The Infant Health and Development Program (IHDP) was designed to promote the development of low-birth weight (up to 2,500 grams) and premature (up to 37 weeks gestational age) infants. There is evidence that the IHDP intervention, a randomly-assigned bundle of services including primarily free, high-quality child care from 12 to 36 months, boosted cognitive and behavioral outcomes by the time participants at the end of the intervention. The literature has established that the intervention was more effective among the subsample of heavier low birth weight (2,000-2,500 grams) than among those born lighter. Among the heavier group, it was more effective for children from lower-income families. Families who participated in the intervention were diverse in key observable characteristics like income, race or ethnicity. In addition, families reallocated their time in different ways when then had the opportunity to use the free services provided by the IHDP. The goal of this paper is to understand the economic decisions and constraints faced by households who gained access to the IHDP and explain their differential behavior. In order to do so, we propose an economic model, construct measures of theoretically-relevant drivers of postnatal investment decisions, and explore patterns of heterogeneity in parental response and child development along these dimensions. (author abstract)