Estimating the Technology of Children's Skill Formation
NBER Working Paper No. 22442
In this paper we study the process of children's skill formation. The identification of this process is challenging because children's skills are observed only through arbitrarily scaled and imperfect measures. Using a dynamic la- tent factor structure, we provide new identification results which illuminate the key identification trade-offs between restrictions on the skill production technology and the measurement relationships. One of our contributions is to develop empirically grounded restrictions on the measurement process that allow identification of more general production technologies, including those exhibiting Hicks neutral total factor productivity (TFP) dynamics and free returns to scale. We then use our identification results to develop a sequential estimation algorithm for the joint dynamic process of latent investment and skill development. Using data for the United States, we estimate different versions of the skill formation model under various identifying assumptions. Although all of our estimated models suggest that investments are particularly productive during early childhood. Moreover, we find that the marginal productivity of early investments is substantially higher for children with lower existing skills, suggesting the optimal targeting of interventions to disadvantaged children. When we compare these estimates to those using models which restrict the technology or ignore measurement error, we estimate policy effects which are substantially smaller, indicating that the generalities we allow are important to answering key policy questions.
Document Object Identifier (DOI): 10.3386/w22442
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