Quantifying the contribution of a subpopulation to inequality an application to Mozambique
In this study, I quantify the contribution of a subpopulation to inequality. This is defined as the sum of the contributions of its members, with these contributions computed as the impact on inequality of a small increase in the population mass at each point of the distribution (using the recentered influence function - RIF).
The decomposition is shown to verify various attractive properties. I also discuss alternative approaches used in the literature of factor inequality decompositions. I show that the RIF and the marginal and Shapley factor contributions are approximately equal in the case of the mean log deviation, the index with the best additive decomposability properties, when the same normalization is used.
In an empirical illustration, I use the approach to identify how the richest, highly educated, and urban population has disproportionally contributed to high and increasing inequality in Mozambique in recent years.