In this appendix, we present our summary and critique of Cunha et al (2010) in some depth, to the extent that we are able as it is a formidable technical edifice. The published paper (Cunha et al 2010) is 50 pages long and is dense with mathematical equations and esoteric economic terminology; the supplement with additional important detail is a further 50 pages, and is equally arcane. Condensing this without distortion has been a challenge, but we have endeavoured to pick out key features, limitations, assumptions and implications. Representing a collaboration of three authors, Cunha, Heckman and Schennach, we will henceforth refer to the model presented in their paper as the CHS model.

Befitting economists, Cunha et al refer to their Model of Skill Formation as a ‘production function’, jargon for a mathematical function which describes the relationship between the input (factors of production, such as labour and capital) and the outputs of a ‘production’ system. Treating skill formation in these terms sees the level of skill, at any period in the development of an individual, as the output of inputs from the previous period. The overall time course of skill formation is divided into a number of stages, with each stage made up of several consecutive periods. In the empirically tested model, as we shall see, two such developmental stages are distinguished: 0 to 6 years, and 7 to 14 years, each comprising four two-year periods (the first period is age 0). The model implies that the shape of the production function is specific to each stage, and makes an important distinction between cognitive (intellectual) and noncognitive (socio-emotional) skills.

Key components of the model are described as follows, simplifying slightly from p 886: