The assessment of the impact of social programs is the subject of lively, sometimes heated debate over whether program evaluation is best conducted either by comparing mean outcomes from a randomized intervention or by using econometric techniques with nonrandom samples. This paper contributes to this debate through an examination of PROGRESA, a Mexican anti-poverty and human resource program, on child nutritional status. PROGRESA was randomly assigned at the locality level. However, a shortage in the availability of one component- a nutritional supplement provided to preschool children -led local administrators to exercise discretion in its delivery, systematically favoring those children with poorer nutritional status. While comparisons of mean outcomes suggest that PROGRESA had no or a negative effect on nutritional status, estimates that control for this heterogeneity using child specific fixed effects find that PROGRESA had significant and substantial positive impacts in increasing stature. The long-term consequences of these improvements are non-trivial; its impact working through adult height alone may result in a 2.9% increase in lifetime earnings.