On Tue, 1 Dec 2020, Sven Schreiber wrote: Thanks, Peter and Sven. But my focus is not so much on judging whether using y or log(y) is better; at this point I'm convinced that log(y) gives a substantially better fit. Let me try to explain my problem more clearly. My dependent variable y can be decomposed as y = y1 + y2, and I have data on the two components. I'm looking for a formal test between these alternatives: Restricted: y = Xb + u Unrestricted: y = y1 + y2 = Xb1 + v + Xb2 + w where in the second case b1 and b2 are to be estimated by separate regressions of y1 on X and y2 on X. (One might think of SUR, but X is the same in the two cases so it's equivalent to per-equation OLS.) I think this would be relatively straightforward if y were just in levels, but coming up with a valid test is complicated by the fact that I actually want to use log(y), log(y1) and log(y2) in the respective regressions. Allin