9. Suppose you estimate a log-level model (yi) = β0 + β1 xi + ui, yi > 0, with E(ui xi) = 0. Using the standard approximation for small changes, which interpretation of β_1 is correct? (A) A one-unit increase in x changes y by exactly β_1 units (B) A one-percent increase in x changes y by approximately β_1 percent (C) A one-unit increase in x changes E(y x) by approximately 100β_1 percent (D) β_1 is the price elasticity of demand

10. Consider the wage equation $\ln(wagei) = \beta0 + \beta1 educi + ui$, where $ui$ contains unobserved ability $abilityi$ and local labor-market quality $Li$. Assume $Cov(educi, abilityi) > 0$ and $Li$ 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 $ Cov(z{i}, e d u c{i}) \neq 0 $, IV 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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