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I want to test whether a fixed or a random effects model is better suited for my data. I am including all variables which don't make the p-value jump, estimate both models and the Hausman test gives me the following output:

 Hausman Test

data:  DV ~ IV + CV1 + CV2 + CV3 + CV4 + CV5 +  ...
chisq = 62.595, df = 9, p-value = 4.227e-10
alternative hypothesis: one model is inconsistent

Soo, very significant, which means I should use a fixed effects model Now, if I add just one more (or multiple) of the variables I have identified as making the p-value jump to 1 the output is the following:

Hausman Test

data:  DV ~ IV + CV1 + CV2 + CV3 + CV4 + CV5 +  ...
chisq = 0.23564, df = 10, p-value = 1
alternative hypothesis: one model is inconsistent

Some of these variables which make the p-value jump so much are very significant in the regression model, so I cannot just exclude them. But I somehow get the feeling, that there is something wrong with my model. A p-value of 1 seems strange. Or is it just what it is, and with these variables included a random effects model should be used?

I am looking forward to your answers!

To estimate the models I use the following code, with CV10 being the variable that makes the p-value jump to 1:

fe_model<-plm(DV ~ IV + CV1 + CV2 + CV3 + CV4 + CV5 + CV6 + CV7 + CV8
+ CV9 + factor(Industry) + CV10, data=sample, index = c("Company", "Year"), model="within", effect="twoways") 

re_model<-plm(DV ~ IV + CV1 + CV2 + CV3 + CV4 + CV5 + CV6 + CV7 + CV8 
+ CV9 + factor(Industry) + CV10, data=sample, index = c("Company", "Year"), model="random", effect="twoways", random.method = "walhus")
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