I've been meaning to write this post for some time. Scott Sumner's post spurs me to write it now.
First let me ask my dumb econometrics question. It's a very simple question, and I really ought to know the answer. But I don't.
Q1. If you estimate a linear regression, using Least Squares or whatever, will the estimated residuals always sum to zero? If the answer is "yes", then skip the next question. [Update: Ben, Norman, and Matthew tell me in comments the answer is "yes", provided there is a constant term in the regression, and I want there to be a constant term.]