A Practitioner’s Note on the Shapley-Owen-Shorrocks Decomposition

Audoly, Richard; McGee, Rory; Ocampo, Sergio; Paz-Pardo, Gonzalo

doi:10.59576/sr.1163

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A Practitioner’s Note on the Shapley-Owen-Shorrocks Decomposition

Abstract: Decomposing empirical or economic phenomena into the contributions of different inputs is a frequent goal of economic analysis. However, in many settings, the quantity of interest depends on many inputs which are aggregated non-linearly. In these settings, decompositions need not sum to one and often depend on the order in which inputs are “zeroed out.” In this note we describe a simple but convenient alternative. We show that using the Shapley-Owen value, extended to inequality decompositions in Shorrocks (1999, 2013), provides an additive decomposition that sums to one and is easily interpretable in terms of the contribution of different inputs (or groups of them) to some aggregate outcome. We provide several examples to help implement the approach. We believe this is exceptionally well-suited to decompositions in rich-structural models of economic phenomena which are typically non-linear.

JEL Classification: B4;

https://doi.org/10.59576/sr.1163