Some pro-choice advocates argue that having an abortion is perfectly morally acceptable, either because a fetus has little to no moral significance, or because a woman’s right to bodily autonomy always prevails over whatever rights a fetus might have. Some even go so far as to celebrate the act of having an abortion as a manifestation of female empowerment — the ultimate middle finger to the patriarchy. They hold that any and all abortion restrictions would amount to a violation of female bodily autonomy.But many pro-choice advocates, especially among the rank-and-file, have a more moderate view. They concede that abortion is (at least usually) morally wrong or bad, perhaps even seriously so — even if women are often not blameworthy for having them. And yet they still believe that abortion should be legal. I would venture to say that this is the most common pro-choice position.Pro-lifers are often baffled by this combination of beliefs, but some moderate pro-choicers have an explanation at the ready: Abortion restrictions don’t work. Instead of lowering the rate of abortion, they simply replace safe abortions with roughly the same number of unsafe “back alley” abortions. If a law does not reduce the incidence of the problematic behavior that it targets, and it also has costs attached to it — such as creating unsafe conditions for women seeking the procedure, or imposing unfair burdens on women in a society that often treats them unjustly — then that law is unjustified, even if abortion is morally wrong or bad.The logic of this argument is above reproach. But the factual assertion at its heart -- that abortion restrictions don’t work -- does not stand up to scrutiny.In order to shore up this causal claim, pro-choice advocates typically rely on large-scale studies, such as a widely reported 2016 piece of research published in the Lancet, that report no correlation — and sometimes even an inverse correlation — between abortion restrictions and the rate of abortion across regions with stricter and looser abortion laws. For a concrete example of such an argument, we need go no further than the Guttmacher Institute, whose research scientist was the lead author of the Lancet study. An oft-referenced infographic on their website summarizes the relevant findings of the study as follows: “Highly restrictive laws do not eliminate abortion. Rather, they make the abortions that do occur more likely to be unsafe.” The graphic shows that the average rate of abortion in countries with strict abortion laws is comparable to the average rate of abortion in countries in which abortion is broadly legal.The key problem with using these estimates as evidence that abortion restrictions don't affect abortion rates is that they do not account for confounding factors -- i.e., they ignore the fact that countries with stricter abortion laws are also different in other ways that may affect abortion rates, a problem that the published study explicitly notes. While the report indeed finds that “abortion rates are not substantially different across groups of countries classified according to the grounds under which abortion is legally allowed,” it goes on to state that “the level of unmet need for contraception is higher in countries with the most restrictive abortion laws than in countries with the most liberal laws, and this contributes to the incidence of abortion in countries with restrictive laws.” Moreover, the vast majority of countries with more restrictive abortion laws are in developing regions, and poverty likely also has an impact on the abortion rates in these countries.It is not at all implausible that the abortion restrictions in these countries do, in fact, prevent many abortions from occurring, and that these countervailing factors act to bring their abortion rates in line with those of wealthier countries that have more liberal abortion laws. Indeed, when studies use rigorous methods to limit the problem of confounding factors, the evidence points in the opposite direction.Some studies, for instance, compare the rates of abortion before and after changes to abortion laws within a particular region, and sometimes track birth rates instead of abortion rates directly, thereby avoiding the problem of overlooking clandestine abortions. These studies support the claim that abortion restrictions lower abortion rates: See, for instance, here, here, here, here, and here. This is certainly not a comprehensive look at all of the available research, and different types of abortion restrictions will have different effects, but the main point here is simply that the picture can change radically once one begins to control for these countervailing factors.Of course, to complete the case for abortion restrictions, pro-lifers must also assess the costs of such restrictions and argue that pro-life laws have a great enough impact on the abortion rates to offset those costs. But if moderate pro-choicers really do believe that abortion should be “rare,” then showing that abortion restrictions actually do lower abortion rates should move them in a more pro-life direction.