The rank of the differenced variance matrix does not equal the number of coefficients being tested

[Clarine Caine]

Hi there,

I have a panel data and I want to do Hausman Test but it keeps on showing this note:

---

. hausman fe re


Note: the rank of the differenced variance matrix (2) does not equal the number of coefficients being tested (3); be sure
this is what you expect, or there may be problems computing the test. Examine the output of your estimators for
anything unexpected and possibly consider scaling your variables so that the coefficients are on a similar scale.

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fe re Difference S.E.
-------------+----------------------------------------------------------------
ENV_w | -.0038478 -.0080422 .0041944 .0020483
RDEV_w | -36.91599 5.822116 -42.73811 7.913736
SIZE_w | .0000109 -7.44e-06 .0000184 9.02e-06
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg

Test: Ho: difference in coefficients not systematic

chi2(2) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 31.32
Prob>chi2 = 0.0000

---

I tried to follow your suggestion on other posts to use sigmamore on my hausman command, but the note still shows.

---

. hausman fe re,sigmamore

Note: the rank of the differenced variance matrix (2) does not equal the number of coefficients being tested (3); be sure
this is what you expect, or there may be problems computing the test. Examine the output of your estimators for
anything unexpected and possibly consider scaling your variables so that the coefficients are on a similar scale.

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fe re Difference S.E.
-------------+----------------------------------------------------------------
ENV_w | -.0038478 -.0080422 .0041944 .0021063
RDEV_w | -36.91599 5.822116 -42.73811 7.999969
SIZE_w | .0000109 -7.44e-06 .0000184 9.10e-06
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg

Test: Ho: difference in coefficients not systematic

chi2(2) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 30.58
Prob>chi2 = 0.0000

---

Why is the note keep showing? Will it affect my regression result? What should I do?



Thank you,
Clarine Caine

[Joro Kolev]

You might also want to show the output of the original regressions, the fixed and random effects regressions that you ran before doing the Hausman test.

[Clarine Caine]

Here you go:


. xtreg ROA_w ENV_w RDEV_w SIZE_w, fe

Fixed-effects (within) regression Number of obs = 1,974
Group variable: ID Number of groups = 282

R-sq: Obs per group:
within = 0.0104 min = 7
between = 0.0554 avg = 7.0
overall = 0.0310 max = 7

F(3,1689) = 5.92
corr(u_i, Xb) = -0.5317 Prob > F = 0.0005

------------------------------------------------------------------------------
ROA_w | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ENV_w | -.0038478 .0039014 -0.99 0.324 -.0114999 .0038042
RDEV_w | -36.91599 9.310212 -3.97 0.000 -55.17676 -18.65523
SIZE_w | .0000109 9.69e-06 1.13 0.260 -8.08e-06 .0000299
_cons | 5.613622 .4412597 12.72 0.000 4.748148 6.479095
-------------+----------------------------------------------------------------
sigma_u | 2.8819728
sigma_e | 1.9380729
rho | .68859562 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(281, 1689) = 10.68 Prob > F = 0.0000

.
. estimates store fe

.
. xtreg ROA_w ENV_w RDEV_w SIZE_w, re

Random-effects GLS regression Number of obs = 1,974
Group variable: ID Number of groups = 282

R-sq: Obs per group:
within = 0.0000 min = 7
between = 0.0769 avg = 7.0
overall = 0.0467 max = 7

Wald chi2(3) = 12.07
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0071

------------------------------------------------------------------------------
ROA_w | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ENV_w | -.0080422 .0033205 -2.42 0.015 -.0145502 -.0015343
RDEV_w | 5.822116 4.90437 1.19 0.235 -3.790272 15.4345
SIZE_w | -7.44e-06 3.55e-06 -2.10 0.036 -.0000144 -4.81e-07
_cons | 5.212351 .2849336 18.29 0.000 4.653892 5.770811
-------------+----------------------------------------------------------------
sigma_u | 2.2716756
sigma_e | 1.9380729
rho | .57875072 (fraction of variance due to u_i)
------------------------------------------------------------------------------

.
. estimates store re

.
. hausman fe re, sigmamore

Note: the rank of the differenced variance matrix (2) does not equal the number of coefficients being tested (3); be sure
this is what you expect, or there may be problems computing the test. Examine the output of your estimators for
anything unexpected and possibly consider scaling your variables so that the coefficients are on a similar scale.

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fe re Difference S.E.
-------------+----------------------------------------------------------------
ENV_w | -.0038478 -.0080422 .0041944 .0021063
RDEV_w | -36.91599 5.822116 -42.73811 7.999969
SIZE_w | .0000109 -7.44e-06 .0000184 9.10e-06
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg

Test: Ho: difference in coefficients not systematic

chi2(2) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 30.58
Prob>chi2 = 0.0000

[Joro Kolev]

I do not see anything irregular here. Neither the fixed nor the random effects regressions are dropping anything, it all seems fine.

If you do not want to bother, just carry on as if everything is fine, and carry on with the fixed effects model, because your test rejects.

If you want do the regression based test with the Mundlak device as explained on this thread here
https://www.statalist.org/forums/for...an-test-result
in my post #10 with the clarification by Eric in #11.

[Clarine Caine]

okay, thank you so much!