纽约联储-关于夏普利-欧文-肖罗克斯（Shapley-Owen-Shorrocks）分解法的实践者笔记（英）

A Practitioner’s Note on the Shapley-Owen-Shorrocks Decomposition Richard Audoly | Rory McGee | Sergio Ocampo | Gonzalo Paz-Pardo NO. 1163 AUGUST 2025 A Practitioner’s Note on the Shapley-Owen-Shorrocks Decomposition Richard Audoly, Rory McGee, Sergio Ocampo, and Gonzalo Paz-Pardo Federal Reserve Bank of New York Staff Reports, no. 1163 August 2025 https://doi.org/10.59576/sr.1163 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 Key words: decomposition, methodology _________________ Audoly: Federal Reserve Bank of New York (email: audolyr@gmail.com). McGee: UWO & IFS (email: rmcgee4@uwo.ca). Ocampo: UWO (email: socampod@uwo.ca). Paz-Pardo: ECB (email: gonzalo.paz_pardo@ecb.europa.eu). The authors are grateful to David Wiczer for first suggesting this approach to them many years ago. They also thank Emmanuel Murray Leclair for research assistance. This previously appeared as an appendix to their paper "The Life-Cycle Dynamics of Wealth Mobility." Ocampo acknowledges financial support from the Research Council of Norway through the project TaxFair, Number 315765. McGee and Ocampo acknowledge financial support from the Social Science and Humanities Research Council of Canada through the Insight Development Grant Number 430-2022-00394. This paper presents preliminary findings and is being distributed to economists and other interested readers solely to stimulate discussion and elicit comments. The views expressed in this paper are those of the author(s) and do not necessarily reflect the position of the Federal Reserve Bank of New York, the Federal Reserve System, the European Central Bank, or the Eurosystem. Any errors or omissions are the responsibility of the author(s). To view the authors’ disclosure statements, visit https://www.newyorkfed.org/research/staff_reports/sr1163.html. Inthisshortnote,weaimtoprovideasimpleoverviewoftheShapley-Owen-Shorrocks decomposition. The objective of the decomposition is toobtain values measuring the contribution of several inputs (or groups of them) to someaggregate outcome. When the outcome can be