Rush Limbaugh has a solution for women who have trouble affording contraception: Have less sex. Instead of asking your employer or college to provide insurance that covers birth control, pay for your birth control yourself. Or get your boyfriend to pay for it. Or just keep your knees together so you won’t have to worry about getting pregnant.

That’s what Limbaugh told Sandra Fluke, the Georgetown University law student who recently argued that health insurers should be required to cover contraception. “Ms. Fluke, have you ever heard of not having sex?” Limbaugh asked on his radio show. “Did you ever think about maybe backing off the amount of sex that you have?” In lieu of birth-control pills, he offered: “I will buy all of the women at Georgetown University as much aspirin to put between their knees as they want.”

Limbaugh has no idea how often Fluke has sex, and none of us knows what went through her mind as she thought about the cost of birth control. But there’s evidence that many college women in her position have done what Limbaugh suggested. Faced with a contraceptive price hike in 2007, they cut back on sex. And yet, the rate of accidental pregnancy among college women didn’t decline. In fact, among those who were financially stressed, the rate increased, apparently because many of them responded to the higher cost of birth-control pills by shifting to cheaper, riskier methods, or to unprotected sex. From a conservative standpoint, the Limbaugh policy—less sex and no contraceptive subsidies—was at best a wash, and arguably a net loss.

The evidence comes from a research paper issued last May by the Population Studies Center at the University of Michigan Institute for Social Research. The draft paper, The Impact of Subsidized Birth Control for College Women: Evidence from the Deficit Reduction Act, was written by Emily Gray Collins and Brad Hershbein. It analyzed what happened in 2007 when a federal law inadvertently eliminated the college discount on birth control pills, causing their price on campus to rise from $5-$10 per month to $30-$50 per month.

Did students buy fewer pills? Did they switch to other birth-control methods? Did they resort to risky tactics such as withdrawal? Or did they cut down on their sexual activity? The answer is: all of the above.

The good news, if you share Limbaugh’s cultural views (but not his apparent behavior), is that many college women did reduce their sexual activity. Among those with health insurance, the number of reported sex partners fell 6 percent. Among those without health insurance, the number of reported partners fell 8 percent. Meanwhile, the proportion of college women who reported that they’d had vaginal sex in the previous 30 days declined by nearly 3 percent among insured women, and by nearly 6 percent among uninsured women.

The bad news is that the reduction in sexual activity was offset by a shift to cheaper, riskier methods of birth control. Among the roughly 100,000 women in the national sample on which the study focused, 40 percent used the pill. Among women engaged in contraception, more than 60 percent used the pill. Women with health insurance were significantly more likely to rely on this method.

When the discount ended and the price shot up, some college women stopped using the pill. Among those who had health insurance, the decline was only 2 to 3 percent. But among those who didn’t have insurance, the drop was much bigger: 9 to 10 percent. Collins and Hershbein checked this discrepancy against a second sample that included older college women. There, they found a similar insurance discrepancy and much bigger proportional effects: a decline of 40 to 50 percent in use of the pill among uninsured women.

In the main sample, Collins and Hershbein expected to see an increase in condom use. No such trend showed up. Instead, they saw an increase in two other practices. One was emergency contraception: high-dose birth-control pills that can prevent pregnancy if taken soon after intercourse. Among women with insurance, there was no change in EC use. But among women without insurance, there was a 17 percent increase. Among sexually active women without insurance, the increase in EC use was 24 percent.

That’s worrisome if, as the data suggest, some uninsured women substituted EC for daily birth-control pills. According to the best Web site on EC (not-2-late.com, run by the Office of Population Research at Princeton University), “any contraceptive you use before or during sex is more effective than emergency contraceptive pills.” Furthermore, “Even though emergency contraceptive pills have no serious or long-term side effects, some women feel sick to their stomach or throw up after taking them. You might also feel tired, get a headache, or have irregular bleeding” after taking them.

The increase in EC is particularly problematic for Limbaugh and other conservatives who have described EC, inaccurately, as “abortion pills.” Mitt Romney, Rick Santorum, and Newt Gingrich have all repeated this falsehood. In reality, to the extent they work, EC pills suppress ovulation and fertilization. (Theoretically, EC could fail to stop ovulation and fertilization and yet somehow succeed in blocking implantation, but that risk is unclear, unsubstantiated, and deeply implausible.) But if you think EC amounts to an abortion, as Romney, Santorum, Gingrich, and Limbaugh do, then one message from the University of Michigan report is that by helping employers withhold contraceptive insurance, you’re causing what you call abortions.

The second practice that spread among college women after the 2007 price hike on birth-control pills was “non-prescription” methods—an umbrella term for withdrawal, periodic abstinence (also known as natural family planning or the calendar or rhythm method), and unprotected sex. These practices didn’t change significantly among sexually active women with health insurance. But among sexually active women who were uninsured, there was a 7 percent increase in such methods.

That’s definitely bad news. For the pill, over the course of a year, the failure rate among typical users—i.e., the unintended pregnancy rate based on imperfect use—is 9 per 100 women. (With perfect use, the failure rate is less than 1 percent.) The failure rate for withdrawal is twice that. The failure rate for periodic abstinence is nearly three times as high. For completely unprotected sex, the failure rate is 85 per 100 women.

So the sex rate went down, but the rate of free, flimsy, and fake contraception went up. Which effect prevailed? What happened to the pregnancy data?

In the sample as a whole, Collins and Hershbein found no significant change in the rate of accidental pregnancy. (On paper, the numbers increased by about 6 percent, but that variation is within the range that could be due to chance.) One logical explanation is that to some extent, the reduction in sexual activity canceled out the reduction in reliable contraception. But when Collins and Hershbein looked at the most financially stressed women—those with more than $2,000 in credit card debt—they found that the rate of accidental pregnancy among these women increased 23 percent.

Collins and Hershbein haven’t submitted their paper for peer review yet, and the birth-control subsidy they examined was a discount, not insurance coverage. But their findings should give pause to both sides of the contraception debate. Forcing college women to pay the full cost of birth-control pills didn’t cause a crisis, contrary to the warnings of Fluke and many Democrats. It did push some students to curb their sexual activity. But it didn’t reduce the accidental pregnancy rate, because many women, instead of giving up sex, switched to cheaper, less reliable, and ad hoc birth-control methods, including what Limbaugh erroneously calls “abortion pills.” In fact, among women least equipped to cope with the price hike, the accidental pregnancy rate went up.

If all you care about is reducing sex on campus or making students shoulder the cost, withdrawing birth-control coverage will probably serve your ends. The question is whether you also care about the consequences.

William Saletan’s latest short takes on the news, via Twitter: