In the present paper we analyze these questions empirically by examining the effect of changes in the supply of public child care services on private child care provision in Brazil. We use  rich municipal-level panel data covering the period 2000–06 to  analyze the effect of increased availability of public child care  centers on the quantity of private supply, as measured by private  enrollment rates and number of private centers. We also check whether increased public supply has any impact on the quality of private child care, as measured by group size, teacher qualification, and quality of infrastructure. To plausibly identify exogenous variation in public supply, we exploit unique features of the allocation mechanism of federal transfers to municipalities in Brazil, where the transfers received by local governments exhibit a non-linear and non-monotonic relationship with given population estimates.  Results from a regression-discontinuity design reveal that  larger federal transfers to a given municipality lead to a significant  expansion of public preschool services (as measured by  the number of municipal centers and enrollment), but show  no evidence that such an expansion crowds-out private enrollment.  If anything, the results suggest that private enrollment also increases. We also find no evidence of adverse effects on the quality of private provision.

To guide the interpretation of our empirical results, we develop a simple theoretical model of vertical differentiation, analyzing the optimal pricing response of a private child care provider to entry of a public competitor. In the model, public preschool education is free of charge (zero price), whereas private providers optimally set prices in a profit-maximizing way and supply higher-quality services. Demand for preschool services comes from two different segments of households, with consumers who differ in average income and therefore differ in willingness-to-pay for preschool education. The private provider optimally chooses between a high-price strategy, serving consumers with high willingness-to-pay only, and a low-price strategy, serving consumers from both segments.  An expansion of public supply has ambiguous effects on private enrollment, depending on the difference in willingness to pay across consumer segments and on the relative size of each segment. Crowding-out effects of more public provision are less likely when the differences in willingness-to-pay across consumer segments are relatively large.

Our paper clearly relates to the more general literature on crowd-out effects of government funding, in particular the strand of the literature dealing with crowd-out effects of public provision of private goods. However, the existing empirical research has mainly been devoted to health care markets.  Cutler and Gruber (1996) and Gruber and Simon (2008) analyze  the extent to which public health insurance crowds out  private insurance, while Cohen, Freeborn, and McManus  (2013) study crowd-out effects of public providers in the US  market for outpatient substance abuse treatment. In each case, sizable crowd-out effects are identified. 

Among the relatively few empirical studies on child care  markets in this strand of the literature, recent contributions  include Bassok, Fitzpatrick, and Loeb (2014) and Bassok,  Miller, and Galdo (2014), who find evidence of significant  crowding-out of private providers as a result of increased  public provision in the child care markets in Oklahoma  and Florida, respectively. Cascio and Schanzenbach (2013) also find evidence of crowd-out effects from the expansion of public preschool in Oklahoma and Georgia, particularly for high-income families. Similarly, Cascio (2009) finds evidence of sizable crowd-out effects using US census data over five decades. These mixed findings for the US and Brazilian settings can be rationalized in the context of our model. As noted above, crowding-out effects of more public provision are less likely when the differences in willingness-to-pay across consumer segments are relatively large. These differences are expected to be generally larger in the Brazilian context, where the levels of inequality in parental income are among the highest in the globe (World Bank, 2004).