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Intergenerational transmission of skills during childhood and optimal public policy

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We characterize the optimal tax policy and quality of day care services in an OLG model in which child care arrangements chosen by parents of different skill types affect the probability that children become high-skilled adults in a type-specific way. With respect to previous contributions, optimal tax formulas incorporate type-specific Pigouvian terms which correct for the intergenerational externality in human capital accumulation. The optimal quality of day care services is determined by equating the total private marginal benefits of a quality increase to its marginal cost, adjusted for the presence of three additional terms capturing respectively the budgetary impact of a change in demand for day care services, the intergenerational externality in human capital accumulation, and the self-selection constraint.

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  1. Havnes and Mogstad (2010) show that the focus on mean impact of day care services on child development can also mask important differences along the earnings distribution. The effects are positive and sizable below the median of the earnings distribution.

  2. A model in which child care enters the human capital production function is analyzed by Casarico and Sommacal (2012) who study the impact on growth of changes in labor income taxation. However, their analysis is not concerned with the design of optimal public policies, which is instead the focus of the current paper.

  3. Heterogeneity in the ability to raise children is also considered by Balestrino et al. (2002, 2003). In these papers, however, the authors only allow for two possible uses of time, market labor supply and parental care, do not explicitly focus on external day care, and work within a static framework. On the other hand, they consider the possibility of endogenous fertility, which we neglect in our paper, and use weaker assumptions regarding the correlation between market ability and ability to raise children.

  4. In a background version of the paper (Casarico et al. 2011), we relax the assumption of perfect correlation between the two types of skills and consider a four-type model.

  5. We assume that the government’s budget is balanced year by year without recurring to debt.

  6. See, for example, Stiglitz (1982) or Edwards et al. (1994).

  7. Note, however, that the conditions required to satisfy the agent-monotonicity assumption are stronger in our setting than those in standard optimal taxation models. In the latter, normality of consumption is a sufficient condition for agent monotonicity. In our setting, this is not enough since a high-skilled mimicker and a true low-skilled agent do not differ only with respect to their labor supply but also with respect to the amount available for private consumption (once expenses on day care services have been subtracted). A more thorough discussion of this issue is provided in a background version of this paper (see Appendix A in Casarico et al. 2011).

  8. We recall that children must be taken care of all the time, either by parents themselves or at day care centers. Therefore, if time spent with parents goes up, time spent in day care centers necessarily goes down.

  9. It is, however, clear from (12) that one should also consider how the numerator of the expression defining the marginal willingness to pay for quality differs for a mimicker and for a true lowly skilled. For simplicity, in our discussion here, we disregard the possibility that this effect more than offsets the effect that works through the difference in the denominators.

  10. This objective function is of the Greenwood-Hercowitz-Huffman type. Note that it is linear in consumption, which implies that there is no income effect on the labor supply, and it is often used in the optimal taxation literature (e.g., see Kleven et al. 2009).

  11. Given that we focus on the steady state, the discount factor ρ is just a scale parameter which does not affect the optimal policies.

  12. Data used are not all available for a single year. The reference period is 1998–2004.

  13. A few remarks are important in interpreting these data. First, we recall that in our model, parents devote time to the child only during his first 6 years of life. In collecting time use data, we therefore only consider time devoted to children over this time span, whereas the overall time endowment refers to a 25-year period. This partly explains the low share of time devoted to child care. Moreover, parental time with children is defined as the sum of the minutes devoted to primary and secondary child care: this amount of time is lower than the total time spent with children, but it better captures deliberate child care by parents. Finally, leisure is defined as a residual category, that is, it is the time not spent either working or doing primary and secondary child care: as a consequence, it is not a measure of pure leisure as it also includes, for instance, housework.

  14. The resulting values of α, β, and γ are, respectively, 0.78, 0.19, and 0.01.

  15. See Giuliano 2008. Similar estimates are provided by Checchi et al. (1999) on older data (1985 rather than 1998). The calibration delivers σ 1 = 0.31 and σ 2 = 2.69.

  16. According to the OECD (2011), the share of Italian graduates in the age group of 25–64 years was 15 % in 2009.

  17. The unitary cost of day care services is calculated by averaging OECD data on the Italian public and private per-child expenditure on preprimary education (children aged 3–6) and Bank of Italy data presented by Zollino (2008) on the public and private per-child expenditure on day care (children aged 0–3). The obtained per-child cost is then converted into an hourly cost assuming that care is available for 11 months, at 8 h per day. The hourly cost is finally divided by the wage rate of type 1 agents: the resulting value is 31 %. The calibration delivers ω = 0.28.

  18. OECD data for a two-earner married couple, with one spouse earning the average wage, the other spouse earning 33 % of the average wage, and two children.

  19. We perform a sensitivity analysis on ψ in the online Appendix.

  20. The only difference concerns the parameters of the utility function. Since the probability of becoming highly skilled π j does not depend on parental time n j, the parameter δ does not affect the allocation of time, and we normalize it to 0. Thus, to match the allocation of time of the two groups, we only have two parameters α and β, given the restriction α + β + γ = 1. These two parameters are used to match the labor supply and the time devoted to children by the lowly skilled l 1 and n 1; l 2 and n 2 are generated by the model.

  21. We here consider an ad valorem tax τ d, whereas Eq. (11) refers to an excise tax τ. Note that setting τ d = τ/p, we obtain for an ad valorem tax an equation which is equivalent to that in (11).

  22. GDP is measured at the optimum of the government’s problem when the right environment is used.


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We thank the two anonymous referees for insightful comments, as well as seminar participants at the SIEP conference in Pavia, the University of Louvain-la-Neuve, the University of St.Gallen, the University of Wien, the CESifo Area Conference on Employment and Social Protection and the IIPF Conference in Uppsala. All the remaining errors are ours. Alessandro Sommacal acknowledges financial support from MIUR within a FIRB project.

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Correspondence to Luca Micheletto.

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Responsible editor: Alessandro Cigno

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Casarico, A., Micheletto, L. & Sommacal, A. Intergenerational transmission of skills during childhood and optimal public policy. J Popul Econ 28, 353–372 (2015).

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