5. In the multiple regression yi = β0 + β1 x1i + β2 x2i + ui, you want to test H0: β1 - β2 = 0 (a single linear restriction).Suppose you have β1 = 0.80, β2 = 0.50, Var(β1) = 0.040, Var(β2) = 0.010, Cov(β1, β2) = 0.005.Compute the $t$-statistic t = (β1 - β2) - 0Var(β1 - β2), Var(β1 - β2) = Var(β1) + Var(β2) - 2Cov(β1, β2).Which is closest?(A) 1.50(B) 2.12(C) 3.00(D) 4.24

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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