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Advances in evidence-based neonatal care have led to large improvements in the survival rates of high-risk newborns. Yet studies have documented wide variation in the care of more prevalent moderate-risk infants, who comprise a much larger proportion of admissions to neonatal care. In this study, we build on a small literature which uses quasi-experimental design to understand the impact of neonatal care, and for the first time, examine this moderate-risk cohort of infants. We use individual-level data on the full population of births in the state of New South Wales, Australia to examine the impact of neonatal care on the healthcare use of moderate-risk infants in the first two years of life. We implement a regression discontinuity design exploiting admission protocols based on birthweight among neonatal units of three different and explicit levels of capability. Unlike previous studies, which examine differences in outcomes across the high-risk cut-off at 1500 g, our study examines differences for moderate-risk infants born near birthweight cut-offs closer to normal birth weight (2500 g). While admission to the neonatal unit jumps across the cut-off, we find modest impacts on downstream healthcare use, including both in-hospital and out-of-hospital care. However, we identify heterogeneous effects across varying capability levels. Moderate risk infants admitted to lower capability neonatal units received more cost-intensive care, resulting in reduced healthcare use following discharge from hospital, while the same was not observed for those admitted to the highest capability units. We suggest that this is due to more aggressive clinical management at lower capability units, and leave this as a priority for future research.