Timothy Taylor looks at various meta-analyses of studies of the possible causal role of the absence of a father on outcomes for the children. He quotes a meta-analysis by Sara McLanahan and others

The research base examining the longer-term effects of father absence on adult outcomes is considerably smaller, but here too we see the strongest evidence for a causal effect on adult mental health, suggesting that the psychological harms of father absence experienced during childhood persist throughout the life course. The evidence that father absence affects adult economic or family outcomes is much weaker. A handful of studies find negative effects on employment in adulthood, but there is little consistent evidence of negative effects on marriage or divorce, on income or earnings, or on college education.

Read Taylor’s whole post. He and the authors he cites are quite aware of the difficulty of distinguishing correlation from causation in this sort of research.