4. Consider the simple regression yi = β0 + β1 xi + u_i. Which condition, if violated alone, implies OLS is generally not BLUE but can remain unbiased?(A) E(ui xi) = 0(B) Var(ui xi) = σ^2 (constant variance)(C) Var(x_i) &gt; 0(D) Linear-in-parameters conditional mean: E(yi xi) = β0 + β1x_i

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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