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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

9. Suppose you estimate a log-level model $\ln(yi) = \beta0 + \beta1 xi + ui, \quad yi > 0,$with $E(ui \mid xi) = 0$. Using the standard approximation for small changes, which interpretation of $\beta_1$ is correct?(A) A one-unit increase in \( x \) changes \( y \) by exactly \( \beta_{1} \) units(B) A one-percent increase in \( x \) changes \( y \) by approximately \( \beta_{1} \) percent(C) A one-unit increase in \( x \) changes \( E(y \mid x) \) by approximately \( 100\beta_{1} \) percent(D) \( \beta_{1} \) is the price elasticity of demand

8. Let a categorical variable $Gi \in \{1,2,3,4\}$ and define dummies $D{ki} = \mathbf{1}\{Gi = k\}$, $k = 1,2,3,4$. Consider the regression with an intercept: $yi = \beta0 + \beta1 D{1i} + \beta2 D{2i} + \beta3 D{3i} + \beta4 D{4i} + ui$. Which statement is correct?(A) The model is identified because the dummies are mutually exclusive(B) The model is not identified because \( \sum{k=1}^{4} D{ki} = 1 \) for all \( i \); drop one dummy or drop the intercept(C) The model is identified if \( n \) is large enough(D) Identification fails only if one group has zero observations試題隨卷繳交接背面4國立臺北大學 115 學年度碩士班一般入學考試試題系(所)組別:經濟學系科 目:統計學第4頁 共4頁☑可 ☐不可使用計算機

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