# st: Negative Hausman Test and FE vs. Pooled

 From Sizhong Sun To statalist@hsphsun2.harvard.edu Subject st: Negative Hausman Test and FE vs. Pooled Date Tue, 30 May 2006 16:52:15 +1000

Dear Listers:

Sorry to bother you all. I am a new stata user, and hope somebody can be kind to answer my question.
I have got a 2-year panel, and did pooled OLS, FE, and RE over the data set (pls see the output in the following). I tried to figure out which estimation is most appropriate. However, for test FE vs. RE, the Hausman test statistics is negative. What is the problem with that? And when testing FE vs. Pooled OLS, I know I can use a F test which can be computed with the R-squared in the two estimations. However, for the R-squared in FE estimation, it reports three: within, between and overall. Which shall I use to computer the F test statistics?

Besides, does using "xtreg y x1 x2, fe robust" command give hetereoskedasticity robust SE?

Any help is very much appreciated!

Best
Sizhong

=================================================================

. reg y lnfai k tao l, robust;

Linear regression Number of obs = 44
F( 4, 39) = 6.83
Prob > F = 0.0003
R-squared = 0.4265
Root MSE = .04115
------------------------------------------------------------------------------------------------------------
| Robust
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------------------------------------
lnfai | .0124241 .007253 1.71 0.095 -.0022464 .0270946
k | .0506836 .1310023 0.39 0.701 -.2142936 .3156608
tao | -.0334697 .0298679 -1.12 0.269 -.0938833 .0269439
l | .3283087 .1075946 3.05 0.004 .110678 .5459394
_cons | -.1579543 .1729375 -0.91 0.367 -.5077533 .1918448
------------------------------------------------------------------------------------------------------------

. xtreg y lnfai k tao l, fe robust;

Fixed-effects (within) regression Number of obs = 44
Group variable (i): icode Number of groups = 22

R-sq: within = 0.7722 Obs per group: min = 2
between = 0.2732 avg = 2.0
overall = 0.3059 max = 2

F(4,18) = 36.77
corr(u_i, Xb) = -0.8336 Prob > F = 0.0000
----------------------------------------------------------------------------------------------------------------------
| Robust
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+--------------------------------------------------------------------------------------------------------
lnfai | .0691566 .0300599 2.30 0.034 .0060032 .13231
k | .2037541 .0774986 2.63 0.017 .0409355 .3665727
tao | .0328561 .0146233 2.25 0.037 .0021337 .0635785
l | .3572544 .158167 2.26 0.037 .0249579 .6895509
_cons | -1.540555 .7221369 -2.13 0.047 -3.057708 -.0234018
-------------+--------------------------------------------------------------------------------------------------------
sigma_u | .07496871
sigma_e | .02094293
rho | .92760976 (fraction of variance due to u_i)
----------------------------------------------------------------------------------------------------------------------

. estimates store fixed;

. xtreg y lnfai k tao l, re robust;

Random-effects GLS regression Number of obs = 44
Group variable (i): icode Number of groups = 22

R-sq: within = 0.7266 Obs per group: min = 2
between = 0.2959 avg = 2.0
overall = 0.3943 max = 2

Random effects u_i ~ Gaussian Wald chi2(5) = 426.53
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
----------------------------------------------------------------------------------------------------------------------
| Robust
y | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lnfai | .0146575 .0078896 1.86 0.063 -.0008059 .0301208
k | .0705568 .1001375 0.70 0.481 -.1257091 .2668227
tao | -.0010638 .0221253 -0.05 0.962 -.0444285 .042301
l | .4420591 .1129879 3.91 0.000 .2206069 .6635114
_cons | -.2164438 .1911119 -1.13 0.257 -.5910163 .1581286
-------------+--------------------------------------------------------------------------------------------------------
sigma_u | .02935355
sigma_e | .02094293
rho | .66267202 (fraction of variance due to u_i)
----------------------------------------------------------------------------------------------------------------------

. xttest0;

Breusch and Pagan Lagrangian multiplier test for random effects:

y[icode,t] = Xb + u[icode] + e[icode,t]

Estimated results:
| Var sd = sqrt(Var)
---------+-----------------------------
y | .0026781 .0517506
e | .0004386 .0209429
u | .0008616 .0293535

Test: Var(u) = 0
chi2(1) = 5.39
Prob > chi2 = 0.0202

. estimates store random;

. hausman fixed random;

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fixed random Difference S.E.
-------------+----------------------------------------------------------------------------------------------
lnfai | .0691566 .0146575 .0544991 .029006
k | .2037541 .0705568 .1331973 .
tao | .0328561 -.0010638 .0339199 .
l | .3572544 .4420591 -.0848047 .1106821
------------------------------------------------------------------------------------------------------------
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(4) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= -8.49 chi2<0 ==> model fitted on these
data fails to meet the asymptotic
assumptions of the Hausman test;
see suest for a generalized test

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