{"title":"Gaussian Transforms Modeling and the Estimation of Distributional Regression Functions","authors":"Richard H. Spady, Sami Stouli","doi":"10.3982/ECTA19153","DOIUrl":null,"url":null,"abstract":"<p>We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative distribution functions, including in finite samples and under general misspecification. We use these representations to provide a unified framework for the flexible maximum likelihood estimation of conditional density, cumulative distribution, and quantile functions at parametric rate. Our formulation yields substantial simplifications and finite sample improvements over related methods. An empirical application to the gender wage gap in the United States illustrates our framework.</p>","PeriodicalId":50556,"journal":{"name":"Econometrica","volume":"93 5","pages":"1885-1913"},"PeriodicalIF":7.1000,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.3982/ECTA19153","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Econometrica","FirstCategoryId":"96","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.3982/ECTA19153","RegionNum":1,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ECONOMICS","Score":null,"Total":0}
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Abstract
We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative distribution functions, including in finite samples and under general misspecification. We use these representations to provide a unified framework for the flexible maximum likelihood estimation of conditional density, cumulative distribution, and quantile functions at parametric rate. Our formulation yields substantial simplifications and finite sample improvements over related methods. An empirical application to the gender wage gap in the United States illustrates our framework.
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Econometrica publishes original articles in all branches of economics - theoretical and empirical, abstract and applied, providing wide-ranging coverage across the subject area. It promotes studies that aim at the unification of the theoretical-quantitative and the empirical-quantitative approach to economic problems and that are penetrated by constructive and rigorous thinking. It explores a unique range of topics each year - from the frontier of theoretical developments in many new and important areas, to research on current and applied economic problems, to methodologically innovative, theoretical and applied studies in econometrics.
Econometrica maintains a long tradition that submitted articles are refereed carefully and that detailed and thoughtful referee reports are provided to the author as an aid to scientific research, thus ensuring the high calibre of papers found in Econometrica. An international board of editors, together with the referees it has selected, has succeeded in substantially reducing editorial turnaround time, thereby encouraging submissions of the highest quality.
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