owned, the portion of the value assigned to each individual is based on the asset share (where available) or equal partitioning of the total asset value between all owners (when shares are not available). To derive a welfare metric for gender asset gaps, we use the well-established Atkinson framework by defining an equally distributed equivalent asset distribution (EDEAD). We use the familiar CES specification for W (·) that allows parametrization of the inequality aversion factor. For a given inequality aversion factor, a welfare measure of gender asset gap is simply the ratio of EDEAD and the total value of assets owned by the household. Thus this welfare metric, GA ∈ (0, 1], represents the fraction of observed household wealth that is needed to reach observed welfare levels if the assets were distributed equally among different members of the household. While the Atkinson framework enables development of a simple welfare metric for gender asset gaps, there are underlying limitations of using such an approach that needs to be carefully addressed. Particular attention needs to be paid to appropriate choice of the social welfare function that can take any form ranging from a utilitarian specification (with no inequality aversion) to the Rawlsian SWF at the other extreme depending on the value taken by the CES parameter. Our paper develops a normative framework for specification of the inequality parameter in an intrahousehold context. In particular we use insights from the capability approach that is particularly well-suited for understanding the relationship between assets and welfare. We argue that for policy praxis a particularly useful specification of the social welfare function is the Foster function. If T i is the Theil index (mean log deviation) for household i calculated on the assets space, we define a gender asset gap metric, GF that is simply the ratio of observed household welfare (as calculated by the Foster function) and potential welfare with perfect equality (Gi F = e −T i ) where T i is the Theil index for the household. This framework also allows us to seamlessly extend welfare metrics for gender asset gaps from the household level to a larger aggregation. While the focus of our paper is on developing welfare metrics when asset values are known, we also allude to how welfare metrics for gender asset gaps can be constructed when only incidence data is available using constructed asset indices. We use individual level assets data, representative for the state of Karnataka in India to empirically illustrate the theoretical framework developed here.