Good point. This article uses quasi-experimental methods and finds important partisan differences in Swedish local government: https://www.jstor.org/stable/40283092?seq=1#metadata_info_ta...
I haven't read the paper yet, but noticed it uses a regression discontinuity design without showing raw data (i.e. a scatterplot).
There have been some cases where such discontinuity analyses were extremely misleading [1], so some caution is advised.
[1] https://statmodeling.stat.columbia.edu/2021/03/11/regression...
Maybe you'll like this better method then: Bayesian counterfactual time-series analysis [1]. In essence, it compares a "neutral" time series and another one affected by a natural experiment and produces bayesian point-estimates for the causal impact.
Super powerful, there's a great R package, and really easy to use.