Math Skills, Selection in Training Firms, and Post-Training Wages

This paper analyzes the association between an individual's mathematical skills in ninth grade, the subsequent selection process in firm-based apprenticeship training, and post-training skilled worker wages. Using data from the National Educational Panel Study and the Institute for Employment Research, we show that math skills are associated with training placements in larger and higher-paying firms, as well as higher subsequent skilled worker wages. Furthermore, we apply instrumental variables regression to account for measurement error in standardized math test scores. We find that a one-standard deviation increase in math skills is initially associated with a 36% increase in initial post-training earnings, reducing to 10% after five years. Our results suggest that math skills help school leavers find an apprenticeship in firms in which they have a comparative advantage, thereby increasing allocation efficiency. Moreover, when we control for observable cognitive and non-cognitive skills, we find that female school-leavers sort into lower-paying training firms. This selection accounts for a significant portion of the gender wage gap observed later among women who continue their careers as skilled workers within their training firms.