Classroom quality is critical for young children's learning, yet evidence suggests that the quality of early care and education (ECE) classrooms varies widely, even within the federally-administered Head Start program. This study uses data from the nationally-representative Head Start Impact Study to examine variation in children's access to formal and high quality ECE by policy characteristics that demonstrate a state's commitment and approach to regulating ECE quality. Findings support existing evidence of the impact of randomization to Head Start on children's access to formal and high quality ECE, and expand our understanding of the ways in which these impacts vary. We find that stronger child care licensing regulations and other indicators of a child-friendly policy climate are associated with a smaller contrast between the Head Start versus control groups' access to both formal and high quality ECE. This study also offers initial evidence that state regulations targeting the quality of an ECE program's professional environment may be particularly critical for high quality classrooms. (author abstract)