阿摩線上測驗 登入

最新科目

最新試卷

最新試題

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 $x1, x2, \ldots, x_n$ is a random sample of size $n$ from a normal distribution with mean $\mu$ and variance $\sigma^2$. What is the Cramér-Rao lower bound for $\sigma^2$? (A) $\frac{\sigma^2}{n}$ (B) $\frac{\sigma^2}{n-1}$ (C) $\frac{2\sigma^4}{n}$ (D) $\frac{2\sigma^4}{n-1}$

8. Suppose $x1, x2, \ldots, xn$ is a random sample of size $n$ from a Poisson distribution with mean $\lambda$, and assume $n = 2k$ for some integer $k$. Consider the following estimator. $\hat{\lambda} = \frac{1}{2k} \sum{i=1}^{k} (x{2i} - x{2i-1})^2$ Which of the following is correct? (A) \(\hat{\lambda}\) is a linear and an unbiased estimator. (B) \(\hat{\lambda}\) is a linear but biased estimator. (C) \(\hat{\lambda}\) is not a linear but an unbiased estimator. (D) \(\hat{\lambda}\) is neither a linear nor an unbiased estimator.

最新申論題

最新課程

最新主題筆記

最新討論