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January 31, 2012
The Distribution of Beta-Hat
We start from a previous equation and list some assumptions.
A little side trip shows that the assumption that the expected value of the errors equals zero is not important because the intercept will "soak up" the mean of the errors if it is not zero.
Our centerpiece proofs of the expected value and variance of the estimated beta:
It is important to understand that these conclusions are only valid if the assumptions hold. Stata will run the calculations in any case so, if the assumptions are not satisfied, the Stata results can be misleading.
We have seen a very similar analysis in ECON 400.
Posted by bparke at January 31, 2012 07:52 PM