Maybe less than you thought, at least after adjusting for other variables. The Economist reports:
In Sweden the age of criminal responsibility is 15, so Mr Sariaslan tracked his subjects from the dates of their 15th birthdays onwards, for an average of three-and-a-half years. He found, to no one’s surprise, that teenagers who had grown up in families whose earnings were among the bottom fifth were seven times more likely to be convicted of violent crimes, and twice as likely to be convicted of drug offences, as those whose family incomes were in the top fifth.
What did surprise him was that when he looked at families which had started poor and got richer, the younger children—those born into relative affluence—were just as likely to misbehave when they were teenagers as their elder siblings had been. Family income was not, per se, the determining factor.
That suggests two, not mutually exclusive, possibilities. One is that a family’s culture, once established, is “sticky”—that you can, to put it crudely, take the kid out of the neighbourhood, but not the neighbourhood out of the kid. Given, for example, children’s propensity to emulate elder siblings whom they admire, that sounds perfectly plausible. The other possibility is that genes which predispose to criminal behaviour (several studies suggest such genes exist) are more common at the bottom of society than at the top, perhaps because the lack of impulse-control they engender also tends to reduce someone’s earning capacity.
The original research, by Amir Sariaslan, Henrik Larsson, Brian D’Onofrio, Niklas Långström and Paul Lichtenstein is here, here is how the authors report the conclusion:
There were no associations between childhood family income and subsequent violent criminality and substance misuse once we had adjusted for unobserved familial risk factors.