Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Part A: Individual-level randomization. For a total sample of 3,600 clients (1,200 being offered the standard loans; 1,200 the tailored loans; and 1,200 the grace-period loans), we will be able to detect increases of 4.2 percentage points (5 percent) in the share of households with a self-employment activity and of 5.3 pp (17 percent) in the share of households where at least one household member does day work. With imperfect compliance, effects among clients that will take up the new loan offers will need to be much larger in order to detect them. For example, for a total sample size of 3,000, standardized MDEs increase to 0.21 for a take-up rate of 0.6 and to 0.31 for a take-up rate of a 0.4. This compares to 0.13 in the ITT scenario. Given the observed take-up rates during the beginning of the experiment implementation, it is important to generate a large enough sample. Our goal is therefore to achieve a total sample size of 3,600 clients (1,200 in each arm).
For continuous outcomes, we will be able to detect increases of 17 percent for profits, 18 percent for sales, and 14 percent for consumption. These magnitudes of the minimum detectable effects are equivalent to 0.11 of a standard deviation. Minimum detectable effects increase as the sample size decreases: standardized effects increase to 0.13 and 0.14 of a standard deviation for sample sizes of 3,000 clients (1,000 in each group) and 2,400 clients (800 in each group), respectively. Standardized detectable effects do not change significantly for this range of sample sizes. Given the large standard deviation of continuous outcomes, a standardized effect of 0.14 translates, however, into larger minimum detectable effects of 21 percent for profits, 22 percent for sales, and 17 percent for consumption.
Part B will take place in eight villages in the catchment area of each of the 40 participating branches. This part thus involves 320 villages. A sample size of 80 villages per treatment group will allow for the detection of impacts on village-level take-up of at least 6.3 percentage points. We calculate these MDE using data from a related study in rural Morocco (Crépon, Devoto, Duflo, and Parienté, 2015) where the standard deviation of this outcome is 0.14.