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The motherhood wage and income traps

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Abstract

We present a simple dynamic model based on on-the-job human capital accumulation affecting the dynamic of wage rates and labor earnings. The model can generate and explain the different dynamics of women’s earnings after childbirth documented in the empirical literature on child penalties. We show that the temporary negative shock in labor supply due to childbearing may create a wage trap and a permanent divergence of labor earnings between genders. Even when the wage trap is avoided, and working mothers are on a path toward a high-wage equilibrium, slow convergence can permanently reduce earnings. We use this model to study the impact of different policies on the gender wage gap and child penalties. We show that mandatory maternal leave exacerbates the shock which pleads against long leaves. Similarly, cash transfers to mothers aggravate gender wage differences via the income effect on labor supply. By contrast, temporary subsidies to mothers’ wages (possibly in the form of income tax credits) are not only useful to exit the wage trap, but also to speed up recovery and reduce the child penalty when the shock in labor supply is small enough to avoid the wage trap. Other family policies, like childcare subsidies and in-kind provision of formal childcare, are potentially useful because they reduce the mothers’ cost of labor supply, but they affect mothers’ choices only indirectly.

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We do not use any data.

Notes

  1. The concept of traps, and particularly poverty traps, has been widely studied in the macroeconomic literature. The seminal paper is Azariadis and Drazen (1990), who show how poverty traps can emerge when human capital is subject to threshold externalities. While traps are often modelled as low-level equilibria in a static model of coordination failures, we discuss the concept in a dynamic setting, following Matsuyama (2008). In a static setting, we would be unable to distinguish poverty traps from (possibly temporary) bad market outcomes, that are also often modelled as low-level equilibriums in a static model of coordination failures; see Matsuyama (2008) for further discussion and references. Furthermore, studying the persistence of a child penalty for years after the initial shock is inherently a dynamic problem.

  2. We could characterize the conditions on the primitives of the model which lead to the considered dynamics. However, this would be a purely technical exercise which would not provide any further intuition.

  3. In Albanesi and Olivetti (2009), a gendered equilibrium realizes from the beginning of a woman’s working life and irrespective of the labor supply shock due to childbearing. Hence, their equilibria do not reproduce the earnings dynamics in Kleven et al. (2019a, 2019b).

  4. Since learning-by-doing is interpreted at the aggregate level, Eq. 5 does not enter the individual’s maximization problem stated in Eq. 1.

  5. Since \(\psi _{A}^{\prime \prime }[\varpi ]=0\) for \(\varpi ^{n_A}=(n_A-1)\theta _A/(1+n_A)\), a necessary and sufficient condition to have \(\psi _{A}[.]\) first convex and then concave in (0, 1) is that \(1>(n_A-1)\theta _A /(1+n_A)\), meaning that \(\theta _A<(1+n_A)/(n_A-1)\). Obviously, \(\theta _A \in (0,1)\) represents a sufficient condition.

  6. Increasing or decreasing depending on the initial level; see our Illustration A and the discussion provided in Section 4.1 for more details.

  7. A steady state is achieved when \(\ell _{t+1}=\ell _t\) so that once this level is achieved, labor supply remains constant and equal to \(\ell ^\star \).

  8. See Fig. 1 and the comments provided there for an illustration.

  9. Increasing or decreasing, depending on \(\ell _{-1}\) or equivalently \(w_{0}\).

  10. Formally, this is established by a simple argument. We have shown above that when \(\varphi [.]\) is an increasing function \(\Delta [.]\) is increasing (and positive). Since \(\psi [.]\) is also an increasing and positive function, it follows that \(\Gamma [.]=\psi [.]\Delta [.]\), which is the product of these two functions, is also increasing and positive and the same applies to the inverse function, \(\Gamma ^{-1}[.]\), given that \(\Gamma ^{\prime }[.]\ne 0\). Consequently, \(\Phi [.]=\Gamma [\Delta [\Gamma ^{-1}[.]]]\) is the composite of three increasing and positive functions.

  11. When \(\Delta [0]>0\) and \(\Delta [1]<1\), it is, for instance, straightforward to show that there exists at least one steady state \(\ell ^{\star }\in (0,1)\).

  12. With some abuse \(\psi ^{2}[.]\) is used to denote \((\psi [.])^{2}\).

  13. If the three dynamics described by Eqs. 6 and 16–18 are defined for \(\ell _{t-1}\ne 0\), \(w_{t}\ne 0\) and \(y_{t}\ne 0\), it is easy to show that \(\Delta [0]=(1+b)a^{2} \varepsilon _A/(1+a^{2}\varepsilon _A)\), \(\Omega [0]=\varepsilon _A\) and \(\Phi [0]=(1+b)a^{2}\varepsilon _A^{2}/(1+a^{2}\varepsilon _A)\).

  14. A very simple way to introduce discrimination could be to make the function \(\psi [.]\), defined by Eq. 5 gender-specific.

  15. We thank a reviewer who pointed out that this property deserves more emphasis.

  16. But, at least in our example, the speed of convergence crucially depends on the extent of the shock. As Fig. 2 shows, \(\ell _{5}=0.8238\) yields very slow convergence.

  17. In their empirical analysis, they consider three types of occupations that have different entry wages and different rates of atrophy (skill depreciation) and wage growth: routine, abstract, and manual occupations.

  18. Del Rey et al. (2017) also find an ambiguous impact but for different reasons. They study the effects of maternity leave on unemployment and wages in a search and matching model of the labor market. Crucial factors in their model are women’s wage bargaining power and the value of the leave for worker relative to the employer.

  19. See also Kleven et al. (2020). Girsberger et al. (2023) find a positive but very modest effect for Switzerland.

  20. Child-related cash transfers to families with children include child allowances and public income support payments which may depend on the child’s age and/or family size and sometimes are income-tested. Income support payments cover periods of parental leave and aid for solo parents’ families. In OECD statistics, cash, and in-kind transfers are lumped together and, on average, represent 1.163 of GDP; see OECD (2022)

  21. See for instance Pestieau and Ponthière (2013).

  22. A large literature has examined the labor supply effects of EITC in the US; see Nichols and Rothstein (2016) for a survey. In the UK, the main in-work benefit is the Working Family Tax Credit, introduced in 1999. A general consensus exists that this policy raised the employment rate of lone mothers by 4–5 percentage points; see, among others, Francesconi and van der Klaauw (2007).

  23. Applying the subsidy in periods 6 and 7 yields similar results but with some extra delay for the recovery of women’s income.

  24. Azmat (2019) argues that the nominal beneficiary of the subsidy matters, which is not in line with conventional wisdom on tax incidence. However, we assume that the subsidy is paid to the worker so that Azmat’s argument is consistent with our assumption that the subsidy benefits the workers.

  25. A possible efficiency-enhancing role of paternity leave is also described by Bastani et al. (2019). In their setting, workers differ in their family orientation (i.e., their propensity to take up parental leave), and the fraction of family-oriented workers is lower among men than among women. Firms are unable to offer distinct contracts to workers differing in their family orientation; thus, a distortion arises, taking the form of an underprovision of workplace flexibility. Parental leave mandates are a means to regulate the extent of workplace flexibility, thereby mitigating the distortion and also promoting redistributive goals by reducing the extent of gender pay gaps.

  26. In Sweden, firms must provide 12 months of parental leave per child, evenly divided between both parents, with 3 months specifically allocated to fathers. This policy may contribute to a slight reduction in Swedish fathers’ earnings due to taking more paternity leave compared to their American or German counterparts. Typically, fathers return to work after 3 months, while mothers often stay home longer.

  27. Considering together parental leave and childcare subsidies and studying the impact of Austrian reforms since the 1950s on the full dynamic of male and female earnings, Kleven et al. (2020, page 1) conclude that “The enormous expansions of parental [for mothers and fathers] leave and childcare subsidies have had virtually no impact on gender convergence.” Our analysis suggests a possible explanation of this result: the beneficial effect of childcare and paternal leave and the negative effect of a relatively long maternity leave might have canceled out.

  28. See for instance d’Albis et al. (2018) or Pestieau and Ponthière (2015).

  29. See Connoly et al. (2023).

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Acknowledgements

The authors would like to thank the anonymous referees for helpful comments and suggestions. We thank Martial Dupaigne and Andrea Ichino for helpful discussions. We also thank the reviewers and the editor, Grégory Ponthière, for their detailed and constructive comments.

Funding

Helmuth Cremer and Emmanuel Thibault gratefully acknowledge financial support from the Chaire “Marché des risques et création de valeur” of the FdR/SCOR and from the Agence Nationale de la Recherche under grant ANR-17-EURE-0010 (Investissements d’Avenir program); Francesca Barigozzi gratefully acknowledges financial support from RFO University of Bologna.

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Authors and Affiliations

  1. University of Bologna, Bologna, Italy

    Francesca Barigozzi

  2. Toulouse School of Economics, University of Toulouse Capitole, Toulouse, France

    Helmuth Cremer

  3. Toulouse School of Economics (University of Perpignan), Toulouse, France

    Emmanuel Thibault

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Correspondence to Helmuth Cremer.

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Barigozzi, F., Cremer, H. & Thibault, E. The motherhood wage and income traps. J Popul Econ 37, 74 (2024). https://doi.org/10.1007/s00148-024-01053-4

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