quantity and quality of center-based care, and we simulated a broader set of households using vouchers, some of which benefit from high-quality centers in terms of child development.

We can compare the effects of our targeted voucher simulations with those of several actual programs. For example, Bettendorf et al. (2015) study a child care policy in the Netherlands, in which the subsidy amount is decreasing in family income and covers between 25 and 95 percent of child care costs. They find only modest increases in maternal employment rate, a result consistent with the relatively small decline in mothers’ participation rates implied by our income-targeted voucher simulations.

Some tax credit policies are similar to our income-based and work-requirement vouchers. Credit fungibility is different, since tax credits can be used to buy any goods and services, but conditionality is the same. For instance, the Earned Income Tax Credit (EITC) requires that at least one household member work, and the benefit amount decreases after an income threshold. There is evidence that EITC raises labor market participation for single mothers but lowers it for secondary earners (Eissa and Hoynes (2006) and Hotz (2003)). Dahl and Lochner (2012), Dahl and Lochner (2017) and Lundstrom (2017) find that EITC expansions improve children’s math and reading achievement. However, Heckman and Mosso (2014) caution against taking these results as evidence that cash transfers substantially improves children’s outcomes because they ignore equilibrium effects on female labor supply. Agostinelli and Sorrenti (2018) improve on this margin by controlling for the endogeneity of family income and maternal labor supply to study the EITC and its impact on single mothers who work. They find that a subsidy of $1,000 a year increases average child development by about 0.044 s.d–an impact bigger than ours.<sup>40</sup> Since our sample children are very young, our cash transfer simulation is comparable to cash transfers for households with newborn or very young children, common in numerous European countries and Canada (OECD, 2011). Gonz ́alez (2013) considers the effect of a large and unanticipated lump-sum universal child cash transfer to mothers with newborn babies. She finds the policy led to a substantially lower use of formal day care services and a temporary reduction in mother’s labor supply, with an increase in maternal care time. Schirle (2015) studies the Canadian Universal Child Care Benefit, which distributes a monthly amount ($100 in 2012) per child under six years of age. She finds substantial reductions in labor supply for mothers with high and low education levels, with stronger impacts for the latter. Milligan and Stabile (2009) studies a transfer expansion to households with children ages zero to five in the Canadian state of Manitoba. They find large differences in labor supply responses by mother’s education and estimate a negative impact only for households with low education levels. In our cash transfer simulation, we also find different effects on labor force participation and child development by mother’s education, with larger effects for college mothers. Since education is correlated with income, these heterogenous effects by mother’s education are consistent with the heterogenous effects by income estimated in the literature (see Løken et al. (2012) using Norwegian data.)

> 40In our simulations, the subsidy and voucher are $40 per day, generating a subsidy of $10,000 a year if the subsidy is used five days a week for about 11 months a year. As shown in Table F.1, the effect of the most effective interventions for married mothers is at most 0.13 s.d. The highest effect is for single mothers under quality-based vouchers (0.16 s.d.). A caveat worth noting is that income enters child development in our model and policy simulations through the choice of child-care mode, unlike in the reduced form literature where income can also affect the use of other goods and services which may directly affect child development.

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