I am working on a paper studying the relative persistence of company profits, that is, the tendency of profits to last between periods. The standard approach in the literature is estimating an AR(1)autoregressive model and taking the autoregression parameter as an estimate of the persistence rate.
Instead, we are using a simple linear growth curve, using time as the only covariate, and including random effects for both intercept and slope. Then we regress the slope on the intercept, and take the (negative) coefficient as evidence of the rate of erosion of differences in firm profits.
Well, we have sent the paper to a journal, and we have received feedback from one reviewer saying that "in an empirical model as yours the result that the initial heterogeneity will regress to the mean is very likely meaningless", and referring to a classical econometric discusson on the "regression to the mean" issue.
We are pretty confident that our model does not suffer from this problem, as we estimate initial heterogeneity using all the available observations, but we would much appreciate your opinion, as well as any references that may us help in convincing the reviewer, if we are indeed right.
Not sure I can help here. This is a tough topic to disentangle, where you would have to argue against the idea that an unusually low/high starting profit for a company necessarily leads to an increased/decreased profit. You can search for references by David Rogosa on regression to the mean. There have been other studies done with s ON i - in achievement research - but I don't think they have had to argue against regression to the mean.