We performed Negative binomial segmented regression (NB) and Autoregressive integrated moving average (ARIMA) models as a preliminary and sensitivity analysis of the main model, Difference-in-Differences. Detailed methods results and output for NB and ARIMA can be found in the Supplementary material .
Difference-in-Differences (DiD) methods compare the mean of the variable of interest for an exposed and control group, before and after a certain interruption point, providing insight on the changes of the variable for the exposed countries relative to the change in the negative outcome group (15 (link)). We cannot draw causal conclusions by simply observing before-and-after changes in outcomes, because other factors might influence the outcome over time. DiD methods overcome this by introducing a comparison between two similar groups exposed to different conditions. First, DiD takes the difference of the variable of interest of both groups before and after the intervention. Then it subtracts the difference of the control group to the difference of the exposed one to control for time varying factors, therefore giving a result which constitutes a difference of the differences. This approximates the clean impact of the intervention. In essence, the DiD estimating equation is the following,
where Ygt is the outcome for an individual in group g and treated unit t, Pt is a binary time variable indicating whether the observation belongs to the period before or after the intervention and Tg is a binary variable indicating whether the observation belongs to the exposed or the controlled group. In this setting, the treatment effect is estimated with the coefficient β3 from the regression.
For this method to be rightly used, all the typical OLS assumptions must be met. The parallel trends assumption, which requires both groups to present similar trends before the intervention time point (16 (link)), must also be satisfied. We tested all these assumptions, and the latter can be visually inspected inFigures 1 –3 .
DiD models produce estimates which consider a counterfactual group, therefore adjusting for unmeasured confounding. This cannot be done by neither of the two previous models. Its biggest limitation is that, in the end, the measured effect can only be attributed to the timepoint chosen. If that is due to the intervention placed then, or to other underlying reasons around the same time, cannot be known by design.
Difference-in-Differences (DiD) methods compare the mean of the variable of interest for an exposed and control group, before and after a certain interruption point, providing insight on the changes of the variable for the exposed countries relative to the change in the negative outcome group (15 (link)). We cannot draw causal conclusions by simply observing before-and-after changes in outcomes, because other factors might influence the outcome over time. DiD methods overcome this by introducing a comparison between two similar groups exposed to different conditions. First, DiD takes the difference of the variable of interest of both groups before and after the intervention. Then it subtracts the difference of the control group to the difference of the exposed one to control for time varying factors, therefore giving a result which constitutes a difference of the differences. This approximates the clean impact of the intervention. In essence, the DiD estimating equation is the following,
where Ygt is the outcome for an individual in group g and treated unit t, Pt is a binary time variable indicating whether the observation belongs to the period before or after the intervention and Tg is a binary variable indicating whether the observation belongs to the exposed or the controlled group. In this setting, the treatment effect is estimated with the coefficient β3 from the regression.
For this method to be rightly used, all the typical OLS assumptions must be met. The parallel trends assumption, which requires both groups to present similar trends before the intervention time point (16 (link)), must also be satisfied. We tested all these assumptions, and the latter can be visually inspected in
DiD models produce estimates which consider a counterfactual group, therefore adjusting for unmeasured confounding. This cannot be done by neither of the two previous models. Its biggest limitation is that, in the end, the measured effect can only be attributed to the timepoint chosen. If that is due to the intervention placed then, or to other underlying reasons around the same time, cannot be known by design.
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