# **<mark>Difference-in-Differences</mark>**

<mark>Although many of the previous studies mentioned in this review have used multiple years of data, this temporal aspect has not been a key component of the estimation strategy. With the differencein-differences approach, changes over time are contrasted. However, in order to avoid other factors influencing the outcomes over time, there is an additional contrast between treated and untreated groups, where treatment is access to childcare. This strategy has been used in many contexts where government has scaled up childcare programs, resulting in variation in coverage over both time and place. We summarize the policies used in DiD studies in Table A1 rather than providing details on each of them in the text. These studies often examine large-scale government changes using national data, resulting in estimates that are more generalizable than those from RCTs or RDD studies.</mark> <mark>For the change between the outcomes of the treated and untreated groups to reflect causal estimates two assumptions need to hold. First, the changes between the groups prior to increase in availability of childcare need to follow a similar trajectory. Second, there cannot be time-variant factors simultaneously correlated with access to childcare and the outcome variables, which researchers do not observe and cannot control for.</mark> <mark>The first assumption can be tested if at least two data points are available prior to rollout of a childcare program. The second one is not a testable assumption. To increase the likelihood that the second assumption holds, some studies refine control groups by adding another dimension in a triple difference framework, such as age of children eligible for institutional childcare. The additional dimension reduces the likelihood that some unobservable factor, which is correlated with access to preschools affects women’s labor market outcomes. Because access to preschool in a triple-difference framework is defined through a combination of three factors (for example, time of the reform, its geographical coverage and age of children), the likelihood of confounding factors varying similarly along these three dimensions is reduced.</mark> <mark>Among 9 papers reviewed, only 3 used a triple differences approach, which we consider a stronger strategy for causal identification, compared to a double differences approach. Calderon (2014) exploits rollout of preschools for low-income families in Mexico, De la Cruz Toledo (2015) relies on changes in Mexican legislation that made preschool education compulsory in 2002, Halim, Johnson, and Perova (2021) examine impacts of public preschool expansion in Indonesia. However, only Halim, Johnson, and Perova (2021) p</mark> rovide convincing evidence that pre-treatment trends in the outcome variables were similar. Calderon (2014) graphically show diverging trends between eligible and synthetic control<sup>11</sup> prior to the treatment. De la Cruz Toledo (2015) does not include a parallel trends test. Of the 6 double difference studies, only Padilla-Romo and CabreraHernandez (2018) reference a parallel trends test, but do not present the results in the paper.

<mark>When discussing results, for comparability we group the studies along two dimensions: treatment variable (categorical or continuous) and the type of intervention (availability of a childcare program or expansion of school day).</mark>

> 11 In absence of a natural control group, Calderon (2014) develops a synthetic control group with comparable skills and experiences.

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