This paper discusses a fundamental problem in measuring the growth of knowledge and comparing the skills of people. New skills emerge that are not just more of the previously acquired skills. Psychometric convention forces these skills into arbitrarily constructed scales, which can severely distort measurement. To formally address this problem, we measure skills using a novel measurement scheme, estimate a stochastic learning process, and reject the common scale assumption across levels for language and cognitive skills. Furthermore, we estimate dynamic complementarity without imposing arbitrary scales for skills.
Heckman et al. (Fri,) studied this question.