$\hat { \beta } - \beta$
A) cannot be calculated since the population parameter is unknown.
B) $= \left( \boldsymbol { X } ^ { \prime } \boldsymbol { X } \right) ^ { - 1 } \boldsymbol { X } ^ { \prime } \boldsymbol { U }$
C) $= \boldsymbol { Y } - \hat { Y }$
D) $= \boldsymbol { \beta } + \left( \boldsymbol { X } ^ { \prime } \boldsymbol { X } \right) ^ { - 1 } \boldsymbol { X } ^ { \prime } \boldsymbol { U }$

Question

Quizplus · Accepted Answer

$\hat { \beta } - \beta = \left( \boldsymbol { X } ^ { \prime } \boldsymbol { X } \right) ^ { - 1 } \boldsymbol { X } ^ { \prime } \boldsymbol { U }$The difference between the estimated coefficient vector and the true coefficient vector is the bias of the estimator. The bias of the OLS estimator is zero, which means that the OLS estimator is unbiased.

β^−β\hat { \beta } - \betaβ^​−β A) Cannot Be Calculated Since the Population Parameter Is Unknown

$\hat { \beta } - \beta$ A) Cannot Be Calculated Since the Population Parameter Is Unknown