題組內容

2. Consider the simple regression model, assume to satisfy ideal conditions:
\( y_t = \beta x_t + \varepsilon_t \quad (2) \)
We now want to consider another estimator $\tilde{\beta}$, defined as follow. You pick two observations at random; say, t = 3 and t = 6.
\( \tilde{\beta} = (y_6 - y_3) / (x_6 - x_3) \quad (3) \)

(a). Consider the estimator \( \tilde{\beta} \). Whether is \( \tilde{\beta} \) unbiased?