The best replacement for natural experiment is field experiment.

The best alternatives to natural experiment are rated as following:
★★★★★  field experiment
★★★★★  quasi experiment
★★★★★  observational study
★★★  true experiment
★★  lab experiment
★  manipulative experiment
★  quasi-experiment

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No companions for natural experiment have been suggested so far.
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Google Trends

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natural experiment
field experiment
quasi experiment