In policy research a frequent aim is to estimate treatment effects separately by subgroups. This endeavor becomes a methodological challenge when the subgroups are defined by post-treatment, rather than pre-treatment, variables because if analyses are performed in the same way as with...

Using data from the Child Care Supplement to the Fragile Families and Child Wellbeing Study, we test associations between the quality of child care and state child care policies. These data, which include observations of child care and interviews with care providers and mothers for 777 children...