Ordinary Least Squares Bias and Bias Corrections for iid Samples

The O(n-1) bias and O(n-2) MSE of OLS are derived for iid samples. An approach is suggested for handling nonexistent finite sample moments. Bias corrections based on plug-in, weighting, jackknife and pairs bootstrap methods are equal to Op(n-3/2). Sometimes they are effective at lowering bias and MSE, but not always. In simulations, the bootstrap correction removes more bias than the others, but has a higher MSE. A hypothesis test is given for the presence of this bias. The techniques are applied to survey data on food expenditure, and the estimated bias is small and statistically insignificant.