We set the _cash transfer_ to the same amount as the voucher ($40 a day.) The transfer is universal, without requirements. Households can use it to purchase child care services–either from centers or from non-relative providers–but also to consume more. This experiment mimics actual cash transfer programs to households with newborn and young children and provides a useful comparison to vouchers.<sup>36</sup> Our _public provision_ simulation mimics a public entity that chooses the lowest-cost firms to operate and caps prices at cost in order to raise affordability. Since we do not model a government, we simulate a benevolent policymaker that controls center-based supply. It observes marginal costs for all potential providers and considers every possible market configuration, choosing that which maximizes social surplus (total household welfare minus center-based costs) subject to zero profits per provider. We assume that households–not the government– pay for the service because even in countries with widespread public provision (e.g., Denmark, Germany, and Sweden) most households still pay. Thus, the “public” aspect in this counterfactual refers to the policy maker’s control of supply, not free provision. Formally, let _Z_ = _{_ ( _c_<sup>_L_</sup> 1<sup>_, cH_</sup> 1<sup>)</sup><sup>_, . . . ,_(</sup><sup>_cL_</sup> _S_<sup>_, cH_</sup> _S_<sup>)</sup><sup>_} × {_0</sup><sup>_, γL, γH}_bethesetofallpossiblemarketconfigurations</sup> and _W_ ( _z,_ **p** ) the social surplus for configuration _z ∈ Z_ and prices **p** . The optimal market configuration maximizes social surplus: where _Ns_ ( **p** ) denotes provider _k_ ’s total enrollment given prices **p** .

To provide intuition for public provision, consider two thought experiments. In the first, households do not have a taste for variety, which leads to only the most efficient provider operating in the market–with minimum costs yet minimum variety. In the second, households have a taste for variety and firms have zero fixed costs, which leads to potentially one firm per household–with maximum variety yet not minimum costs. By maximizing social surplus subject to zero profits, public provision strikes a balance between costs and variety and is reminiscent of the social optimum in monopolistic competition (Dixit and Stiglitz, 1977). In general, then, public provision yields fewer providers and lower prices than the baseline.

# **6.2 Results**

Table F.1 shows detailed simulation results for all policies. The magnitude of policy impacts varies across policies partly reflecting their eligibility and take-up rates (top panel of Table 6). All households are eligible for the cash transfer, universal voucher, quality-based voucher, and public provision, but only 46 and 25 percent of households are eligible for the employmentbased and income-targeted vouchers, respectively. Moreover, not all eligible households use a policy. Only 55 percent of households take up the universal voucher, with even lower take-up rates for conditional vouchers: 48, 42, and 8 percent respectively for quality-based, employment-based, and income-targeted vouchers. Take-up rates are also low for public provision, as only 27 percent of households use child care centers.

> 36Universal child benefits, frequently in the form of cash transfers, are common in numerous European countries and Canada. See for example, OECD (2011), Gonz ́alez (2013), and Schirle (2015).

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