Abstract

An important class of structural models investigates the determinants of skill formation and the optimal timing of interventions. To achieve point identification of the parameters, researcher typically normalize the scale and location of the unobserved skills.  This paper shows that these seemingly innocuous restrictions can severely impact the interpretation of the parameters and counterfactual predictions. For example, simply changing the units of measurements of observed variables might yield ineffective investment strategies and misleading policy recommendations. To tackle these problems, this paper provides a new identification analysis, which pools all restrictions of the model, characterizes the identified set of all parameters without normalizations, illustrates which features depend on these normalizations, and introduces a new set of important policy-relevant parameters that are identified under weak assumptions and yield robust conclusions. As a byproduct, this paper also presents a general and formal definition of when restrictions are truly normalizations.

Professor Joachim Freyberger is an econometrician at the University of Bonn. Before joining Bonn, he was an Assistant Professor at the University of Wisconsin-Madison. His work has focuses on identification, estimation, and inference issues in nonparametric models with endogeneity as well as empirical applications in industrial economics and finance.

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