Identical OLS and Random Effect Model; Why is my theta/individual effect variance zero? I have a panel data set with companies and some variables expressed as changes year-to-year from 2017-2018 (2018) to 2020-2021 (2021). I am trying to estimate a regression estimating the effect of all variables on "OPEX" with the plm-function in R (from package plm).



R tells me "n = 254, T = 4, N = 1016" and then I guess due to NAs "n = 225, T = 1-4, N = 679".
Anyways, when running Pooled OLS, FE and RE regressions I recognized that the RE and Pooled model were identical. I suspect this is because theta=0 and this in respect is because the individual effects variance is 0. I found this in the RE model:



Consistent to that the Lagrange Multiplier Test gave a p-value of 1 (When using type "bp" the value was very small): plmtest(pooledols, effect="individual")



The F-Test for the Pooled and the FE also gave a p-value of 1: pFtest(fixedeff,pooledols)



For the Pooled and RE I included time-invariant variables but excluded them for FE. None of the variables were significant in any regression and the R-squared always was very low.
Did I do something wrong? Might there be a problem because I used changes year-to-year instead of the actual values?
My interpretation is that the fixed effects are the same for all companies and therefore the variance is zero and the RE becomes identical to a pooled OLS. I have not found any explanation why this could have happened on the internet and it feels off. Therefore, I am very happy for any help. If you need further screenshots or explanations please do not hesitate to ask.

It is standard practice for econometrics software to set variance estimates to 0 if a negative variance is estimated for the random effects estimators which do not garantuee non-zero variance estimation.
A hint about this you find in, e.g. one of the plm's package Vignettes where such an example is presented: https://cran.r-project.org/web/packages/plm/vignettes/B_plmFunction.html

The estimated variance of the time component is negative for the
Wallace-Hussain as well as the Swamy-Arora models and plm sets it to
0.

In this case, the Swamy-Arora estimation degenerates to a pooled estimation.
Good econometric textbooks mention this shortcoming of some of the RE estimators. For a reference to Wooldridge, see my answer here: https://stats.stackexchange.com/a/181444/94889
