a discount, on average, increases this share to 29%. Under _SDM_ , however, the uptake of LARCs at full price jumps to 35% - an increase of over 300% over _IDM_ . Interestingly, _SDM_ seems to also cause clients to become less sensitive to LARC prices: offering them discounts makes no difference to the adoption of LARCs. The difference in the effect of _Discounted_ LARCs between _IDM_ and _SDM_ is 18.1 pp (p=0.097).

In Appendix Section C, we present a model of individual utility maximization, where the clients care about the price of LARCs and the perceived returns to adopting them. This model provides straightforward implications that is consistent with _SDM_ causing a decline in the price elasticity of demand for LARCs. Importantly, follow-up surveys with clients indicate that this counseling approach maintained respect for their autonomy in decision-making: we found no differences between the two randomized counseling arms in a checklist of quality of service indicators, clients’ level of satisfaction with their counseling session, or their willingness to return to the hospital for FP services in the future (Table A10).

# **4.3 Heterogeneity of impacts**

In this sub-section, we ask, “What characterizes the client segment that is more likely to be persuaded by price discounts?” To answer this question, we first estimate the conditional average treatment effect (CATE) on LARC adoption of switching from _High_ prices to _Low_ or _Mid_ prices (as in the previous section, we binarized the treatment by pooling all the discounted prices). Then, we say an individual is relatively “strongly” affected by discounts if their estimated CATE on LARC adoption is above the median estimated CATE in the data, and relatively “weakly” affected otherwise, where we hold out folds of data in estimating the CATE so that an individual’s own outcome does not influence its subgroup assignment. We calculate the average treatment effect (ATE) for each subgroup. Finally, we compare the average value of each covariate of interest across the two subgroups. See, e.g., Chernozhukov et al. (2018, Section 3.2) or Athey and Wager (2019, Section 2.2) for similar methods.

We estimate the CATE non-parametrically by fitting three causal forests<sup>18</sup> (Athey et al., 2019). As our analysis in the previous section strongly suggests that individuals react differently to treatment depending on counseling regimes, we split our data into three separate subsets by counseling regime ( _MiM_ , _IDM_ or _SDM_ ), and fit a separate causal forest for each subset. We then concatenated their predictions to compute the results in this section; this is essentially equivalent to forcing the trees to split by counseling regime. Details are provided in Appendix Section F.

The first row in Panel A of Table 2 presents the ATE of discounts on LARC adoption by subgroup. For the _strongly_ -affected subgroup, we estimate an ATE of about 27 percentage points (pp), significant at the 1% level. Among those _weakly_ -affected by discounts, we cannot distinguish the effect from zero. The difference in ATE between the two groups is significantly different than zero at the 1% level. The second row in Panel A estimates the subgroup-specific ATE using augmented inverse propensity scores (AIPW), cross-fitted so that an individual’s outcome is not used to estimate the conditional mean or propensity score for themselves, enabling estimates with lower variance. The results are very similar across the two methods.

> 18Using the function `causal_forest` function implemented in the `R` package `grf` .

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