Intergenerational transmission of skills during childhood and optimal public policy

Abstract

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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Notes

  1. 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. 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. 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. 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. 5.

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

  6. 6.

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

  7. 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. 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. 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. 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. 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. 12.

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

  13. 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. 14.

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

  15. 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. 16.

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

  17. 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. 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. 19.

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

  20. 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. 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. 22.

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

References

  1. Balestrino A (2000) Mixed tax systems and the public provision of private goods. Int Tax Public Financ 7:463–478

    Article  Google Scholar 

  2. Balestrino A, Cigno A, Pettini A (2002) Endogenous fertility and the design of family taxation. Int Tax Public Financ 9:175–193

    Article  Google Scholar 

  3. Balestrino A, Cigno A, Pettini A (2003) Doing wonders with an egg: optimal re-distribution when households differ in market and non-market abilities. J Public Econ Theory 5:479–498

    Article  Google Scholar 

  4. Bernal R (2008) The effect of maternal employment and child care on children’s cognitive development. Int Econ Rev 49:1173–1209

    Article  Google Scholar 

  5. Bernal R, Keane M (2010) Quasi-structural estimation of a model of child-care choices and child cognitive ability production. J Econ 156:164–189

    Article  Google Scholar 

  6. Bernal R, Keane M (2011) Child care choices and children’s cognitive achievement: the case of single mothers. J Lab Econ 29:459–512

    Article  Google Scholar 

  7. Blomquist S, Christiansen V, Micheletto L (2010) Public provision of private goods and nondistortionary marginal tax rates. Am Econ J: Econ Policy 2:1–27

    Google Scholar 

  8. Casarico A, Sommacal A (2012) Labor income taxation, human capital and growth: the role of child care. Scand J Econ 114:1182–1207

    Google Scholar 

  9. Casarico A, Micheletto L, Sommacal A (2011) Intergenerational transmission of skills during childhood and optimal public policy. CESifo working paper series 3343. CESifo Group, Munich

    Google Scholar 

  10. Checchi D, Ichino A, Rustichini A (1999) More equal but less mobile? Education financing and intergenerational mobility in Italy and in the US. J Public Econ 74:351–393

    Article  Google Scholar 

  11. Cremer H, Pestieau P (2006) Intergenerational transfer of human capital and optimal education policy. J Public Econ Theory 8:529–545

    Article  Google Scholar 

  12. Cunha F, Heckman J (2007) The technology of skill formation. Am Econ Rev 97:31–47

    Article  Google Scholar 

  13. Cunha F, Heckman J, Lochner L, Masterov D (2005) Interpreting the evidence on life cycle skill formation. In: Hanushek E, Welch F (eds) Handbook of the economics of education. North Holland, Amsterdam

    Google Scholar 

  14. Edwards J, Keen M, Tuomala M (1994) Income tax, commodity taxes and public good provision: a brief guide. FinanzArch 51:472–487

    Google Scholar 

  15. Giuliano P (2008) Culture and the family: an application to educational choices in Italy. Riv Polit Econ 98:3–38

    Google Scholar 

  16. Glomm G, Kaganovich M (2008) Social security, public education and the growth inequality relationship. Eur Econ Rev 52:1009–1034

    Article  Google Scholar 

  17. Glomm G, Ravikumar B (1992) Public versus private investment in human capital: endogenous growth and income inequality. J Polit Economy 100:818–834

    Article  Google Scholar 

  18. Guryan J, Hurst E, Kearney M (2008) Parental education and parental time with children. J Econ Perspect 22:23–46

    Article  Google Scholar 

  19. Havnes T, Mogstad M (2010) Is universal child care leveling the playing field? Evidence from non-linear difference-in-differences. Discussion paper 4978. Institute for the Study of Labor (IZA), Bonn

    Google Scholar 

  20. Heckman J, Masterov D (2007) The productivity argument for investing in young children. Working papers 13016. NBER, Cambridge

    Google Scholar 

  21. Juster FT (1985) A note on recent changes in time use. In: Juster FT, Stafford FP (eds) Time, goods, and well-being. Institute for Social Research, University of Michigan, Ann Arbor

    Google Scholar 

  22. Kleven HJ, C T Kreiner, Saez E (2009) The optimal income taxation of couples. Econometrica 77:537–560

    Article  Google Scholar 

  23. Kopczuk W (2013) Incentive effects of inheritances and optimal estate taxation. Am Econ Rev: Pap Proc 103:472–477

    Article  Google Scholar 

  24. Li W, Sarte P-D (2004) Progressive taxation and long-run growth. Am Econ Rev 94:1705–1716

    Article  Google Scholar 

  25. McDaniel C (2007) Average tax rates on consumption, investment, labor and capital in the OECD 1950–2003. Mimeo

  26. Mirrlees JA (1971) An exploration in the theory of optimum income taxation. Rev Econ Stud 38:175–208

    Article  Google Scholar 

  27. OECD (2011) Education at a glance 2011. OECD, Paris

    Google Scholar 

  28. Ruhm CJ (2004) Parental employment and child cognitive development. J Human Res 39:155–192

    Article  Google Scholar 

  29. Schokkaert E (2006) The empirical analysis of transfer motives. In: Kolm S-C, Ythier JM (eds) Handbook of the economics of giving, altruism and reciprocity. North-Holland, Amsterdam, pp 128–181

    Google Scholar 

  30. Stiglitz JE (1982) Self-selection and Pareto efficient taxation. J Public Econ 17:213–240

    Article  Google Scholar 

  31. Zollino F (2008) Il difficile accesso ai servizi di istruzione per la prima infanzia in Italia: i fattori di offerta e di domanda. Questioni di Economia e Finanza (Occasional Papers) 30, Bank of Italy, Economic Research Department

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Acknowledgments

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). https://doi.org/10.1007/s00148-014-0505-0

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Keywords

  • Optimal taxation
  • Day care quality
  • Intergenerational transmission of skills
  • Early childhood environment
  • Warm glow

JEL Classifications

  • H21
  • J22
  • J24