Discuss the use of natural experiments in causal inference.

Instruction: Provide an example of a natural experiment and explain how it can be utilized to infer causality.

Context: Candidates should demonstrate understanding of natural experiments, including the identification of exogenous variations and their application in causal analysis.

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A natural experiment uses an externally generated assignment process that may create plausibly exogenous treatment variation. The claim depends on how assignment actually worked, not on calling an event a shock.

Consider a hypothetical oversubscribed training program whose available places are allocated by a documented lottery among eligible applicants...

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