and education, initial child development, preferences, availability of informal care, and location. Child care providers are heterogeneous in their marginal costs–capturing, for instance, heterogeneous managerial ability.

To see the relevance of the equilibrium mechanisms in our model, consider a policy that provides child care vouchers to all households. Such policy would raise the demand and use of child care and, if the supply of child care centers did not change, it would raise prices by a given amount. Our model, however, allows incumbents to alter their supply and also allows for the entry of new providers, leading to a lower price increase (or even a decrease) and a greater expansion of child care use than if supply did not change. These equilibrium effects are crucial when evaluating the large-scale policies often proposed to increase access to center-based care.

We estimate the model’s structural parameters by Simulated Method of Moments (SMM) using data from the Early Childhood Longitudinal Study (ECLS). We focus on the ECLS birth cohort (ECLS-B), which is a nationally representative sample of children born in 2001 and followed from birth through kindergarten. We use the second wave, conducted between January 2003 and December 2003, when the children were two years old. The data are well suited for our study because they contain information parental labor supply, child development, child care modes, and providers’ quality. We focus on households with two-year-old children because the child care market for this age features mostly private providers and has a large expansion potential.<sup>5</sup> The estimated model fits the data well. It replicates the patterns of child care quality and price across households of different parental income, education, labor supply, and marital status. It also replicates the variation of child care markets across locations, which we define based on size (children population) and income (median family income). The point estimates show that parents value child development and mothers’ time inputs are very effective in producing child development. A novel result for children of this age is the high substitutability between time with parents and time with other care providers. Location-specific parameters imply that parental wage offers and cost of care rise with location size and income, albeit not at the same rate. As a result, high-quality child care centers are less costly relative to wages in large, high-income locations than in others.

We use the estimated model to simulate two types of policies: subsidy-based policies (vouchers and cash transfers) and public provision (e.g., public control of supply). We consider universal vouchers as well as vouchers provided only to individuals that satisfy income or work requirements, or that can only be used to attend high-quality centers. The simulations, which take into account child care market equilibrium effects, deliver large effects for universal, employment-based, and quality-based vouchers, and small effects for cash transfers, income-targeted vouchers, and public provision. All policies raise average child development relative to the baseline but the increase is small and mostly driven by children who switch from low- to high-quality centers. The impact on mothers’ labor supply is more substantial, and highest among mothers with less than a college degree. Comparing vouchers with and without work requirements shows that if access to center-based care were subsidized, many

> 5Enrollment rates in center-based care at ages 3 to 5 are relatively high in developed countries (Laughlin (2013) and Chzhen et al. (2019)), and provision is frequently public. The US has seen a stable increase in public preschool programs targeting children ages three and four but not two.

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