Shapley Decomposition by Components of a Welfare Aggregate

Abstract

We present an exercise to account for changes in an indicator into components of a welfare aggregate. The decomposition presented in this paper focus on the distribution of the welfare variable rather than a decomposable indicator. Thus, it is a statistical exercise in which we assume that we can in fact modify one factor at a time and keep everything else constant. This paper contributes to the existing literature by applying the concept of a Shapley decomposition to deal with the path dependence that arises from changing one element at a time. Although, the interpretation changes, the proposed decomposition is applicable to both the case of panel data as well as repeated cross section and allows accounting the contribution of each component to change in any given indicator.