Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
We start with 80 villages, and randomly sample 20 households in each village. We will block villages at the commune level with 8 villages per commune. We then proceed to estimate the minimum detectable effect (MDE) for the economic outcomes of interest: consumption, fertilizers, cultivated area, and education, using data from the Burkina Faso 2010 DHS (for education) and from the Ministry of Agriculture of Burkina Faso for the remaining outcomes (the construction of the latter variables are described in Kazianga and Wahhaj (2017). The data are summarized in Table 02 attached. We calculate the MDE under two scenarios. In the first case, we treat any rural household in a treated link as treated. We also account for the proportion of variance explained by blocking. We assume 20% take-up rate. Under these assumptions and with the figures shown, we can detect a minimum change equivalent to roughly 40% of the standard deviation. This MDE corresponds to CFA 198,802 increase in consumption, 17.6 KG increase in fertilizers, 1.7 ha increase in cultivated area, and 19% increase in current enrollment for education.
In the second case, we consider comparing V0U1 with V0U0, and V1U1 with V1U0. In this case, we can again ignore the intra-cluster correlation (as when comparing take-up) and block at the village level. Assuming again a take-up rate of 20%, the MDE is, in this case, about 0.30 for the outcomes we consider.