The authors interpret their findings to mean that family structure may not be as consequential as many people think:
Various scholars (Cherlin, 2014; McLanahan and Percheski, 2008; Putnam 2016; Wax 2007) have claimed that family structure (and single motherhood in particular) is an important factor explaining differences in life outcomes across socioeconomic groups in Western countries.The problem with the authors' interpretation is, however, that their comparison is between children whose parents were married and then either separated or stayed together. The authors whom they cite are much more focused on out-of-wedlock childbearing. As I have noted myself, especially in reference to the work of Isabel Sawhill, but also to that of Andrew Cherlin (a Past President of the Population Association of America), the evidence is very strong that children growing up in a single-parent household (typically the mother, and sometimes without any recognition of the existence of the birth father) are at a disadvantage relative to other children. The relationship may be complex, but it cannot be dismissed.