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

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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.

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  • Richard Audoly & Rory McGee & Sergio Ocampo & Gonzalo Paz-Pardo, 2025. "A Practitioner’s Note on the Shapley-Owen-Shorrocks Decomposition," Staff Reports 1163, Federal Reserve Bank of New York.
    • Handle: RePEc:fip:fednsr:101431
    DOI: 10.59576/sr.1163
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    1. Osnat Israeli, 2007. "A Shapley-based decomposition of the R-Square of a linear regression," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(2), pages 199-212, August.
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    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology

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