5. Consider the linear model with intercept:
$y_t = \alpha + \beta x_t + u_t$
If the $A = \sum_{i=1}^{n} (x_i - \bar{x})^2$ is positive definite and $E(u_i \mid x_i) = 0, \forall t = 1, 2, \dots, T$, which statement is true under sample size $T \to \infty$.
(A) $ \hat{\beta} $ is consistent, but we cannot judge whether $ \hat{\beta} $ is efficiency
(B) $ \hat{\beta} $ is unbiased and efficiency
(C) $ \hat{\beta} $ is consistent and efficiency
(D) $ \hat{\beta} $ is, but we cannot judge whether $ \hat{\beta} $ is efficiency
(E) $ \hat{\beta} $ is unbiased and consistent.

阿摩線上測驗 · 2026-10-16T14:40:35+08:00

5. Consider the linear model with intercept: y_t = α + β x_t + u_t If the A = Σ_i=1^n (x_i - x)^2 is positive definite and E(u_i x_i) = 0, t = 1, 2, , T, which statement is true under sample size T → ∞. (A) β is consistent, but we cannot judge whether β is efficiency (B) β is unbiased and efficiency (C) β is consistent and efficiency (D) β is, but we cannot judge whether β is efficiency (E) β is unbiased and consistent.