Hausman test results: fe vs re model?

[Tatenda Smith]

Working on a panel data set of 27 countries across 6 years worth of observations (2005-10) and trying to pick the right model. My specification is as follows for fixed or random effects:

xtreg lnlifeexp lngdp lniws lnphealth lnwbaid lnadbaid yr1 yr2 yr3 yr4 yr5, cluster(country_id)

I used N-1 time dummies (5). When I run my hausman test this is what I get:


. estimate store random

. hausman fixed random, force

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fixed random Difference Std. err.
-------------+----------------------------------------------------------------
lngdp | .0628643 .0606692 .0021951 .0128097
lniws | .0195612 .0186782 .0008831 .0181452
lnphealth | -.0026833 -.0023503 -.000333 .
lnwbaid | -.0005814 -.0004911 -.0000904 .0003009
lnadbaid | -.0003736 -.0003668 -6.81e-06 .0001944
yr1 | -.0362377 -.0366296 .0003919 .0021936
yr2 | -.0273504 -.0277966 .0004462 .0020063
yr3 | -.0214533 -.0216657 .0002123 .0013544
yr4 | -.0147298 -.0148276 .0000977 .0007549
yr5 | -.0062909 -.0063835 .0000926 .0004695
------------------------------------------------------------------------------
b = Consistent under H0 and Ha; obtained from xtreg.
B = Inconsistent under Ha, efficient under H0; obtained from xtreg.

Test of H0: Difference in coefficients not systematic

chi2(10) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 0.01
Prob > chi2 = 1.0000
(V_b-V_B is not positive definite)


When I try drop the time dummies, I get this:
hausman fixed random, force

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fixed random Difference Std. err.
-------------+----------------------------------------------------------------
lngdp | .1355259 .1238774 .0116485 .0249016
lniws | .2351917 .2210201 .0141715 .0310882
lnphealth | -.0022339 -.0007919 -.001442 .
lnwbaid | -.0030356 -.0032161 .0001805 .0002083
lnadbaid | .0011601 .0011044 .0000556 .0002451
------------------------------------------------------------------------------
b = Consistent under H0 and Ha; obtained from xtreg.
B = Inconsistent under Ha, efficient under H0; obtained from xtreg.

Test of H0: Difference in coefficients not systematic

chi2(5) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 2.22
Prob > chi2 = 0.8184
(V_b-V_B is not positive definite)


I've read similar threads, but to no avail. In my regressions, the time dummies all have P values of 0, and are therefore significant, but the hausman model including them has a P>CHi2 of 1? Surely something must be wrong? Or does this just mean I go with the Random Effects model?

[Tatenda Smith]

My regression results: . xtreg lnlifeexp lngdp lniws lnphealth lnwbaid lnadbaid yr1 yr2 yr3 yr4 yr5, cluster(country_id) fe

Fixed-effects (within) regression Number of obs = 161
Group variable: country_id Number of groups = 27

R-squared: Obs per group:
Within = 0.8778 min = 5
Between = 0.0953 avg = 6.0
Overall = 0.1225 max = 6

F(10,26) = 42.58
corr(u_i, Xb) = -0.0986 Prob > F = 0.0000

(Std. err. adjusted for 27 clusters in country_id)
------------------------------------------------------------------------------
| Robust
lnlifeexp | Coefficient std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
lngdp | .0628643 .0272356 2.31 0.029 .0068808 .1188478
lniws | .0195612 .0568237 0.34 0.733 -.0972415 .136364
lnphealth | -.0026833 .0035992 -0.75 0.463 -.0100815 .0047149
lnwbaid | -.0005814 .0011484 -0.51 0.617 -.0029421 .0017792
lnadbaid | -.0003736 .0006218 -0.60 0.553 -.0016517 .0009045
yr1 | -.0362377 .005669 -6.39 0.000 -.0478906 -.0245849
yr2 | -.0273504 .0049214 -5.56 0.000 -.0374664 -.0172344
yr3 | -.0214533 .0033783 -6.35 0.000 -.0283976 -.0145091
yr4 | -.0147298 .0020393 -7.22 0.000 -.0189216 -.010538
yr5 | -.0062909 .0010955 -5.74 0.000 -.0085428 -.0040389
_cons | 3.543396 .2670822 13.27 0.000 2.994401 4.092391
-------------+----------------------------------------------------------------
sigma_u | .08536895
sigma_e | .00682317
rho | .99365243 (fraction of variance due to u_i)
------------------------------------------------------------------------------

. estimate store fixed

. xtreg lnlifeexp lngdp lniws lnphealth lnwbaid lnadbaid yr1 yr2 yr3 yr4 yr5, cluster(country_id) re

Random-effects GLS regression Number of obs = 161
Group variable: country_id Number of groups = 27

R-squared: Obs per group:
Within = 0.8778 min = 5
Between = 0.0962 avg = 6.0
Overall = 0.1237 max = 6

Wald chi2(10) = 436.68
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

(Std. err. adjusted for 27 clusters in country_id)
------------------------------------------------------------------------------
| Robust
lnlifeexp | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
lngdp | .0606692 .0240351 2.52 0.012 .0135612 .1077771
lniws | .0186782 .0538487 0.35 0.729 -.0868633 .1242197
lnphealth | -.0023503 .0036925 -0.64 0.524 -.0095874 .0048868
lnwbaid | -.0004911 .0011083 -0.44 0.658 -.0026634 .0016812
lnadbaid | -.0003668 .0005906 -0.62 0.535 -.0015243 .0007908
yr1 | -.0366296 .0052274 -7.01 0.000 -.0468751 -.0263841
yr2 | -.0277966 .0044939 -6.19 0.000 -.0366044 -.0189888
yr3 | -.0216657 .003095 -7.00 0.000 -.0277317 -.0155997
yr4 | -.0148276 .0018944 -7.83 0.000 -.0185406 -.0111146
yr5 | -.0063835 .0009898 -6.45 0.000 -.0083235 -.0044434
_cons | 3.559195 .2391799 14.88 0.000 3.090411 4.027979
-------------+----------------------------------------------------------------
sigma_u | .09111631
sigma_e | .00682317
rho | .99442362 (fraction of variance due to u_i)
------------------------------------------------------------------------------

. estimate store random

[Andrew Musau]

You should not use hausman after estimation with clustered standard errors as it does not implement the robust version of the test. Instead, see

ssc install xtoverid
help xtoverid

for a test of overidentifying restrictions.

[daniel klein]

Statistical tests are fine and all but I would rather look at the coefficients and ask myself whether the difference between, e.g., .0195612 and .0186782 are really meaningful substantively. If so, I would consider the precision with which those two coefficients are estimated and how that precision relates to the observed differences.