ECON 710 Midterm: ECON 710 UW Madison Midterm 2010a
Document Summary
The assumption that the observations are iid implies nothing about the relationship between yi and xi . It does not imply that the linear equation yi = x0 i(cid:12) + ei is a regression. (calling it a regression does not make it one!) From the fwl theorem, we have the expression. 1x2 which happens when x 0 for ~(cid:12)2 and substitute in the ols estimates on the full model. 2x1 = 0: another way to see the di erence is to take the expression to (cid:133)nd. ^(cid:12)2 6= ^(cid:12)2 where the second-to-last equality uses m1x1 = 0 and m1^e = m1m y = 0: yes, it is consistent. There are two key steps to this observation. Two, the subsample has n = n=2 observations and n ! Since the observations are selected randomly from the the dataset, this is equivalently to taking a sample of size n from the population.
