An interesting study by: W. Bradford Wilcox and Laurie DeRose
Our results suggest that there is something about marriage per se that bolsters stability. It could be the elaborate ritual marking the entry into marriage; the norms of commitment, fidelity, and permanence associated with the institution; the distinctive treatment of family and friends extended to married couples; or, most likely, a combination of all these things and more — that promotes greater commitment and stability.
By contrast, the very freedom and flexibility that makes cohabitation so attractive to some adults means that cohabitation is per se less institutionalized and therefore less stable. That’s why, even in highly developed and secular societies found in Europe, the institution of marriage is imbued with a stability advantage that benefits children.