Quasi-structural estimation of a model of childcare choices and child cognitive ability production

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Abstract

This article evaluates the effects of maternal vs. alternative care providers’ time inputs on children’s cognitive development using the sample of single mothers in the National Longitudinal Survey of Youth. To deal with the selection problem created by unobserved heterogeneity of mothers and children, we develop a model of mother’s employment and childcare decisions. We then obtain approximate decision rules for employment and childcare use, and estimate these jointly with the child’s cognitive ability production function. To help identify our selection model, we take advantage of the plausibly exogenous variation in employment and childcare choices of single mothers generated by the variation in welfare rules across states and over time created by the 1996 welfare reform legislation and earlier State waivers.

Introduction

The effects of home inputs on child cognitive development have been widely analyzed, especially in the psychology and sociology literatures. Much prior work has focused on the effects of maternal time vs. alternative provider time, and the effects of goods inputs or household income. Economists have recently become quite interested in these questions. One motivation comes from recent studies in the human capital literature, such as Keane and Wolpin, 1997, Keane and Wolpin, 2001, Keane and Wolpin, 2006 and Cameron and Heckman (1998), which suggest that labor market outcomes in later life (e.g., wages, employment) are largely determined by skill “endowments” already in place by around ages 14–16. But the early determinants of these teenage skill “endowments” remain largely a black box. Hence, the human capital literature needs to place more emphasis on investments in children at early ages, including parental time and goods inputs into child development.

Extensive research shows that early cognitive achievement is a strong predictor of later life outcomes—e.g., high early achievers tend to have higher educational attainment and higher earnings; and are less likely to have teenage births, be on welfare or participate in crime. Bernal and Keane (2008) show, using the National Longitudinal Survey of Youth (NLSY), that the test scores as early as ages 4–6 are strongly correlated with the completed education for children of single mothers.1 Thus, understanding the determinants of early cognitive achievement may be critical for the design of public policy aimed at improving subsequent labor market outcomes (see Cunha et al. (2006)). However, the question of what determines child cognitive achievement in general, and the role of parental time and goods inputs in particular, remains largely unresolved.

Two key problems hamper research in this area: (1) a paucity of good data on inputs into child cognitive development, and (2) the difficult selection problem arising because inputs into child development may be correlated with unobserved characteristics of parents and children. In this article, we tackle a small aspect of this general problem, by looking at the effects of maternal vs. alternative care provider time inputs, and household income, on child cognitive ability test scores recorded at ages 4–6. For this purpose, we use data on single mothers from the 1979 NLSY. It is useful to focus only on single mothers for reasons we describe below.

In studying the effects of maternal time inputs on child outcomes, two sources of selection bias are of key concern: (1) women that work/use childcare may differ systematically from those that do not; (2) child cognitive ability may itself influence a mother’s decisions about work/childcare. To illustrate problem (1), suppose that high-skilled women are more likely to have high cognitive ability children, and more likely to work/use childcare. Then, a statistical analysis may find a spurious positive effect of maternal employment/childcare use on cognitive outcomes. To illustrate (2), suppose mothers of low ability endowment children compensate by spending more time with them, and thus tend to work less. Again, the estimated effect of maternal employment/childcare on child cognitive outcomes is upwardly biased. Clearly, these selection issues make evaluating effects of women’s decisions on child outcomes very difficult.

The data on single mothers in the NLSY79 provide an important opportunity to address these selection problems. A subset of these women was affected by the 1996 reform of the US welfare system that created the Temporary Aid to Needy Families (TANF) program, or by earlier State welfare waivers, and/or by substantial increases in childcare subsidy spending by the ChildCare Development Fund (CCDF). These rule changes had strong effects on the incentives for single mothers to work and use childcare. In fact, the percentage of single mothers who work increased from 67% in 1992 to 79% in 2001, with even larger increases for certain subgroups.2

Thus, for women in the NLSY79 whose children reached ages 4–6 after the start of the reforms, there was a strong and plausibly exogenous increase in their incentive to work/use childcare prior to our observations on their children’s test scores. Women whose children reached ages 4–6 prior to the start of the reforms were not affected by these changes. This source of variation helps identify the effect of maternal work/childcare use on child outcomes.3

This discussion gives an intuition for our approach, but it may seem to suggest a simple before-and-after welfare reform comparison of test score outcomes and levels of maternal work—as in the natural experiment/instrumental variable (IV) literature. But this over-simplifies the approach we actually take. As Rosenzweig and Wolpin (2000) stress, what IV estimates depends on what one controls for. For example, welfare reform may have altered goods inputs, not just time inputs. Thus, to interpret our estimates, we must (i) adopt a particular theoretical model, including a specification of a child cognitive ability production function, and (ii) consider how this relates to the outcome equation we actually estimate (i.e., not all production function inputs are observed due to data limitations, complicating interpretation. We discuss this in Section 4.1).

Hence, our empirical work is guided by a structural model of mothers’ employment and childcare decisions described in Section 4.1. Using this model, we obtain approximate decision rules for employment and childcare use, and estimate these jointly with a child cognitive ability production function and mother’s wage function—an approach we call “quasi-structural.” In our selection model, welfare rules provide natural exclusion restrictions, as it is plausible they enter decision rules for employment and childcare use, but not the cognitive ability production function. We use local demand conditions as additional instruments (i.e., exclusions), as it also seems natural these enter the decision rules for work/childcare but not the cognitive ability production function. Our results imply that one year of full-time work and childcare use reduces child cognitive ability test scores by roughly 2.7% on average, or 0.14 standard deviations of the score distribution.

This result is similar to a −3.2% annual effect estimate we obtain using a single-equation IV approach, using the same welfare rule and local demand instruments. Each approach relies on somewhat different identifying assumptions; particularly, in terms of the exact form of the decision rules for work and childcare (whose form the IV approach leaves implicit). Hence, each implements a somewhat different correction for the selection of different types of children into childcare. Thus, it is comforting that the results are so similar across the two approaches.

A key advantage of a quasi-structural approach over linear IV is we can accommodate unobserved heterogeneity in effects of maternal work and childcare use on child outcomes. We find evidence of substantial observed and unobserved heterogeneity in childcare effects. Negative effects are larger for better-educated mothers and children with higher skill endowments.

Another advantage is that, by estimating the work and childcare decision rules, the wage function and the production function as a system, we achieve a rather substantial efficiency gain. Indeed, the standard error on the cumulative childcare use coefficient in the log test score equation falls by a factor of 7.4, giving us much greater confidence in the estimated effect size.4 This occurs in part, because the wage equation residual conveys information about the mother’s unobserved skill endowment, and, hence, about the unobservable in the test score equation.

On the other hand, a disadvantage of the quasi-structural approach is that mis-specification of the joint distribution of the unobservables in the four-equation system may lead to inconsistency.5 Another advantage of single equation IV is its relative simplicity of implementation which, in Bernal and Keane (2008), enables us to examine a large number of alternative specifications of the child cognitive ability production function.6 Given the time required to estimate the quasi-structural system, such extensive testing is not practical here.

A key difference between either a quasi-structural or single-equation IV approach and a full solution/full information maximum likelihood (FIML) is that FIML requires one to fully specify the process by which agents form expectations of the forcing variables. For instance, we could assume perfect foresight regarding future welfare rules, or myopia (i.e., each rule change comes as a surprise), or rational expectations (i.e., agents know the process generating the rules). The IV and quasi-structural approaches allow us to sidestep this issue in estimation.

This has both advantages and disadvantages. While it may provide more robust estimates, the failure to fully specify the model creates problems when it comes to policy simulation. For instance, a change in welfare policy may have very different effects on maternal work/childcare use, and goods inputs, depending on whether it is perceived as permanent or transitory.7 Thus, to simulate effects of policy changes on maternal decisions and child outcomes, we cannot avoid making assumptions (either explicitly or implicitly) about expectations.8

Our study of single mothers extends earlier work by Bernal (2008) on children of married women in the NLSY. Using a fully structural approach, she found that one year of maternal full-time work and childcare results in an 1.8% reduction in child cognitive ability test scores. A key motivation of our work was to see if that result generalizes from married to single mothers. Our estimate for single mothers is larger (2.7%), but the similarity of the results is still striking.

Bernal (2008) relied on very different exclusion restrictions from those used here. She treats age profiles of husband and wife earnings as exogenous, in that: (1) only parents’ skill endowments, and not their age, affect the skill the child inherits, and (2) only skill endowments and permanent income of mothers and husbands, and not short run fluctuations in household income (e.g., due to movement along the wage/age path) affect investment in children. Thus, otherwise identical women who have children when they or their husbands are at different points in the life-cycle will have different incentives to work. This creates exogenous variation in work/childcare use that helps identify the effects of maternal time inputs.9 We find this approach appealing, but exogeneity of the welfare policy rules used here seems less subject to challenge.

Besides the advantage of having highly plausible instruments (i.e., welfare rules), the study of single mothers is also of special policy interest, given that welfare policy changes have substantially increased their work and childcare usage in recent years. If childcare has negative effects on the test scores of their children, it suggests an additional cost of these policies that should be considered when evaluating their overall success.

Section snippets

Literature review

Many prior studies, mostly in developmental psychology, use the NLSY to assess effects of maternal employment or childcare on child cognitive development. For reviews see Haveman and Wolfe (1994), Lamb (1996), Love et al. (1996), Blau (1999), Ruhm (2002) and Bernal and Keane (2008). Most studies present simple correlations of inputs and child outcomes, not controlling for family or child characteristics. Rarely are controls for selection bias implemented.10

Construction of instruments using welfare rules and other policy variables

To deal with the selection problem arising because children placed in childcare may differ systematically from those who are not, we use welfare policy rules as instruments (or exclusion restrictions) to help identify our selection model. Welfare rules have a large impact on labor supply of single mothers (see Moffitt (1992)). To construct our instruments, we collected very detailed information on State welfare policies. The working article version contains a detailed list of sources, and more

Structural and quasi-structural models

We first present a structural model of single mother’s decisions about work and childcare use, and how these affect child outcomes. Rather than presenting a general model, we detail a specific model we might actually estimate, given available data and computational limitations. This helps clarify the type of assumptions needed to solve and estimate such a model. Next, we describe a “quasi-structural” approximation to the model. This clarifies how some assumptions required for structural

Individual level data

We use data from the NLSY 1979 youth cohort (NLSY79). This consists of 12,686 individuals, approximately half of them women, who were 14–21 years of age as of January 1, 1979. It includes a core random sample and over-samples of blacks, Hispanics, poor whites and the military. Interviews have been conducted annually from 1979 through 1994, and biannually since 1994. The NLSY79 has regularly collected pre- and postnatal care information from the sample women as they became mothers. In 1986, a

Estimation results for the quasi-structural model—homogenous effects case

In this section, we present parameter estimates for the “quasi-structural” model of Section 4.2. That is, we jointly estimate the approximate decision rules for work and childcare use, with the maternal wage and child cognitive ability production functions. Specifically, we maximize the likelihood given by approximate decision rules for work and childcare (see Eq. (12)), and the wage and test score density functions implied by Eqs. (13), (14).

Table 6 presents the estimates of the cognitive

Conclusions

This article evaluates the effects of maternal work and childcare use on child cognitive development, using the sample of single mothers in the NLSY. In particular, we assess the effects of maternal vs. alternative care provider time inputs, and household income, on child cognitive test scores recorded at ages 3, 4, 5 and 6. To deal with the potential bias created by unobserved heterogeneity of mothers and children, and systematic selection of certain types of children into childcare, we

Acknowledgements

We acknowledge support from the Australian Research Council grants FF0561843 and DP0774247 as well as several grants from the Minnesota Supercomputing Institute. We wish to acknowledge helpful comments from Robert Moffitt, Kenneth Wolpin, and other participants to the Conference on “Structural Models in Labor Aging and Health”- UNC and Duke (2005) and one anonymous referee.

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