Spatial Panel Models with Heterogeneous Coefficients: A Scalable, Integrated Hamiltonian Monte Carlo Estimation Framework

Spatial Panel Models with Heterogeneous Coefficients: A Scalable, Integrated Hamiltonian Monte Carlo Estimation Framework | 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 Spatial Panel Models with Heterogeneous Coefficients: A Scalable, Integrated Hamiltonian Monte Carlo Estimation Framework Yuheng LING, Peiyi Wu, Lei JIANG This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8938359/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Spatial panel models with heterogeneous coefficients provide a flexible framework for capturing region-specific spillovers, but their practical use is often constrained by two challenges: (i) existing estimators primarily justified under large-\(\:T\) asymptotics, leaving unit-specific effects imprecisely estimated in the short panels common in regional science; and (ii) allowing spatial dependence and slopes to vary across units yields a high-dimensional parameter space that is difficult to estimate efficiently. This paper proposes a hierarchical Bayesian spatial model with heterogeneous coefficients that addresses both issues through hierarchical priors and an integrated Hamiltonian Monte Carlo estimation framework. The hierarchical prior induces partial pooling across units, shifting inference toward low-dimensional population hyperparameters while stabilizing unit-level estimates in finite samples, particularly when \(\:N>T\). Furthermore, we develop scalable evaluation of the log-determinant term using a power-series expansion and Hutchinson stochastic trace estimation, and we exploit sparse matrix-vector multiplication and parallel computing to improve computational efficiency. Comprehensive simulation experiments demonstrate that the proposed Bayesian framework delivers reliable finite-sample inference and improved estimation accuracy relative to maximum likelihood in short panels. The results also show that heterogeneous spatial dependence is sensitive to the density of the spatial weights matrix than slope coefficients, offering practical guidance for applied research. JEL Classification : C11 · C13 · C23 Bayesian spatial panel models heterogeneous coefficients hierarchical prior Hamiltonian Monte Carlo Hutchinson stochastic trace estimator Full Text Additional Declarations No competing interests reported. Supplementary Files Appendixv1.pdf Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version 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. 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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-8938359","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":596735774,"identity":"73f60ef1-b5bd-45b5-9870-564e81b57b0c","order_by":0,"name":"Yuheng LING","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwUlEQVRIiWNgGAWjYBACPgYeCIMfRCQUEKGFDaZFsgGkxYAULQYHwCQxWiRyjz34UGEnb3x+deKHBwYM8vxiBwhpyUs3nHEm2XDbjbebJYAOM5w5O4GQlhwzad62AwlmN85uAGlJMLhNjJa/QC3GM85u/kG8FkagFgP+3m1E2sLzxkyyB+iXGTd4t1kkGEgQ9gs/e46ZxA9giPH3n91880eFjTy/NAEtDAIwBRJghgQB5WBrDqAzRsEoGAWjYBSgAQBd6z7dKCDihwAAAABJRU5ErkJggg==","orcid":"","institution":"Hainan Normal University","correspondingAuthor":true,"prefix":"","firstName":"Yuheng","middleName":"","lastName":"LING","suffix":""},{"id":596735777,"identity":"fd7b6e73-7ec3-41fa-87d3-cefc4f8d4518","order_by":1,"name":"Peiyi Wu","email":"","orcid":"","institution":"Hainan Normal University","correspondingAuthor":false,"prefix":"","firstName":"Peiyi","middleName":"","lastName":"Wu","suffix":""},{"id":596735778,"identity":"d4a111f9-dbe4-407e-8da9-6fd17ccd9f73","order_by":2,"name":"Lei JIANG","email":"","orcid":"","institution":"Guangzhou University","correspondingAuthor":false,"prefix":"","firstName":"Lei","middleName":"","lastName":"JIANG","suffix":""}],"badges":[],"createdAt":"2026-02-22 10:08:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8938359/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8938359/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104401026,"identity":"01c81bab-7667-4827-a430-13e499904db6","added_by":"auto","created_at":"2026-03-11 12:11:42","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":877936,"visible":true,"origin":"","legend":"","description":"","filename":"MainManu.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8938359/v1_covered_d5e565dc-9a15-4019-96a2-8f9e7338364a.pdf"},{"id":103843459,"identity":"77aaec7e-7028-41d3-9024-7a34788ca379","added_by":"auto","created_at":"2026-03-03 15:14:15","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":1623141,"visible":true,"origin":"","legend":"","description":"","filename":"Appendixv1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8938359/v1/ac7b8315d5bf5d9975603213.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Spatial Panel Models with Heterogeneous Coefficients: A Scalable, Integrated Hamiltonian Monte Carlo Estimation Framework","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"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":"Bayesian spatial panel models, heterogeneous coefficients, hierarchical prior, Hamiltonian Monte Carlo, Hutchinson stochastic trace estimator","lastPublishedDoi":"10.21203/rs.3.rs-8938359/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8938359/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eSpatial panel models with heterogeneous coefficients provide a flexible framework for capturing region-specific spillovers, but their practical use is often constrained by two challenges: (i) existing estimators primarily justified under large-\\(\\:T\\) asymptotics, leaving unit-specific effects imprecisely estimated in the short panels common in regional science; and (ii) allowing spatial dependence and slopes to vary across units yields a high-dimensional parameter space that is difficult to estimate efficiently. 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