(amount in pesos), due date, date of payment, days overdue, means of payment (cash or electronic), type of account (residential, retail store, factory), gender of the account holder, age of the account holder, linear front meters of the lot/property, assessed value of the property.

The municipality authorities required us to target blocks with eight to fifty accounts, neither very sparse nor very dense, which was the target for their mailing campaign. Figure 1 shows the distribution of accounts per block. Table A2 shows some descriptive statistics for the year 2019. Our sample size consists of 68,808 accounts distributed in 3,982 blocks. The frequency of payments is highly polarized. About 45 percent of the accounts paid the twelve 2019 monthly bills, and about 35 percent did not pay any bill at all.<sup>10</sup> We call these two core groups _always payers_ and _never payers_ , respectively. The proportion of always payers is relatively low (45 percent) and, therefore, leaves room for potential behavioral responses from non-compliant and partially-compliant neighbors, and this was compounded by the context of the pandemic, during which lockdown measures reduced payments even from highly compliant individuals.

For the randomization, power calculations, and simulations, we use baseline data from the year 2019. We rely on three different pre-treatment outcomes: (i) an indicator equal to 1 if the account paid the twelve monthly bills of 2019, (ii) an indicator equal to 1 if the account paid at least one bill in 2019, and (iii) an indicator equal to 1 if the account paid six bills or more in 2019.

# **4.3 Experimental Design and MDEs**

Following the notation in Section 3, the block-level treatment indicator is denoted by _Tg ∈{_ 0 _,_ 1 _,_ 2 _,_ 3 _}_ with distribution P[ _Tg_ = _t_ ] = _qt_ for _t_ = 0 _,_ 1 _,_ 2 _,_ 3 where _Tg_ = 0 indicates the pure control blocks, _Tg_ = 1 indicates the blocks with 20% treated, _Tg_ = 2 indicates blocks with 50% treated, and _Tg_ = 3 indicates blocks with 80% treated. The account-level treatment indicator is _Dig ∈{_ 0 _,_ 1 _}_ .

We use an independent within-cluster treatment assignment and constant within-cluster treatment probabilities. In the absence of data from a pilot experiment, we assume equal moments across assignments _σ_<sup>2=</sup><sup>_σ_2</sup><sup>_μg_(</sup><sup>_d, t_)</sup><sup>_−μn_(</sup><sup>_d, t_)=</sup><sup>_μg_(0</sup><sup>_,_0)</sup><sup>_−μn_(0</sup><sup>_,_0)and</sup><sup>_ρg_(</sup><sup>_d, t_)=</sup><sup>_ρg_(0</sup><sup>_,_0)forall</sup><sup>_g, d, t_.We</sup> _g_<sup>(</sup><sup>_d, t_)</sup> _g_<sup>(0</sup><sup>_,_0),</sup> further assume that the intracluster correlation is constant across clusters. We then impute all these magnitudes based on our baseline data. The parameters of interest are the difference in means between treated or untreated units in each treated group and the pure control units, _βn_ ( _d, t_ ) for _d_ = 0 _,_ 1 and _t_ = 1 _,_ 2 _,_ 3.

The municipality authorities requested that the total number of letters sent be set to _L_ = 25 _,_ 061. To incorporate this constraint into the choice of the saturation probabilities _qt_ , we set up a system of equations as follows. The expected number of treated units is _n_ 1 = _n_ (0 _._ 2 _q_ 1 + 0 _._ 5 _q_ 2 + 0 _._ 8 _q_ 3). Since the assignments _Tg_ = 1 and _Tg_ = 3 can be seen as symmetric, we set _q_ 1 = _q_ 3. Finally, we add an equation that ensures that the variance of the effect at 50% saturation is equal to the variance for the “small” cells (treated units in 20% clusters and untreated units in 80% clusters), so that V[ _β_<sup>ˆ</sup> ( _d,_ 2)] = V[ _β_<sup>ˆ</sup> (0 _,_ 3)] = V[ _β_<sup>ˆ</sup> (1 _,_ 1)]. This 10 For the full distribution, see Figure B.15.

21