average log size in panel data

[Luc de Ridder]

Hello,

I have a random effects model with clustered errors and I would like to add the log size to the model. When I generate the log and regress it remains insignificant. Is this due to that the size is an average for each fund so it does not change over time?

[Clyde Schechter]

If this were a fixed-effects model and log(size) does not change within fund over time, then it would be omitted entirely from the model due to colinearity with the fund fixed effects. In a random effects model that does not happen. The random effects model estimates a blend of the between-fund and within-fund effects. You have constructed the variable so that there are no within-fund effects at all for log(size) because it does not vary over time. So all that is left is to estimate the between-fund effects. But these are also being picked up by the random intercepts at the fund: level, and those two are competing to reflect it. In this case, at least, the random effects are winning that competition and log(size) is getting a small coefficient. But, it is nevertheless strongly correlated with the fund random effects, and the latter "steal the variance" away from log(size), so you get a small coefficient.

[Luc de Ridder]

Thanks for your help Clyde. Would it in this case be better to use different sub-samples and look at the differences between them? For example the smallest 25%, middle 50% and largest 25%.

[Clyde Schechter]

In general, taking a continuous variable and breaking it into categories degrades the analysis, rather than improving it. There are some exceptions. If the relationship between exreturn and log(size) is strongly non-linear, then categorizing it can overcome that difficulty--but for that purpose you would be better off with a larger number of categories than three. But if non-linearity is not really an issue here and the problem is what I pointed out in #2, then you won't have any better luck with categories because the same reasoning will still apply.