Journal of Productivity Analysis

, Volume 38, Issue 1, pp 29–44 | Cite as

Child maturation, time-invariant, and time-varying inputs: their interaction in the production of child human capital

  • Mark D. Agee
  • Scott E. Atkinson
  • Thomas D. Crocker


We model the relationship over time between multiple good and bad inputs to the child development production process and the multiple good and bad outcomes which are generated. Doing this avoids several well-known empirical problems associated with construction and use of aggregated inputs and outputs, the assumption of separability among inputs and outputs, and the estimation of reduced forms. Using time-demeaned data for a balanced panel of families from the National Longitudinal Survey of Youth–Child Sample for 1994–2000, we estimate an output-oriented directional distance function that simultaneously relates good and bad inputs from home, school, and environment, to good and bad outcomes, measured as children’s math and reading test scores as well as parent-reported behavior problems. We are able for the first time to compute partial effects among endogenous outputs. Recovering consistent estimates of time-invariant coefficients using a second-stage estimator, we find that some time-invariant variables are significant. We also measure productivity growth, technical change, efficiency change, and technical efficiency. Children’s productivity growth is highest at age 5 years and diminishes thereafter. Finally, we investigate the effect on these estimates of the choice of alternative direction vectors for the good and bad outputs.


Child human capital Stochastic frontiers Productivity change 

JEL Classification

I12 J13 C14 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Mark D. Agee
    • 1
  • Scott E. Atkinson
    • 2
  • Thomas D. Crocker
    • 3
  1. 1.Department of EconomicsPennsylvania State UniversityAltoonaUSA
  2. 2.Department of EconomicsUniversity of GeorgiaAthensUSA
  3. 3.Department of Economics and FinanceUniversity of WyomingLaramieUSA

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