  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.
