Final Regression Results on the Cognitive Achievement of Children in the Christchurch Health and Development Study with Corrections for Attrition from this Longitudinal Study

Econometric analyses of the cognitive development of children have been hampered by data limitations and a variety of methodological and specification issues. Structural models allow for complex causal relationships between child achievement and inputs from parents, schools and communities, but these effects are difficult to isolate. Even reduced-form models suffer from both omitted-variable (e.g., unobserved family and community investments) and simultaneous-equation bias (e.g., endogenous private schooling and class size). The use of panel data offers the best non-experimental solution to these estimation issues. With multiple observations on test performance of children between the ages of 8 and 13 in the Christchurch Health and Development Study, we are able to hold constant individual- specific, time-invariant factors that influence cognitive achievement. These data permit several insights into the dynamic nature of this cognitive achievement process. We cannot reject the null hypothesis that the lagged dependent variable serves as a “sufficient statistic” for all past determinants of cognitive achievement. This provides the first statistical justification for the “value-added approach” recommended of Hanushek (1986), and actually diminishes the need for these longer longitudinal studies. Procedures are developed for testing for the presence of unobserved fixed-effects in this cognitive development process, and correcting for the effects of attrition from this panel. No evidence is found that the value-added to cognitive achievement is influenced by the number of parents in the family, the work status of the mother, the benefit status of the family, the income of the family and the type of school attended. Evidence is also found of a positive effect of class size on cognitive development. Our interpretation is that class size is endogenous, and the causality may be reversed (i.e., children with poor reading performances are intentionally placed in smaller classes). Yet, no evidence is found of the hypothesised negative effect of class size on cognitive achievement with an anti- instrumental-variable approach.