The inter-generational fertility effect of an abortion ban

Abstract

This study examines the extent to which banning women from having abortions affected the fertility of their children, who did not face a similar legal constraint. Using multiple censuses from Romania, I follow men and women born around the time Romania banned abortion in the mid-1960s to investigate the demand for children over their life cycle. The empirical approach combines elements of regression discontinuity design and the Heckman selection model. The results indicate that individuals whose mothers were affected by the ban had significantly lower demand for children than those who were not. One-third of the decline is explained by inherited socio-economic status.

Appendices

Appendix: A

Computing the inverse mills ratio

Regression (17) requires the computation of the inverse mills ratio λ(.) to include it as a covariate. Following Heckman (1979), the inverse mills ratio can be obtained by estimating a probit model for the probability that a pregnant woman chose to give birth instead of aborting. The probit model can be written in latent variable form, which is derived from Eqs. 3 and 4 after assuming (i) the functional form g(X^f,ξ^f) = X^fα − ξ^f, and consequently $\tilde {\xi }_{x} = X \alpha$ in regression (17), and ii) the distribution of fertility preferences ξ^f to be normal.

$$ \begin{array}{@{}rcl@{}} a*_{i} &= {X_{i}^{f}} \alpha - {\xi_{i}^{f}} \end{array} $$

(18)

$$ \begin{array}{@{}rcl@{}} a_{i} &= \begin{cases} 1 & \text{if} \ \ a*_{i} > 0,\\ 0 & \text{if} \ \ a*_{i} \leq 0. \end{cases} \end{array} $$

(19)

Equations 18 and 19 give the standard expressions for the probability of giving birth $P(a=0|X^{f}) = {\Phi }({X_{i}^{f}} \alpha )$ and the inverse mills ratio $\lambda ({X_{i}^{f}} \alpha )=\phi ({X_{i}^{f}} \alpha )/ 1- {\Phi }({X_{i}^{f}} \alpha )$. The estimation of the model is not straightforward with the structure of the data available. The standard probit requires classifying women into those who had an abortion (a = 1) and those who gave birth (a = 0). The information contained in censuses is insufficient to make such classification. However, overcoming this problem is possible.

In any pre-policy period, knowing who carried the pregnancy to term is possible, because all the children are in the data but not who aborted.²² Given the absence of the pregnancy status of women in the data, women who did not give birth in the months before June 1967 either aborted or were simply not pregnant. Conversely, none of the women who were in their first trimester of pregnancy had the option to abort after the decree was enforced. If compliance was high, then, the number of children born in July–September of 1967 should be the same as the number of pregnant women with pregnancy due date in that trimester (see Fig. 1). Thus, the unconditional probability of not having an abortion is the ratio of the cohort size born in July–Sept 1966 (i.e., the number of women who decided not to abort when abortion was legal) to the cohort size born in July–Sept 1967 (i.e., the total number of pregnant women). Formally, the variables b are defined as follows:

$$ \begin{array}{@{}rcl@{}} b_{i} &= \begin{cases} 1 & \ \ \text{if woman \textit{i} gave birth in Jan--Mar 1967},\\ 0 & \ \ \text{if woman \textit{i} gave birth in Jul--Sep 1967}. \end{cases} \end{array} $$

(20)

Additionally, let s be the number of women with pregnancy due date in Jan–Mar 1967, and n the total number of women for which b is defined. Then, the unconditional probability of not having an abortion before the implementation of the pro-natalist policy is

$$ \begin{array}{@{}rcl@{}} P(a_{i}=0) &=& \frac{{\sum}_{i=1}^{n} b_{i}}{s} \end{array} $$

(21)

$$ \begin{array}{@{}rcl@{}} &=& \frac{{{\sum}_{i}^{n}} b_{i}}{{\sum}_{i=1}^{n} (1-b_{i})} \end{array} $$

(22)

$$ \begin{array}{@{}rcl@{}} &=& \frac{{{\sum}_{i}^{n}} b_{i}}{n} \times \frac{n}{{\sum}_{i=1}^{n} (1-b_{i})} \end{array} $$

(23)

$$ \begin{array}{@{}rcl@{}} &=& \frac{P(b_{i}=1)}{P(b_{i}=0)} \end{array} $$

(24)

Equalities (21)–(24) prove the assumptions needed to compute the probit model. The right-hand side of Eq. 21 indicates that the probability of not having an abortion is, by definition, the ratio of births in Jan–Mar 1967 to the number of pregnant women who were supposed to give birth in that period had none of them aborted. The denominator s is not observed but can be replaced by a similar quantity under two assumptions.

Assumption A1

The number of women with pregnancy due date in Jan–Mar 1967 was the same as the number of women with pregnancy due date in Jul–Sep 1967.

Figure 1 suggests that Assumption A1 is plausible. The cohort size before the pro-natalist policy was relatively constant over time, which is consistent with stable pregnancy and abortion rates in the absence of the policy.²³ More stringently, this assumption also says that the implementation of the decree occurred suddenly and prevented women with pregnancy due date in Jul–Sep 1967 from adjusting their behavior in anticipation of the policy. Assumption B1 relaxes this assumption.

Assumption A2

Full compliance with the anti-abortion decree in the short run.

Assumption A2 implies that the total number of pregnancies due in Jul–Sep 1967 effectively resulted in births up to a regular miscarriage rate. That is, no pregnant woman violated the anti-abortion decree (see assumption B1 below for a relaxation of A2).

Under assumptions A1 and A2, the denominator in Eq. 21 can be replaced by the number of births in Jul–Sep 1967, resulting in expression (22). Then, multiplying the numerator and the denominator by n in Eq. 23 provides the final result in Eq. 24.

Equalities (21)-(24) also hold when the probabilities are written conditional on covariates X^f. Then, they can be used in a likelihood function to compute the probit model (18)-(19).

$$ L = \prod\limits_{i=1}^{n} P(b_{i}=1|{X_{i}^{f}})^{b_{i}} \left( 1-P(b_{i}=1|{X_{i}^{f}}) \right)^{1-b_{i}} $$

(25)

Equation 25 is the likelihood function for a binary model with dependent variable b_i, as defined in Eq. 20, and regressors ${X_{i}^{f}}$. The relationship (26) between the conditional probabilities in Eq. 25 and the corresponding probabilities of not having an abortion are obtained from equalities (21)- (24).

$$ \begin{array}{@{}rcl@{}} P(b_{i}=1|{X_{i}^{f}}) &=& \frac{P(a_{i}=0|{X_{i}^{f}})}{1+P(a_{i}=0|{X_{i}^{f}})} \end{array} $$

(26)

$$ \begin{array}{@{}rcl@{}} & = & \frac{\Phi(X_{i} \alpha)}{1+{\Phi}(X_{i} \alpha)} \end{array} $$

(27)

The specific functional form in Eq. 27 comes directly from the normality assumption of probit model (18)-(19). Replacing (27) into (25) gives the computationally feasible likelihood function (28).

$$ L(\alpha) = \prod\limits_{i=1}^{n} \left( \frac{\Phi(X_{i} \alpha)}{1+{\Phi}(X_{i} \alpha)}\right)^{b_{i}} \left( 1-\frac{\Phi(X_{i} \alpha)}{1+{\Phi}(X_{i} \alpha)}\right)^{1-b_{i}} $$

(28)

Under assumptions A1 and A2, the coefficients $\widehat {\alpha }$ obtained from maximizing the function (28) are identical to those from the unfeasible standard probit for the probability of not aborting on a sample of pregnant women s.²⁴ After $\widehat {\alpha }$ is obtained, the computation of the inverse mills ratio to include it as a regressor in Eq. 17 is straightforward.

The selection probabilities from the maximization of Eq. 28 are downwardly biased if either some women anticipated the anti-abortion policy and took precautions not to get pregnant (violation of assumption A1), or some women who were already pregnant when the decree was issued aborted anyway despite the ban (violation of assumption A2). The World Bank country report describing the social and economic environment in socialist Romania mentions that five abortions were committed for every live birth in 1965, the year before the anti-abortion decree was issued (Dethier et al. 1994; p. 142). Assumption B1 takes this abortion rate as an alternative to assumptions A1 and A2.

Assumption B1::

The ratio of abortions for every live birth prior to the anti-abortion decree was 5 to 1 (Dethier et al. 1994).

Under assumptions A1 and A2, Fig. 1 indicates only 1.5 abortions for every live birth, much lower than what assumption B1 states. Using assumption B1 instead of A1 and A2 requires “inflating” the probabilities of abortion. The modified likelihood function 30 does it by including an additional parameter ψ. The value of this new parameter is obtained after imposing that the unconditional probability of not having an abortion is 1/6 (i.e., 5 abortions per live birth). Results for assumptions A1 and A2, as well as for assumption B1 are computed below.²⁵

$$ L(\alpha, \psi) = \prod\limits_{i=1}^{n} \left( \frac{\Phi(X_{i} \alpha + \psi)}{1+{\Phi}(X_{i} \alpha + \psi)}\right)^{b_{i}} \left( 1-\frac{\Phi(X_{i} \alpha + \psi)}{1+{\Phi}(X_{i} \alpha + \psi)}\right)^{1-b_{i}} $$

(30)

Computing the standard deviation of fertility preferences

Regression (17) is the fertility equation of second-generation women. The dependent variable, the number of children ever born, is observed in Censuses 1992, 2002, and 2011 when they were adults. On the other hand, the inverse mills ratio λ(.) and all the information about the socio-economic status of second-generation women at the beginning of their reproductive life X^s are obtained from Census 1977, when these women were children. Because it is not possible to link individuals across census years, these covariates are included in the regression after being aggregated at the cohort level. This aggregation procedure, together with appropriate clustered standard errors, does not affect the estimation of regression coefficients. But, it affects the standard deviation of the residuals.

$$ \begin{array}{@{}rcl@{}} chborn_{ict} &=& \beta_{0} + \beta_{\lambda} \ pre_{c} \ \lambda(\tilde{\xi}_{xi}) + \eta_{1} W_{c} \ pre_{c} + \eta_{2} W_{c} \ (1-pre_{c}) + X_{ic}^{s} \ \beta_{s} + \xi^{s}_{ic} \end{array} $$

(31)

$$ \begin{array}{@{}rcl@{}} &=& \beta_{0} + \beta_{\lambda} \ pre_{c} \ \bar{\lambda}(\tilde{\xi}_{x}) + \eta_{1} W_{c} \ pre_{c} + \eta_{2} W_{c} \ (1-pre_{c}) + \bar{X}_{c}^{s} \ \beta_{s} + {\dots} \\ && \ \ \ \ \ {\dots} \underbrace{\beta_{\lambda} \ pre_{c} \ (\lambda(\tilde{\xi}_{xi}) - \bar{\lambda}(\tilde{\xi}_{x})) + (X_{ic}^{s} - \bar{X}_{c}^{s}) \ \beta_{s} + \xi^{s}_{ic}}_{\epsilon_{ict}} \end{array} $$

(32)

The ideal fertility (31) contains regressors $\lambda (\tilde {\xi }_{xi})$ and $X_{ic}^{s}$ at the individual level. Adding and subtracting cohort aggregates for these covariates gives the computationally feasible (32). The error term 𝜖_ict contains not just preferences $\xi _{ic}^{s}$ but deviations of individual regressors from cohort averages. Then, since $(X_{ic}^{s} - \bar {X}_{c}^{s})$ is orthogonal to $\xi ^{s}_{ic}$, the variance of 𝜖_ic for those born in Jul–Sep 1967 (i.e., pre_c = 0, which eliminates the term $(\lambda (\tilde {\xi }_{xi}) - \bar {\lambda }(\tilde {\xi }_{x}))$ from the error 𝜖_ict) is:

$$ Var(\xi^{s}_{ic}) = Var(\epsilon_{ic}) - Var((X_{ic}^{s} - \bar{X}_{c}^{s}) \ \beta_{s}) $$

The estimator for V ar(𝜖_ic) is the sample variance of the residuals in Eq. 32 for women born in Jul–Sep 1967. The estimator for $Var((X_{ic}^{s} - \bar {X}_{c}^{s}) \ \beta _{s}$ is computed in two steps. First, $\widehat {\beta _{s}}$ is obtained from regressing (32) using Censuses 1992, 2002, and 2011. Second, this estimated vector of coefficients is used to build the single index $(X_{ic}^{s} - \bar {X}_{c}^{s}) \ \widehat {\beta }_{s}$ in Census 1977 and compute its sample variance. Then, the estimator for the intergenerational transmission of preferences specified in Eq. 17 is

$$ \begin{array}{@{}rcl@{}} \widehat{\rho} &=& \frac{\widehat{\beta_{\lambda}}}{\widehat{\sigma^{s}}} \end{array} $$

(33)

$$ \begin{array}{@{}rcl@{}} &&\ \ \ s.t. \ \ \widehat{\sigma^{s}} = \sqrt{\widehat{Var}(\widehat{\epsilon}_{ic}) - \widehat{Var}((X_{ic}^{s} - \bar{X}_{c}^{s}) \ \widehat{\beta}_{s})} \end{array} $$

(34)

where the two sample variances on the right-hand side of expression (34) are computed as previously explained. Notice that using only women born Jul–Sep 1967 to compute $\widehat {\sigma ^{s}}$ have the advantage not only of eliminating the inverse mills ratio from the residuals in Eq. 32, but also the usual heteroscedasticity that arises in standard selection models (Greene 1981).

Appendix: B

Tables 6 and 7 show the descriptive statistics from the 1977 Census, when second-generation individuals born at the policy cutoff, i.e., in June 1967, were 9 years old and living with their parents.

Table 6 Demographics and house characteristics (Census 1977 - 9 years old)^(a)

Table 7 Characteristics of the father and the mother (Census 1977 - 9 years old)^(a)

Table 8 shows the descriptive statistics for relevant variables in Censuses 1992, 2002, and 2011. I use these Census data to analyze the fertility choices of second-generation individuals at different points in their lives (ages 24, 34, and 44). I separately study men and women because the information available for women is more accurate than those of men. Only women reported the number of children ever born and the age when they first got married.

Table 8 Own characteristics at different ages in adulthood