Family size, cognitive outcomes, and familial interaction in stable, two-parent families: United States, 1997-2002.

Measures of children's time use, particularly with parents and siblings, are used to evaluate three hypotheses in relation to the vocabulary and mathematical skills development: (1) the resource dilution hypothesis, which argues that parental and household resources are diluted in larger families; (2) the confluence hypothesis, which suggests that the intellectual milieu of families is lowered with additional children; and (3) the admixture ("no effect") hypothesis, which suggests that the negative relationship between family size and achievement is an artifact of cross-sectional research resulting from unobserved heterogeneity. Each hypothesis is tested using within-child estimates of change in cognitive scores over time with the addition of new children to families.