Table 6 reports the results of this analysis. We run the algorithm using our main outcome variable _loan repaid_ . Our main coefficient of interest is the difference in treatment effect between the relationship and the regulator offer, so we include borrowers in either of those two conditions, and compare the relationship offer as the "treatment" to the regulator offer as the "control" in this analysis. The GATES analysis finds an estimated treatment effect of 0.074 on the most-affected quintile _γ_ 5, nearly double the main effect on the overall population. The estimated treatment effect in the least-affected quintile _γ_ 1, on the other hand, is zero. Because of sample size limitations we lack sufficient statistical power in the loan level analysis to reject the null hypothesis that the treatment effect is homogeneous across the population.

While there is no statistical evidence that treatment effect heterogeneity is large in our setting, we do find some evidence that the effect of the relationship offer on repayment is larger for borrowers with larger loans and shorter remaining loan durations. Turning to heterogeneity among borrower characteristics, the results show that the treatment effect is larger for borrowers with lower initial credit scores and a shorter credit history (and thus worse outside options in the credit market), borrowers who suffered especially large income losses during the pandemic, and borrowers who are especially concerned about maintaining a good credit score. The treatment effect of the relationship offer on loan repayment is also larger for borrowers who state that they would not expect banks to help customers who are facing difficulties making their payments. In other words, borrowers respond more strongly if they are _surprised_ to be offered forbearance by their lender.

These results highlight that overall, borrowers for whom the repayment offer is immediately valuable, for example, borrowers who have larger loans outstanding, borrowers who suffered especially large income losses, or borrowers who are worried that their temporary inability to repay will tarnish their credit score, are more responsive to the relationship offer.<sup>23</sup>

# **4 Debt Moratoria and Banking Relationships: The Product Adoption Experiment**

In this section, we examine whether debt forbearance offers extended by the lender can strengthen banking relationships in the longer term. This also tests the intuition that forbearance offers improve repayment because borrowers interpret them as an investment in the relationship that makes the option value of a continued association with the lender salient to the borrower.

> which of these correlated variables is responsible for the heterogeneity.

> 23 In Appendix Table B.8, we supplement this analysis with a conventional heterogeneous treatment effect analysis. Specifically, for each variable in the vector of borrower and loan characteristics _Zi_ considered in the machine learning analysis, we construct an indicator _I_ ( _Zi_ ) = 1[ _Zi > Zmedian_ ] equal to 1 if borrower _i_ has an above-median value of _Zi_ and zero otherwise. We then estimate variations of equation (1) that include interactions between the relationship offer treatment dummy _Ti_<sup>1and the loan and borrower characteristics indicators</sup><sup>_I_(</sup><sup>_Zi_) (along with both terms uninteracted).While specific</sup> estimates naturally differ between the two exercises, some of the main characteristics along which treatment effects are heterogeneous are similar in the two exercises, such as the remaining duration of the loan, and the extent to which borrowers care about maintaining a good credit score. Because some borrower characteristics used in the heterogeneity analysis are elicited in an endline survey, several months after participants received one of the treatment or control messages, we verify that the treatments have no effect on survey responses. The results, reported in Appendix Table B.9, show that there are no treatment effects on any of the survey outcomes.

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