based on survey questions that refer to one randomly-selected child in the household.<sup>18</sup> Finally, we measure in-person school attendance ( _inperson_ ) if children report to be regularly attending school at the time of the interview. This information is available for all children in the household. Therefore, to analyze to what extent the take-up of remote and alternative learning options, as well as the rates of return to school (once the restrictions were lifted), differed according to socio-economic characteristics, we estimate the following (weighted) OLS model: where, for child _i_ , in household _h_ , in county _c_ , during wave _t_ , the binary dependent variable (yict) stands for either remote education, alternative education (both between September and November 2020) or school attendance (between January and March 2021). In addition to the explanatory variables of interest, we include a vector (Xihct) containing the control variables previously mentioned as well as county fixed effects (δct), which eliminates (unobserved) county-specific characteristics that are common to all households in a given county.<sup>19</sup> Whenever data from more than one wave is included in the analysis (i.e., when we examine well-being), we add also wave fixed effects (φt) to capture crosssection variation that is common to all households during each wave. The robust standard error (uihct) is corrected according to the survey design.

Furthermore, to assess the consequences of the pandemic for child well-being, we track changes in children’s behaviors across six different dimensions. If parents report that their children have been (i) crying more, (ii) more defiant, (iii) destroying more, (iv) speaking less, (v) more withdrawn and/or (vi) more irritable than usual, we consider this to be a sign of (internalizing and externalizing) changes in behavior ( _behavior_ ), which is our main measure to capture emotional well-being. We also split these six indicators into two different groups: externalizing (i, ii, iii) and internalizing (iv, v, vi) behaviors. Simply put, the former attitudes are directed outwards, “generating discomfort and conflict in the surrounding environment,” while the latter manifest inwardly, leading to “distress in the individual” (Forns et al. 2011, p. 1464). The main objective is to understand to what extent the recent increase in mental health issues reported in children is explained by the (change in) exposure to the three different types of learning described above (i.e., remote, alternative, and in-person education).<sup>20</sup> To account for parent attitudes that are likely to be associated with the probability of children exhibiting changes in behavior, in this part we control for two additional binary indicators: whether parents stimulate and engage with their children ( _engagement_ ), and whether they apply harsh disciplinary methods ( _discipline_ ). Engagement is defined as any of the following activities: playing, reading books, telling stories or singing songs to the child, whereas harsh discipline includes calling the child names (e.g., dumb or lazy), spanking, hitting or beating the child.

As these internalizing and externalizing behavioral questions were only introduced in January 2021 (wave four of the RRPS), we first pool observations from waves four and five and run a (weighted) OLS regression similar to the one described above, but with behavioral changes ( _behavior_ ) as the dependent

> 18 In this part of the analysis, as the outcome variables capture formal education (either in-person, remote or alternative learning), we exclude children below pre-primary age (i.e., age three and younger) from the sample, as they are below the age of government-provided education and usually have no access to alternative forms of early learning or childcare. Furthermore, considering the fundamental differences between children in different age cohorts and that remote education in particular is more easily adopted by older children, we split our analysis, whenever possible, between age groups.

> 19 Vector Xihct includes: nchildhct, ageihct, agesqihct, weekcounthct, feelanxioushct.

> 20 Note that the variable _inperson_ can be defined based on two different questions in the survey. One of these questions is available to all children in the sample, while the other is only posed to a randomly-selected child in each household. While the former has the advantage of a larger sample size, the latter can be matched to other characteristics that are also only available to the selected respondent, such as _remote_ and _alternative_ . As the two approaches yield similar results, we rely on the definition that we believe is most appropriate in each section of this paper. We indicate the use of the full-sample alternative with _inperson (all)_ .

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