This article describes a conceptual and empirical approach for estimating a human capital production function of child development that incorporates mother- or child-fixed effects. The use of mother- or child-fixed effects is common in this applied economics literature, but its application is often inconsistent with human capital theory. We outline the problem and demonstrate its empirical importance with an analysis of the effect of Head Start and preschool on child and adult outcomes. The empirical specification we develop has broad implications for a variety of applied microeconomic analyses beyond our specific application. Results of our analysis indicate that attending Head Start or preschool had no economically or statistically significant effect on child or adult outcomes.