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Why did rich families increase their fertility? Inequality and marketization of child care

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Abstract

A negative relationship between income and fertility has persisted for so long that its existence is often taken for granted. One economic theory builds on this relationship and argues that rising inequality leads to greater differential fertility between rich and poor. We show that the relationship between income and fertility has flattened between 1980 and 2010 in the US, a time of increasing inequality, as high income families increased their fertility. These facts challenge the standard theory. We propose that marketization of parental time costs can explain the changing relationship between income and fertility. We show this result both theoretically and quantitatively, after disciplining the model on US data. We explore implications of changing differential fertility for aggregate human capital. Additionally, policies, such as the minimum wage, that affect the cost of marketization, have a negative effect on the fertility and labor supply of high income women. We end by discussing the insights of this theory to the economics of marital sorting.

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Notes

  1. Galor and Moav (2002) argue that the opposite is true before the demographic transition. Relatedly, Vogl (2016) indeed finds that the income-fertility gradient was positive in less developed countries before they experienced the demographic transition.

  2. See Autor et al. (2008) and Heathcote et al. (2010) regarding rising inequality and Hazan and Zoabi (2015) regarding changing fertility patterns.

  3. We measure marketization expenditures as the relative expenditures on childcare, as calculated from the Survey of Income and Program Participation (SIPP). See “Appendix A” for details.

  4. We define these sectors as in Mazzolari and Ragusa (2013).

  5. See http://berniesanders.com/issues/a-living-wage.

  6. Doepke and Kindermann (2016) argue that policies that lower the childcare burden on mothers are significantly more effective at increasing fertility as compared to general child subsidies. We argue that the minimum wage is a policy that increases the childcare burden on mothers, and hence decreases fertility.

  7. Notice that this tackles inequality from another direction. Rather than focus on a rise in inequality due to rising wages among high income households, she is studying an increase in the supply of low wage workers. Our mechanism is agnostic as to the source of rising inequality.

  8. Using data from Hong Kong, Cortés and Pan (2013) show that the ability to hire foreign workers as live-in help increases labor force participation of mothers. They argue that child care cost reduction through immigration is a market alternative to child care subsidies.

  9. The literature on women’s labor force participation is too vast to summarize here. However, a few papers showing how women’s labor supply is related to structural transformation and taxes are worth noting, as they illuminate further potential effects of marketization on the economy. Akbulut (2011) argues that work at home, in which women have a comparative advantage, and work in services are quite similar. Thus, when demand for services rises, women’s labor force participation rises as well. Buera et al. (2013) develop this argument further: they use a quantitative model of sectoral reallocation and specialization between men and women to evaluate various causes of structural transformation. Cerina et al. (2018) argue that the rise of high skill women entering the labor force, due to the increased skill premium, contributed to job polarization. When these women enter the labor force the high skill employment shares increase. As a side effect of their employment, these women also must now marketize their home production, leading to an increase in low skill employment in the HPS sector. Rendall (2018) argues that women’s labor force participation and the service sector are strongly affected by taxes. Kaygusuz (2010) and Bar and Leukhina (2009) study the effects of changes in married couples’ taxation on the rise of married female labor force participation in the US, while Guner et al. (2012) argue that participation would be even higher if the U.S. were to adopt a system of individual based taxation of married households. Duernecker and Herrendorf (2018) argue that labor productivity in home production in the US has stagnated in recent decades, while it has risen in other places such as Germany. Their result is based on the fact that wages of household workers, what we call HPS workers, have stagnated in the US but risen in Germany. They explain the US stagnation with the prevalence of cheap immigrant labor, which has become more widely used by richer Americans in home production.

  10. Hazan and Zoabi (2015) show a very similar pattern when restricting the data to white non-Hispanic women.

  11. Formally, \(HFR_t=n_{24,t}+\sum _{a=25}^{55}AFR_{at}\), where \(n_{24,t}\) is the average number of children ever born at age 24 in year t and \(AFR_{at}\)is the age-specific fertility rate for women of age a in year t. We estimate HFR separately for each education group.

  12. Additionally, when using the sample of all native-born American women, as in Fig. 1, and replacing high income women with women with advanced degrees, the regression coefficient is practically the same as in Fig. 5.

  13. Time directly devoted to children actually remained roughly unchanged for the top income families, partly because their fertility increased and partly due to the more inclusive definition of time spent in direct child care activities applied in later survey years.

  14. An alternative formulation would allow for the uncertainty over college to be resolved child-by-child. The advantage to our approach is that it allows for a closed-form solution to the model.

  15. Notice that this function is not bounded between 0 and 1. However, this is not an issue in our calibration, as for any range of e chosen, it is possible to pick parameters such that \(\pi (e) \in [0,1]\). Becker and Tomes (1976) discuss conditions necessary on the \(\pi \) function such that it would yield a negative relationship between income and fertility, specifically that the elasticity of the human capital production function with respect to e is increasing. See also Jones et al. (2010) Our functional form both meets this criteria and yields a closed form solution.

  16. We show the existence of a unique solution to the household problem in Section B.1 of the Online Appendix.

  17. Additionally, if \(\rho >0\), there is an increase in relative spending on market substitutes, i.e. \(\frac{p_m m}{w_f t_f}\) rises.

  18. Notice that if \(p_n\) is proportional to \(w_f\), and \(w_m = 0\), then (15) collapses to the optimal fertility solution as in de la Croix and Doepke (2003) and Moav (2005).

  19. For an analysis on how parents bargain over the allocation of time to childcare, see Gobbi (2018).

  20. We show this formally in Section D of the Online Appendix. We delve into further detail on \(p_{m,1980}\) as it relates to \(w_{hps,1980}\) and \(p_{d,1980}\) in Sect. 4.3, below.

  21. Regarding the index of marketization, we use the childcare module of the Survey of Program Participation and Income (SIPP) to estimate relative uses of market substitutes. Our index measures are based off expenditures on childcare hours purchased in the marketplace. Since this is only one aspect of marketization, we use this to target the relative use of marketization across deciles, rather than taking the absolute expenditure levels literally. The implicit assumption is that there is a strong correlation between the use of childcare and other market substitutes for parents’ time. See “Appendix A” for more details.

  22. The imperfect fit results from a corner solution in education for the first two deciles.

  23. There is well known bias in CEX data, such that comparing the CEX and the National Income and Product Accounts (NIPA) over time shows substantial divergences. Attanasio et al. (2012) surveys some of the literature on this subject. As a result, we only use CEX to examine relative expenditures on different types of goods, rather than absolute expenditures.

  24. For durables, we calculate expenditures using house furnishing and equipment expenditures (“houseeqcq”). For demand for HPS workers, we use babysitters and housekeepers expenditures (“domsrvcq” in 2010, and “housopcq” in 1980).

  25. Sato (1967) derives an equivalent expression for this elasticity using expenditure shares of the inputs.

  26. The decile specific \(\epsilon \) is monotonically increasing and is in the range of 1.54–1.73.

  27. There is one point worth discussing about time allocations. Our model focuses on understanding time allocation between home production and work, implicitly assuming that the total time on non-leisure activities has not revealed a systematic trend. American Time Use Survey (ATUS) data, however, suggests that leisure may have slightly declined between 1975 and 2003 for the group of married females that we consider: by 6 h per week for the top deciles and 3.5 h for the bottom deciles. These are based on our own calculation, and we note that the 1975 ATUS gets reduced to a very small sample once we apply our sample restrictions. If this extra time is devoted towards quantity of children, rather than quality (time spent reading to children, other education), then our results may be slightly biased for 2010. However, the basic point that the model broadly captures trends in the data is unaffected by this potential mismeasurement.

  28. In Section C of the Online Appendix we include changes in college tuition and the college premium as additional exogenous forces. The results remain largely unchanged, as these shocks exhibit offsetting effects and do not interact with wages or \(p_m\).

  29. This is the range of their IV estimates. See their Table 2.

  30. Formally, high income fertility is expressed as \(\frac{n(10) + n(9)}{2}\), MDF1 is expressed as \(\frac{n(10) + n(9)}{2} / n(2)\), and MDF2 is expressed as \(\sum _{i = 6}^{10}n(i) / \sum _{i = 1}^{5}n(i) \), where n(i) is the fertility rate of decile i.

  31. Formally, the fertility-driven measure of college attainment is computed as \(CG = \sum _{d} \frac{n(d)}{\sum _{d}n(d)} \pi ^{data}_{1980}(d)\), where \(\pi _{1980}^{data}(i)\) is the empirical college graduation rate of children born in decile i in 1980.

  32. When calculating the college attainment rates in the model using the \(\pi \) in the main experiment, the college attainment rate rises from 38.3% in 1980 to 42.8% in 2010, an even larger increase.

  33. As can be seen from Eqs.  (11) and (12), this implies that \(\frac{t_f}{m}\) remains constant, by decile, over time.

  34. We leave out the first decile in Fig. 8, because the model generates a corner solution and because couples in this decile qualify for various welfare programs that our model does not capture. This is not crucial as the effects of marketization on the first decile are minimal.

  35. Notice that the level of fertility is lower for all deciles. This is due to the fact that female wages grew more than male wages. Specifically, as can be seen from Eq. (15), the positive income effect generated by male wage growth is counterbalanced by a larger increase in the price children driven by rising female wages.

  36. Notice that the standard theory does not allow for any marketization, while in our counterfactual exercise we do not allow the relevant cost of marketization to fall over time. Thus, while the two exercises are not perfectly comparable, the underlying economics is similar.

  37. The opposite happens for the low end of the distribution where male real incomes actually fell over time.

  38. Notice that these two exercises show that marketization and the income effect do not add up to the total effect. This is because there is an interaction between the two mechanisms; when \(p_m\) decreases, the positive effect of \(w_f\) on the price of children (\(p_n\)) weakens, as seen in Equation (6) of the Online Appendix, thereby allowing the income effect of wages on fertility to grow in strength.

  39. The selection of these industries follows Mazzolari and Ragusa (2013).

  40. The data source for the minimum wage by state and year is Vaghul and Zipperer (2016).

  41. Our results below show that this variable is not important quantitatively or statistically for our findings.

  42. For example, about 9% of workers in this sector are in managerial occupations, of whom 90% earn wages above the minimum wage with an average of 2.5 times the minimum wage.

  43. We calculate this average wage without workers in the home production substitute sector in order to avoid the reflection problem (Manski 1993).

  44. We use the average of their nominate measure of state government ideology from 1960–1980. The index of state liberalism has a range of 1–100, with more liberal states receiving a higher score, with an average (standard deviation) of 62.3 (11.3).

  45. We also estimated (21) in log–log specifications which follow Table 3. In all specifications we obtain estimates that are highly significant and approximately equal to 0.5, with no clear difference between the OLS and the 2SLS estimates. An elasticity of 0.5 would imply a somewhat larger effect of changing the minimum wage on \(p_m\) than the one implied by the level regressions reported in Table 3.

  46. We are unsure why a person in our sample is earning less than minimum wage. It could be that this is a result of misreported data, lack of enforcement of the minimum wage, or an uncovered sector (waiters). To be conservative, we assume these people are unaffected by the minimum wage. Had we assumed them to be affected, then the counterfactual wage estimated here would be even higher, yielding a greater estimated impact of the minimum wage on home production substitute sector wages.

  47. We drop 1% of outlying observations, specifically those groups with top wages of less than 10.9 dollars per hour or more than 60 dollars per hour, measured in 1999 dollars.

  48. Note that if instead we were to impute wages for non-working females via a Heckman procedure and then take average wages for each decile, our model would not be able to accurately match both female income and female hours. Both of these quantities are critical to our analysis.

  49. Why not include younger women in our analysis and use the standard measure of TFR? We model time allocation between work and home production, and therefore prefer to focus on couples that completed educational investments. Using the hybrid fertility measure then enables us to correctly account for the number of children.

  50. We use the 1990 childcare module as a proxy for the 1980 index of marketization, as this is the earliest available data. We use the 2008 module to derive the 2010 index.

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Authors and Affiliations

  1. San Francisco State University, San Francisco, USA

    Michael Bar

  2. CEPR, Tel-Aviv University, Tel Aviv, Israel

    Moshe Hazan

  3. Federal Reserve Bank of St. Louis, St. Louis, USA

    Oksana Leukhina

  4. Tel Aviv University, Tel Aviv, Israel

    David Weiss

  5. New Economic School, Moscow, Russia

    Hosny Zoabi

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  1. Michael Bar
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  2. Moshe Hazan
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  3. Oksana Leukhina
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  4. David Weiss
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  5. Hosny Zoabi
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Correspondence to Moshe Hazan.

Additional information

We thank three anonymous referees, Paul Beaudry, Alma Cohen, Mariacristina De Nardi, Matthias Doepke, Axelle Ferriere, Oded Galor, Jeremy Greenwood, Nezih Guner, Lutz Hendricks, Yishay Maoz, Omer Moav, Marla Ripoll, Analia Schlosser, Itay Saporta-Eksten, Tom Vogl, David Weil, Alan Weiss, Yaniv Yedid-Levi and seminar participants in various seminars, workshops, and conferences for helpful comments. We thank Sergei Filiasov and Yannay Shanan for excellent research assistance. Moshe Hazan acknowledges financial support provided by the Israel Science Foundation and the Falk Institute for the quantitative part of the paper. Hosny Zoabi acknowledges the financial support of the Russian Science Foundation, Grant #18-18-00466 for supporting the theoretical part of the paper. This paper was previously circulated under the title “Is The Market Pronatalist? Inequality, Differential Fertility, and Growth Revisited.”

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A Data

A Data

We employ the 1980 Census and the American Community Survey (ACS) 2010 Ruggles et al. (2010) for measuring incomes, fertility and work hours of each spouse. Additionally, we use the National Longitudinal Study of Youth 1997 (NLSY 97) for measuring educational attainment of children born around 1980, by family income. Finally, we employ the Survey of Program Participation and Income for measuring childcare expenditure by family income. In this study, we focus on the growth of inequality between 1980 and 2010. These years are chosen to allow us to follow the cohort from the NLSY 97 (born around 1980) for measuring their educational attainment by their parental income, while still studying the period of rising income inequality as defined by Autor et al. (2008).

1.1 A.1 Mapping of model objects to the data

The mapping between the model and the data is not trivial. In the model, there is one period of adult life which aims to capture the entire working-age lifecycle. In the data, we observe choices of various couples of different age (fertility, work hours, etc) for a period of one year. To map the model to the data, we take the view that a model couple goes through its lifecycle by behaving according to the average age-specific behavior of those couples in the data that it represents.

There are ten types of couples in the model, each of measure 0.1. Each type of couple stands in for exactly 10% of the entire population of married couples of working age. Married couples in the data are allocated into these deciles according to their observed income. We do so based on the ranking of the couples’ observed annual income in their group, defined by the wife’s age.

From the 1980 Census and 2010 ACS data, we need to derive decile-specific empirical moments for household lifetime income, male lifetime income, male and female wages, male and female lifetime work hours, and couple’s lifetime fertility, \(I_{f,i}^{year},I_{m,i}^{year},w_{f,i}^{year},w_{m,i}^{year},hours_{f,i}^{year},n_{i}^{year},hours_{m}^{1980}\) for each decile \(i\in \left[ 1,2,\ldots 10\right] \) and \(year=1980,\text { }2010\). We state income and hours moments in annualized terms and report wages in hourly terms. This is done for clarity.

We restrict attention to white non-Hispanic married couples, aged 25–55, with the husband working at least 35 h per week and at least 40 weeks per year, following Autor et al. (2008). We also drop the couples in the bottom and top 2% of the male income distribution.

All data couples assigned to a particular income decile are used to derive the average statistics for the model couple representing that decile. To compute the decile-specific lifetime income and hours moments for men, we first average the appropriate quantity within the decile-age cells. For each decile, we then sum across ages.

In the model, all men work full time throughout their life cycle, which is normalized to be 1. This corresponds to the average lifetime hours of full-time male workers in 1980, \(hours_{m}^{1980}\) (\(\sim \,2300\) h in annualized terms). We infer the data counterpart of \(w_{m,i}^{year}\) as \(I_{m,i}^{year}/hours_{m}^{1980}\). Note that the 1980 average hours are used to derive \(w_{m,i}^{year}\) in each year. This method ensures that the observed variation of total male incomes across deciles and time will be fully reflected in the purchasing power of couples in the model.

Note that when we consider say a 37 year old woman in 1980 in a given decile, we observe her work hours, which partly reflect her number of children and their age distribution. Our goal here, however, is to derive average working hours for a hypothetical woman that experiences her lifecycle according to the cross-sectional profile. We need to proxy the hours each woman would work if she were to follow the 1980s cross-sectional fertility profile, not that of her own cohort. To this end, we regress female work hours in a given year on the actual age distribution of her children (i.e. number of children under 2, 2–3, 4–6, 7–10, 11–17), income decile and age dummies. We then predict the average adjusted female hours in each decile and for each age using the children’s age distribution implied by the cross-sectional fertility profile. For each decile, we sum these average adjusted hours across age groups to obtain \(hours_{f,i}^{year}\) and infer the data counterpart of time spent in home production \(t_{f,i}^{year}\) as

$$\begin{aligned} 1-hours_{f,i}^{year}/hours_{m}^{1980}. \end{aligned}$$

We infer the data counterpart of \(w_{f,i}\) as \(I_{f,i}^{year}/hours_{f,i}^{year}\) (about 2050 h in annualized terms).Footnote 48 We infer the empirical counterpart of \(n_{i}\) as a decile-specific hybrid Total Fertility Rate (TFR), as in Shang and Weinberg (2013). We first compute the average age-specific-birth-rate, based on all women in decile i. We then sum across all ages to compute decile-specific TFR. To obtain decile-specific hybrid TFR, we add on the average lifetime fertility among the 25 year-old women in the appropriate decile.Footnote 49

We estimate college attainment for 1980 from NLSY97. Specifically, using the 2011 wave, we observe non-black non-Hispanic individuals, born between 1980 and 1982, and assign them into income deciles according to their parental household income in 1996. We assume that individuals with at least four years of college are college graduates. We measure college attainment \(\pi _{i}^{1980}\) as the fraction of children with a college degree among all children in the appropriate decile.

Finally, we use the childcare module of the Survey of Program Participation and Income (SIPP) to estimate relative uses of market substitutes.Footnote 50 Our index measures are based off of expenditures on childcare hours purchased in the marketplace. Since this is only one aspect of marketization, we use this to target the relative use of marketization across deciles, rather than taking the absolute expenditure levels literally. The implicit assumption is that there is a strong correlation between the use of childcare and other market substitutes for parents’ time. To calculate childcare expenditures across deciles, we break households into 5-year age groups from 25–30 until 50–55. Within each group, we divide households into deciles according to their income. We then sum the childcare expenditures for each decile over the lifecycle. The index is this measure relative to the expenditures on childcare used by decile 1. As before, our sample is married, white, non-Hispanic households.

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Bar, M., Hazan, M., Leukhina, O. et al. Why did rich families increase their fertility? Inequality and marketization of child care. J Econ Growth 23, 427–463 (2018). https://doi.org/10.1007/s10887-018-9160-8

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