Normalizations and Misspecification in Skill Formation Models

• 成果类型: Article; Early Access
• 署名作者: Freyberger, Joachim
• 署名单位: University of Bonn
• 刊物名称: REVIEW OF ECONOMIC STUDIES
• ISSN/ISSBN: 0034-6527
• DOI: 10.1093/restud/rdaf078
• 发表日期: 2025
• 关键词: identification; TECHNOLOGY; INEQUALITY

摘要

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.