Experimental Design
For each borrower in the sample, the lender will send a settlement offer (the “effective discount” below) based on random assignment (the “assigned discount” below) subject to the lender’s three standard operational constraints on the discount offer’s composition and maximum allowable amount:
1)on unpaid interest and late fees, offer up to a 100% haircut (i.e., complete debt forgiveness)
2)on unpaid principal, offer a maximum of:
25% haircut for 91-120 days late borrowers
40% haircut for 121-150 days late borrowers
50% haircut on loan principal for 151-180 days late borrowers
Each month, each borrower in the sample to one of five discount values: zero (control group), 10%, 20%, 30%, 40%. The randomization will be stratified across six groups. These six groups are created by dividing the sample across two variables: (a) 3 bins reflecting whether the borrower was late by 91-120 days, 121-150 days or 151-180 days during the experiment month; and (b) whether the borrower never made a non-zero payment after loan origination (“never payer”) as defined in the month they first become part of the experiment sample. However, the effective discount that a borrower will receive could be lower than the randomized discount, because of the constraints described above. To be precise, the effective discount is defined as min(Assigned Discountit, Maximum Allowable Discountit), where i indexes borrowers and t the month of randomization.
We will use the conditionally assigned discount for any intent-to-treat (ITT) analysis. However, the effective discount will be useful for descriptive purposes, for measuring compliance (in econometric terms) with the random assignment, and possibly for estimating ITT heterogeneous treatment effects and/or IV estimates.
We will analyze the take-up rate of the settlement offers using the following specification:
y_it = a + b1 * T_it1 + b2 * T_it2 + b3 * T_it3 + b4 * T_it4 + m * X_it + s_it + u_it
where y_it is one of the second-stage outcomes defined above, and T_itg is takes the value of 1 if borrower i in randomization month t belonged to the treatment arm g={1,2,3,4}. Control group is the omitted category. s_it represents strata x experiment month fixed effect, where strata is one of the 6 groups defined by combination of the three days late bin and whether the borrower was a “never payer”. X_it is a vector of indicators reflecting the borrower’s randomly assigned discount(s) in any prior month(s).