It's an experimental study. These designs attempt to create a treatment and control to account for this problem.
Others in the thread point out how it's not easy to implement, but there is a methodological attempt at casual inference in the design.
It is not an experimentally study. It's observational, e.g. from the paper: "we exploit the abrupt end of United Kingdom sugar rationing in September 1953 as a natural experiment."
They didn't perform an experiment, they took someone else's observational data from a real-world event, and attempted to interpret it as if it had been an experiment.
It’s really not experimental though.
Assuming their math and design are good, this is pretty strong, as these things go. But there were a lot of other things that were different between the groups that could reasonably be affecting results.
The article itself is careful to deny drawing any prescriptive conclusions from this research — a tacit acknowledgement that the causal connection isn’t entirely clear.
This is interesting and fairly strong, and potentially important, but definitely needs more work before we start acting on it.