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Parenting style as an investment in human development

A Correction to this article was published on 11 April 2020

This article has been updated

Abstract

We propose a household production function approach to human development that explicitly considers the role of parenting style in child rearing. Specifically, parenting style is modeled as an investment that depends not only on inputs of time and market goods, but also on attention. Our model relates socioeconomic disadvantage to parenting style and human development through the constraints that disadvantage places on cognitive capacity. We find empirical support for key features of our model. Parenting style is a construct that is distinctive to standard parental investments and is important for young-adult outcomes. Effective parenting styles are negatively correlated with disadvantage.

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Fig. 1

Change history

  • 11 April 2020

    It has been brought to our attention that the comparative statics derived in Section 3.3.1 of our paper and presented in Table 1 (p. 1326) are wrong.

Notes

  1. Fiorini and Keane (2014) argue that studies which focus on single inputs into child development and do not consider the trade-offs between alternative inputs provide limited and potentially misleading information.

  2. Socioeconomic disadvantage, for example, has been linked to increased risk-taking, more impatience, and diminished self-control (Haushofer and Fehr 2014; Bernheim et al. 2015).

  3. Ermisch (2003) provides an excellent overview.

  4. Lillard and Willis (1997) provide extensive descriptions of each of these motives in a developing country context.

  5. The empirical evidence on cultural transmission is somewhat limited, but nonetheless suggests that interactions within families and local communities play a role in shaping, for instance, ethnic and religious identities (Bisin and Verdier 2010), risk preferences (Dohmen et al. 2011), and attitudes towards welfare (Barón et al. 2015).

  6. Interestingly, Michael and Becker (1973) model home production as a function of time inputs, market goods, a3.1nd the “environment” in which production takes place. The role of environmental inputs, however, has not received much attention in the home production literature. More recently, economists have explicitly begun to consider the role of inattention in inter-temporal decision-making (see Taubinsky 2014), however, as yet these models have not been applied to parental decision-making.

  7. Although parenting-related investments can also have consumption benefits for parents and thus children can provide utility directly to them (Becker 1960, p. 210), we abstract from that here in order to focus on the potential for mechanisms that are not preference-based to account for the relationship between socioeconomic disadvantage and human development.

  8. See Gorman (1959) for the formal conditions underpinning utility separability.

  9. See Del Boca et al. (2014) for a less general model that explicitly accounts for parents’ trade-off between child rearing and other consumption.

  10. We simplify notation by considering x to be a “basket of goods” priced by an index p.

  11. Our choice of attention-augmented earnings follows the same rationale as Becker’s (1985) model of effort allocation in the household, which incorporates energy—the parallel of attention in our model—into the allocation of resources across economic activities. In fact, the interaction between attention and time in the production of earnings in our model is a specific case of Becker’s earnings specification where “firms are indifferent to the distribution of hours among identical workers” (Becker 1985, p. S44). Alternatively, it is possible to assume that w = w(a), with w > 0 and w′′ < 0. The central intuition behind our model does not change under this more general framework.

  12. The tunneling that scarcity induces—i.e. the heightened focus on the most salient issues to the exclusion of others—is not specific to poverty, but rather holds across a broad range of contexts (Shah et al. 2012; Mullainathan and Shafir 2013). Those who are hungry focus on food-related cues, for example, while those who are busy focus more intensely on task deadlines (see Shah et al. 2012 and the references therein.)

  13. To see this, substitute Equations (4) and (5) into Equation (6) and rearrange.

  14. The counterpart to Equation (10) when there is joint production—i.e. the use of an input in the production of more than one investment at the same time—captures the same intuition but adds notational burden (see Michael and Becker 1973).

  15. Comparative statics can also be derived in the case of joint production and multiple parental investments of the same type. However, the results are only informative under additional functional form assumptions and they add little to the intuition of the model.

  16. For details, see Breunig et al. (2007, 2009) and http://youthinfocus.anu.edu.au.

  17. Australia’s social security system is nearly universal because many family-related payments are either not means-tested at all or have very high income thresholds. For example, the Family Tax Benefit is an income tax credit for families with children that is denied only to families in the top 20% of the income distribution. To place these benefits in context, similar benefits in the United States are provided to families through the tax system in the form of child care rebates and standard deductions for dependent children.

  18. The loadings of the first five main components, with eigenvalues larger than one, are reported in Table 8 in the Appendix.

  19. These results are presented in Tables B4 and B5 in the Appendix.

  20. The value of differentiating between goods- and time-related inputs is shown in Attanasio et al. (2015).

  21. PCA and factor analysis are frequently used to construct indices of latent parenting constructs from multiple items (e.g., Ermisch 2008; Fiorini and Keane 2014).

  22. The use of the Oblimax rotation results in factors that are non-orthogonal and are, in fact, clearly linked through the common loadings on the last two measures.

  23. Doepke and Zilibotti (2017) compare parenting styles across countries. In aggregate, parenting style has a relatively uniform distribution in Australia with approximately one third of parents falling into each of the three main categorizations (authoritarian, authoritative, permissive). Relative to US parents, Australian parents are somewhat less likely to employ authoritative parenting (see Doepke and Zilibotti 2017; Figure 1 p. 1337).

  24. Our two indices can be used to categorize parents into four mutually exclusive types: authoritative (highly respectful and highly monitoring), authoritarian (not respectful and highly monitoring), permissive (highly respectful and not monitoring), and disengaged (not respectful and not monitoring). These four categories are commonly used in the developmental psychology literature (e.g., Baumrind 1967; Maccoby and Martin 1983) and have recently been incorporated into economic models of preference transmission (Doepke and Zilibotti 2017). Results using the four-way classification are available upon request.

  25. For example, among the supporting studies cited by Bradley and Robert (2002), some report only heavily mediated effects which are hard to interpret (e.g., Conger et al. 1992). Others combine warmth, nurturance and other parenting practices together, making it impossible to infer the relationship between disadvantage and separate parenting constructs (e.g., Lempers et al. 1989; Conger et al. 1992; McCoy et al. 1999). Of the studies with good measures of economic disadvantage and parental warmth, at least one does not find a strong association between the two (McLoyd et al. 1994). Several studies find no (or only a weak) relationship between socioeconomic status and parental warmth (e.g., Patterson et al. 1989; Dodge et al. 1994; Davis et al. 2001; Davis-Kean 2005), while Guo and Harris (2000) and Yeung et al. (2002) are somewhat unique in reporting some evidence of a negative relationship.

  26. Specifically, high-school graduates who meet certain minimum coursework requirements (e.g., with respect to minimum credit hours, English requirements, school attendance) are assigned a percentile ranking based on their academic performance in grades 11 and 12. Rankings are based on a combination of in-class performance, performance on standardized state-based exams, and the degree of difficulty in students’ curriculum. Although each of Australia’s six states and two territories calculates this ranking differently, a national conversion allows comparisons to be made across students educated in different jurisdictions. These rankings are high-stakes in that places for specific degree programs at Australian universities are centrally allocated in rank order on the basis of students’ entrance rankings (see Marks et al. 2001).

  27. We also created and analyzed indicators for each of our eight forms of risky behavior separately. Respectful parenting is correlated with significantly lower levels of risky behavior across the board. Monitoring parenting is correlated with lower levels of getting in trouble with the police and using illicit drugs.

  28. For simplicity, we ignore here the role of non-market income, VP.

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Acknowledgements

The data used for this research come from the Youth in Focus Project which is jointly funded by the Australian Government and the Australian Research Council (Grant Number LP0347164) and carried out by the Australian National University. The research was also supported by the Australian Research Council through a Discovery Program Grant (DP140102614) and the Centre of Excellence for Children and Families over the Life Course (project number CE140100027). The Centre is administered by the Institute for Social Science Research at The University of Queensland, with nodes at The University of Western Australia, The University of Melbourne and The University of Sydney. We thank Dan Hamermesh, David Ribar, two anonymous referees, and the editor of this Journal for their comments on earlier drafts of this paper, and several seminar participants and conference attendees for their useful comments. The views expressed herein are solely those of the authors.

Funding

The data used for this research come from the Youth in Focus Project which is jointly funded by the Australian Government and the Australian Research Council (Grant Number LP0347164) and carried out by the Australian National University. The research was also supported by the Australian Research Council through a Discovery Program Grant (DP140102614) and the Centre of Excellence for Children and Families over the Life Course (project number CE140100027).

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Appendices

Appendix 1

Parenting Model with Linear Parenting Technologies and Cobb-Douglas Human Development

In this appendix, we develop the comparative statics presented in Section 3.3.1 of the paper, making two key assumptions that allow us to find closed form analytical solutions. First, we assume that parenting technologies are linear, which implies that each additional unit of input produces a constant amount of parenting investment. Second, we assume that the human development function is Cobb-Douglas, which implies that parental investments have a constant elasticity of substitution of one in the production of human development (i.e., a 1% change in the relative marginal productivity of parental investments will result in a 1% change in their relative use). The equations in this appendix are numbered parallel to the equation numbering in the main text, so that the results here can be easily mapped into the general discussion of the paper.

From the simplified version of the model discussed in Section 3.3.1 and our additional assumptions, we can express human development as

$$ Q=\Theta {\left({Z}_x\right)}^{\alpha_x}{\left({Z}_t\right)}^{\alpha_t}{\left({Z}_a\right)}^{\alpha_a} $$
(A2)

where each of the parental investments is

$$ {Z}_x={\beta}_xx $$
(A3.1)
$$ {Z}_t={\beta}_tt $$
(A3.2)
$$ {Z}_a={\beta}_aa $$
(A3.3)

In Eq. (A2), Θ is the total factor productivity for human development and αj, j = x, t, a are Cobb-Douglas output elasticities. In Equations (A3.1) through (A3.3), βj are the marginal productivities for a unit of each input. The usual restrictions apply, meaning that αj, βj > 0 ∀ j, ∑jαj = 1, and ∑jβj = 1. The household’s input constrains, which are simplifications of Equations (4), (5), and (6) areFootnote 28

$$ {T}^P={t}_w+t $$
(A4)
$$ {A}^P={a}_w+a $$
(A5)
$$ w{t}_w{a}_w= px $$
(A6)

The Lagrangian for this maximization problem is therefore:

$$ L=\Theta {\left({\beta}_xx\right)}^{\alpha_x}{\left({\beta}_tt\right)}^{\alpha_t}{\left({\beta}_aa\right)}^{\alpha_a}+\lambda \left[w\left({T}^P-t\right)\left({A}^P-a\right)- px\right] $$
(A9)

The usual first-order conditions for an interior solution are characterized by a system of four equations (the partial derivatives of L against x, t, a, and λ, all equal to zero) and four unknowns (x, t, a, and λ). Solving this system yields:

$$ {x}^{\ast }=\frac{A^P{T}^Pw{\alpha}_x^2}{p\left({\alpha}_x+{\alpha}_t\right)\left({\alpha}_x+{\alpha}_a\right)} $$
(13a)
$$ {t}^{\ast }=\frac{T^P{\alpha}_t}{\alpha_x+{\alpha}_t} $$
(13b)
$$ {a}^{\ast }=\frac{A^P{\alpha}_a}{\alpha_x+{\alpha}_a} $$
(13c)

These solutions can be seen as expressions of the optimal (Marshallian) demands of parents for parenting inputs of market goods, time, and attention, all of which are expressed as functions of factors that are exogenous from the perspective of the parents. Substituting these solutions into Zj = βjj for j = x, t, a yields the optimal choice of parenting investments \( {Z}_x^{\ast } \), \( {Z}_t^{\ast } \), and \( {Z}_a^{\ast } \).

These results make it straight-forward to obtain comparative statics that describe the predicted change in parenting styles associated with changes in parenting attention, the price of market goods, and wage rates. Appendix Table 5 presents the same set of comparative statics as given in Table 1. As a result of the additional functional form assumptions made here, the comparative statics in Appendix Table 5 can be unambiguously signed, leading to predictions regarding the response of parental investments to exogenous changes in parenting attention, prices, and wages.

Table 8 Exploratory principal component analysis of all parent-child interactions

Strictly positive quantities are shown in bold. When parenting technologies are linear in their inputs and human development is Cobb-Douglas in parenting investments, our model unambiguously predicts, for example, that an exogenous increase in parenting attention (AP) will increase parents’ use of market goods-intensive investments relative to time-intensive investments. To see this, consider the following. The results in Appendix Table 5 indicate that the derivative of \( {R}_x^t \) with respect to AP is positive. Recall that \( {R}_x^t \) is defined in in Equation (11a) as \( \frac{\partial Q}{\partial {Z}_t}/\frac{\partial Q}{\partial {Z}_t} \), i.e., the relative marginal productivities of time-intensive versus goods-intensive parenting investments. As these marginal productivities change, there is a corresponding change in the optimal level of time-intensive (Zt) relative to goods-intensive (Zx) parenting investments. The consequences of an increase in \( {R}_x^t \) are illustrated in Appendix Fig. 1. The graph on the right depicts the optimal level of time-intensive parenting investments, while the graph on the left depicts optimal goods-intensive investments. Suppose that initially (period 0) investments are given by \( {Z}_t^0 \) and \( {Z}_x^0 \) implying that the relative productivity of these alternative investment types (\( {R}_x^{t0} \)) is given by the ratio of the slopes of their tangent lines. An increase in the marginal productivity of time-intensive investments relative to goods-intensive investments in period 1, i.e., \( {R}_x^{t1}>{R}_{x,}^{t0} \), will be associated with an increase in Zx relative to Zt. This general intuition can be applied for to the interpretation of all comparative statics in Tables 1 and Appendix Table 5.

Table 9 Correlations between parenting indices
Table 5 Comparative statics with linear parenting technologies and a cobb-douglas child development function

Appendix 2

Table 7 Summary statistics

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Cobb-Clark, D.A., Salamanca, N. & Zhu, A. Parenting style as an investment in human development. J Popul Econ 32, 1315–1352 (2019). https://doi.org/10.1007/s00148-018-0703-2

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Keywords

  • Parenting style
  • Cognitive load
  • Locus of control
  • Socioeconomic disadvantage
  • Parental investments
  • Human development

JEL classification

  • D13
  • I31
  • J13