Signal-to-noise ratios.

Parental behavior is paramount to child health and skill formation, explaining a significant portion of differences in developmental outcomes. However, little is known regarding the distributional effects of parental time allocation at different levels of children’s outcomes. I use a national administrative dataset of Chilean pre-school students to the estimate production functions for socioemotional development and body mass index z-scores at every decile of the distribution at baseline. Modest average effects conceal significant heterogeneity on the returns to parental time investments. Children in the bottom of the socioemotional development distribution could gain up to 0.4 standard deviations for a one standard deviation increase in time investments. A similar increase can lead to a reduction of 0.8 standard deviations in body mass index among severely obese students. Evidence reveals that children with high developmental scores are unlikely to benefit from additional parenting time.