Random-Effects: R2, Coef. & many variables - interpretations and limits for interpretation?

[Eva Lan]

Hello everyone,

Up to now, I ran Random-Effects Models. Due to quite small outcomes wether significances I struggle with the interpretations. I have quite similar problems with the DiD esmimation and the same dataset. Might it be a problem with the data?


Input: xtreg ..., re (proofed by hausman & LM)

Output:

Random-effects GLS
Group variable: per
[…]
Obs per group: min = 7
avg = 8.0
max = 16

R-sq: within = 0.0000
between = 0.0523
overall = 0.0214

Wald chi2(11) = 55.00
Prob > chi2 = 0.0000

corr(u_i, X) = 0 (assumed)


My questions would be:

1. I have about 10 independent variables in that -re- model. Does the modelfit count for each of those variables nevertheless? So if the model predicts the dependent variable e.g. to 10% each of my variable predicts the dependent variable to 10%? That doesn’t really make sense to me.
2. Due to the fact that I have quite a lot independent variables, might that be a reason for the rather small R2? So can I take it for granted or isn’t it that precise or even valid/relevant anymore?
   I have read that I had to take care with the interpretation of R2, because data may be quite different, although the R2-outcome stays the same.
3. The question that arises for me is whether - with such a small predictive value, even if the model is significant - I can expect a real effect of my independent variables? Does the coefficient is more important than R2? So how do I predict a quite high coefficient although the R2value might be quite small for example? Or is the coefficient irrelevant in this context? Then it wouldn’t matter if the coefficient were a significant value of -coef.=4.52 or coef.=-0.002, because in any cases the variable would only makes a 2.1% prediction for the dependent varaible anyway.

(Furthermore about the reporting: )

1. Prob > chi2 is significant. That means I can declare the -re- as „valid“? Or would I have to call it differently?
2. Within my persons the my output can predicted the effect on my dependent variable of 0% - so it can’t predict it? Between the single persons (so the differences between person A and person B) are predictable to 5,23% and over the whole dataset (so for every single line in my dataset) to 0,214%?
3. corr is "0". In my -fe- models it’s above 0. FE Modellen war corr. immer größer null. Is this a problem?

I would be very thankful, if someone could explain my questions to me (especially 1-3!). It doesn’t make sense to me to have multiple predictive values for my dependent variable AND to have such small ones.
The modelfits and the interpretation represents a real hurdle form me.

Thank you very much in advance!

[Carlo Lazzaro]

Eva:
1-3): just like your DID, I think that your -xtreg, re- model (please share with the list what you typed and what Stata gave you back via CODE delimiters, outcome table included. Thanks) suffers from omitted variable bias.

About reporting:
- a statistically significant Prob chi2 >0 simply tells that, taken together, the coefficients of your model are different from zero. This is not enough to state that your model gives a fair and true view of the data generating process;
- the sole R-sq that deserves consideration under -xtreg,re- is the between R-sq;
- you seem to forget that corr=0 is the (sometimes untenable) assumption of the -re- specification, whereas correlation differen from zero is its counterpart under -fe- specification (If I interpret your German phrasing correctly, you stated that, under -xtreg,fe- the correlation between variables was always>0). Correlation refers to the panel-wise effect (u_i) and the vector of regressors. Take a look at -xt- entries in Stata -pdf manual and any decent textbook on panel data econometrics. Even better if you can discuss your concerns with a colleague who is skiled in panel data econometrics and/or with your professor/teacher/mentor/supervisor (who, all in all, you pay for that).

[Eva Lan]

Hello Carlo,
thank you very much for your response! That is very helpful!
Unfortunately, I don't have any omitted variables in my models.
Yes, I mixed the correlations up. Thank you!

[Carlo Lazzaro]

Eva:
as you're surely aware of, omitted vraibale bias can also imply the existence of a non-linear relationship between a given predictor and the dependent variable.
This is often the case with predictors such as age; working_experience and tenure.

[Eva Lan]

Okay. Thank you! No, i didn't keep that in mind, to be honest. I am not at all used to panel analyses and probably I mixed up quite a lot. Is there any test I can use to check the mentioned case above?

[Carlo Lazzaro]

Eva:
-estat ovtest- is the test to be run.
Unfortunately, it does not work with -xt- commands.
The workaround is to perform -regress- with standard error clustered on -paneiid- and then invoke it.

[Eva Lan]

Thank you very much, Carlo!!
I am going to run that test.