## 3 Results
### Assessment of the Timely Lifting of Quarantine Measures through Augmented Synthetic Control Method  
Another relevant aspect of the analysis of the role of mobility restriction measures is precisely the timely lifting of these measures, especially quarantine. Since 15 May 2020, a long period of quarantine has been implemented in the MR. Although the measure was taken for practically all the communes of the MR simultaneously, the de-confinement occurred gradually. The communes were coming out of quarantine as the number of cases decreased. The first to leave were Colina, La Reina, Las Condes, Lo Barnechea, Til Til, and Vitacura (basically some rural communes, along with the communes with the highest income). On the other hand, the communes with the longest confinement time are at a partial level: Puente Alto, specifically the western sector, which was under the measure for 172 days; and in their territorial totality: El Bosque and Quinta Normal, where quarantines were in force for 158 days (all these communes are low-income). The case of Puente Alto is particularly interesting, given that it is the commune with the most COVID-19 cases in the country and where the lockdown measures were, therefore, inefficient. We used synthetic control [67] to estimate the effect that the lifting of the quarantine had on the number of cases and also on the mobility of the affected communes. For the  
Figure 12: The mobility index vs. the cumulative number of cases per 100.000 inhabitants after relaxing the confinement measures. analysis, we consider that the communes in the \"pre-treatment\" stage are all those that are in quarantine (practically all the communes of the MR for the observation time interval considered). In this case, the \"treatment\" is lifting the quarantine, which the communes were gradually leaving. To consider this staggered lifting of the confinement measures and to be able to estimate the \"treatment effects\", we used the augmented synthetic control method (ASCM) [67; 68; 69]. The objective here is to estimate its consequences on mobility and the number of COVID-19 cases for these communes by comparing with the opposite option, that is, having spent more days in quarantine. The idea is to construct a weighted average of donor communes, known as a synthetic control, that matches the pre-treatment results of the treated communes. The estimated effect is then the difference in post-treatment outcomes between the treated communes and the synthetic control. The donors for the estimation were determined from the available group of communes and their memberships to different clusters previously defined from the similarities in mobility and also considering the socioeconomic conditions of the communes. Figure 13 shows the estimate of the effect of lifting the quarantine in the Recoleta, San Ramon, La Cisterna, La Granja, San Joaquin, and San Miguel communes (all of them with low income) compared to the synthetic control built from other communes with similar socioeconomic characteristics that subsequently abandoned the quarantine (Quinta Normal, La Pintana, Lo Prado, Cerro Navia, Conchali, Puente Alto and Lo Espejo). The figure describes how, initially, the number of COVID-19 cases, on average, for the treated communes tends to fall after lifting the restriction measure. However, this number is rapidly growing again, indicating that the measure may have caused a resurgence of contagion in the treated communes. On the other hand, Figure 14 shows the gradual increase in mobility after relaxing the confinement measure. Because the lifting of the quarantine was not total and the communes went to the so-called Phase 2 of the \"Step by Step\" plan (i.e., the quarantine measure was maintained only on weekends), periodicity is observed in the estimation of the mobility difference. On weekends, the difference with the mobility of the synthetic control decreases as, once again, the communes are temporarily quarantined.