6. Consider the structural model yi = β0 + β1 xi + ui, where Cov(xi, ui) ≠ 0. You have one instrument $zi$ satisfying Cov(zi, xi) ≠ 0 (relevance), $Cov(zi, ui) = 0$ (exogeneity).Assume all variables are mean-zero for simplicity. The just-identified IV estimand isβ1^IV = (Cov(zi, yi))/(Cov(zi, x_i))Suppose $Cov(zi, yi) = -0.18$ and $Cov(zi, xi) = 0.12$. What is β_1^IV?(A)-0.67(B)-0.5(C) 0.5(D)-1.50

10. Consider the wage equation $\ln(wagei) = \beta0 + \beta1 educi + ui$, where ui contains unobserved ability abilityi and local labor-market quality Li. Assume Cov(educi, abilityi) > 0and Li directly affects wages. A proposed instrument is distance to nearest college, zi. Suppose zi is strongly correlated with Li (e.g. urban areas have smaller distance and higher wages even holding education fixed), and $L_i$ is omitted from the regression. Which statement is most correct?(A) The exclusion restriction may fail because $ z{i} $ can affect $ \ln (wage{i}) $ through $ L{i} $, so $ Cov(z{i},u_{i}) $ may be nonzero.(B) If is always consistent regardless of $ L_i $(C) Adding an intercept is sufficient to control for $ L_{i} $(D) If OLS is biased, IV must be unbiased in finite samples

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