Why do larger families reduce parental investments in child quality, but not child quality per se?

Becker's Quantity-Quality model (Becker in Demographic and economic change in developed countries, Princeton University Press, Princeton, pp 209-240, 1960; Becker and Lewis in J Polit Econ 81(2): S279-S288, 1973; Becker and Tomes in J Polit Econ 84(4): S143-S162, 1976) suggests a trade-off between family size and parental investments in children. To date, only Caceras-Delpiano (J Hum Resour 41(4): 738-754, 2006) tests this theory by considering private school enrolment. This study extends this work by using a unique data set containing a broader range of parental investments that are arguably linked to parental intentions for producing higher quality children, such as overall and nonsectarian private school enrolment, the number of computers in the home per child, and saving for the child's education. Both studies find that fertility reduces parental investments. However, the literature generally finds that fertility has no impact on child outcomes. The study offers three potential explanations for this 'puzzle'.