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

Liam Puknys

Papers from arXiv.org

Abstract: Program evaluations routinely find larger returns to investment in low-skill children, while structural models of skill formation typically find that skill and investment are complements. I show that these findings are not in tension: they measure different objects. The Beckerian schedule of returns (BSR) is the elasticity of output with respect to an input, holding all inputs at fixed values; average marginal returns (AMR) average that elasticity over the joint distribution of inputs. Revisiting Cunha, Heckman, and Schennach (2010)'s model of child skill formation on the Children of the NLSY79, I find that skill and investment are complements, but that low-skill children receive so much less investment that their AMR to investment is higher in early childhood --- a pattern that reverses at later ages. The framework also provides a natural way to sign bias from curvature in log-linear models with interaction terms, which conflate the BSR and AMR and accurately estimate neither; adding quadratic terms both reduces this bias and often strengthens estimated interaction effects. Methodologically, I model discrete proxies with an ordered probit measurement system --- treating them as continuous biases AMR estimates and fails to detect that low-skill children have higher AMR than high-skill children in early childhood --- and introduce effective factors, a scaling system that allows latent factors to take different effective scales when producing different skills in the same period. Finally, conditional on maternal permanent income, current household income has no predictive power for parental investment, undermining the exogenous variation on which the standard control-function approach relies and cautioning a descriptive interpretation of my estimates.

Date: 2026-10
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