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

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Staff Reports

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

Number 1163
August 2025

JEL classification: B4

Authors: Richard Audoly, Rory McGee, Sergio Ocampo, and Gonzalo Paz-Pardo

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.

Full Article

Author Disclosure Statement(s)

Richard Audoly
The author declares that he has no relevant or material financial interests that relate to the research described in this paper. Prior to circulation, this paper was reviewed in accordance with the Federal Reserve Bank of New York review policy, available at https://www.newyorkfed.org/research/staff_reports/index.html.

Rory McGee
The author declares that he has no relevant or material financial interests that relate to the research described in this paper.

Sergio Ocampo
I am Sergio Ocampo, one of the authors in "A Practitioner’s Note on The Shapley-Owen-Shorrocks Decomposition" [Audoly, McGee, Ocampo, Paz-Pardo]. I declare that I do not have relevant or material financial interests that relate to the research described in this paper.

Gonzalo Paz-Pardo
The author declares that he has no relevant or material financial interests that relate to the research described in the paper.

Suggested Citation:
Audoly, Richard, Rory McGee, Sergio Ocampo, and Gonzalo Paz-Pardo. 2025. “A Practitioner’s Note on the Shapley-Owen-Shorrocks Decomposition.” Federal Reserve Bank of New York Staff Reports, no. 1163, August. https://doi.org/10.59576/sr.1163

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