In the potential outcomes framework, suppose that program eligibility is randomly assigned but participation cannot be enforced. To formally describe this situation, for each person i, z_i is the eligibility indicator and xi is the participation indicator. Randomized eligibility means z_i is independent of [y_i(0), y_i(1)] but xi might not satisfy the independence assumption.

(i) Explain why the difference in means estimator is generally no longer unbiased.

(ii) In the context of a job training program, what kind of individual behavior would cause bias?