# st: Re: hausman after xtreg

 From Kit Baum <[email protected]> To [email protected] Subject st: Re: hausman after xtreg Date Thu, 2 Oct 2003 09:09:15 -0400

```On Thursday, Oct 2, 2003, at 02:33 US/Eastern, Paula wrote:

```
I have used the xthausman command, however, I am very surprised by some results. When I use whatever of the following alternatives:

1)xtreg y x, fe
est store fixed
xtreg y x, re
hausman fixed .
or
2) xtreg y x, re
estimates store random_effects
xtreg y x, fe
hausman . random_effects
or
3) xtreg y x, fe
hausman, save
xtreg y x, re
hausman

I get always the same result:

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| Consistent Efficient Difference S.E.
------------- ----------------------------------------------------------------
invl1 | 1.974847 1.860985 .1138621 .0419927
desipoterl1 | .9808413 .5775732 .4032681 .1703565
desliqotvl1 | 2.269129 -1.008472 3.277601 .7864388
CPIBreal | .0036555 .0056068 -.0019513 .002446
tendencia | .0000698 .0000947 -.0000249 .0000122
----------------------------------------------------------------------- -------
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)
= -65.02 chi2<0 ==> model fitted on these
data fails to meet the asymptotic
assumptions of the Hausman test;
see suest for a generalized test

This would tell me that I do not have enough information to reject the null, so I have to use random effects. However, if I use the xthausman command, I get:

. xthausman
(Warning: xthausman is no longer a supported command; use -hausman-. For instructions, see help hausman.)

Hausman specification test

---- Coefficients ----
| Fixed Random
nfond | Effects Effects Difference
- ------------- -----------------------------------------
invl1 | 1.974847 1.860985 .1138621
desipoterl1 | .9808413 .5775732 .4032681
desliqotvl1 | 2.269129 -1.008472 3.277601
CPIBreal | .0036555 .0056068 -.0019513
tendencia | .0000698 .0000947 -.0000249

Test: Ho: difference in coefficients not systematic

chi2( 5) = (b-B)'[S^(-1)](b-B), S = (S_fe - S_re)
= 18.01
Prob>chi2 = 0.0029

which tells me that I have to use fixed effects.

How is this possible?
I don't know. I just tried invoking both commands, and got exactly the same chi^2 from hausman and xthausman:

. webuse grunfeld,clear

. qui xtreg invest mvalue kstock, fe

. est store fixed

. qui xtreg invest mvalue kstock, re

. hausman fixed .

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fixed . Difference S.E.
------------- +----------------------------------------------------------------
mvalue | .1101238 .1097811 .0003427 .0055213
kstock | .3100653 .308113 .0019524 .0024516
------------------------------------------------------------------------ ------
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)
= 2.33
Prob>chi2 = 0.3119

. xthausman
(Warning: xthausman is no longer a supported command; use -hausman-. For
instructions, see help hausman.)

Hausman specification test

---- Coefficients ----
| Fixed Random
invest | Effects Effects Difference
-------------+-----------------------------------------
mvalue | .1101238 .1097811 .0003427
kstock | .3100653 .308113 .0019524

Test: Ho: difference in coefficients not systematic

chi2( 2) = (b-B)'[S^(-1)](b-B), S = (S_fe - S_re)
= 2.33
Prob>chi2 = 0.3119

.
Kit

*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/