A Recursive Framework for Consistent Sectoral Real Value-Added in Chain-Weighted National Accounts

A Recursive Framework for Consistent Sectoral Real Value-Added in Chain-Weighted National Accounts | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A Recursive Framework for Consistent Sectoral Real Value-Added in Chain-Weighted National Accounts Jaewon Park This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6756289/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract Chain-weighted Fisher indexes are widely used in modern national accounts for their theoretical strengths and ability to capture changes in relative prices over time. However, the fundamental limitations of this approach are non-additivity and inconsistency - the sum of sectoral real value-added does not equal aggregate real GDP, and the sum of sectoral contributions to growth does not match the aggregate economic growth rate. This difference complicates empirical analysis and undermines the interpretability of sectoral dynamics. To resolve this issue, we extend the recursive method proposed by Choi and Pyo (2025), adapting it to the U.S. National Income and Product Accounts (NIPA), based on the Fisher Ideal Index. By constructing symmetric, Fisher-compatible growth contributions and embedding them in a recursive structure, we generate sectoral real value-added series, both level- and growth-additive. Empirical validation using U.S. BEA data confirms that our method fully restores internal consistency, offering a theoretically sound and operationally effective solution to the non-additivity problem in chain-weighted systems. Macroeconomics Econometrics Economic Theory non-additivity chain-weighted indexes recursive estimation Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6756289","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":473692830,"identity":"bf6d0193-4dee-42d3-817a-abb242ca1731","order_by":0,"name":"Jaewon Park","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzklEQVRIiWNgGAWjYBACxgYQrrDh4YfwmYnVciZNRrKBWC1gbY1th2wMDhCrhXl287OPM9gO8BifX50mwVBhndhA0IY5x4xnbuC5w2N24+02CYYz6URomZFgzPhA4hlQy9ltEoxth4nRkv6Z8YHBYR7jGSAt/4jSkmPMuCHhMI8Bfy9QSwMxWuacKWaccSCNR+IG72aLhGPpxgS1GM5u38zY+8/Gnr//7MYbH2qsZQlrmQFjSSQwMCQQUg4C8hIwFv8BYtSPglEwCkbBSAQAjIlD5M36n6MAAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0001-2783-9143","institution":"George Mason University","correspondingAuthor":true,"prefix":"","firstName":"Jaewon","middleName":"","lastName":"Park","suffix":""}],"badges":[],"createdAt":"2025-05-27 07:03:33","currentVersionCode":2,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-6756289/v2","doiUrl":"https://doi.org/10.21203/rs.3.rs-6756289/v2","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":85088176,"identity":"ebb99940-69d6-4545-a738-916593c783e1","added_by":"auto","created_at":"2025-06-20 20:51:32","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":254547,"visible":true,"origin":"","legend":"","description":"","filename":"PrePrint.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6756289/v2_covered_a3ee9396-4290-4483-8601-22ec63bb1d2a.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"A Recursive Framework for Consistent Sectoral Real Value-Added in Chain-Weighted National Accounts","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"George Mason University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"non-additivity, chain-weighted indexes, recursive estimation","lastPublishedDoi":"10.21203/rs.3.rs-6756289/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6756289/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eChain-weighted Fisher indexes are widely used in modern national accounts for their theoretical strengths and ability to capture changes in relative prices over time. 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