{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T18:31:12Z","timestamp":1772303472131,"version":"3.50.1"},"reference-count":43,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T00:00:00Z","timestamp":1694736000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Grants-in-Aid for Scientific Research","award":["19K02006"],"award-info":[{"award-number":["19K02006"]}]},{"name":"Grants-in-Aid for Scientific Research","award":["22K01431"],"award-info":[{"award-number":["22K01431"]}]},{"name":"Grants-in-Aid for Scientific Research","award":["22H00834"],"award-info":[{"award-number":["22H00834"]}]},{"name":"Grants-in-Aid for Scientific Research","award":["23K01689"],"award-info":[{"award-number":["23K01689"]}]},{"name":"Grants-in-Aid for Scientific Research","award":["2023-ISMCRP-2017"],"award-info":[{"award-number":["2023-ISMCRP-2017"]}]},{"name":"Grants-in-Aid for Scientific Research","award":["jh231001"],"award-info":[{"award-number":["jh231001"]}]},{"name":"ISM Cooperative Research Program","award":["19K02006"],"award-info":[{"award-number":["19K02006"]}]},{"name":"ISM Cooperative Research Program","award":["22K01431"],"award-info":[{"award-number":["22K01431"]}]},{"name":"ISM Cooperative Research Program","award":["22H00834"],"award-info":[{"award-number":["22H00834"]}]},{"name":"ISM Cooperative Research Program","award":["23K01689"],"award-info":[{"award-number":["23K01689"]}]},{"name":"ISM Cooperative Research Program","award":["2023-ISMCRP-2017"],"award-info":[{"award-number":["2023-ISMCRP-2017"]}]},{"name":"ISM Cooperative Research Program","award":["jh231001"],"award-info":[{"award-number":["jh231001"]}]},{"name":"Joint Usage\/Research Center for Interdisciplinary Large-scale Information Infrastructures","award":["19K02006"],"award-info":[{"award-number":["19K02006"]}]},{"name":"Joint Usage\/Research Center for Interdisciplinary Large-scale Information Infrastructures","award":["22K01431"],"award-info":[{"award-number":["22K01431"]}]},{"name":"Joint Usage\/Research Center for Interdisciplinary Large-scale Information Infrastructures","award":["22H00834"],"award-info":[{"award-number":["22H00834"]}]},{"name":"Joint Usage\/Research Center for Interdisciplinary Large-scale Information Infrastructures","award":["23K01689"],"award-info":[{"award-number":["23K01689"]}]},{"name":"Joint Usage\/Research Center for Interdisciplinary Large-scale Information Infrastructures","award":["2023-ISMCRP-2017"],"award-info":[{"award-number":["2023-ISMCRP-2017"]}]},{"name":"Joint Usage\/Research Center for Interdisciplinary Large-scale Information Infrastructures","award":["jh231001"],"award-info":[{"award-number":["jh231001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Based on corporate financial data for almost all companies listed on the Prime Market of the Tokyo Stock Exchange in fiscal year 2021, we gradually refine a model to explain firms\u2019 sales by the number of employees and total assets. Starting from a Cobb\u2013Douglas-type functional form linearized by a log transformation, the assumption of a skew-symmetric distribution in the error structure and the introduction of industry dummies are shown to be useful not only in searching for a good-fitting model, but also in ensuring the accuracy of important parameters such as the labor share. The introduction of industry dummies helps to improve the accuracy of the model as well as to allow for interpretation as sector-wise total factor productivity.<\/jats:p>","DOI":"10.3390\/sym15091772","type":"journal-article","created":{"date-parts":[[2023,9,17]],"date-time":"2023-09-17T06:36:45Z","timestamp":1694932605000},"page":"1772","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Statistical Modeling of Financial Data with Skew-Symmetric Error Distributions"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0010-2798","authenticated-orcid":false,"given":"Masayuki","family":"Jimichi","sequence":"first","affiliation":[{"name":"School of Business Administration, Kwansei Gakuin University, 1-155 Ichiban-cho, Uegahara, Nishinomiya 662-8501, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1830-223X","authenticated-orcid":false,"given":"Yoshinori","family":"Kawasaki","sequence":"additional","affiliation":[{"name":"Department of Statistical Modeling, The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa 190-8569, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0967-9040","authenticated-orcid":false,"given":"Daisuke","family":"Miyamoto","sequence":"additional","affiliation":[{"name":"Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2603-5100","authenticated-orcid":false,"given":"Chika","family":"Saka","sequence":"additional","affiliation":[{"name":"School of Business Administration, Kwansei Gakuin University, 1-155 Ichiban-cho, Uegahara, Nishinomiya 662-8501, Japan"}]},{"given":"Shuichi","family":"Nagata","sequence":"additional","affiliation":[{"name":"School of Business Administration, Kwansei Gakuin University, 1-155 Ichiban-cho, Uegahara, Nishinomiya 662-8501, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,15]]},"reference":[{"key":"ref_1","first-page":"139","article-title":"A Theory of Production","volume":"18","author":"Cobb","year":"1928","journal-title":"Am. 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