Hausmann Test: the rank of the differenced variance matrix (12) does not equal the number of coefficients being tested (13)

[Julie Balaz]

Hello,

I performed a Hausman test to check for fixed versus random effect model. The result show that I should use fixed effects model. However, I do not understand the NOTE.
Can someone just please tell me what I can do to not get this NOTE after running the command?

Thanks in advance and best regards

Julie

[Carlo Lazzaro]

Julie:
you can run the Stata comunity-contributed module -xtoverid- on -xtreg,re- and see if the null (that is, -re- is the way to go) is rejected.
As -ctoverid- do not allow -fvvarlist- notation, see -xi:-.

[Sebastian Kripfganz]

This is likely because of the time dummies, which do not provide a useful signal for the RE vs. FE comparison. You can adjust the degrees of freedom manually with the df() option of the hausman command. In your case, this would be df(7) when you count the coefficients excluding the time dummies.

Aside from that, the test computed by the hausman command is not robust to heteroskedasticity. Carlo gave a useful suggestion in this regard. Also, there is a generalized regression-based version of the Hausman test that can be used with robust standard errors; search for keywords "correlated random effects" and "Mundlak".

[Andrew Musau]

This is likely because of the time dummies, which do not provide a useful signal for the RE vs. FE comparison.

I agree that the time dummies do not provide a useful signal for the RE vs. FE comparison, and I support the recommendation to use the generalized regression-based version of the Hausman test, which is programmed in StataNow 18.5 and later versions. However, regarding the cause of the error, my money is on the coefficient of "avg_cal", which is too small and gets dropped when hausman attempts to take differences. You should consider rescaling this variable.

replace avg_cal= avg_cal/1e+6
label variable  avg_cal "Whatever (in millions of x units)"

Then re-run the commands with the rescaled variable.