{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T19:59:16Z","timestamp":1783454356027,"version":"3.55.0"},"reference-count":39,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2025,9,4]],"date-time":"2025-09-04T00:00:00Z","timestamp":1756944000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/100010663","name":"European Research Council","doi-asserted-by":"publisher","award":["ERC-2020-STG-949319"],"award-info":[{"award-number":["ERC-2020-STG-949319"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,7,7]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>An important class of structural models studies the determinants of skill formation and the optimal timing of interventions. In this article, I provide new identification results for these models and investigate the effects of seemingly innocuous scale and location restrictions on parameters of interest. To do so, I first characterize the identified set of all parameters without these additional restrictions and show that important policy-relevant parameters are point identified under weaker assumptions than commonly used in the literature. The implications of imposing standard scale and location restrictions depend on how the model is specified, but they generally impact the interpretation of parameters and may affect counterfactuals. Importantly, with the popular constant elasticity of substitution (CES) production function, commonly used scale restrictions fix identified parameters and lead to misspecification. Consequently, simply changing the units of measurements of observed variables might yield ineffective investment strategies and misleading policy recommendations. I show how existing estimators can easily be adapted to solve these issues. As a byproduct, this article also presents a general and formal definition of when restrictions are truly normalizations.<\/jats:p>","DOI":"10.1093\/restud\/rdaf078","type":"journal-article","created":{"date-parts":[[2025,8,29]],"date-time":"2025-08-29T11:43:00Z","timestamp":1756467780000},"page":"2574-2604","source":"Crossref","is-referenced-by-count":1,"title":["Normalizations and Misspecification in Skill Formation Models"],"prefix":"10.1093","volume":"93","author":[{"given":"Joachim","family":"Freyberger","sequence":"first","affiliation":[{"name":"University of Bonn ,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2025,9,4]]},"reference":[{"key":"2026070714414788500_rdaf078-B1","doi-asserted-by":"crossref","first-page":"1569","DOI":"10.1093\/restud\/rdac062","article-title":"Managerial Quality and Productivity Dynamics","volume":"90","author":"Adhvaryu","year":"2023","journal-title":"The Review of Economic Studies"},{"key":"2026070714414788500_rdaf078-B2","author":"Agostinelli","year":"2016"},{"key":"2026070714414788500_rdaf078-B3","author":"Agostinelli","year":"2016"},{"key":"2026070714414788500_rdaf078-B4","doi-asserted-by":"crossref","first-page":"846","DOI":"10.1086\/733396","article-title":"Estimating the Technology of Children\u2019s Skill Formation","volume":"133","author":"Agostinelli","year":"2025","journal-title":"Journal of Political Economy"},{"key":"2026070714414788500_rdaf078-B5","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/s11129-014-9147-5","article-title":"Identification and Counterfactuals in Dynamic Models of Market Entry and Exit","volume":"12","author":"Aguirregabiria","year":"2014","journal-title":"Quantitative Marketing and Economics"},{"key":"2026070714414788500_rdaf078-B6","author":"Anderson","year":"1956"},{"key":"2026070714414788500_rdaf078-B7","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1257\/aer.20150183","article-title":"Estimating the Production Function for Human Capital: Results from a Randomized Control Trial in Colombia","volume":"110","author":"Attanasio","year":"2020","journal-title":"American Economic Review"},{"key":"2026070714414788500_rdaf078-B8","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1146\/annurev-economics-092821-053234","article-title":"Early Childhood Development, Human Capital, and Poverty","volume":"14","author":"Attanasio","year":"2022","journal-title":"Annual Review of Economics"},{"key":"2026070714414788500_rdaf078-B9","doi-asserted-by":"crossref","first-page":"2511","DOI":"10.1093\/restud\/rdaa026","article-title":"Human Capital Development and Parental Investment in India","volume":"87","author":"Attanasio","year":"2020","journal-title":"The Review of Economic Studies"},{"key":"2026070714414788500_rdaf078-B10","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/j.red.2017.02.002","article-title":"Human Capital Growth and Poverty: Evidence from Ethiopia and Peru","volume":"25","author":"Attanasio","year":"2017","journal-title":"Review of Economic Dynamics"},{"key":"2026070714414788500_rdaf078-B11","doi-asserted-by":"crossref","first-page":"2905","DOI":"10.1086\/715417","article-title":"The Path to College Education: The Role of Math and Verbal Skills","volume":"129","author":"Aucejo","year":"2021","journal-title":"Journal of Political Economy"},{"key":"2026070714414788500_rdaf078-B12","author":"Bolt","year":"2024"},{"key":"2026070714414788500_rdaf078-B13","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1086\/704759","article-title":"Early and Late Human Capital Investments, Borrowing Constraints, and the Family","volume":"128","author":"Caucutt","year":"2020","journal-title":"Journal of Political Economy"},{"key":"2026070714414788500_rdaf078-B14","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.jeconom.2015.01.001","article-title":"Nonparametric Identification and Estimation of Transformation Models","volume":"188","author":"Chiappori","year":"2015","journal-title":"Journal of Econometrics"},{"key":"2026070714414788500_rdaf078-B15","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1111\/j.1475-5890.2011.00138.x","article-title":"Recent Developments in the Identification and Estimation of Production Functions of Skills","volume":"32","author":"Cunha","year":"2011","journal-title":"Fiscal Studies"},{"key":"2026070714414788500_rdaf078-B16","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1257\/aer.97.2.31","article-title":"The Technology of Skill Formation","volume":"97","author":"Cunha","year":"2007","journal-title":"American Economic Review"},{"key":"2026070714414788500_rdaf078-B17","doi-asserted-by":"crossref","first-page":"738","DOI":"10.1353\/jhr.2008.0019","article-title":"Formulating, Identifying and Estimating the Technology of Cognitive and Noncognitive Skill Formation","volume":"43","author":"Cunha","year":"2008","journal-title":"Journal of Human Resources"},{"key":"2026070714414788500_rdaf078-B18","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1162\/JEEA.2009.7.2-3.320","article-title":"The Economics and Psychology of Inequality and Human Development","volume":"7","author":"Cunha","year":"2009","journal-title":"Journal of the European Economic Association"},{"key":"2026070714414788500_rdaf078-B19","doi-asserted-by":"crossref","first-page":"883","DOI":"10.3982\/ECTA6551","article-title":"Estimating the Technology of Cognitive and Noncognitive Skill Formation","volume":"78","author":"Cunha","year":"2010","journal-title":"Econometrica: Journal of the Econometric Society"},{"key":"2026070714414788500_rdaf078-B20","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1093\/restud\/rdt026","article-title":"Household Choices and Child Development","volume":"81","author":"Del Boca","year":"2013","journal-title":"The Review of Economic Studies"},{"key":"2026070714414788500_rdaf078-B21","doi-asserted-by":"crossref","first-page":"1256","DOI":"10.1002\/jae.2929","article-title":"Identification of Dynamic Latent Factor Models of Skill Formation with Translog Production","volume":"37","author":"Del Bono","year":"2022","journal-title":"Journal of Applied Econometrics"},{"key":"2026070714414788500_rdaf078-B22","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1017\/S0266466611000831","article-title":"Some Extensions of a Lemma of Kotlarski","volume":"28","author":"Evdokimov","year":"2012","journal-title":"Econometric Theory"},{"key":"2026070714414788500_rdaf078-B23","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1086\/677232","article-title":"How the Allocation of Children\u2019s Time Affects Cognitive and Noncognitive Development","volume":"32","author":"Fiorini","year":"2014","journal-title":"Journal of Labor Economics"},{"key":"2026070714414788500_rdaf078-B24","doi-asserted-by":"crossref","first-page":"1824","DOI":"10.1093\/restud\/rdx052","article-title":"Nonparametric Panel Data Models with Interactive Fixed Effects","volume":"85","author":"Freyberger","year":"2018","journal-title":"Review of Economic Studies"},{"key":"2026070714414788500_rdaf078-B25","author":"Gallipoli","year":"2023"},{"key":"2026070714414788500_rdaf078-B26","author":"Gao","year":"2021"},{"key":"2026070714414788500_rdaf078-B27","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1080\/07474930701220329","article-title":"Normalization in Econometrics","volume":"26","author":"Hamilton","year":"2007","journal-title":"Econometric Reviews"},{"key":"2026070714414788500_rdaf078-B28","doi-asserted-by":"crossref","first-page":"2052","DOI":"10.1257\/aer.103.6.2052","article-title":"Understanding the Mechanisms Through Which an Influential Early Childhood Program Boosted Adult Outcomes","volume":"103","author":"Heckman","year":"2013","journal-title":"American Economic Review"},{"key":"2026070714414788500_rdaf078-B29","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1016\/j.jdeveco.2010.03.001","article-title":"The Formation and Evolution of Childhood Skill Acquisition: Evidence from India","volume":"95","author":"Helmers","year":"2011","journal-title":"Journal of Development Economics"},{"key":"2026070714414788500_rdaf078-B30","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1007\/s13524-017-0554-6","article-title":"Children\u2019s Development and Parental Input: Evidence from the UK Millennium Cohort Study","volume":"54","author":"Hern\u00e1ndez-Alava","year":"2017","journal-title":"Demography"},{"key":"2026070714414788500_rdaf078-B31","doi-asserted-by":"crossref","first-page":"351","DOI":"10.3982\/QE1253","article-title":"Identification of Counterfactuals in Dynamic Discrete Choice Models","volume":"12","author":"Kalouptsidi","year":"2021","journal-title":"Quantitative Economics"},{"key":"2026070714414788500_rdaf078-B32","doi-asserted-by":"crossref","first-page":"1153","DOI":"10.3982\/QE675","article-title":"Joint Analysis of the Discount Factor and Payoff Parameters in Dynamic Discrete Choice Models","volume":"9","author":"Komarova","year":"2018","journal-title":"Quantitative Economics"},{"key":"2026070714414788500_rdaf078-B33","doi-asserted-by":"crossref","first-page":"835","DOI":"10.1257\/jel.20181361","article-title":"The Identification Zoo: Meanings of Identification in Econometrics","volume":"57","author":"Lewbel","year":"2019","journal-title":"Journal of Economic Literature"},{"key":"2026070714414788500_rdaf078-B34","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/BF02289693","article-title":"Instrumental Variables in Factor Analysis","volume":"29","author":"Madansky","year":"1964","journal-title":"Psychometrika"},{"key":"2026070714414788500_rdaf078-B35","author":"Matzkin","year":"1994"},{"key":"2026070714414788500_rdaf078-B36","author":"Matzkin","year":"2007"},{"key":"2026070714414788500_rdaf078-B37","doi-asserted-by":"crossref","first-page":"S99","DOI":"10.1086\/683779","article-title":"Human Capital Investment, Inequality, and Economic Growth","volume":"34","author":"Murphy","year":"2016","journal-title":"Journal of Labor Economics"},{"key":"2026070714414788500_rdaf078-B38","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1111\/j.1467-937X.2009.00578.x","article-title":"Structural Vector Autoregressions: Theory of Identification and Algorithms for Inference","volume":"77","author":"Rubio-Ram\u00edrez","year":"2010","journal-title":"The Review of Economic Studies"},{"key":"2026070714414788500_rdaf078-B39","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1080\/07474938.2018.1550042","article-title":"Identification of the Linear Factor Model","volume":"39","author":"Williams","year":"2020","journal-title":"Econometric Reviews"}],"container-title":["Review of Economic Studies"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/restud\/advance-article-pdf\/doi\/10.1093\/restud\/rdaf078\/64204886\/rdaf078.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/restud\/article-pdf\/93\/4\/2574\/64204886\/rdaf078.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/restud\/article-pdf\/93\/4\/2574\/64204886\/rdaf078.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T18:41:56Z","timestamp":1783449716000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/restud\/article\/93\/4\/2574\/8247752"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,4]]},"references-count":39,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,9,4]]},"published-print":{"date-parts":[[2026,7,7]]}},"URL":"https:\/\/doi.org\/10.1093\/restud\/rdaf078","relation":{},"ISSN":["0034-6527","1467-937X"],"issn-type":[{"value":"0034-6527","type":"print"},{"value":"1467-937X","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,7]]},"published":{"date-parts":[[2025,9,4]]}}}