IDEAS home Printed from https://ideas.repec.org/p/fip/fednsr/101431.html

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

Author

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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: https://www.newyorkfed.org/medialibrary/media/research/staff_reports/sr1163.pdf
    File Function: Full text
    Download Restriction: no
    File URL: https://www.newyorkfed.org/research/staff_reports/sr1163.html
    File Function: Summary
    Download Restriction: no
    File URL: https://libkey.io/10.59576/sr.1163?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. David Pérez-Mesa & à ngel S. Marrero, 2024. "Adult health and inequality of opportunity in Spain," Working Papers 671, ECINEQ, Society for the Study of Economic Inequality.
    2. L'Roe, Jessica & Detoeuf, Diane & Wieland, Michelle & Ikati, Bernard & Enduyi Kimuha, Moïse & Sandrin, François & Angauko Sukari, Odette & Nzale Nkumu, Junior & Kretser, Heidi E. & Wilkie, David, 2023. "Large-scale monitoring in the DRC’s Ituri forest with a locally informed multidimensional well-being index," World Development, Elsevier, vol. 169(C).
    3. Gregorio Gimenez & Ana Isabel Gil-Lacruz & Marta Gil-Lacruz, 2021. "Is Happiness Linked to Subjective Life Expectancy? A Study of Chilean Senior Citizens," Mathematics, MDPI, vol. 9(17), pages 1-12, August.
    4. Dan Givoly & Yifan Li & Ben Lourie & Alexander Nekrasov, 2019. "Key performance indicators as supplements to earnings: Incremental informativeness, demand factors, measurement issues, and properties of their forecasts," Review of Accounting Studies, Springer, vol. 24(4), pages 1147-1183, December.
    5. Pérez-Mesa, David & Marrero, Gustavo A. & Darias-Curvo, Sara, 2021. "Child health inequality in Sub-Saharan Africa," MPRA Paper 108801, University Library of Munich, Germany.
    6. Nikolova, Milena, 2016. "Minding the happiness gap: Political institutions and perceived quality of life in transition," European Journal of Political Economy, Elsevier, vol. 45(S), pages 129-148.
    7. Hu'e Sullivan & Hurlin Christophe & P'erignon Christophe & Saurin S'ebastien, 2022. "Measuring the Driving Forces of Predictive Performance: Application to Credit Scoring," Papers 2212.05866, arXiv.org, revised Jan 2025.
    8. Shabana Mitra, 2016. "Synergies Among Monetary, Multidimensional and Subjective Poverty: Evidence from Nepal," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 125(1), pages 103-125, January.
    9. Rafael P. Ribas, 2014. "Liquidity Constraints, Informal Financing, and Entrepreneurship: Direct and Indirect Effects of a Cash Transfer Programme," Working Papers 131, International Policy Centre.
    10. Omoniyi B Alimi & David C Maré & Jacques Poot, 2020. "The effects of immigration and skills on urban income inequality in New Zealand: two decomposition approaches," RFBerlin Discussion Paper Series 2023, ROCKWOOL Foundation Berlin (RFBerlin).
    11. Xingwei Hu, 2018. "A Theory of Dichotomous Valuation with Applications to Variable Selection," Papers 1808.00131, arXiv.org, revised Mar 2020.
    12. Asuyama, Yoko, 2021. "Determinants of job interestingness: Comparison of Japan and other high-income countries," Labour Economics, Elsevier, vol. 73(C).
    13. Fabián Slonimczyk, 2013. "Earnings inequality and skill mismatch in the U.S.: 1973–2002," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 11(2), pages 163-194, June.
    14. Nikolova, Milena & Cnossen, Femke, 2020. "What makes work meaningful and why economists should care about it," Labour Economics, Elsevier, vol. 65(C).
    15. Beatriz Barrado & Gregorio Gimenez & Jaime Sanaú, 2021. "The Use of Decomposition Methods to Understand the Economic Growth Gap between Latin America and East Asia," Sustainability, MDPI, vol. 13(12), pages 1-18, June.
    16. Erin Lentz & Elizabeth Bageant & Sudha Narayanan, 2021. "Empowerment and nutrition in Niger: insights from the Women’s Empowerment in Nutrition grid," Food Security: The Science, Sociology and Economics of Food Production and Access to Food, Springer;The International Society for Plant Pathology, vol. 13(5), pages 1227-1244, October.
    17. Halleck Vega, Solmaria & Elhorst, J. Paul, 2016. "A regional unemployment model simultaneously accounting for serial dynamics, spatial dependence and common factors," Regional Science and Urban Economics, Elsevier, vol. 60(C), pages 85-95.
    18. Yihua Wang & Tomoko Kinugasa, 2022. "The relationship between demographic change and house price: Chinese evidence," International Journal of Economic Policy Studies, Springer, vol. 16(1), pages 43-65, February.
    19. Jean-Marie Grether & Nicole Mathys & Jaime de Melo, 2009. "Scale, Technique and Composition Effects in Manufacturing SO 2 Emissions," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 43(2), pages 257-274, June.
    20. Filotto, Umberto & Caratelli, Massimo & Fornezza, Fabrizio, 2021. "Shaping the digital transformation of the retail banking industry. Empirical evidence from Italy," European Management Journal, Elsevier, vol. 39(3), pages 366-375.

    More about this item

    Keywords

    ;
    ;

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fip:fednsr:101431. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Gabriella Bucciarelli (email available below). General contact details of provider: https://edirc.repec.org/data/frbnyus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.