題組內容

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

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