Correlated random effects model

[Joe Randolf]

I have a panel data set with mainly time variant regressors but 2 regressors which remain pretty much constant for most units (and are completely time-invariant for many units). My question is am I justified in using a correlated random effects model? A hausman test excluding the "relatively time invariant" regressors tells me a fixed effects model is most appropriate but this would remove a high proportion of the data for the two variables. I understand I do not strictly speaking have any time-invariant regressors but I still feel like the correlated random effects model would be the best approach.

Thanks in advance,
Joe

[Rhys Williams]

Hi Joe,

Q1.) Why do you run the FE model excluding relatively time invariant regressors?
Q2.) Why would the FE model remove a high proportion of the data for the two variables?

The answers may well be linked to the explanation on your previous post (in terms of your ticket price var having limited obs), so it might be a good idea to link to that post, so people have a better idea of what is going on.

In my mind, the benefit of a FE model is that you exclude unobserved time-invariant variables (i.e. not variables you have in your dataset (which you can control for), but variables that you can't control for which may be driving your result (omitted variable bias)). It seems that the Hausman test also supports this conclusion so I am not sure why you feel that the correlated random effects model would be a better approach? Is there something in the literature of your study, or econometric theory which makes you think that or are you results just "better" under this model (sadly, that may not be the best reasoning to take).

If you use the RE model and it is unjustified then you run the risk of not using a consistent estimator.

Best,
Rhys

[Joro Kolev]

You might want to show your output and state the question in terms of actual output. At the level of generality at which you speak, I cannot understand what you mean.

[Joe Randolf]

Hi Rhys and Joro.

Apologies, I really should have been more specific. Here is a link to my previous post Removing variable completely changes regression output - Statalist which goes into more detail about the model I want to estimate (looking at the impact of a number of variables on English football attendance).

The 2 variables I refer to are stadium capacity and population. For the vast majority of clubs, stadium capacity remains the same for the entire time period (only a few clubs move into new stadia). Similarly, the local area population does not fluctuate very much at all. My understanding of the fixed effects model is that it uses the within transformation to essentially remove the average of each variable for each unit (please correct me if I am wrong on that). This would mean that using a fixed effects model would mean that the impact of stadium capacity would be estimated using only that small sample of clubs that have moved into new stadia. Additionally, the magnitude of population would essentially be removed. The fixed effects model would therefore fail to account for the full impact of these 2 variables.

As I understand it, the correlated random effects model (Mundlak approach) would allow me to the retain the effects of these 2 variables whilst also keeping all the advantages of the fixed effects model by adding cluster means of the time-variant regressors (hence why I only perform the hausman test on these variables). Essentially like a hybrid model of fixed and random effects.

Generally, the CRE model is only used when there are variables that are completely time-invariant so I am not sure if I can justify using it here. Also I have an unbalanced data set so I don't know if that would make any difference.

Sorry if I have explained that really badly.

[Rhys Williams]

Hi Joe,

I am not sure I agree with your description of the FE estimator - by removing the effect of (relatively) time-invariant variables you will not be able to estimate the effect on your time-invariant variables (stadium capacity and population, in your case) because the standard errors will likely be high (when the variable is completely time-invariant it won't be "estimatable" at all). However, this does not mean that FE model fails to account for the full impact of these 2 variables. Your estimator of interest (scr) will be better estimated using FE as it is possible to remove any time-invariant omitted variable bias.

Unfortunately, I don't know much about the CRE model so can't comment on that.

Best,
Rhys