Consider a simple model of classical regression as Yi where ui stands for random...........

Economics-I Statistical and Econometric Methods

Consider a simple model of classical regression as Y_i = $\small \beta X _{i} + u_{i}$ , where u_i stands for random disturbance term with the standard assumptions and u_{i ~ N(0, ),}and X_iis non-stochastic and i = 1,2,.....,n.

Prove that $\small \bar{\beta }= \frac{\bar{Y}}{\bar{X}}$ , where $\small \bar{Y}$ and $\small \bar{X}$ are means respectively , is unbiased but less efficient estimator of $\small \beta$ than $\small \hat{\beta }$ _OLS.(150 words) (10 Marks)