The superior methods (from a causal id perspective) also have problems, or to put it more positively, cross-sections offer some advantages relative to them. The advantages relate to generalizability.
Natural experiments tend to analyze a very specific case, and it remains unclear to what extent the specific results hold across contexts. A good example is the relationship between social media use and depressions.
Economists recently used the geographically staggered rollout of Face-book in a natural experiment for causal estimates. This is great, but what about social media use in other countries?
I have a similar reservation regarding experiments. Of course, it would be possible to set up a survey or lab experiment that analyzes the research question at hand, for example by triggering people to see their government as incompetent, etc.
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