where i is an outcome for household in group at survey wave _t_ , and i is a dummy equal to 1 if household gg _i_ in group is offered public works. All regressions control for group effects gg yy ii gg TT ( ), strata fixed effects ( ), with an ANCOVA specification, and controlling for a vector of gg baseline (pre-determined) covariates ( ).<sup>15</sup> The impact of the public works offer is gg ss λλ λλ captured by _β_ . We estimate this equation separately at two points in time: during the public ii0 XX works program (M, midline) and after the program ended (E, endline).

In order to improve precision of the estimates and to account for random imbalance on observable characteristics, our regressions include the following set of baseline regressors: age of female beneficiary and her husband (if present), number of household members, number of children aged 0-5 years, number of children aged 6-15 years, an indicator for whether the woman is working, share of household members who are inactive, and whether the household is among the poorest 25<sup>th</sup> percentile of the food per capita expenditure distribution. We use this equation to estimate the effects presented in Tables 4 to 9. We also included survey-time indicators.<sup>16</sup>

# _Heterogeneity Analysis_

Our standard attempts to find heterogeneous effects are limited by the parametric modeling assumptions and by one-at-a-time testing for heterogeneity using interaction terms with adjustments for multiple hypotheses testing. Given the large array of potential sample splits for detecting heterogeneity, choosing ad hoc subgroups ex-post creates the possibility of overfitting. To this end, we aimed to minimize the concerns of specification searching by applying a machine learning approach to guide the selection of the relevant dimension of heterogeneity. We follow Chernozhukov et al.’s (2018) general framework, which provides valid inference to test whether there is heterogeneity in impact based on a set of baseline covariates. If heterogeneity is detected, then Chernozhukov et al.’s method makes it possible to (i) compute the magnitude of such heterogeneity and characterize the difference in the treatment effect across the most and least impacted groups, and (ii) identify the key observable correlates of the most and least impacted groups. Annex C contains a more detailed discussion on this approach.

We applied these methods to test for heterogeneity on key primary outcomes of interest, such as the woman and husband’s employment status, the woman’s labor income, and

> 15 Since the unit level of randomization is the household and within-cluster dependence of the main outcomes is not meaningful, we do not cluster at the site level. Therefore, the baseline intra-cluster correlation for women’s employment is 0.006 and for women’s inactivity is 0.004.

> 16 These indicators control for the possibility of arising or worsening economic conditions emerging after the baseline to midline and the endline surveys. Notably, we do not find any evidence for this after examining time patterns in total per capita expenditure for control households while leveraging 8 survey data points (month/years) from the baseline through to the last endline surveys.

16