# **5. Empirical strategy**

We estimate the ‘value of treatment,’ or VT, using a simple reduced-form linear model: (1), tt,ii ii ii tt=0,ii tt=0,ii rr tt,ii where is an outcome variable measured at time YY = αα+ ββTT<sup>BB</sup> + θθ XX for household + φφ(TT<sup>BB</sup> XX) . + μμ is a binary treatment indicator which + εε takes the value of 1 if household tt,ii was eligible to receive transfers at baseline, ii is thus our coefficient of YY tt ii TT<sup>BB</sup> interest. denotes a vector of covariates, which includes the value of the outcome at baseline and the ii ββ propensity score, both centered.tt=0,ii<sup>24</sup> All covariates are centered by subtracting the sample mean from each XX observation and are interacted with the treatment indicator. Finally, denotes stratum fixed effects for the five regions by which the survey was stratified. We estimate heteroskedasticity-robust standard errors.rr<sup>25</sup> All μμ estimates are weighted by sampling weights multiplied by the inverse propensity weights, which were described in section 4.1.

We then supplement the VT estimation with instrumental variable (IV) estimates, where we instrument the receipt of cash transfers at each follow-up with eligibility at baseline, i.e. with the treatment indicator from specification (1) described above. This is akin to the familiar estimation of the LATE, where take-up of treatment is instrumented with the original assignment to the treatment group. The estimated coefficient can thus be interpreted as the value of treatment for compliers , or the LAVT, i.e. the households who received cash transfers if they were assigned to the treatment group at baseline and did not otherwise. The IV model we estimate is analogous to specification (1), shown in (2) below: (2), tt,ii ii ii tt=0,ii ii tt=0,ii rr ii where is a binary indicator for whether the household is currently receiving transfers.YY = αα+ ββTT<sup>CC</sup> + θθ XX + φφ(TT<sup>CC</sup> XX) + μμ + εε<sup>26</sup> The first stage equation is exactly equivalent to specification (1), where the dependent variable is beneficiary status at time ii _t_ . TT<sup>CC</sup>

> 24 Our pre-analysis plan (PAP) stated that all five eligibility criteria would be included as controls but we chose to include the propensity score instead because it contains the five eligibility criteria (see section 4.1 and Appendix Table 1). 25 The PAP mentions clustering standard errors are the province level, but this was due to the study team’s uncertainty surrounding the sampling strategy at the time. As we now know that the sample was drawn as a simple random sample within each of the five strata, there is no need to cluster standard errors at the province level (Abadie et al. 2020). However, Sävje, Aronow, and Hudgens (2019) show that conventional variance estimators might not capture the loss of precision that can result from interference and propose alternative estimators. Aronow, Samii, and Wang (2020) show that if the interference is spatial in nature and there is homophily in treatment effects on the space (i.e. points that generate largerthan-average effects reside close to each other), then clustering the standard errors at the region level will suffice if interference is contained within the region. Clustering the standard errors at the region level does not alter the main findings here. Appendix Table 8 replicates Table 6 (with our main impact estimates) using cluster robust inference.

> 26 This variable is constructed using data collected by the program administrators and is not self-reported by the household survey respondents.

22