women would choose to work even in the absence of work requirements. Interestingly, most policies lead to a decline in the average price of center-based care although they expand its demand because of equilibrium effects on the supply side. Indeed, the policies lead the most efficient incumbents to expand and offer high-quality services while encouraging the entry of additional providers. Accounting for equilibrium effects also illustrates that some voucher policies could “pay for themselves” by increasing mothers’ labor supply and aggregate household income, thereby lowering the implicit tax rate needed to finance the policies. Location characteristics affect some policy implications. For example, vouchers-based policies expand the use of child care centers in all locations but to a greater extent in large, high-income locations due to two equilibrium channels. On the demand side, higher-income locations have a higher share of college-educated households, in which mothers have greater incentives to join the workforce and hire center-based care. On the supply side, larger locations have a larger customer base, favoring the entry of more centers in the market.

Which policy is preferable depends on the policy maker’s objective. If the goal is maximizing aggregate household income through increases in female labor supply, then vouchers with work requirements are the best choice according to our simulations. If the goal is maximizing child development gains, then vouchers to attend high-quality centers are the best choice. Further, the preferable policy varies across locations. For example, quality-based vouchers are the best option to maximize child development gains in large locations but universal vouchers are best for small locations. In a large location, limiting vouchers to high-quality centers does not impose a substantial constraint because the large size encourages entry by high-quality providers under _any_ voucher program. In contrast, a small location may not support many high-quality providers, which hinders the usefulness of quality-based vouchers. Regardless of specific features and locations, what makes vouchers effective is that, by harnessing the power of the market, they trigger a supply expansion and deliver widespread gains, whereas attempts to publicly control supply shrink the market and only benefit those initially using center-based provision.

Although no other study models both supply and demand of child care, numerous contributions have focused on a single side of the market. On the demand side, a large literature looks at parental labor supply, child care use, and child development. The first strand of this literature starts with the early contributions based on static labor supply models with unitary households that make employment and child care decisions.<sup>6</sup> These papers use various US datasets and estimate reduced form and structural models to identify the effect of child care costs on female labor supply and child care demand. They find that, consistent with the neoclassical model, maternal employment and use of formal child care are sensitive to child care costs. Child care subsidies, particularly for the poor, can substantially increase labor force participation and child care use. Our modeling of parents’ labor supply is similar to that of these first-generation papers.

The second strand of the demand-side literature conducts impact evaluation of child care subsidy policies to estimate their effect on maternal employment and child development outcomes.<sup>7</sup> For example, Baker et al. (2008) analyze the introduction of the $5-dollar-a-day

> 6See, for example, Heckman (1974b), Blau and Robins (1988), Ribar (1992), Kimmel and Connelly (2007).

> 7There is a growing literature on child development impacts of parental leave policies (e.g., Dustmann and Schonberg (2012) and Carneiro et al. (2015)).

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