_d_<sup>_R_</sup> ( _j_ ) = 1) but do not know _all_ households that have it available. In principle, we could estimate the proportion of such households from the data because we model the choice of nonrelative care and observe the households using it. Since the proportion is poorly identified in the data, we calibrate it. Compton and Pollak (2015) use data from the second wave of the National Survey of Families and Households (NSFH) to estimate distances from the husband’s mother and the wife’s mother conditional on their education. Using their estimates and our sample data on household parental education, we arrive at 40% of households having relative care available.<sup>24</sup> Parents in the two low-income locations, in turn, are more likely to have relative care available than others (Table D.2).

# **4.3 Estimation Method**

We estimate the model by Simulated Method of Moments. This is particularly well-suited for our model, which lacks a closed-form solution. Let **_θ_** be a column vector of dimension _P_ , equal to the number of parameters to be estimated. Our estimator, **_θ_**<sup>ˆ</sup> SMM, is such that: where **z** is the column vector of _B > P_ sample moments to match, and **s** ( **_θ_** ) is the column vector of the corresponding moments evaluated at **_θ_** . Weighting matrix **W** is diagonal; weights are the bootstrapped standard deviations of the sample moments.<sup>25</sup> We perform full-solution estimation, which requires equilibrium computation for every value of **_θ_** .

We estimate the model in two steps. In the first step, we match 77 moments aggregated over the four locations and recover the structural parameters common to all of them. In the second step, we match 24 moments for each location to estimate location-specific parameters. Besides being computationally convenient, this approach helps us overcome small sample issues generated by our modest sample size. By aggregating moments over locations, we can condition on a rich set of household-specific observables while having an acceptable number of observations per moment. This criteria, together with our identification strategy (Sections 4.2 and D.1) guides the selection of moments for estimation, which include moments on child care markets, child development, and parental labor market outcomes. Mothers are the unit of observation for most moments.<sup>26</sup> While ideally we would condition on mother’s marital status, educational attainment, work status, and location for every moment and location, this is not always possible because some cells contain very few observations, leading us to only use moments with at least 50 observations.

The second column of Table E.1, _Sample_ , shows aggregate moments; the third, fifth, seventh, and ninth columns of Table E.2 show location-specific moments. The first column

> 24We use the aggregate proportions conditional on parental education provided in Table V of Compton and Pollak (2015), and assume that only grandmothers living within 30 miles are available for child care. Conditioning on education is important. For example, when both spouses have a college degree, the proportion of married couples living more than 30 miles _away_ from both grandmothers is 49.4%; when neither spouses has a college degree, it falls to 18.9%.

> 25The weighting matrix is useful to give all moments a similar scale and to reduce the estimation’s sensitivity to imprecise sample moments.

> 26In our sample we only have one child per mother. Fathers’ labor market moments are the only ones using fathers as the unit of observation, and we match them exactly (Section 4.2.3.)

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