Here is a puzzle: if promiscuity has increased over the past century and if the cause of that increase was really a fall in the risk of pregnancy, then why have out-of-marriage births increased as well?
Over the whole of the twentieth century premarital sex rates for women increased; from 6% in 1900 to 75% in 1999.* Before the turn of the century, the only really safe form of sex, in terms of risk of pregnancy, was sex within marriage. As new technologies appeared, premarital sex became less "costly" and, as we know, when the price of anything falls, we demand more of it.
The only problem is that the share of all pregnancies that are outside of marriage hasn’t fallen; they have increased from 2% in the 1920’s to 33% in the 1999.
Clearly this isn’t simply a case of individuals weighing the benefit against cost of their behavior; there has to be more to the story. I would argue that advances in birth control technology might have started the quake, but it was the tidal wave of social change that has really made the difference.
For most of human history the only way to have sex and avoid pregnancy was coitus interruptus—aka withdrawal. Condom use appears to go back 3,000 years but it wasn’t until 1844 when techniques were available to vulcanize rubber, that anything was produced that you might actually want to put on your penis. Even that is questionable, as the original condoms were re-usable and (apparently) uncomfortable.
Speaking of discomfort, it is said that Casanova used lemons cut in half in the way that the modern diaphragm is used, the invention of which had to wait until 1882.
The IUD was invented in 1909 and latex condoms were produced in 1912 making them, thankfully, disposable. As most of us already know, the birth control pill arrived on the market in 1960.
Given that technology for controlling fertility was advancing so quickly over the end of the nineteenth and the beginning of the twentieth century, it isn’t surprising that those who had been cautious about engaging in pre-marital sex began to "enter the market," so to speak. If everyone was making their decisions based solely on pregnancy risk, we would never have seen the increase in pregnancy outside of marriage; in fact, we might have expected to see it fall. Birth control is part of the story, certainly, but the effect is not just that the behavior of pregnancy-minimizing individuals changed.
The story is that when enough pregnancy-minimizing individuals changed their behavior, pre-marital sex became more and more acceptable and others, presumably not minimizing their risk for pregnancy outside of marriage, followed suit. The effect is advances in birth control technology plus social change.
Think of it another way. Let’s say it is 1900 and assume that everyone wants to have sex regardless of whether or not they are married. There is little birth control available, so that if you have sex there is a very good chance (about 85%) that you will get pregnant, even if withdrawal is used (22%). Also, having sex outside of marriage is heavily stigmatized. In fact, for a woman having premarital sex might make it difficult for you to ever marry in the future because it sends a bad signal to any future husband regarding your ability to be faithful.
Now birth control is available and, while it is still stigmatized, a small number of people willing to break the social norm start being more adventurous, presumably those that care more about pregnancy and less about the stigma. Over time the number of people in that promiscuous group increases and the behavior becomes more and more socially acceptable. Others begin to enter the group not because pregnancy risk has decreased but because the costs related to stigmatization are falling.
There is a chance of pregnancy any time two people have sex. As the share of sexual "events" that are between two people who are not married increases, the share of pregnancies in that situation is bound to increase. Add to that the fact that the availability of birth control has also decreased the total number of pregnancies within marriage; the rise in the share of pregnancies outside of marriage was mathematically inevitable.
So is the invention of the birth control pill responsible for the rise in out-of-marriage pregnancies? Well, not really. The effect of one particular contraceptive is quite small. Economists have estimated that less than 1% of the increase in pre-marital sex among teenagers is the result of the invention of the pill.* It isn’t that contraceptives are not important; it's just that the pill is just one of many viable birth control options.
*Greenwood, Jeremy and Nezih Guner (2009). “Social Change: The Sexual Revolution.” Population Studies Center PSC Working Paper Series University of Pennsylvania.