According to The Impact of Legalized Abortion on Crime, in THE
QUARTERLY JOURNAL OF ECONOMICS Vol. CXVI May 2001 Issue 2 by John Donohue III and Steven Levitt (one of the authors of Freakonomics):
We offer evidence that legalized abortion has contributed signicantly to
recent crime reductions. Crime began to fall roughly eighteen years after abortion
legalization. The ve states that allowed abortion in 1970 experienced declines
earlier than the rest of the nation, which legalized in 1973 with Roe v. Wade.
States with high abortion rates in the 1970s and 1980s experienced greater crime
reductions in the 1990s. In high abortion states, only arrests of those born after
abortion legalization fall relative to low abortion states. Legalized abortion appears to account for as much as 50 percent of the recent drop in crime.
The authors posit the basis for this, in the conclusion:
According to a
recent National Academy report, there appears to be “a causal
and adverse effect of early childbearing on the health and social
and economic well-being of children; this effect is over and above
the important effects of background disadvantages” [Institute of
Medicine 1995, p. 58]. Moreover, unintended pregnancies are
associated with poorer prenatal care, greater smoking and drinking during pregnancy, and lower birthweights. Consequently, the
life chances of children who are born only because their mothers
could not have an abortion are considerably dampened relative to
babies who were wanted at the time of conception. The drop in the
proportion of unwanted births during the 1970s and early 1980s
appears to be the result of the increasing availability and resort
to abortion.
And finally:
These estimates suggest that legalized abortion is a primary
explanation for the large drops in murder, property crime, and
violent crime that our nation has experienced over the last decade. Indeed, legalized abortion may account for as much as
one-half of the overall crime reduction.
Obviously there is bias in the source I've given because it's the same author as the claim being analyzed. However, the paper spells out in better detail the actual claims Levitt has made, and further it provides the basis and references for those claims — The evidence put forward in the paper supports the conclusions in the book.
Clearly, analysis by individuals other than the author of the book would better illuminate how well supported the conclusions are, but I wasn't able to find any right away.