hausman test interpretation

[Chiara Tasselli]

Good evening to everyone,
someone could help me in the interpretation of the Hausman test? I used an instrumental variable (namely "near_college" on a dummy variable for those who have a college degree "college"), and now I wan't to compare the model with instrument with the one with the simple OLS, what should i look?

hausman iv ols  

Note: the rank of the differenced variance matrix (22) does not equal the number of coefficients being tested (23); 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))
iv          ols         Difference       Std. err.

graduate     1.286624     .4050783        .8815458        .4655217
age     .0787274     .0553255        .0234018        .0141504
ageSq    -.0007348    -.0004779       -.0002569        .0001565
female    -.4129626    -.3075613       -.1054012         .057833
Dumregio1     .6351721     .3067958        .3283763               .
Dumregio2     1.020149     .6391724        .3809765        .0634536
Dumregio3     .7535022     .3861025        .3673998               .
Dumregio4     .6646546     .3689129        .2957417               .
Dumregio5     .6112953     .2792785        .3320168               .
Dumregio6     .6466768     .2502819        .3963949               .
Dumregio7      .589291     .2341512        .3551398               .
Dumregio8     .5523138     .3218681        .2304458               .
Dumregio9     .5710511     .3227754        .2482757               .
Dumregio10     .4627912     .1617768        .3010144               .
Dumregio11     .2001652    -.0945038         .294669               .
Dumregio12     .4523748     .1722981        .2800767               .
Dumregio13      .378258     .1425761        .2356819               .
Dumregio14     .4860104     .1729525        .3130578               .
Dumregio16     .2888901    -.0010325        .2899226               .
Dumregio17     .3862235     .0827122        .3035114               .
Dumregio18     .1315079    -.1997876        .3312955               .
Dumregio19     .2970778    -.0495494        .3466272               .
Dumregio20      .298561    -.0478439        .3464049               .

b = Consistent under H0 and Ha; obtained from ivregress.
B = Inconsistent under Ha, efficient under H0; obtained from regress.

Test of H0: Difference in coefficients not systematic

chi2(22) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= -6.30

Warning: chi2 < 0 ==> model fitted on these data
fails to meet the asymptotic assumptions
of the Hausman test; see suest for a
generalized test.

Many thanks in advance for your time!

[Carlo Lazzaro]

Chiara:
I would start with creating a 20-level unique categorical variable for -region-, re-run both regressions, save their estimates and go -hausman- again.

[Chiara Tasselli]

Many thanks here are the results:

Note: the rank of the differenced variance matrix (23) does not equal the number of coefficients being    tested (24); 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))
iv          ols         Difference       Std. err.

graduate     1.286624     .4050783        .8815458        .4655217
age     .0787274     .0553255        .0234018        .0141504
ageSq    -.0007348    -.0004779       -.0002569        .0001565
female    -.4129626    -.3075613       -.1054012         .057833
Dumeregio 
2      .3849768     .3323766        .0526002        .1414082
3      .1183301     .0793067        .0390235        .0677823
4      .0294825     .0621171       -.0326346        .0405115
5     -.0238768    -.0275173        .0036405        .0755711
6      .0115047    -.0565139        .0680186        .0826549
7      -.045881    -.0726446        .0267635        .0435554
8     -.0828583     .0150723       -.0979305        .0764992
9      -.064121     .0159796       -.0801006         .058946
10     -.1723809     -.145019       -.0273619         .044751
11     -.4350069    -.4012996       -.0337073        .0633472
12     -.1827973    -.1344977       -.0482996        .0556423
13     -.2569141    -.1642197       -.0926944        .0641664
14     -.1491617    -.1338433       -.0153185        .0599795
15     -.3115943    -.3067958       -.0047985        .0974678
16      -.346282    -.3078283       -.0384537        .0455481
17     -.2489486    -.2240836       -.0248649        .0472539
18     -.5036642    -.5065834        .0029192         .094649
19     -.3380943    -.3563452        .0182509         .050589
20     -.3366111    -.3546397        .0180286        .0439386
21     -.6351721    -.6827686        .0475965        .0705742

b = Consistent under H0 and Ha; obtained from ivregress.
B = Inconsistent under Ha, efficient under H0; obtained from regress.

Test of H0: Difference in coefficients not systematic

chi2(23) = (b-B)'[(V_b-V_B)^(-1)](b-B)
=   3.59
Prob > chi2 = 1.0000

Moreover, besides the Hausman test, the coefficient of graduate in the IV seems unrealistic, isn't it??

[Carlo Lazzaro]

Chiara:
Prob>chi2=1.000 is also strange.
Have you checked correlation and robusteness of the instrument?
In addition, use -fvvarlist- notation to make age and its squared term more efficient:

c.age##c.age