### **Definition 1** **_Equilibrium Definition._**

_An equilibrium in this model specifies the set of child care providers available to households as well as their prices and qualities, and the decisions made by households with respect to work and child care, such that: (1) the child care providers in parental choice sets are indeed available in the market; (2) every child care provider in the market makes non-negative profits, and (3) neither parents nor child care providers wish to alter their decisions._ Due to the discreteness of household and firm choices, as well as the finite number of household types and potential firms, the equilibrium does not have a closed-form solution and must be solved numerically for a given set of parameter values. Appendix B.1 describes the quantitative version of our model, and Appendix B.2 describes the equilibrium computation.

# **3 Data**

## **3.1 Sources**

We estimate the model with data from the US Early Childhood Longitudinal Study birth cohort (ECLS-B), which follows individuals from birth through kindergarten for a nationally representative sample of children born in 2001 and includes several waves to capture children’s development as they grow. We use the second wave, collected between January and December 2003, when the children are two years old. In this wave the ECLS-B uses instruments to assess child development in the physical, cognitive, and socio-emotional domains. We focus on the cognitive domain, assessed with the Bayley-Short Form instrument (Research EditionMental), which contains measures of general cognitive ability such as problem solving and language acquisition.

The ECLS-B also collects household demographic data (household members; parents’ education, age, and marital status; living arrangements) and parental labor market information (labor force participation, hours of work, and hourly wages). It contains detailed information on child care modes (parental care, relative care, non-relative care, center-based care), hours of use for each one, and hourly child care expenses. Further, it provides an assessment of the quality of center-based care using an instrument designed by developmental psychologists, the ITERS (Infant/Toddler Environment Rating Scale).<sup>13</sup> Scores range from 1 to 7 (inadequate and excellent quality, respectively). ITERS scores are only available for the centers that agreed to be observed (45 percent of centers, enrolling about half of the children.) Starting from the second wave’s full dataset, we arrive at our estimation sample by imposing three main restrictions: we focus on two-parent and one-parent households with only one child, who is two years old; we restrict one-parent household to cases where the parent is the mother; and we focus on households in which the father, if present, works full time. The first restriction greatly reduces the problem’s dimensionality as child care is chosen for only one child. It also avoids modeling fertility or scale economies in child care. The second restriction reflects that virtually all one-parent households in our sample are led by women. The

> 13 The ITERS scale contains 39 items in seven sub-scales: space and furnishings, personal care routines, listening and talking, activities, interaction, program structure, and parents and staff. We focus on the overall score (mean over the seven sub-scales.)

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