# Enabling Decision Making with the Modified Causal Forest: Policy Trees for Treatment Assignment
## 3 Empirical Studies
### Study 3: Interest Rates and Loan Returns  
In 2003, ref. [28] conducted a randomised controlled trial to examine the impact of personalised pricing by a microfinance lender in South Africa. They randomised interest rates to study the effect on the decision to borrow (extensive margin) and, among other outcomes, on the lender's revenues (intensive margin). Considering the intensive margin, the overall findings suggest that lower interest rates only marginally decrease profits. This study is particularly relevant because microfinance initiatives may serve broader purposes beyond profit maximisation. They can play a crucial role in promoting financial inclusion among specific population subgroups. Moreover, any initial losses incurred by the lender could be offset by a wider uptake of microfinance services. Therefore, this study employs the same data and the intention-to-treat strategy of [28] to investigate the impact of receiving a mail invitation with different interest rates on the lender's returns. Ref. [29] also leverages this dataset to propose policy allocations aimed at maximising the lender's revenue while considering fairness implications. This paper does not explicitly take a stance on fairness. Consequently, we include variables commonly regarded as sensitive in the literature. The dataset includes 48,852 individuals who received an invitation letter to apply for a loan at the offered interest rate. Differently from the study of [28], our specification incorporates socio-demographic information (see Tables A3 and A6 in Appendix A for the complete variable list and descriptive statistics) collected from the bank operator before the randomisation. While not crucial for treatment effects identification, these variables are important for exploring heterogeneity and conducting policy learning analysis. In addition, we discretise the treatment variable in three different interest rate groups: low, medium, and high rates, based on the client's risk profile. The cut-offs are indicated in [28] and are based on the risk category of clients pre-approved by the lender. The discretisation into three groups enhances the interpretability of results from a policy perspective, particularly when employing policy trees. As for the other applications, our heterogeneity analysis is based on the distribution of the IATEs. Specifically, we compare the medium- and high-interest rate treatment groups with respect to the low-rate group and the high-interest rate group with the medium-rate group. As illustrated in Figure 5, all distributions show positive and negative treatment effects. Examining the medium- and high-interest rate groups compared to the low-rate group, the effects range from ZAR -1520 (ZAR -1656) to ZAR 1610 (ZAR 2327), with an average effect of ZAR 78 (ZAR 163) and an average standard error of ZAR 506 (ZAR 487). When comparing the high-rate group to the medium-rate group, the effects range from ZAR -1748 to ZAR 2393, with an average effect of ZAR 81 and a standard error of ZAR 547. Figure 5: Distribution of IATE. Note: Means of the IATEs for the high- (medium-) vs. low-interest rate groups: ZAR 78 (ZAR 163). Average standard errors of the IATEs for the high- (medium-) vs. low-interest rate groups: ZAR 506 (ZAR 487). For the high- vs. medium-interest rate group, the mean is ZAR 81 with an average standard error of ZAR 547. These findings indicate the existence of effect heterogeneity, which could be used to potentially enhance the allocation mechanism. As for the previous studies, we use policy trees of different depths and compare the welfare produced by the different allocations with the welfare from random and observed allocations. Due to this application's relatively larger sample size, we also demonstrate the performance of both shallow and deeper trees. Additionally, we explore various combinations of trees: optimal, optimal with one final sequentially optimal tree (+1), and optimal with two final sequentially optimal trees (+2).