Help with time-invariant variable in panel data

[Murielle Fuchs]

Good morning,

I am new here and would greatly appreciate some help. I would like to run a regression in order to see the effect of several variables (GDP, urbanisation rate...) on the production of waste.
I have an unbalanced panel data with 930 observations for 27 EU countries between 1995 and 2017.

In my regression, I would like to include a variable on "environmental awareness" that does not change across time (discrete variable with values ranging from 0 to 5). Nevertheless, running a fixed-effect models results in an omitted variable (as it is time-invariant). My main reason for using a FE model is that the result of my Breusch-Pagan Lagrange multiplier test indicated no significant difference across units (thus indicating that random effects are not appropriate, if I am not mistaken). I am not completely sure of my choice between random and fixed models though.

I am now thinking of using a random-effect mode (which does not omit my variable) l but I would like to know whether I am allowed to do that or whether there is a way I could include my "environmental awareness" variable in the FE model.

All my gratitude goes to whoever takes the time to read this and could help me!

[Carlo Lazzaro]

Murielle:
welcome to this forum.
You do not report the outcome of the F-test appearing as a footnote of the -xtreg,fe- oucome table. If it does not reach statistical significance, you canot go -fe-either. Hence, the alternative is a pooled OLS. Conversely, if it eaches statistical significance and you want to investigate the time invariant predictor, you can consider the user-written programme -mundlak- (type -search mundlak- from within Stata to spot and install it) and https://blog.stata.com/2015/10/29/fi...dlak-approach/.
As an aside, the reference test to compare -fe-vs -re- specification is -hausman-.
Eventually, as you N and T dimensions are similar, you may want to take a look at -xtregar-.

[Murielle Fuchs]

Dear Carlo,
Thank you very much for your answer.

The outcome of my F-test of the -xtreg,fe- regression is F(26,206)=84.02, which gives Prob>F=.0000. It thus reaches statistical significance.

Your idea of the mundlak test is a very interesting one, I did not know about this test. I tried it and concluded that I can reject the null hypothesis and that a fixed-effect model is appropriate.
Do you think that there is any way I can still include my time invariant in a fixed-effect model? I am quite confused since I feel that I should use a fixed-effect model but can't find a way to include this variable (constant yet quite important in my model).

Thank you again for your time.

PS: It is indeed the Hausman test that I had in mind and not the Breusch-Pagan Lagrange, sorry about that!

[Carlo Lazzaro]

Murielle:
thanks for providing further clarifications.
Innaddition to the mundlak test, there's also the user-written -mundlak- command (type -search mundlak- from within Stata to spot and install it), that allows you to estimate the coefficient of time-invariant predictors.

[Phil Bromiley]

There is also user-written xthybrid which has similar capabilities.