Sixth, we define four composite locations (henceforth, locations) based on population and income. Population (number of children below age 5) captures potential market size for child care services while (median family) income captures the ability to pay for them. We assign households to locations based on their observed place of residence and 2000 census county data on population and family income (see Appendix C.2.2 for further details). Locations 1 through 4 are defined as follows: low population (“small”), low income; low population, high income; high population (“large”), low income; and high population, high income, respectively. While admittedly coarse, these locations clearly vary in _ex ante_ household characteristics. For instance, low-income locations have a higher share of single-mother households and a lower share of college-educated parents than high-income locations (Table C.2.) Marital status does not vary much by location size conditional on location income yet parental education rises substantially with location size. In our empirical implementation, locations differ not only as described but also in location-specific parameters such as parental wage offer distributions and center costs, as explained below.

This setting gives rise to four heterogeneous, distinct child care markets. For example, the large, high-income location includes a large amount and share of college-educated parents and supports greater quality and variety in center-based care than other locations. What this setting does not feature, however, is heterogeneity _within_ locations, such as differences among a city’s high- and low-income neighborhoods. Since our dataset is representative of the US population, it does not allow us to characterize child care markets at the neighborhood level. Nonetheless, we argue that neighborhood-level differences are less important in child care markets than in K-12 school markets, where catchment areas impose a strong geographic dimension to the choice set. Child care services for 2-year-olds are less subject to such constraints, as parents use child care providers located not only in their neighborhood but also close to their workplace or even at relatives’ homes. As a result, the relevant child care choices are geographically located in the same broad area where parents supply labor. Heterogeneity across such broad areas is what our setting is best equipped to capture.

# **4.2**

The model includes four sets of parameters, related to household utility and constraints, child development production, parental wage offers, and child care providers. Given the model’s nature, there is no direct mapping between empirical features and model parameters. However, some empirical features play a greater role than others to identify specific parameters. Our discussion below follows this intuition and focuses on aggregate-level parameters, common to all locations. Appendix D.1 discusses identification of location-specific parameters.

## **4.2.1 Household utility and constraints**

These parameters fall into three groups. The main one includes parameters for heterogeneous preferences over consumption, leisure, and child development: _{μvc, μvq, μvf }_ and _{σvc, σvq, σvf }_ (equation (17)). These preferences affect trade-offs among leisure, consumption, and child development. We observe wages, labor supply, and child care choices for each 17