between time inputs by exploiting the variation in parental time inputs and child care choices conditional on educational attainment and marital status.

# **4.2.3 Parental wage offers**

Parameters in equations (22) and (23) include the gender- and education-specific parameters of the lognormal wage offers distributions, _{μwf_ ( _ef_ ) _, σwf_ ( _ef_ ) _}_ for fathers and _{μmf_ ( _ef_ ) _, σmf_ ( _ef_ ) _}_ for mothers, and the _{ρ_ 0 _, ρ_ 1 _}_ parameters of assortative mating in married parents’ wage offers. Since fathers always work in the model, their wage offer distribution is equal to the observed (accepted) wage offer distribution, allowing us to directly estimate the former from the empirical wage distribution. Mothers, instead, decide on labor supply, thereby making the observed distribution of accepted wages a truncation of the unobserved distribution of wage offers. Since the lognormal distribution is recoverable and we characterize mother’s optimal labor supply decision, we can identify wage offer parameters from observed hourly wages. We identify gender- and education-specific parameters from the observed wage distribution conditional on these observables and identify the assortative mating parameters from correlations in spousal wages conditional on education.

# **4.2.4 Child care providers**

The identification of their productivity for child development is discussed in Section 4.2.2; here we focus on the remaining parameters. For child care centers, these are the fixed costs _{F_<sup>_L_</sup> _, F_<sup>_H_</sup> _}_ and the lognormal distributional parameters for heterogeneous variable costs, _{μ_<sup>_L_</sup> _c_<sup>_, σ_</sup> _c_<sup>_L}_and</sup><sup>_{μH_</sup> _c_<sup>_, σ_</sup> _c_<sup>_H}_.Sinceourdatadonotallowustoidentifyfixedcosts,wecalibrate</sup> them using industry cost reports. Using data from the Generic Cost Model for child care centers provided in Mitchell and Stoney (2012), we obtain fixed cost values of $128.90 and $322.25 a day for low-quality and high quality centers, respectively.<sup>23</sup> Regarding variable costs, we face the usual selection problem in that we do not observe all potential entrants but only those that do enter, and not even for these do we observe variable costs. Identification is therefore based on observed price and quality. We observe prices as reported by centers and observe quality in the high/low quality aggregate fashion described above. Given fixed costs, the observed market shares for high- and low-quality and the price distribution by quality identify variable cost parameters because active firms make non-negative profits and the lognormal distribution is recoverable.

For non-relative caregivers, no additional parameters are left to be identified. For relative care, we have one remaining parameter: the proportion of households with available relative care. We observe some households using relative care (which therefore have it available, or

> 23 The Generic Cost Model for child care centers provided in Mitchell and Stoney (2012) is compiled by the _Alliance for Early Childhood Finance_ to model “budgets for a proposed center and to understand the costs of operating a better quality center”. In the fixed cost calculation we include non-personnel costs for the building (rent/lease, insurance, utilities, maintenance/repair/cleaning) and setup costs (audits, fees and permits, telephone, and Internet). We compute all costs at 2003 prices and assume that the typical center size is two and five classrooms for low- and high-quality centers, respectively, reflecting differences in spaces for play, music, and other enrichment activities. These values are comparable with the $200 a day fixed cost from occupancy and overhead reported in previous studies such as Helburn and Howes (1996).

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