To estimate the effect of breastfeeding initiation and duration on child development outcomes. 3,271 children and their mothers participating in the Child Development Supplement of the Panel Study of Income Dynamics provide data for these analyses. Main outcomes include Woodcock Johnson Psycho-Educational Battery-Revised (WJ-R) test score (letter word, passage comprehension, applied problem, and broad reading), and Wechsler Intelligence Scale for Children-Revised (WISC-R) test score at the 2002 survey. Controlled variables include family, maternal, and child characteristics, many of which can be traced back to the year the child was born. The analytic technique is propensity score matching with multiple imputations. After using propensity scores to adjust for confounding factors, breastfeeding initiation showed statistically significant effects but the practical scale remains small. Breastfeeding duration showed a non-linear effect on those outcomes and most of the effects are not significant. The effects of breastfeeding on child's cognitive outcomes are modest in practical terms. The non-linear effects suggest that selection into breastfeeding may account for the increased score of children who are breastfed.