Early Investment Snowballs for Low-Skill Children: Average Marginal Returns and the Dynamics of Skill Formation

Program evaluations routinely find larger effects of investment in low-skill children, while structural models of skill formation typically find that skill and investment are complements. I reconcile these findings by introducing the Average Marginal Return (AMR), which averages the marginal return to an input over the distribution of other inputs, providing a structural analogue to the average treatment effects estimated in program evaluations. The AMR reveals why input scales and distributions matter for the economic interpretation of structural estimates, why reduced-form interaction coefficients need not identify technological complementarity, and why dynamic complementarity can be difficult to detect in reduced-form work. I estimate AMRs to parental investment using a dynamic factor model of cognitive and noncognitive skill formation for ages 5-14 in the Children of the NLSY79. I accommodate binary and Likert measures using ordered probits, showing that treating them as continuous substantially biases estimates, and introduce effective factors to extend the scale-invariant normalization of Freyberger (2026) to models with multiple skills per period. Investment in early childhood generates larger long-run gains in cognitive skill than investment at later ages. Although skill and investment are complements, the AMR to early investment is initially flat across skill levels but becomes sharply decreasing in initial skill over time. By ages 13-14, children at the 10th percentile of early cognitive skill gain roughly twice as much from early investment as children at the 90th.