(CATE) on subgroups in our experimental sample (De Neve et al., 2021)<sup>30</sup> . Causal forests predict CATE for each taxpayer, taking the average effects estimated from several _causal trees_ : similarly to decision trees, which partition data in order to find best predictions of some observed label, causal trees partition data in order to maximize heterogeneous effects across partitions (leaves). Since treatment effects are not observed but estimated from the data, Athey & Imbens (2016) recommend using "honest trees", which use separate sub samples to perform partition and estimate treatment effects.

In Figure 4 we present a histogram of predicted treatment effect on the filing probability for our entire sample<sup>31</sup> . The distribution of CATE is centered around zero and 90% of predicted effects fall in the range [-3.7,+3.2] percentage points. Overall, the null average treatment effect does not seem to be driven by a large positive effect for some group of taxpayers and negative effects for others, but is more consistent with null effects for the majority of subjects in the experiment.

One specific dimension of interest for targeting these interventions is whether taxpayers deemed to be high-risk are more responsive. In Figure 5, panel A, we document that is not the case. The scatter plot of predicted treatment effect using the causal forest model and the continuous risk measure used by the tax authority shows a slightly negative correlation: predicted treatment effects are positive, albeit small, for taxpayers with very low risk, and become negative for taxpayers with higher assessed risk. We summarize that relationship in panel B, where we present the average predicted treatment effect (weighted by baseline declared revenue) across the five risk-categories created from the continuous risk measure. The average is positive and small for taxpayers in the low and medium-low risk-levels, and negative for taxpayers with higher assessed risk<sup>32</sup> .

# **5.5 Costs of the experiment**

While the marginal cost of sending emails is zero, any campaign involving thousands of taxpayers requires several activities from dozens of workers in the tax authority<sup>33</sup> . These include meetings to define the content of messages, time to prepare databases, train frontline workers who might receive calls or visits from taxpayers, among others. Using back-of-the-envelope calculations of time invested and hourly wage of involved workers,

> 30For a detailed explanation of the causal forest algorithm and application in economics, see Davis & Heller (2017).

> 31We show in Figure A1 that results are similar if we consider the amount of gross revenue declared as the outcome of interest.

> 32Magnitudes are different from our estimated heterogeneous effects obtained in Table 6, where we present results linear regressions that interact the dummy for treatment with baseline assessed risk. In here we estimate a much more flexible model, using causal trees and a richer set of covariates, and then aggregate the predicted effects based on the baseline risk.

> 33While the intervention discussed in this paper required further time from researchers outside the tax authority (e.g. developing experts’ forecast survey, preparation of the pre-analysis plan and preregistration), this cost-benefit analysis focus on what an "usual" intervention, developed entirely by the tax authority, would cost.

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