{"id":68559,"date":"2023-12-01T23:07:55","date_gmt":"2023-12-01T22:07:55","guid":{"rendered":"https:\/\/www.wifo.ac.at\/publication\/two-part-models-for-fractional-responses-defined-as-ratios-of-integers\/"},"modified":"2025-10-22T22:24:37","modified_gmt":"2025-10-22T20:24:37","slug":"two-part-models-for-fractional-responses-defined-as-ratios-of-integers","status":"publish","type":"publication","link":"https:\/\/www.wifo.ac.at\/en\/publication\/68559\/","title":{"rendered":"Two-Part Models for Fractional Responses Defined as Ratios of Integers"},"content":{"rendered":"","protected":false},"featured_media":0,"template":"","class_list":["post-68559","publication","type-publication","status-publish","hentry"],"acf":{"subtitle":"","text":"This paper discusses two alternative two-part models for fractional response variables that are defined as ratios of integers. The first two-part model assumes a Binomial distribution and known group size. It nests the one-part fractional response model proposed by Papke and Wooldridge (1996) and, thus, allows one to apply Wald, LM and\/or LR tests in order to discriminate between the two models. The second model extends the first one by allowing for overdispersion in the data. We demonstrate the usefulness of the proposed two-part models for data on the 401(k) pension plan participation rates used in Papke and Wooldridge (1996).","onlinedate":"2014-09-01 02:00:00","lang":"English","publication_series":"","publication_date":"20140901","publication_date_year":"","publication_date_full":false,"publication_num_pages":"","keywords":"[\"fractional response models for ratios of integers\",\"one-part versus two-part models\",\"Wald test\",\"LM test\",\"LR test\"]","jelcodes":"[]","related_publications":"[]","pdf":null,"zip":null,"link":"","monthly_report":false,"monthly_report_main":false,"monthly_report_volume":"2","monthly_report_pages":"123-144","monthly_report_pages_sort":"123","issue":"3","journal":"Econometrics","publisher":"","invisible":false,"external":true,"embargo_date":null,"types":[83083],"research_groups":[3491],"collaboration":"","persons":[3600,3785],"persons_data":"[{\"personId\":3600,\"personName\":\"Harald Oberhofer\",\"organisationNames\":[]},{\"personId\":3785,\"personName\":\"Michael Pfaffermayr\",\"organisationNames\":[]}]","clients":[],"subclients":[],"partners":[],"topics":[],"host_publication_title":"","host_publication_subtitle":"","place_of_publication":"","host_publication_editors":"[]","type_description":"","output_media":"","chapter":"","article_number":"","scientific_assistance":"[]","scientific_review":"[]","version":"","release_date":null,"expiration_date":null,"surveyor":"","research_assistance":"","edv":"","additional_info_de":"","additional_info_en":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.3) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Two-Part Models for Fractional Responses Defined as Ratios of Integers - WIFO<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wifo.ac.at\/en\/publication\/68559\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Two-Part Models for Fractional Responses Defined as Ratios of Integers\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wifo.ac.at\/en\/publication\/68559\/\" \/>\n<meta property=\"og:site_name\" content=\"WIFO\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/WIFOat\/\" \/>\n<meta property=\"article:modified_time\" content=\"2025-10-22T20:24:37+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.wifo.ac.at\/wp-content\/uploads\/2024\/05\/WIFO-Gebaeude-FotoAlexanderMueller-www.alexandermueller.at-IMG_6326-Bearbeitet-1.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1280\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@WIFOat\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.wifo.ac.at\\\/en\\\/publication\\\/68559\\\/\",\"url\":\"https:\\\/\\\/www.wifo.ac.at\\\/en\\\/publication\\\/68559\\\/\",\"name\":\"Two-Part Models for Fractional Responses Defined as Ratios of Integers - WIFO\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.wifo.ac.at\\\/en\\\/#website\"},\"datePublished\":\"2023-12-01T22:07:55+00:00\",\"dateModified\":\"2025-10-22T20:24:37+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/www.wifo.ac.at\\\/en\\\/publication\\\/68559\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/www.wifo.ac.at\\\/en\\\/publication\\\/68559\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/www.wifo.ac.at\\\/en\\\/publication\\\/68559\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Startseite\",\"item\":\"https:\\\/\\\/www.wifo.ac.at\\\/en\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Two-Part Models for Fractional Responses Defined as Ratios of Integers\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/www.wifo.ac.at\\\/en\\\/#website\",\"url\":\"https:\\\/\\\/www.wifo.ac.at\\\/en\\\/\",\"name\":\"\u00d6sterreichisches Institut f\u00fcr Wirtschaftsforschung\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\\\/\\\/www.wifo.ac.at\\\/en\\\/#organization\"},\"alternateName\":\"WIFO\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/www.wifo.ac.at\\\/en\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/www.wifo.ac.at\\\/en\\\/#organization\",\"name\":\"\u00d6sterreichisches Institut f\u00fcr Wirtschaftsforschung\",\"alternateName\":\"WIFO\",\"url\":\"https:\\\/\\\/www.wifo.ac.at\\\/en\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/www.wifo.ac.at\\\/en\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/www.wifo.ac.at\\\/wp-content\\\/uploads\\\/2024\\\/05\\\/WIFO_kurz_rechts-2-1920x412.jpg\",\"contentUrl\":\"https:\\\/\\\/www.wifo.ac.at\\\/wp-content\\\/uploads\\\/2024\\\/05\\\/WIFO_kurz_rechts-2-1920x412.jpg\",\"width\":2000,\"height\":429,\"caption\":\"\u00d6sterreichisches Institut f\u00fcr Wirtschaftsforschung\"},\"image\":{\"@id\":\"https:\\\/\\\/www.wifo.ac.at\\\/en\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/WIFOat\\\/\",\"https:\\\/\\\/x.com\\\/WIFOat\",\"https:\\\/\\\/linkedin.com\\\/company\\\/wifoat\\\/\",\"https:\\\/\\\/www.youtube.com\\\/@WIFO_at\"],\"description\":\"Das WIFO, 1927 von Friedrich August von Hayek und Ludwig von Mises zur Konjunkturanalyse gegr\u00fcndet, ist heute das f\u00fchrende Institut f\u00fcr angewandte empirische Wirtschaftsforschung in \u00d6sterreich mit starkem Engagement auf europ\u00e4ischer Ebene.\",\"email\":\"office@wifo.ac.at\",\"telephone\":\"+43 1 798 26 01 \u2013 0\",\"legalName\":\"\u00d6sterreichisches Institut f\u00fcr Wirtschaftsforschung\",\"foundingDate\":\"1927-01-02\",\"numberOfEmployees\":{\"@type\":\"QuantitativeValue\",\"minValue\":\"51\",\"maxValue\":\"200\"},\"publishingPrinciples\":\"https:\\\/\\\/www.wifo.ac.at\\\/institut\\\/mission-und-strategie\\\/\",\"ownershipFundingInfo\":\"https:\\\/\\\/www.wifo.ac.at\\\/institut\\\/organisation\\\/\",\"actionableFeedbackPolicy\":\"https:\\\/\\\/www.wifo.ac.at\\\/aktuelles\\\/presse\\\/\",\"correctionsPolicy\":\"https:\\\/\\\/www.wifo.ac.at\\\/institut\\\/kontakt\\\/\",\"ethicsPolicy\":\"https:\\\/\\\/www.wifo.ac.at\\\/institut\\\/evidenzbasierung-transparenz-und-unabhaengigkeit\\\/\",\"diversityPolicy\":\"https:\\\/\\\/www.wifo.ac.at\\\/institut\\\/gleichstellung\\\/\",\"diversityStaffingReport\":\"https:\\\/\\\/www.wifo.ac.at\\\/institut\\\/gleichstellung\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Two-Part Models for Fractional Responses Defined as Ratios of Integers - WIFO","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.wifo.ac.at\/en\/publication\/68559\/","og_locale":"en_US","og_type":"article","og_title":"Two-Part Models for Fractional Responses Defined as Ratios of Integers","og_url":"https:\/\/www.wifo.ac.at\/en\/publication\/68559\/","og_site_name":"WIFO","article_publisher":"https:\/\/www.facebook.com\/WIFOat\/","article_modified_time":"2025-10-22T20:24:37+00:00","og_image":[{"width":1920,"height":1280,"url":"https:\/\/www.wifo.ac.at\/wp-content\/uploads\/2024\/05\/WIFO-Gebaeude-FotoAlexanderMueller-www.alexandermueller.at-IMG_6326-Bearbeitet-1.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_site":"@WIFOat","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.wifo.ac.at\/en\/publication\/68559\/","url":"https:\/\/www.wifo.ac.at\/en\/publication\/68559\/","name":"Two-Part Models for Fractional Responses Defined as Ratios of Integers - WIFO","isPartOf":{"@id":"https:\/\/www.wifo.ac.at\/en\/#website"},"datePublished":"2023-12-01T22:07:55+00:00","dateModified":"2025-10-22T20:24:37+00:00","breadcrumb":{"@id":"https:\/\/www.wifo.ac.at\/en\/publication\/68559\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.wifo.ac.at\/en\/publication\/68559\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.wifo.ac.at\/en\/publication\/68559\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Startseite","item":"https:\/\/www.wifo.ac.at\/en\/"},{"@type":"ListItem","position":2,"name":"Two-Part Models for Fractional Responses Defined as Ratios of Integers"}]},{"@type":"WebSite","@id":"https:\/\/www.wifo.ac.at\/en\/#website","url":"https:\/\/www.wifo.ac.at\/en\/","name":"\u00d6sterreichisches Institut f\u00fcr Wirtschaftsforschung","description":"","publisher":{"@id":"https:\/\/www.wifo.ac.at\/en\/#organization"},"alternateName":"WIFO","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.wifo.ac.at\/en\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/www.wifo.ac.at\/en\/#organization","name":"\u00d6sterreichisches Institut f\u00fcr Wirtschaftsforschung","alternateName":"WIFO","url":"https:\/\/www.wifo.ac.at\/en\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.wifo.ac.at\/en\/#\/schema\/logo\/image\/","url":"https:\/\/www.wifo.ac.at\/wp-content\/uploads\/2024\/05\/WIFO_kurz_rechts-2-1920x412.jpg","contentUrl":"https:\/\/www.wifo.ac.at\/wp-content\/uploads\/2024\/05\/WIFO_kurz_rechts-2-1920x412.jpg","width":2000,"height":429,"caption":"\u00d6sterreichisches Institut f\u00fcr Wirtschaftsforschung"},"image":{"@id":"https:\/\/www.wifo.ac.at\/en\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/WIFOat\/","https:\/\/x.com\/WIFOat","https:\/\/linkedin.com\/company\/wifoat\/","https:\/\/www.youtube.com\/@WIFO_at"],"description":"Das WIFO, 1927 von Friedrich August von Hayek und Ludwig von Mises zur Konjunkturanalyse gegr\u00fcndet, ist heute das f\u00fchrende Institut f\u00fcr angewandte empirische Wirtschaftsforschung in \u00d6sterreich mit starkem Engagement auf europ\u00e4ischer Ebene.","email":"office@wifo.ac.at","telephone":"+43 1 798 26 01 \u2013 0","legalName":"\u00d6sterreichisches Institut f\u00fcr Wirtschaftsforschung","foundingDate":"1927-01-02","numberOfEmployees":{"@type":"QuantitativeValue","minValue":"51","maxValue":"200"},"publishingPrinciples":"https:\/\/www.wifo.ac.at\/institut\/mission-und-strategie\/","ownershipFundingInfo":"https:\/\/www.wifo.ac.at\/institut\/organisation\/","actionableFeedbackPolicy":"https:\/\/www.wifo.ac.at\/aktuelles\/presse\/","correctionsPolicy":"https:\/\/www.wifo.ac.at\/institut\/kontakt\/","ethicsPolicy":"https:\/\/www.wifo.ac.at\/institut\/evidenzbasierung-transparenz-und-unabhaengigkeit\/","diversityPolicy":"https:\/\/www.wifo.ac.at\/institut\/gleichstellung\/","diversityStaffingReport":"https:\/\/www.wifo.ac.at\/institut\/gleichstellung\/"}]}},"_links":{"self":[{"href":"https:\/\/www.wifo.ac.at\/en\/wp-json\/wp\/v2\/publication\/68559","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wifo.ac.at\/en\/wp-json\/wp\/v2\/publication"}],"about":[{"href":"https:\/\/www.wifo.ac.at\/en\/wp-json\/wp\/v2\/types\/publication"}],"version-history":[{"count":1,"href":"https:\/\/www.wifo.ac.at\/en\/wp-json\/wp\/v2\/publication\/68559\/revisions"}],"predecessor-version":[{"id":414549,"href":"https:\/\/www.wifo.ac.at\/en\/wp-json\/wp\/v2\/publication\/68559\/revisions\/414549"}],"acf:post":[{"embeddable":true,"href":"https:\/\/www.wifo.ac.at\/en\/wp-json\/wp\/v2\/person\/3785"},{"embeddable":true,"href":"https:\/\/www.wifo.ac.at\/en\/wp-json\/wp\/v2\/person\/3600"},{"embeddable":true,"href":"https:\/\/www.wifo.ac.at\/en\/wp-json\/wp\/v2\/research_group\/3491"},{"embeddable":true,"href":"https:\/\/www.wifo.ac.at\/en\/wp-json\/wp\/v2\/publication_type\/83083"}],"wp:attachment":[{"href":"https:\/\/www.wifo.ac.at\/en\/wp-json\/wp\/v2\/media?parent=68559"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}