child care policy in Quebec, Canada. They find an increase in child care use and maternal employment yet negative effects on child outcomes. Havnes and Mogstad (2011b) find that universal child care in Norway crowds out informal care modes but does not increase maternal employment. The impact on long-run children’s outcomes is heterogeneous, with positive effects at the bottom of the income distribution and negative at the top. Our model captures such effects by introducing rich heterogeneity in demand and supply while allowing some structural parameters to vary with mothers’ education.

The third strand of the demand-side literature studies the effect of maternal time as an input for child development. The earlier papers estimate hybrid equations, where parameters embody both technological properties of the production function and the effect of mediating variables. For example, Ruhm (2004) uses data on the children of individuals from the National Longitudinal Survey of Youth (NLSY), and finds that maternal employment during the first three years of life is negatively associated with children outcomes at ages three to five. Bernal and Keane (2011) evaluate the effect of child care versus maternal time using single mothers from the NLSY79. Exploiting exogenous variation in welfare policy rules, they find a negative effect of child care relative to maternal care on child development. Attanasio et al. (2020) estimate dynamic factor models of child cognitive and socio-emotional skills as a function of endogenous material and time investments, and find that time inputs are an important determinant of child outcomes.<sup>8</sup> Our model includes both mother’s and father’s time as inputs in child development production as well as time with non-parental providers, whose impact varies across providers.

The fourth strand of the demand-side literature employs a fully structural approach. Bernal (2008) estimates a dynamic model of employment, child care use, and production of child cognitive ability, which allows her to handle endogeneity in maternal employment and perform counterfactuals. She estimates the model on a sample of single mothers from the NLSY79, and finds that a child care subsidy would increase overall parental utility yet at the expense of child development. Also in the context of dynamic structural model of skill formation, Del Boca et al. (2014) use the Child Development Supplements of the Panel Study of Income Dynamics and exploit detailed data on parental time use with children rather than the usual, coarse measure of maternal employment. Consistent with the rest of the literature, they find that parental time inputs are relatively more important than material resources for children’s cognitive development.<sup>9</sup> Our paper also seeks to recover the structural parameters underpinning parents’ decision. In addition, it models the supply side of the market. To handle the inherent complexity of endogenizing both demand and supply, it uses a static rather than a dynamic framework.

The supply-side literature is much more limited in number of papers and scope. Blau and Mocan (2002) estimate the relationship between cost and child care quality with data from a US sample of child care centers. Using a center quality measure similar to ours, they show that the supply of quality is moderately elastic with respect to prices and child

> 8Cunha et al. (2010) and Agostinelli and Wiswall (2016) also estimate dynamic models but do not separate returns to material and time investments.

> 9Within this structural approach, Liu et al. (2010) is a rare contribution estimating a dynamic model which includes a location decision affected by K-12 school quality, in addition to labor supply and child quality production. This paper does not include maternal time as an input in child development.

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