2.1. Teenage childbearing

The patterns of teenage childbearing differ significantly across developed countries. The teenage birth rate represents the number of births per 1000 women between the ages of 15 and 19 years. It ranges from 6 births per 1000 adolescent females in Sweden, Italy, and Denmark to around 9 births in Norway, Germany, and France, and to 38 births in the USA in the second half of the 2000s—see Fig. 1a.Footnote ¹⁵ Do differences in overall fertility play a role in generating these sharp disparities in teenage childbearing across countries? Controlling for the total fertility rate does not change the overall patterns of teen births—see Fig. 1a. We define the probability of a teen birth as the number of teenage births per woman as a fraction of her total fertility rate, or in other words, teenage births as a fraction of all births. This probability is almost six times higher in the USA than in Denmark.Footnote ¹⁶ It is hard to rationalize the huge differences in teenage childbearing between the USA and, especially, the Scandinavian countries because both regions have similar levels of economic development and sexual activity/contraception practices among adolescents.Footnote ¹⁷

Figure 1. Teenage birth rates across countries (2006–2010). Note: (a) The teenage birth rate is defined as the number of births per 1000 women aged 15–19 years, and the data are from the Worldbank’s World Development Indicators (series SP.ADO.TFRT). (b) The probability of teen birth is defined as the share of teenage births out of total births. It is computed by adjusting the teenage birth rate by the total fertility rate (series SP.DYN.TFRT.IN).

A look at the probability of teen birth at different sections of the income distribution of households with female teenagers in the USA reveals that the high number of teenage births comes from the lower end of the distribution—see Fig. 2a. At the same time, the fraction of sexually active female teenagers is roughly constant across the distribution at around 41 percent with a very mild hike at the very bottom of the distribution (53 percent)—see Fig. 2b. These observations point to the fact that teenage childbearing is high in the USA mainly because teenagers at the bottom of the distribution do not exert as much birth control effort as in the higher income categories.

Figure 2. Teenage births and sex initiation across income groups, USA (2006–2010). Note: (a) The income groups are defined using total income of the respondent’s family (variable totincr) from the 2006–2010 NSFG. The probability of teen birth is defined as in Fig. 1. It is computed from the variable hasbabes and indicates if a respondent ever had a live birth. (b) The probability of sex initiation is the share of teenagers that become sexually active before they turn 20. It is computed based on the variable rhadsex. Details for the definition of the income groups and the computation of the probability of teen birth and the probability of sex initiation can be found in Appendix C.

Suppose we separate the parental households of female teenagers into two groups. The first group consists of households in which the parent, that is the mother, has had a teenage birth, while the second is of households with mothers who did not have a teenage birth. What is the probability that the female teenagers living in these households would have a teenage birth themselves? As shown by Fig. 3a, the probability of teenage birth is much higher in households with parents who also had a teenage birth. Thus, teenage childbearing is correlated across generations. If teenage childbearing has a detrimental effect on future income of teenagers, then it must be that teen births persistence would contribute to the persistence of poverty across generations. Sex initiation rates are also slightly higher in families with parents who have had a teenage birth (Fig. 3b). However, disparities of sex initiations, based on the teenage childbearing status of the parent in the household, are not so high as compared to teenage births.

If higher parental investments at the bottom of the income distribution suppress the number of teenage births by increasing the penalty of a birth to the future income of the affected teenagers, then societies which provide more income redistribution toward relatively poor families through taxation and transfers will tend to have lower teenage birth rates. A good proxy for the cross-sectional degree of redistribution of a society is the difference between the Gini coefficients of gross and net household income (Reynolds and Smolensky (Reference Reynolds and Smolensky1977)). Fig. 4a plots this measure of redistribution against the teenage birth probability for a sample of OECD countries with available data on these two variables. The correlation between the cross-sectional redistribution measure and the probability of teenage birth rate is -0.65. The basic intuition from above is confirmed—countries with high levels of redistribution of household income tend to have lower number of teenage births as a fraction of all births.

Figure 3. Teenage births and sex initiation across income groups conditional on parent childbearing status, USA (2006–2010).Note: The probability of teen birth and the probability of sex initiation are defined and computed as in Fig. 2. The division of data by parent childbearing status is based on variable agemomb1 from the NSFG 2006–2010.

Figure 4. Teenage births and the welfare state (2006–2010).Note: (a) Redistribution is measured by the Reynolds–Smolensky index, that is, net income Gini coefficient minus the gross income Gini coefficient. (b) Public education expenditures per student are normalized to the annual average wage. We employ data from OECD.Stat.

Figure 5. Teenage births, child poverty, income inequality, and intergenerational mobility (2006–2010).Note: (a) We measure inequality using the net income Gini coefficient from OECD.Stat. (b) The child poverty rate represents the percentage of children living in households with incomes below 50% of national median income and refers to time points around the year 2000. We employ the data from UNICEF (2007). (c) The generational earnings elasticity measures the percentage of parental earnings advantage passed on to the children. We present father–son earnings elasticities computed by Corak (Reference Corak2013). They refer roughly to the 1990s.

Another important mechanism of redistribution that provides investments for generating future income to children of poor parents is public education. Fig. 4b provides evidence that countries which spend more on primary and secondary education per student (relative to the average household income) have lower teenage birth rates. The correlation between the public education expenditure per student and the teenage birth rate is –0.44.Footnote ¹⁸

If high-income inequality, in particular a pronounced lower tail of the income distribution, is an evidence of lack of economic opportunities for some fraction of the population, one would expect that inequality and teenage birth rates are correlated. This conjecture turns out to be true in a cross-country context—see Fig. 5a. Moreover, we find a positive correlation between child poverty and teenage birth rates across the OECD countries—see Fig. 5b.Footnote ¹⁹ It is natural to think that limited and predetermined economic opportunities stem from the lack of adequate investments in children. High poverty rates, and in general, high-income inequality limit resources available to poor parents. This translates into lower levels of intergenerational income mobility in a society. Fig. 5c confirms that intergenerational mobility is negatively correlated with teenage childbearing across countries.Footnote ²⁰

So far, we have argued that crucial factors which generate cross-country differences in teenage birth rates, are attributes of the welfare state such as cross-sectional redistribution through taxation and intergenerational redistribution through public education. Later in the paper, the quantitative model of teenage childbearing is fit to US data and is used to explore the interactions between taxation, public education, and teenage childbearing. We examine this interaction by introducing the Norwegian welfare state institutions into the US economy. We select to study the disparities in teenage childbearing between the USA and Norway because these two countries have very different patterns of teenage childbearing. The USA has the highest teenage birth rate in the industrialized world, while Norway is a typical representative of the Scandinavian/Central European countries with low teenage childbearing rates. A secondary but very important reason for this selection is the availability of relevant data used in the quantitative analysis.

2.2. The welfare state

A brief preview of the welfare state institutions in these two countries is in order. Norway has a more progressive tax and transfer system than the USA (see Holter (Reference Holter2015)). The level and distribution of public education expenditures across students ordered by their household income differs significantly between the two countries as well (see Herrington (Reference Herrington2015)). Fig. 6 presents the tax and transfer systems of the USA and Norway. This is the implied relationship between household net and gross labor income, where the measurement scale is relative to average household labor income in the respective country. The Norwegian tax and transfer schedule guarantees a higher minimum income for the poorest families, but calls for higher taxes when income rises. Consequently, as gross income rises, net income goes up less in Norway than in the USA. This is so, because average tax rates increase faster with income in Norway. Summing up, the Norwegian tax and transfer system is more progressive than the American one, because it is more beneficial to the poor and taxes richer households more.

Figure 6. Taxes and transfers, USA and Norway.Note: Net income schedules are obtained from OECD wage benefits data. One unit corresponds to the average annual wage. Appendix C.6 provides further information on computational details.

Fig. 7a and b plot the distributions of public education expenditures per student in primary/middle/high school on the median household labor income of counties in the USA and municipalities in Norway. The circles in the scatter plots are proportional to the number of students in each county or municipality, respectively, and the regression lines are weighted by the number of students. Public expenditure per student is positively correlated with the median household income in counties in the USA, whereas in Norway the opposite pattern occurs.Footnote ²¹

Figure 7. Public education expenditures by counties/municipalities.Note: (a) We employ public expenditure data for the USA from the National Center for Education Statistics Common Core of Data through the Elementary/Secondary Information System (ELSi) application. We use the variable total current expenditures on instruction per student at county level and plot it against the median household income as reported by the 2006–2010 American Community Survey 5-Year Estimates. (b) For Norway we use data from the Statistics Norway website through the StatBank application. We plot the net operating expenditure on teaching at primary and lower- and upper-secondary level (Tables 04684 and 06939) at a municipality level against the median gross income for residents 17 years and older (Table 05854).

Another insightful observation based on the information in Fig. 7 is that the dispersion of education expenditures, across counties/municipalities ordered by median income, differs significantly between the USA and Norway. To capture the differences in dispersion and average public education expenditures across counties/municipalities, we estimate public education expenditure distributions by deciles of the country-wide labor income distribution. We assume that the county/municipality-level income distribution is log-normal. For each county/municipality, the parameters of the log-normal income distribution are given by the observed mean and median of labor income. Using the county/municipality-level income distributions and the distribution of students across counties/municipalities, we simulate a country-wide income distribution. We pair the draws in the simulation with the public education expenditures for the corresponding counties/municipalities to create a sample of related incomes and public education expenditures. Then, we separate the simulated country-wide income distribution into deciles and compute the empirical distribution functions of the public education expenditures for each of these income groups. The results are presented in Fig. 8. We plot the median, as well as the 10th and 90th percentile of the public education expenditure distribution for all income groups.

Figure 8. Estimated public education distributions.Note: We estimate the distribution of public education expenditures by centile of the income distribution using the data from Fig. 7.

The distribution of public education expenditures in the USA is much more dispersed than the Norwegian one and dispersion is increasing with income. Norwegian public spending is less progressive than what could be expected from Fig. 7b. In particular, the estimates suggest that Norwegian education spending on the rich and the poor is similar in terms of median values. However, these median values in Norway are higher than in the USA for almost all income groups.

3.1. Teenagers

Teenagers live with their parents and receive investments $b$ from them. The government spends $g$ on education per teenager. The public and private investments are inputs in the production of future income of the teenagers.

Teenagers receive a sex taste shock $\xi$ . They make a decision of whether to have sex summarized by the indicator function $s$ . If $s=1$ , the teenager is initiated, whereas $s=0$ implies sexual abstinence. Active teenagers can exercise birth control effort $e\in [0,\infty )$ , which comes at a utility cost modeled by a differentiable and increasing cost function $c(e)$ . The probability of teenage birth for an initiated teenager is given by the probability function $\Xi (e)$ , which is differentiable, decreasing, and convex.

The occurrence of a teenage birth is summarized by the indicator function:

\begin{equation*} y'=\begin {cases} 1, & \text{with probability } {\Xi (e)}\\ \mbox {0}, & \text{with probability } {1-\Xi (e)} \end {cases}. \end{equation*}

It takes the value 1 if a teenage birth occurs, and 0 otherwise.Footnote ²⁴

3.1.1. Income

The future household income of the teenager when she becomes a parent is denoted by $a'=\mathbf{a}(b,g,y')$ , a function of private and public investments $b$ and $g$ and the teenage birth indicator $y'$ . In particular, future log-income is given by:

(1) \begin{equation} \log (\mathbf{a}(b,g,y'))=(1-\theta _{0}y')\,(b+g)^{\lambda }. \end{equation}

Investment inputs here are perfectly substitutable and the parameter $\lambda \in \left (0,1\right )$ implies decreasing returns to total investment.Footnote ²⁵ A teenage birth can have some negative consequences for future income. This is portrayed by the parameter $\theta _{0}$ . Whenever a teenager experiences a birth, that is, $y'=1$ , future income decreases for given investment levels $b$ and $g$ . Moreover, the cost of teenage childbearing in terms of lost income is increasing in investments. This implies that teenagers with high investment levels would be more attentive to the consequences of teenage sex, which is in line with the cross-sectional evidence presented in Fig. 2. A graphical representation of this argument is outlined in Fig. 9 below.

Figure 9. Income and investments—the role of a teen birth.

The production function (1) describes the creation of the household income and accounts for patterns of assortative mating and non-tangible investments in the human capital of the children. The parameter $\theta _{0}$ captures not only the direct cost of teenage birth on the mother’s skill formation but also the decline in her marriage perspectives in terms of spousal labor market skills (Fernández et al. (Reference Fernández, Guner and Knowles2005)).

3.1.2. Sexual initiation and birth control

Teenagers derive utility $\xi$ from having sex. The preference shock $\xi$ comes from a distribution $F$ . If a teenager forgoes this utility and stays sexually abstinent, her instantaneous utility level is normalized to zero. Teenagers value their expected income as adults. Their preferences are given by

\begin{equation*} \left (1-\delta \right )(\xi -c(e))s+\delta \mathbf {E}\log (a'), \end{equation*}

where $\delta$ is the utility weight on the expected future income. The first term of the expression above describes the net utility derived out of sex. The cost of birth control effort, $c(e)$ is subtracted from the utility of sex $\xi$ . The utility term of future income is assumed to be logarithmic. Future income is not determined at the time the teenager makes her decision about sexual initiation and birth control. In this sense, sexual activity is risky because it may decrease the level of income if a teen birth is realized. This gives an incentive to sexually active teenagers to exert birth control effort.

3.1.3. Teenager’s decision making

Consider a teenager who is sexually initiated and makes a decision on the level of birth control. A teenager who has sex and receives investments $b$ and $g$ , and a sex taste $\xi$ , faces the following problem:

(2) \begin{equation} \begin{split}\widetilde{V}^{1}(b,g,\xi ) & =\underset{e\geq 0}{\max }\left (1-\delta \right )(\xi -c(e))\\ \\ & +\delta \Xi (e)\log (\mathbf{a}(b,g,\mathbf{1}))\\ \\ & +\delta (1-\Xi (e))\log (\mathbf{a}(b,g,\mathbf{0})). \end{split} \end{equation}

The teenager has to choose an optimal level of birth control $e$ . In doing so, she maximizes the weighted sum of her instantaneous utility from sex and the expected utility out of her household income in the future. The expected utility out of future income is formally expressed in the second and third lines of problem (2). The expectation is formed with respect to the odds of having a teenage birth in the future conditional on the amount of exerted birth control effort. The teenager chooses an optimal level of effort such that it balances the instantaneous utility cost and the benefits of decreasing the probability with which future income is reduced. We call this potential utility loss the option value of avoiding teenage childbearing and define it as:

\begin{equation*} \Lambda (b,g)=\log (\mathbf {a}(b,g,\mathbf {0}))-\log (\mathbf {a}(b,g,\mathbf {1})). \end{equation*}

One can show that the option value is increasing in both private and public investments and is a concave function.Footnote ²⁶ If the teenager has a level of birth control effort $e$ , with probability $\Xi (e)$ she would have a teenage birth and consequently her future income would be determined by the function $\mathbf{a'}(b,g,\mathbf{1})$ . With the complementary probability $1-\Xi (e)$ the teenager will manage to avoid a teen birth and the future level of income would be determined by $\mathbf{a'}(b,g,\mathbf{0})$ . Denote the decision rule of the initiated teenager with respect to birth control as $\mathbf{e}(b,g)$ .

Next, consider a teenager who decides on sexual initiation. We define the indirect utility function of abstinence as

\begin{equation*} \widetilde {V}^{0}(b,g)=\delta \log (\mathbf {a}(b,g,\mathbf {0})). \end{equation*}

The instantaneous utility level in the case of sexual abstinence is normalized to zero. Therefore, the indirect utility function for the abstinent teenager is the utility of future income without a teen birth.

The teenager will engage in sex whenever the value of being sexually initiated is higher than the value of being abstinent. The initiation problem is formalized as:

(3) \begin{equation} V(b,g,\xi )=\underset{s\in \{0,1\}}{\max }\{(1-s)\underset{{\mbox{Abstinence}}}{\underbrace{\tilde{V}^{0}(b,g)}}+s\underset{{\mbox{Sex}}}{\underbrace{\tilde{V}^{1}(b,g,\xi )}\}} \end{equation}

and the corresponding decision rule is given by:

\begin{equation*} \mathbf {s}(b,g,\xi )=\begin {cases} 1\mbox { if} & \tilde {V}^{1}(b,g,\xi )\geq \tilde {V}^{0}(b,g)\\ 0\mbox { if} & \tilde {V}^{1}(b,g,\xi )\lt \tilde {V}^{0}(b,g) \end {cases}. \end{equation*}

Teenagers are indifferent between sexual initiation and abstinence if the realization of the sex taste shock $\xi ^{\star }$ is such that $\tilde{V}^{1}(b,g,\xi ^{\star })=\tilde{V}^{0}(b,g)$ . Teenagers with a taste for sex below $\xi ^{\star }$ would be abstinent, while teenagers with a taste shock above it would be sexually active. The threshold value of the sex taste shock $\xi ^{\star }=\mathbf{\xi }^{\star }(b,g)$ can be represented as a function of private and public investment in the teenager’s future.

3.2. Parents

Parents value household consumption, $c$ , and are paternalistic in the sense that they care about the future expected income $a'$ of the child (Doepke and Zilibotti (Reference Doepke and Zilibotti2017)). Parental preferences are given by:

\begin{equation*} \left (1-\alpha \right )\log (c)+\alpha \mathbf {E}\log (a'), \end{equation*}

where $\alpha$ is the degree of paternalism of parents. Future income of teenagers is not determined at the time of decision-making of parents, thus the expectation operator in the expression above.

3.2.1. Parent’s decision making

The parent observes public education expenditures $g$ to her teenager. She has a household income $a$ which is taxed at an average tax rate given by the increasing function $\tau (a)$ . The parent decides how to allocate net income between household consumption, $c$ , and the investment in the future income of her child, $b$ . The parent knows how investment $b$ influences her teenage daughter’s decisions about sexual initiation, $\mathbf{s}(b,g,\xi )$ , and birth control, $\mathbf{e}(b,g)$ , and she takes into account these decision rules when making the investment. However, the parent does not know the preferences of the teenager over sex, $\xi$ . Also, at the time parental decisions are made, the realization of the potential birth to the teenager, $y'$ , is not yet known.

The decision problem of the parent is given by:

(4) \begin{equation} \begin{split}W(a,g) & =\underset{b\in [0,(1-\tau (a))a]}{\max }\left (1-\alpha \right )\log (c)\\ \\ & +\alpha{{{\int _{\xi }\bigg \{}}}(1-\mathbf{s}(b,g,\xi ))\log (\mathbf{a}(b,g,\mathbf{0}))\\ \\ & +\mathbf{s}(b,g,\xi )\Xi (\mathbf{e}(b,g))\log (\mathbf{a}(b,g,\mathbf{1}))\\ \\ & +\mathbf{s}(b,g,\xi )(1-\Xi (\mathbf{e}(b,g)))\log (\mathbf{a}(b,g,\mathbf{0}))\bigg \} dF(\xi ) \end{split} \end{equation}

subject to

\begin{equation*} (1-\tau (a))a=c+b. \end{equation*}

The parent has to choose an optimal level of household consumption, $c$ , and the investment to the teenager, $b$ . In doing so, she needs to maximize a weighted sum of the utility out of consumption and the expected utility out of the income of the teenager when she becomes an adult parent herself. The expected utility out of the income of the teenager in the future is expressed in the second, third, and fourth lines of problem (4). For a particular mix of investments, $b$ and $g$ , and sex taste, $\xi$ , the teenager may decide to stay sexually abstinent, that is $\mathbf{s}(b,g,\xi )=0.$ In this case, her future income will be given by $\mathbf{a}(b,g,\mathbf{0})$ . This is the case depicted in the second line of the problem. However, if the teenager has sex, $\mathbf{s}(b,g,\xi )=1$ , she faces a teenage birth with probability $\Xi (\mathbf{e}(b,g))$ . In this case her future income is determined by $\mathbf{a}(b,g,\mathbf{1})$ . Of course, she might avoid giving birth while a teenager with probability $1-\Xi (\mathbf{e}(b,g))$ . In this case, her income in the future is defined by $\mathbf{a}(b,g,\mathbf{0})$ . To form the final expression for the expected utility of the parent out of the future income of the teenager, one needs to integrate over all possible realizations of the taste for sex, $\xi$ . The decision rule of the parent with respect to investments is $\mathbf{b}(a,g)$ .

3.3. Equilibrium characterization

Each parent–teenager pair play a game in which the parent moves first and decides how much to invest in her teenage child. The teenager observes the investment, learns her sex taste and makes a decision on sexual initiation. In addition, she decides how much birth control effort to exert if she is sexually active. The natural way to solve this problem is using backward induction. Start at the final decision node, that is when parental investment and sex taste are realized and the teenager has to make her decisions. The optimal behavior of the teenager is summarized by the decision rules $\mathbf{s}(b,g,\xi )$ and $\mathbf{e}(b,g)$ . Now move to the decision problem of the parent. She takes into consideration the optimal behavior of her teenage daughter and makes an investment decision $\mathbf{b}(a,g)$ . The solution concept applied to the outcomes of each household in the economic environment is sub-game perfect Nash equilibrium. The concept requires that the decision rules of the teenager, $\mathbf{s}(b,g,\xi )$ and $\mathbf{e}(b,g)$ , are optimal given that the parent has already determined the investment level $b$ . This implies that the teenager cannot internalize the decision-making process of the parent when it comes to private investments.

If the equilibrium is unique, the derived decision rules of parents and teenagers constitute a unique sub-game perfect Nash equilibrium. The two decision sub-problems of the teenager (2) and (3) yield a unique solution in terms of decision rules $\mathbf{e}(b,g)$ and $\mathbf{s}(b,g,\xi )$ . The assumptions on the probability function of having a teenage birth, $\Xi (e)$ , and on the cost function, $c(e)$ , ensure that the sufficient second-order condition in problem (2) is satisfied. If the solution of the parental problem (4) yields a unique solution, then the sub-game perfect Nash equilibrium is also unique.Footnote ²⁷

The decision problem of a sexually initiated teenager depicted in (2) gives rise to the following optimality condition (in the case of an interior solution) for the choice of birth control effort, $e$ ,

(5) \begin{equation} -\left (1-\delta \right )c'(e)=\delta \Xi '(e)\Lambda (b,g). \end{equation}

Condition (5) above states that the marginal utility cost of birth control effort should be equal to the marginal benefit of effort in terms of future expected income. Using the Implicit Function Theorem we can show that the decision rule function $\mathbf{e}(b,g)$ exists and the level of optimal effort rises with both investments (see Lemma 2 in Appendix B).

The decision problem of the parent can be rewritten in a more convenient way. First, define the perceived probability of a teenage birth to the parent of the teenager as a function of her investments $b$ and the government investments $g$ as $\Xi ^{\star }\left (b,g\right )$ . Recall that the parent does not know the realized sex taste of her teenager. Thus, the probability of a teen birth can be expressed as:

\begin{equation*} \Xi ^{\star }\left (b,g\right )=\int _{\xi }\mathbf {s}\left (b,g,\xi \right )dF\left (\xi \right )\Xi \left (\mathbf {e}(b,g)\right )=\left (1-F(\mathbf {\xi }^{\star }(b,g))\right )\Xi \left (\mathbf {e}(b,g)\right ). \end{equation*}

The probability of a teenage birth perceived by the parent decreases in investments $b$ and $g$ (see Lemma 6 in Appendix B). We can reformulate the decision problem (4) of the parent using this probability:

(6) \begin{equation} \begin{split}W(a,g) & =\underset{b\in [0,(1-\tau (a))a]}{\max }\left (1-\alpha \right )\log (c)\\ \\ & +\alpha (1-\Xi ^{\star }\left (b,g\right ))\log (\mathbf{a}(b,g,\mathbf{0}))\\ \\ & +\alpha \Xi ^{\star }\left (b,g\right )\log (\mathbf{a}(b,g,\mathbf{1})) \end{split} \end{equation}

subject to

\begin{equation*} (1-\tau (a))a=c+b. \end{equation*}

The decision problem (6) of a parent who invests resources for her daughter’s future has the following optimality condition in case of an interior solution for the invested amount $b$ ,

(7) \begin{equation} \frac{1-\alpha }{\tilde{a}}=\alpha \left [1-\Xi ^{\star }\left (b,g\right )\right ]\frac{\frac{\partial \mathbf{a}}{\mathbf{\partial }b}(b,g,0)}{\mathbf{a}\left (b,g,0\right )}+\alpha \Xi ^{\star }\left (b,g\right )\frac{\frac{\partial \mathbf{a}}{\mathbf{\partial }b}(b,g,1)}{\mathbf{a}\left (b,g,1\right )}-\alpha \frac{\partial \boldsymbol{\Xi }^{\star }}{\mathbf{\partial }b}(b,g)\Lambda (b,g), \end{equation}

where $\tilde{a}=(1-\tau (a))a$ is net income of the parent. Condition (7) states that at the optimal level of investment $b$ , the marginal utility of a unit of forgone consumption equals the marginal benefit of investing an extra unit into the future of the teenager. The expression for this marginal utility benefit on the left-hand side of condition (7) consists of three parts. The first and the second summands represent the marginal utility gained due to the increase in the future income of the teenager holding the probability of a teenage birth constant. The third term stands for the marginal utility benefit related to the declining probability of teenage birth holding constant the option value of avoiding teenage childbearing. The decision rule $\mathbf{b}(\tilde{a},g)$ associated with condition (7) exists and the level of parental investment rises with net income of the household but decreases with government investments (see Lemma 7 in Appendix B).

Proposition 1. The probability of a teenage birth as a function of parental net household income $\tilde{a}=(1-\tau (a))a$ and the government investment $g$ , while taking into account the optimal behavior of the parent and the teenager is defined as:

\begin{equation*} \Xi ^{\star \star }\left (\widetilde {a},g\right )=\Xi ^{\star }\left (\mathbf {b}(\widetilde {a},g),g\right ). \end{equation*}

It can be shown that this probability is decreasing in net income and is decreasing in government investments, that is, $\frac{\partial \Xi ^{\star \star }}{\partial \widetilde{a}}(\widetilde{a},g)\lt 0$ and $\frac{\partial \Xi ^{\star \star }}{\partial g}(\widetilde{a},g)\lt 0$ .

This result points out that the unconditional probability of a teenage birth occurrence goes down when net parental income rises. Similarly, when public investments rise, teenager births decline. Thus, the economic model captures the basic intuition outlined in the introductory paragraphs. Larger amount of redistribution, that is, a rise in net income in the lower fractions of the income distribution would bring about a declining trend of teenage childbearing among the affected teenagers. The same is true for an increase in public education expenditures. Which of these effects is stronger? Are these channels at work only at the bottom of distribution? That is, suppose income is redistributed from the top of the distribution to the bottom. Can a declining trend in teenage childbearing at the bottom of the distribution be offset by a rise in teenage births at the middle or at the top of the distribution due to such redistributive policies? These questions are quantitative in nature. We can only address them by bringing the economic model to the data.

4.1. Features of the quantitative model

The theoretical model described in the previous section has to be augmented in several dimensions before using it for quantitative work. These adjustments are made without distorting the main mechanisms at work in the model.

Birth Control and Childcare Expenses. In the model introduced in Section 3, greater tax progressivity has the unambiguous effect of reducing the teenage birth rate because low-income parents can afford to invest more in their children’s education. In reality, however, families also have to contemplate the potential cost of raising a grandchild born to a teenage daughter. Parents are incentivized to invest in their children’s education not only out of altruism but also to reduce the likelihood of having grandchildren born to their teenage daughters. Greater tax progressivity can ease the financial burden of raising a grandchild for low-income families, potentially weakening the incentive to prevent the arrival of a grandchild. Considering the cost of raising a grandchild, the effect of tax progressivity on the teenage birth rate becomes an open quantitative question.

To better capture the interplay between the welfare state and the teenage fertility decision, we introduce a childcare cost in the case of teenage child birth in our quantitative model. We also allow for a monetary cost of birth control that incurs to the parents of teenage girls. We assume the cost of raising a grandchild born to a teenage daughter is $\kappa$ share of the parent’s income. In addition to the private education investment $b$ , parents choose to spend $d$ on birth control, which reflects the costs of contraception and abortion. The birth control expenditure translates into a maximum birth control effort $\bar{e}(d)$ that the daughter can exert, which is an increasing function in $d$ . That is, a sexually active daughter can only exercise safe sex or get an abortion if the parent is willing to pay for these birth control measures.

Specifically, a sexually active teenager’s problem (equation (2)) becomes

\begin{equation*} V^1(b,d,g,\xi ) = \max _{e} \left \{(1-\delta ) (\xi - c(e)) + \delta \Xi (e) \log (\mathbf {a}(b,g,1)) + \delta (1-\Xi (e)) \log (\mathbf {a}(b,g,0)) \right \}, \end{equation*}

subject to

\begin{equation*} e\geq 0, \quad e\leq \bar {e}(d). \end{equation*}

The parent’s problem (equation (6)) becomes

\begin{eqnarray*} W(a,g) &=& \max _{b,d} \left \{\Xi ^*(b,d,g)\left [ (1-\alpha ) \log (c^1) + \alpha \log (\mathbf{a}(b,g,1)) \right ] \right . \\ && \left . + (1-\Xi ^*(b,d,g))\left [ (1-\alpha ) \log (c^0) + \alpha \log (\mathbf{a}(b,g,0)) \right ] \right \}, \end{eqnarray*}

subject to

\begin{eqnarray*} c^1 &=& (1-\kappa )(1-\tau (a))a - b - d, \\ c^0 &=& (1-\tau (a))a - b - d, \\ b &\geq & 0, d \geq 0, \end{eqnarray*}

where $\Xi ^*(b,d,g)$ is the probability of a teen birth, which now also depend on the birth control expenditure $d$ because the optimal birth control effort depends on $d$ . $c^0$ and $c^1$ are the consumption of the parent in the case without and with teen birth, respectively.

Intergenerational Transmission of Teenage Childbearing. As shown in Fig. 3a, a teenager is much more likely to have a birth if the parent of the teenager had a teenage birth herself, irrespective of the position in the parental household income distribution. In order to allow the model to replicate this feature of the data, we introduce an additional cost in the income process. The income process is now defined as

(8) \begin{equation} \log (a')=(1-\theta _{0}y')(1-\theta _{1}M)(b+g)^{\lambda }. \end{equation}

If the teenager was born to a teenage mother $\left (M=1\right )$ , private and public investments are less efficient in generating future income. This inefficiency is captured by the parameter $\theta _{1}$ .Footnote ²⁹ The parameter $\lambda$ controls the efficiency of investments and allows us to adjust the marginal returns on parental investments in estimation. In line with the existing literature (Holter (Reference Holter2015) and Herrington (Reference Herrington2015)), we assume that the investment inputs $b$ and $g$ are perfect substitutes. In a series of robustness checks, we relax this assumption and obtain similar quantitative results.Footnote ³⁰

Disutility of exerting birth control effort. We allow for a fixed component in the utility cost of exerting birth control effort, $c(e)$ . This fixed cost helps us to match the high teenage birth rates at the lower end of the income distribution.Footnote ³¹ We assume that the disutility of the birth control effort, $c(e)$ , is given by:

\begin{equation*} c(e)=\mathbb {I}_{\{e\gt 0\}}\left (\omega _{0}+\omega _{1}e\right ). \end{equation*}

Other functional form assumptions. The probability function of a teenage birth conditional on the exerted effort, $\Xi (e)$ in assumed to be

\begin{equation*} \Xi (e)=\exp\!({-}e). \end{equation*}

The distribution of the sex preference shock, $\xi$ , is assumed to follow a normal distribution conditional on the status of the mother as a teenage parent. The distribution of $\xi$ for those who did not born to a teenage parent has mean $\mu _0$ and variance $\sigma _0^{2}$ . For those born to a teenage parent, the mean and variance are $\mu _1$ and variance $\sigma _1^{2}$ .

4.2. A priori information

4.2.3. Birth control and childcare expenses

Guner et al. (Reference Guner, Kaygusuz and Ventura2012) estimate that the cost of raising a child between age 0 and 5 years is about 10% of the average household income in 2005 based on data from the Survey of Income and Program Participation. We use this to calibrate the cost of raising a child to be $\kappa =0.1$ .

To calibrate the function $\bar{e}(d)$ , the maximum birth control effort given expenditure $d$ (as a fraction of the mean annual gross income), we note the maximum birth control effort translates into the maximum birth control success probability given by $\bar{\Xi }(\bar{e})\equiv 1-\Xi (\bar{e})=\exp\!({-}\bar{e})$ . We can then write the relationship between birth control expense $d$ and maximum birth control success probability $\Xi$ as follows:

\begin{equation*} \bar {e}(d)=-\ln (\bar {\Xi }). \end{equation*}

We use the observed relationship between birth control expenses and success rates to calibrate the function $\bar{e}(d)$ . At zero birth control expense, the birth control success rate is 0%. According to Frost et al. (Reference Frost, Zolna, Frohwirth, Douglas-Hall, Blades, Mueller, Pleasure and Kochhar2019), the annual cost of contraception in the USA is $316. The annual safe sex success rate is 72% according to Fernández-Villaverde et al. (Reference Fernández-Villaverde, Greenwood and Guner2014). Planned Parenthood estimates that the average cost of an abortion (before the overturn of Roe v. Wade) is around $1500. The abortion completion rate is 99.7% according to Weitz et al. (Reference Weitz, Taylor, Desai, Upadhyay, Waldman, Battistelli and Drey2013). Using these data points, we calibrate the function $\bar{e}(d)$ to be a linear function with a zero intercept and a slope equal to 157.18.Footnote ³⁴

4.3. Estimation

The estimation procedure involves 9 parameters. There are six preference parameters, $\{\alpha,\delta,\mu _0,\sigma _0,\mu _1,\sigma _1\}$ , three parameters for the income process, $\{\lambda,\theta _{0},\theta _{1}\}$ and two parameters for the birth control effort function, $\{\omega _{0},\omega _{1}\}$ .

These parameters are estimated to match as close as possible the following list of 24 data targets:

1. 1. Teenage birth rates and sex initiation rates for five parental household income groups and conditional on whether the parent of the teenager has a teenage birth herself. In essence, these are the 20 data moments presented in Fig. 3a and b.

2. 2. Average income cost of a teenage birth. This target is computed as the average income loss associated with a birth to the teenager.

3. 3. Share of sexually active teenagers who do not use any contraceptive technique.

4. 4. Income inequality. We use the Gini coefficient of household income of families with teenage children.

5. 5. Intergenerational mobilty of household income. We use the intergenerational income elasticity of females with respect to their parents.

Before proceeding with the estimation procedure and the resulting model fit, let us take a detour and discuss in depth the utilized data targets and how they help in the process of estimation of the model parameters. The parameter $\theta _{0}$ determines the cost of having a teenage birth in terms of future household income in the model. We follow Fletcher and Wolfe (Reference Fletcher and Wolfe2009) who compute the income loss associated with teenage motherhood using The National Longitudinal Study of Adolescent to Adult Health (Add Health). For the estimation, they use as a control group the teenagers that had a late miscarriage. The procedure controls for community fixed effects too. Fletcher and Wolfe (Reference Fletcher and Wolfe2009) estimate significant reductions in income due to teenage childbearing. We use their estimates and set the income loss due to a teenage birth to be approximately 17%.

The fixed cost of effort $\omega _{0}$ influences the share of teenagers who do not exert birth control effort in the model. Therefore, we recover the value of this parameter by targeting the fraction of sexually active teenagers who do not use any contraceptive technique. This data target is derived from the National Survey of Family Growth (NSFG) 2006–2010.

The remaining parameters are identified by the distributions of teenage birth rates and sexual initiation rates across income groups. We utilize again data from the NSFG for the period 2006–2010 to construct these distributions. In Appendix C.1 we describe how we adjust the teenage birth rates derived from the NSFG to make them consistent with aggregate data. Fig. 3 in Section 2 shows that teenage birth rates and sexual initiation rates decrease with parental income and are higher for teenagers with mothers who had teenage births themselves.

In our model, a teenager decides whether to be sexually active or not by comparing the value of the sex taste shock $\xi$ to the threshold $\mathbf{\xi ^{\star }}(b,g)$ . If the realization of the taste shock is below the threshold, the teenager remains abstinent. Thus, the parameters $\mu _M$ and $\sigma _M$ for $M=0,1$ of the distributions of $\xi$ are set to match the overall distribution of sex initiation by the status of the parent as a teenage mother ( $M$ ). The parameter $\theta _{1}$ controls the degree of investment inefficiency associated with a parent who had a teenage birth herself. Therefore, we can identify this parameter by matching the observed differences in teenage birth and initiation rates based on the teenage childbearing status of the parent.

We use the intergenerational income mobility to recover the utility weight $\alpha$ . The utility weight determines how much parents value the future income of their daughters and determines the level of private investment. Raaum et al. (Reference Raaum, Bratsberg, Røed, Österbacka, Eriksson, Jäntti and Naylor2007) find that the intergenerational elasticity of family income of a female with respect to her parents’ income is 0.408 in the USA. The parameter $\lambda$ determines the curvature of the income production function and influences the dispersion of future income. We use the Gini coefficient of gross household income of families with teenagers of 0.423 as a target.

The utility weight $\delta$ controls how much teenagers care about the income loss related to having a teenage birth. Therefore, an increase in $\delta$ leads to lower sexual initiation rates and teenage childbearing. An increase in the slope parameter of the effort cost function $\omega _{1}$ makes it more costly to exert effort. Consequently, initiated teenagers exert less effort increasing the probability of having a teenage birth rate. However, higher utility costs of effort reduce the incentives to be sexually active and reduces sex initiation rates.

The discussion above points out that the parameters $\mu _0$ , $\sigma _0$ , $\mu _1$ , $\sigma _1$ , $\delta$ , and $\omega _{1}$ are jointly determined by the level and shape of the teenage birth and sex initiation distributions. In Appendix D, we further discuss how these six parameters influence the targeted distributions.

4.3.1. Simulated method of moments

We define the parameter vector to be estimated as $\Theta =\{\alpha,\delta,\mu,\sigma,\theta _{0},\theta _{1},\lambda,\omega _{0},\omega _{1}\}$ and compute the difference between the simulated model moments $\hat{m}_{i}(\Theta )$ and the data moments $m_{i}$ as $g_{i}(\Theta )=m_{i}-\hat{m}_{i}(\Theta )$ . Let $g(\Theta )=(g_{1}(\Theta ),\ldots,g_{24}(\Theta ))$ be a vector that contains all these differences. The estimation of the parameter vector amounts to choosing parameter values that minimize the squared deviation between the data and the model:

\begin{equation*} \hat {\Theta }=\underset {\Theta }{\min }g(\Theta )'\mathcal {W}g(\Theta ), \end{equation*}

where $\mathcal{W}$ is a diagonal weighting matrix. The difference between data and model moments is weighted by the inverse of the observed data moment. The individual bins of the teenage birth and initiation rate distributions are also weighted by their relative population size to account for their importance in the total distribution. Standard errors of the parameter estimates are computed using the methodology proposed by Lee and Ingram (Reference Lee and Ingram1991). Table 1 reports the parameter estimates and the corresponding standard errors. The parameters are tightly estimated as evident by the 95% confidence intervals.

Table 1. Estimated parameters

Parents put a high value on their child’s future outcomes, $\alpha =0.916$ . The parent’s utility weight on future outcomes of the child is also larger than the teenager’s utility weight, $\delta =0.183$ . Thus, parents act in a paternalistic fashion when investing in their children. The fixed cost of exerting birth control effort is 0.022, which constitutes around 82% of the total birth control disutility cost incurred to a sexually active teenager from an average-income household with a parent who did not have a birth as a teenager.

4.4. Model fit

The model matches remarkably well the overall teenage birth and sexual initiation rates, as well as the rest of the targets for the USA (see Table 2). As Fig. 10a illustrates, the model has no trouble capturing the teenage childbearing levels by parental income groups (left panel). Moreover, this behavior is matched for teenagers with a parent who has had a teenage birth as well ( $M=1$ ) and for teenagers with a parent who has not experienced a teenage birth ( $M=0$ ); see the right panel. Teenage childbearing in the model is exacerbated at the lower end of the income distribution and within the group of teenagers with a parent who has also been a teenage mother in line with the observed patterns in the data. The model captures well the sexual initiation rates (Fig. 10b) but it misses the high rate of sexual initiation of teenagers at the bottom of the income distribution and with a parent who has also been a teenage mother.

Table 2. Model fit—aggregate statistics

Figure 10. Model fit—distributions.

4.4.1. Decisions in the baseline economy

Figs 11a and b show how the optimal decisions of parents depend on their net income $\tilde{a}$ and public education expenditure $g$ . Richer parents are able to spend more on their children in education investment and birth control. Birth control expense is smaller than private education investment because a small birth control expense can already achieve a high maximum birth control effort. Public education expenditure crowds out private education investment as the two are substitutes, but the effect is small quantitatively. A higher public education expenditure leads to higher future incomes of the daughter in equilibrium, and thus a higher opporunity cost of a teenage birth. Therefore, parents spend more on birth control when $g$ is higher.

Fig. 11c shows the optimal birth control effort decision of a teenager who faces a non-binding maximum effort constraint. The teenager’s optimal effort decision increases in both private and public education spending ( $b$ and $g$ ). Higher education spendings increase the opportunity of a teenage birth, leading the teenager to exert more effort in birth control. The fixed cost $\omega _0$ of birth control effort causes the optimal effort to have a discrete upward jump. When the sum of public and private education spending is too low, a sexually active teenage chooses to exert zero birth control effort because the marginal cost of effort at zero is high due to the fixed cost. Once the teenage decides to exert effort, she faces a lower marginal cost.

Figure 11. Household policy function.Note: The policy functions are plotted for families with parents who were not a teenage mother. Panel (c): Effort decision is for the case when the maximum birth control constraint is not binding.