The pill and partnerships: the impact of the birth control pill on cohabitation

Abstract

This paper investigates the impact on cohabitation behavior of the introduction and dispersion of the birth control pill in the USA during the 1960s and early 1970s. A theoretical model generates several predictions that are tested using the first wave of the National Survey of Families and Households. Empirically, the causal effect is identified by exploiting plausibly exogenous variation in state laws granting access to the pill to unmarried women under age 21. The evidence shows that the pill was a catalyst that increased cohabitation’s role in selecting marriage partners, but did little in the short run to promote cohabitation as a substitute for marriage.

Appendix

Lemma 4

Assume conditions 1–3. A woman will advance a dating relationship to marriage or cohabitation if she sees x ₁ = h, and will break off the relationship otherwise. In addition, a woman who is currently cohabiting will break off the cohabitation if she observes x ₂ = l, and will continue cohabiting or choose to marry otherwise.

Proof

Firstly, consider a woman who is dating and observes x ₁ = l. If she chooses to marry or cohabit with her partner, her payoff would be − ∞ . Continually dating her partner gives a lifetime utility of $\frac{ k+\varepsilon _{i}}{1-\delta }>-\infty .$ But breaking up and searching for a new partner is the best option because she receives k + ε _i in every period of dating and there is a strictly positive probability that x ₁ = h with the next person she dates. When this happens, she can increase her expected flow payoff to $\max \left\{ pq_{h}+(1-p)q_{l}+k+\varepsilon _{i},pq_{h}+(1-p)q_{l}\right\} >k+\varepsilon _{i}$ by choosing cohabitation or marriage. (Recall that pq _h  + (1 − p)q _l  > 0).

Now consider a woman who is dating and observes x ₂ = h. If she chooses to break up (or to continually date), she receives $\frac{k+\varepsilon _{i} }{1-\delta }$ in lifetime expected utility. Marriage gives an expected lifetime utility of $\frac{pq_{h}+(1-p)q_{l}}{1-\delta },$ and cohabitation gives an expected lifetime utility of at least $\frac{pq_{h}+(1-p)q_{l}+k+ \varepsilon _{i}}{1-\delta }$ since this would be the expected lifetime utility to cohabitation if cohabitation were irreversible. Hence, choosing cohabitation or marriage is optimal since this gives at least $\max \left\{ \frac{pq_{h}+(1-p)q_{l}+k+\varepsilon _{i}}{1-\delta },\frac{ pq_{h}+(1-p)q_{l}}{1-\delta }\right\} >\frac{k+\varepsilon _{i}}{1-\delta }.$

Now consider a woman who observed x ₁ = h while dating, chose cohabitation and observes x ₂ = h. The highest possible flow payoff any woman can achieve is $\max \left\{ q_{h}+k+\varepsilon _{i},q_{h}\right\}$, so it follows that any woman will lock in this payoff by choosing either a permanent cohabitation or to marry.

Finally, consider a woman who observed x ₁ = h while dating, chose cohabitation and observes x ₂ = l. Breaking up results in a payoff equal to $V_{i}^{d}-c$ and continually cohabiting or marrying results in a payoff equal to $\max \left\{ \frac{q_{l}+k+\varepsilon _{i}}{1-\delta },\frac{q_{l} }{1-\delta }\right\} .$ We must show $V_{i}^{d}-c>\max \left\{ \frac{ q_{l}+k+\varepsilon _{i}}{1-\delta },\frac{q_{l}}{1-\delta }\right\} .$

Firstly, consider the case k + ε _i  ≥ 0. We must show $V_{i}^{d}-c>\frac{q_{l}+k+\varepsilon _{i}}{1-\delta }.$ But $V_{i}^{d}\geq \frac{k+\varepsilon _{i}}{1-\delta }$ since one can guarantee $\frac{k+\varepsilon _{i}}{1-\delta }$ by continually dating, so it is sufficient to show $\frac{k+\varepsilon _{i}}{1-\delta }-c>\frac{ q_{l}+k+\varepsilon _{i}}{1-\delta },$ or $-c\geq \frac{q_{l}}{1-\delta },$ but this is true by assumption.

Next consider the case k + ε _i  < 0. We must show $V_{i}^{d}-c> \frac{q_{l}}{1-\delta }.$ Suppose instead that $V_{i}^{d}-c\leq \frac{q_{l} }{1-\delta }.$ Then a woman will convert her cohabitation to marriage regardless of the realization of x ₂ since we know she will do so if x ₂ = h. Consequently $V_{i}^{c}=\frac{pq_{h}+(1-p)q_{l}}{1-\delta } +k+\varepsilon _{i}$. But then $V_{i}^{c}<\frac{pq_{h}+(1-p)q_{l}}{ 1-\delta },$ and the individual would not be cohabiting in the first place. That is, she would have chosen marriage over cohabitation upon seeing x ₁ = h while dating, a contradiction.□