Deterministic vs. Stochastic Methods for Frontier Estimation:  Update and Illustration

Deterministic vs. Stochastic Methods for Frontier Estimation: Update and Illustration | 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 Deterministic vs. Stochastic Methods for Frontier Estimation: Update and Illustration William Weber, Shawna Grosskopf, Kathy Hayes, Heike Wetzel This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4258389/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 We compare an updated version of Aigner-Chu (1968) deterministic frontierestimation to stochastic frontier estimation. This comparison is illustrated byestimation of the Lerner index of monopoly power for a public sector producer.For the deterministic method we apply the bootstrap of Simar and Wilson(1998) and the m out of n bootstrap of Simar and Wilson (2011) as suggestedby Amsler et al. (2013) to construct confidence intervals for the Lerner indexand its price and marginal cost components. Marginal cost estimates arederived from a translog cost function. Since market prices are typically notobserved for public sector producers we use duality theory and derive price1from observed costs and an estimated translog input distance function. Datafrom German public theaters’ production of performances to attract spectatorsusing inputs of artistic staff, administrative staff, and other operatingexpenditures are used as an example. We find no evidence of monopoly power. JEL codes: D24, D42 Lerner index public sector managerial behavior Aigner-Chu deterministic method bootstrapping Full Text Additional Declarations No competing interests reported. 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. 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-4258389","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":293704952,"identity":"a2d1f541-9b69-4e4b-b37e-ec77701b3431","order_by":0,"name":"William Weber","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAt0lEQVRIiWNgGAWjYDACdgYGZiAlB+UyE6GFGaLMmHQtiQ1EazE4zGP4uKDiXvr89u7EBwwV1jC9eLUYG884U5y74czZzQYMZ9IJazE7zLtNmrctIXeDRO42Cca2w0Rp2f6b919Cuvz8t0At/4jTso2ZtyEhgeEGL1BLAxFa7A/zf5aecSzBcMOZ3M0GCcfSjQlqkWxvS/xcUJMgL99+duODDzXWsgS1oIIE0pSPglEwCkbBKMAFAGjCPZcpJ6UNAAAAAElFTkSuQmCC","orcid":"","institution":"Southeast Missouri State University","correspondingAuthor":true,"prefix":"","firstName":"William","middleName":"","lastName":"Weber","suffix":""},{"id":293704961,"identity":"5e34a82b-ee22-4d0f-a5b8-b6ac1ade1de8","order_by":1,"name":"Shawna Grosskopf","email":"","orcid":"","institution":"Oregon State University","correspondingAuthor":false,"prefix":"","firstName":"Shawna","middleName":"","lastName":"Grosskopf","suffix":""},{"id":293704962,"identity":"d80c300e-b3a8-4d17-b460-1c3ab384720a","order_by":2,"name":"Kathy Hayes","email":"","orcid":"","institution":"Southern Methodist University","correspondingAuthor":false,"prefix":"","firstName":"Kathy","middleName":"","lastName":"Hayes","suffix":""},{"id":293704963,"identity":"9af20f82-a68e-4ddb-8f63-3fd7970565f7","order_by":3,"name":"Heike Wetzel","email":"","orcid":"","institution":"University of Kassel","correspondingAuthor":false,"prefix":"","firstName":"Heike","middleName":"","lastName":"Wetzel","suffix":""}],"badges":[],"createdAt":"2024-04-12 14:35:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4258389/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4258389/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":55629796,"identity":"e6addac0-6a66-4d7b-8a87-4016004a1251","added_by":"auto","created_at":"2024-04-30 19:12:20","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":238543,"visible":true,"origin":"","legend":"","description":"","filename":"ANoterevised.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4258389/v1_covered_074e3072-dec0-42c8-aad9-a33dffe5c45c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Deterministic vs. Stochastic Methods for Frontier Estimation: Update and Illustration","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"Lerner index, public sector managerial behavior, Aigner-Chu deterministic method, bootstrapping","lastPublishedDoi":"10.21203/rs.3.rs-4258389/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4258389/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe compare an updated version of Aigner-Chu (1968) deterministic frontierestimation to stochastic frontier estimation. 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