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The report, published today by the Family First lobby group, says the near-trebling of sole parents from 10 per cent of families with dependent children in 1976 to 28 per cent of families in the last two censuses is "the elephant in the room" in the child poverty debate.
Child poverty has tracked sole parenting almost exactly. Children in homes earning below 60 per cent of the median household income rose from 14 per cent in 1982 to 30 per cent in 2001, then declined to 22 per cent by 2007, although they have risen again recently.
"The correlation between sole parent and child poverty rates is stronger than between unemployment and child poverty rates," says the report, by welfare commentator Lindsay Mitchell.
"Unemployment, low wages, high housing costs and insufficient social security benefits are consistently blamed for child poverty, yet a major culprit (if not the major culprit) is family malformation, that is, a lack of two married committed parents."
Sole parents are naturally poorer than couples, on average, because they have only one potential income earner who often can't work fulltime because of the children.
In 2014, 62 per cent of sole parents' children lived in homes earning less than 60 per cent of the median income, compared with only 15 per cent of children in two-parent homes.
The report links the rise of separated parents to the growing acceptance of living together outside formal marriage. Children born to legally married couples plunged from 95 per cent of births in 1961 to 51.3 per cent in 2010, before recovering in each year since then to 53.5 per cent in the latest March year.
For Maori, children born to legally married parents collapsed even more spectacularly from 72 per cent of Maori births in 1968 to just 20.9 per cent in 2011, recovering to 21.6 per cent in the latest year.
The report quotes Australian data showing that de-facto couples are much more likely than married couples to break up within five years, and that the five-year separation rate increased much faster for de-facto couples (from 25 per cent in the 1970s to 38 per cent in the 1990s) than for married couples (from 7 per cent to 9 per cent).
It says another factor promoting separation was the creation of the sole parent benefit in 1974, making parents who are both unemployed better off by splitting to get two separate benefits.
This factor was more important when unemployment was high in the 1990s, and the decline in unemployment since may help to explain the recent slight decline in sole parenting.
However, Dr Susan St John of the Child Poverty Action Group said the report ignored the fact that marriage was not always good for women or their children.
"Intimate partner violence is not mentioned, nor the high rate of incarceration, especially of Maori males," she said. "The policy implications of this report, to reduce the safety net yet further and stigmatise the unwed, are extremely dangerous."