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Measuring the effect of the timing of first birth on wages

Abstract

I study the effect of first-birth timing on women’s wages, defining timing in terms of labor force entry, rather than age. Considering the mechanisms by which timing may affect wages, each is a function of experience rather than age. This transformation also highlights the distinction between a first birth after labor market entry versus before. I show that estimates based on age understate the return to delay for women who remain childless at labor market entry and have obscured the negative return to delay—to a first birth after labor market entry rather than before—for all but college graduates. My results suggest, however, that these returns to first-birth timing may hold only for non-Hispanic white women.

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Notes

  1. Although K 1 reflects potential experience, in practice, it reflects actual experience for the vast majority of these women; in the NLSY79, 98 % work each year before K 1 (93 % at a rate of at least 1000 h per year).

  2. See the math in Appendix Section A.1 (available online) for a more detailed description. This drop in the wage growth rate at t = K 1 may arise, for instance, from a change in labor supply or in effort per hour worked (Becker 1985). Yet, since the magnitude of this change may be endogenous to K 1, I do not incorporate such labor supply behaviors directly into the model, in order to capture the full effect of timing on wages. (In contrast, Happel et al. (1984), Moffitt (1984), and Cigno and Ermisch (1989) and Walker (1995) assume an exogenously-defined level of maternal time associated with child-raising.) One might instead assume a temporary drop in the wage growth rate at motherhood (Wilde et al. 2010); I use this specification given Fig. 5a, which shows little evidence of a return to the pre-birth growth rate.

  3. As written, w 0 is unrelated to K 1, yet for pre- t 1 mothers one might anticipate that w 0 is at least a function of the presence of children. In Section 5, I therefore report results both with and without controlling for w 0.

  4. Note that holding constant the year of first birth, as women delay entering the labor force, K 1 becomes increasingly negative (and their first child becomes older at labor market entry). Likewise, all else equal, women with earlier first births (K 1 more negative) will have more children by t 1.

  5. This will hold only if \(g_{0}^{^{\prime }}<0\), and when measured when \( \theta =-g_{0}^{^{\prime }}\tau \).

  6. Because the NLSY79 is well known, I leave a more detailed discussion of the data to Appendix Section B.1. Appendix Sections B.2 and B.3 discuss how I define my variables, and whether my sample selection criteria may influence my results, respectively. My sample builds from both the cross-sectional and minority supplemental samples, thus throughout I report weighted results.

  7. In determining the “graduation year,” I allow gaps in post-high school education, as long as upon return, a woman completes more years of schooling at a sufficient pace. See appendix footnote 4 for more detail.

  8. Although the timing of labor market entry may not be clear cut, raising the possibility of measurement error, if I limit the analysis to women who work at least 1500 h in t 1, my results are very similar.

  9. This is primarily an issue for high school dropouts; among those who ever work, I lose 5.6 %, compared to only 1.5 and 0.3 % of high school and college graduates, respectively.

  10. Among mothers observed at least 10 years beyond B 1, 83 and 88 % return to work within 36 and 60 months, respectively, thus most women with K 1 ≤ 17 will be back to work by t 19 to t 24.

  11. Approximately 50 % of NLSY79 pre- t 1 mothers are living with a parent at first birth, with parental income their primary source of support; during the following pre- t 1 years support from spouses increases, with welfare reflecting a relatively modest source of income. These patterns are surprisingly similar between pre- t 1 mothers who take a long time to enter the labor force, and those who start working promptly, with the financial resources of the earliest mothers if anything slightly worse.

  12. Wilde et al. also highlights the limitations of using non-mothers as a comparison group.

  13. As written, I am ignoring the question of marriage. By comparison, Happel et al. (1984) and Moffitt (1984), and Cigno and Ermisch (1989) treat the timing of first marriage as the start of the planning horizon (taking its timing, and a woman’s human capital at that point, as exogenous).

  14. These three are the key sources of bias that the literature focuses on.

  15. Given the model described above, in Appendix Section A-2, I formalize the economic conditions under which bias may be captured in the OLS-estimated return to delay, \(\hat {\theta }\).

  16. As drawn here, to translate this link between θ and ability into the terms of Eq. 1, I assume g 1i = g 1(a i ), with \(g_{1}^{\prime }>0\) and g 2 constant. I also maintain the assumption of equal starting wages.

  17. As drawn here, I assume the wage growth rate g is increasing in ability. Alternatively, per Blackburn et al. (1993), women with high ψ may invest less in human capital: g i = g(ψ i ), g <0.

  18. As drawn, in the last panel of Fig. 3, I assume that women take roughly the same amount of time to conceive and give birth, \( {K_{1}^{L}}-{K_{1}^{E}} \approx {t_{c}^{L}}-{t_{c}^{E}}\).

  19. To consider how women jointly choose \(B_{1}^{\ast }\) and \(t_{1}^{\ast }\) requires a much richer model of lifetime utility that incorporates marriage (e.g., match quality, partner earnings, and the consequences of a pre-marital first birth). Given my results suggesting that many women would have higher long-run wages with a pre- t 1 first birth, this question of marriage may be especially important. Since many women instead have a first birth shortly after t 1, this suggests that some other element of the utility function is driving this delay, such as the penalty for a pre-marital first birth.

  20. In Section 5.1, I consider how t 1, and the sorting into a pre- or post- t 1 first birth, vary with individual characteristics. One might also worry, however, that this sorting may be correlated with the wage equation parameters. For instance, if g 2i g 0i , and their difference varies with i, then this sorting may be endogenous to their relative size, such that E[g 0i |p t 1 = 1]>E[g 0i ] and E[g 2i |p t 1 = 0]>E[g 2i ]. Given my goal to estimate δg 0g 2 (see Eq. 4), since my OLS coefficient will reflect E[g 0i |p t 1 = 1]−E[g 2i |p t 1 = 0], the net direction of this potential bias is ambiguous. Alternatively, if \(g_{0 \mathit {i}}=g_{2 \mathit {i}} \equiv g_{\mathit {i}}^{ \mathit {post}}\)i, since by my results \(\hat {\delta }>0\), women with higher \(g^{post}_{\mathit {i}}\) must systematically choose B 1<t 1: \( E\left [g^{post}_{\mathit {i}}|pt_{1}=1\right ]>E\left [g^{post}_{\mathit {i}}|pt_{1}=0\right ]\). (These two possibilities are the equivalent of Scenarios #2 and #3 above, where \(\hat { \delta }\) is biased by endogeneity or unobserved heterogeneity, respectively.) Although I cannot directly test whether this sorting is correlated with these parameters, observable characteristics such as ability may drive much of their variation.

  21. Variation may also arise from factors outside of the model in Section 4, such as marriage timing, or spousal preferences and earnings. I do not control for marital timing in these specifications because women may marry promptly in order to have an early first birth.

  22. For instance, among pre- t 1 mothers, for a given year of birth, B 1, K 1 becomes increasingly negative as women wait longer to enter the labor market. Since women who face higher potential wages may start working sooner, the endogeneity of t 1 may influence my estimates of both slope parameters, \(g_{0}^{\prime }\) and θ (see Fig. 1).

  23. As reported in the first row of Table 2, the average length of time off was 7 years among pre- t 1 mothers, but only 0.4 years among post- t 1 mothers, where 78 % went straight from school to work. Within my analysis sample, 80 % of post- t 1 mothers go straight to work: 53 % of high school dropouts, 81 % of high school graduates, and 89 % of college graduates.

  24. In footnote 20, I raise the possibility that my estimates \( \hat {\delta }\) are biased because the sorting into a pre- or post- t 1 first birth may be a function of g 0 and g 2. Yet, unless variation in these parameters arises from factors completely uncorrelated with the characteristics shown here, the results in Fig. 4 argue against either scenario discussed there.

  25. I see the same pattern if I plot hours worked over time or the proportion in the labor force; labor supply moves together before first birth and diverges only at t = K 1. Likewise, the labor supply pattern of pre- t 1 mothers mirrors the pattern in Fig. 5b. I also find that for post- t 1 mothers, the wage and labor supply disruption is peculiar to the first birth.

  26. Note that the kink at each vertical line in Fig. 5a is driven by the wages of the earliest mothers in each timing group and is not evident for the later mothers in each group until the year that they, in turn, have their first child. Yet, in Scenario #4, the kink in the wage path might still line up with K 1 if women can both perfectly anticipate when their wages will stall, and perfectly time their first birth accordingly. My identification strategy discussed later in this section does not directly address reverse causality. Yet, if I regress a woman’s wage level at t 5 on her subsequent first-birth timing (among women with K 1 > 5), I find no “effect” of K 1, as one would anticipate if wages drive timing. (This holds, even though roughly 40 % of these women have their first child within the next 2 years.)

  27. The composition of women in the labor force over time is likewise unrelated to ability. For instance, if I recreate Fig. 5a using average AFQT scores, but including in each year’s average only those women with an observed wage, AFQT scores within each timing group are very flat over time, with no kink at K 1. (The same holds if I plot average education.) Thus, although each point in Fig. 5 captures data only for women with observed wages in the given year, changes in composition do not drive the pattern in Fig. 5a.

  28. I control for both the calendar year of w 20, and its career year, since this varies from t 19 to t 24.

  29. The former includes where she lived at t 1 and t 20, and the local unemployment rate at labor market entry. The latter includes total children by t 20 (so that I do not capture the indirect effect on wages of timing’s influence on total fertility), spousal support from the year of first birth through t 20 (his earnings when married and alimony/child support when not), and a measure of spousal “quality” (since via assortative mating, “higher income-type” men tend to marry “higher income-type” women). Lastly, I control for years education at t 1. See the notes to Table 3 for additional controls, and Appendix Section B.2 for details on how I define them.

  30. Since Table 2 shows that pre- t 1 mothers with higher potential wages take fewer years off before t 1, and Column (3) of Table 3 also shows a negative link between years off and w 20, this suggests that years off may be a proxy for labor market quality. Yet, among pre- t 1 mothers, years off is highly (negatively) correlated with K 1—perfectly so for the 68 and 50 % of high school dropouts and graduates, respectively, who have their first birth by the end of the calendar year following their “graduation year.” Thus, when I control for years off in Eq. 4, \(\hat {\gamma }\) will be estimated off only the remaining women. Yet, this does not drive my results. For instance, among pre- t 1 high school graduates, if I reestimate Eq. 4 excluding \(k_{1}^{pt_{1}}\), the coefficient on years off is very similar for the “perfectly correlated” subset and for the remaining women. But when I instead run (4) excluding years off, while the slope on \(k_{1}^{pt_{1}}\) for the “perfectly correlated” subset is approximately the reverse of the previous coefficient on years off, the coefficient on \(k_{1}^{pt_{1}}\) for the remaining women is insignificantly different from zero. This suggests that the key relationship is between w 20 and years off.

  31. All of the elements of \(X_{\psi _{\mathit {i}}}\) are significantly correlated with first-birth timing for at least one education group, although among post- t 1 mothers, the link is more common with predicted than observed timing.

  32. In most survey waves, women were asked when they expected to have their next child, which for childless women reflects their predicted timing of first birth.

  33. Across education groups, K 1 increases by 0.3, 0.5, and 0.8 years for each 1-year increase in \(K_{1}^{pred}\).

  34. Note that I do not control for factors that may reflect the mechanism by which first-birth timing affects wages (Buckles 2008), because doing so may absorb part of the effect of K 1.

  35. If I follow Miller (2011) (as amended in Herr (2008)) in using miscarriages and contraceptive failures as instruments for first-birth timing, I again find no evidence of positive bias in θ O L S .

  36. Figure 7b shows average residual long-run wages from a regression of w 20 on the full set of controls excepting k 1, \( k_{1}^{pt_{1}}\), p t 1, and \(K_{1}^{pred}\) and “years off.” I exclude \( K_{1}^{pred}\) because its inclusion complicates the interpretation of \(\hat { \delta }\). And given the discussion in footnote 30, I exclude years off because of its strong correlation with K 1 for pre- t 1 mothers; one might otherwise worry that the change in slope for pre- t 1 mothers from Figs. 7a to b is because I am controlling for something strongly correlated with K 1. If I instead include years off, the slope in Fig. 7b is even flatter and slightly negative. These figures are similar if I use all education levels combined.

  37. The estimates in Chandler et al. (1994) and Miller (2011), 2.1 and 3.0 %, respectively, are much higher than \(\hat {\theta }\) for my pooled sample (1.4 %), driven by their sample selection criteria, which capture a subset of “high type” mothers (married and working full time, and with a first birth after 21, respectively). Building a sample consistent with Chandler et al., I find that the return measured in terms of “career timing” is 55 % larger than when measured in terms of age. By contrast, using a sample consistent with Miller, the career timing return is only 19 % larger, since only a small portion of her sample have a pre- t 1 first birth.

  38. Another possibility is that the effect of children on a woman’s wage path is unrelated to K 1, but evolves over time, in which case at t 20 I am capturing these women at different stages of this process. To consider this, I compare \(\hat {\theta }\) measured at t 15 and t 20 for women with K 1 ≤ 12 (approximately 85 % of each education group). In both education levels, the estimates are very similar, with \(\hat {\theta }_{20}\) approximately 10 % smaller than \(\hat {\theta }_{15}\).

  39. I also consider whether θ varies over time or across women. Including the quadratic of k 1 in Eq. 4, I find no evidence of a decreasing return. In the pooled sample, I do find that θ is significantly increasing in education (by 0.3 percentage points for each year of schooling at t 1), but not increasing in ability. And within education levels, I find no additional variation in θ, which, in turn, helps explain why we see no evidence of endogenous sorting in response to the large return to delay.

  40. The magnitude of \(\hat {\delta }\) is not driven by mothers who complete their childbearing before t 1; controlling for this lowers \(\hat {\delta }\) by less than 5 % for both education levels.

  41. Measuring from t 1 to t 20, pre- t 1 mothers work on average 18 and 6 % more hours, for high school dropouts and graduates, respectively. By comparison, in the 20-year stretch after leaving school, pre- t 1 mothers work on average 8 and 13 % less.

  42. Replacing w 20 with the wage level approximately 20 years after a woman’s “graduation year”, \(\hat {\delta }\) is 0.116 (s.e. 0.088) and 0.152 (s.e. 0.048) for high school dropouts and graduates, respectively.

  43. If I replace w 20 with measures of lifetime earnings, the estimates \( \hat {\delta }\) remain significantly positive throughout, whether measured in terms of own or household earnings, and over the window from either t 1 to t 20 or age 20 to 40 years. Household earnings (including spouse’s income when married, and alimony and child support when not) capture information on the men these women marry; measuring from age 20 to 40 years allows for the possibility that women make their fertility and career choices in terms of age rather than career timing.

  44. On average, black mothers take significantly more time off before working than non-Hispanic whites (2.2 versus 1.8 years), in large part because of the higher proportion with a pre- t 1 first birth. Yet, among post- t 1 mothers, blacks still take longer to start working, while among pre- t 1 mothers, they enter the labor market much more quickly.

  45. When I run a pooled regression, I cannot reject that the estimates of θ, γ, and δ are equal across all three groups. I can only reject, at the 5 % level, that δ W = δ B .

  46. This last factor is the average annual husband earnings (or alimony and child support) from first birth to t 20.

  47. If I rerun the results reported in Table 3 using only non-Hispanic white women, the results are very similar, suggesting that the pattern across education levels is not driven by variation in the racial composition (\(\hat {\delta }_{lHS}=0.242\), \(\hat {\delta }_{HS}=0.196\), \(\hat { \theta }_{HS}=0.017\), and \(\hat {\theta }_{C}=0.033\), each significant at least the 5 % level).

  48. Given my results above, this difference would have to be separate from the difference due to marriage patterns.

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Acknowledgments

I would like to thank David Card, Ronald Lee, Guido Imbens, Jesse Shapiro, Derek Neal, Elizabeth Weber Handwerker, Melanie Guldi, Emily Oster, Colleen Manchester, Sarah Hayford, Lucie Schmidt, Don Cox, Jenna Johnson-Hanks, Ashley Langer, Kevin Stange, Donna Ginther, Martha Bailey, Rachel Sullivan Robinson, two anonymous referees, and participants of the U.C. Berkeley labor seminar series, the University of Chicago’s Booth applied microeconomic series, the Federal Reserve Bank of Chicago’s seminar series, and the Wellesley College labor lunch series for helpful comments. Lastly, I would like to thank the Center for Human Potential and Public Policy at the University of Chicago’s Harris School, and its director, Ariel Kalil, for support and guidance. Financial support for this work was provided by the National Institute for Child Health and Human Development (Interdisciplinary Training Grant No. T32-HD007275).

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Correspondence to Jane Leber Herr.

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Herr, J.L. Measuring the effect of the timing of first birth on wages. J Popul Econ 29, 39–72 (2016). https://doi.org/10.1007/s00148-015-0554-z

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Keywords

  • First-birth timing
  • Women
  • Wages

JEL Classification

  • J13
  • J31
  • J16