more than 0.15 SD; and self-control by more than 0.04 SD. For the different measures of decisionmaking abilities, the lower bounds of the of the 95% confidence intervals permit ruling out that attending daycare for one year _improved_ decision-making abilities by more than 0.22 SD (transitivity in toys task); 0.18 SD (transitivity in sharing task); 0.18 SD (dominated risk choices); and 0.11 SD (transitivity or monotonicity in risk task).<sup>24</sup> These null results are also consistent with Attanasio et al. (2022) who find that the intervention had no sustainable effects on cognitive function, including on executive function.

Notice the confidence intervals are in a way artificially inflated because the types of experimental measures studied are known to be noisy (Gillen et al. 2019). To illustrate, we take advantage that multiple trials were conducted in the toys task, risk task, and sharing task to estimate the amount of measurement error in the measures of decision-making abilities.<sup>25</sup> We estimate that the confidence intervals are from 20% to 25% larger because of measurement error.

Because Figure 4 estimates effects on eight different outcomes, there is naturally a concern about multiple hypothesis testing (List et al. 2019). We proceed therefore to calculate RomanoWolf p-values which adjust for multiple hypothesis testing (Romano and Wolf 2005a; 2005b). One advantage of this approach is that it takes into account the dependence structure of the test statistics. We find the effect of daycare attendance on aversion to disadvantageous inequality remains statistically significant even after one adjusts for multiple hypothesis testing (p-value of 0.014). The p-values for all other outcomes are above 0.63 – see Appendix Table 4.<sup>26</sup> It is also reassuring that the finding that daycare attendance increased aversion to disadvantageous inequality is consistent with the results of Cappelen et al. (2020), who studied the Chicago Heights Early Childhood Center (CHECC) project.<sup>27</sup> The project randomly assigned

> 24 These estimates take into account that on average the treatment group attended daycare for 0.643 more years than the control group.

> 25 To illustrate, take the measure of dominated choices in the risk task. There were eight trials that included a dominated choice. We randomly split these eight trials into two sets with 4 trials each. Let DMA1 be the number of dominated risk choices in the first set and DMA2 be the number of dominated risk choices in the second set. We then ran a regression of DMA1 on DMA2. The coefficient on DMA2 corresponds to the “true variance” in this metric of decision-making ability divided by the sum of the true variance and the variance of measurement error.

> 26 The p-values for the other outcomes are: 0.682 (risk tolerance); 0.948 (aversion to advantageous inequality); 0.627 (delayed gratification); 0.629 (violations of transitivity in toys task); 0.948 (violations of transitivity in the sharing task); 0.948 (dominated choices in the risk task); and 0.948 (violations of transitivity or of monotonicity in the risk task).

> 27 Andreoni et al. (2019) study the effects of CHECC on time preferences and find no effects. Recent work by Chuan et al. (2022) study the impacts of the program on a broader set of time preferences. They also investigate whether the impacts vary by curriculum.

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