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A natural experiment is an empirical study in which the experimental conditions (i.e., which units receive which treatment) are determined by nature or by other factors out of the control of the experimenters and yet the treatment assignment process is arguably exogenous. Thus, natural experiments are observational studies and are not controlled in the traditional sense of a randomized experiment. Natural experiments are most useful when there has been a clearly defined and large change in the treatment (or exposure) to a clearly defined subpopulation (and no change to a comparable subpopulation), so that changes in responses may be plausibly attributed to the change in treatments (or exposure).
An example of a natural experiment occurred in Helena, Montana during the period from June 2002 to December 2002 when a smoking ban was in effect in all public spaces in Helena including bars and restaurants. Helena is geographically isolated and served by only one hospital. It was observed that the rate of heart attacks dropped by 60% while the smoking ban was in effect. 
Sargent RP, Shepard RM, Glantz SA (2004). Reduced incidence of admissions for myocardial infarction associated with public smoking ban: before and after study.. BMJ 328 (7446): 977-980.
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