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Interpreting Different Results when Working with Noncompliance

Suppose you run an experiment where individuals are randomly selected to receive a voucher for free healthcare (as in the Oregon experiment), but only half of the recipients use the voucher. You suspect that the choice to take use the voucher may be related to your health status. To deal with noncompliance but still find a causal effect, you try all four approaches: bounds analysis, assuming random compliance, intention-to-treat analysis, and instrumental variables. That gives you four results. What should you expect to see?

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