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RE: st: Panel Data-FIXED, RANDOM EFFECTS and Hausman Test
Muhammad,
The "negative Hausman statistic" problem comes up from time to time on
Statalist. A couple of my own responses:
http://www.stata.com/statalist/archive/2006-10/msg00599.html on how to
guarantee a postive Hausman stat in an FE vs RE test
http://www.stata.com/statalist/archive/2007-10/msg00819.html on an
add-in (-xtoverid-) that will do this automatically plus give you a
cluster-robust test statistic if you want it.
...but I think Kirimi and David make some fundamental points that are
probably more important than just this technical issue of getting a
positive test stat.
--Mark
Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University
Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3296
http://ideas.repec.org/e/psc51.html
> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]] On Behalf Of
> David Greenberg
> Sent: 26 February 2009 21:26
> To: [email protected]
> Subject: Re: st: Panel Data-FIXED, RANDOM EFFECTS and Hausman Test
>
> With a small number of nations and more years than nations
> you may be better off using panel-corrected standard errors
> than the approach you are taking. David Greenberg, Sociology
> Department, New York University
>
> ----- Original Message -----
> From: Muhammad Billal Malik <[email protected]>
> Date: Thursday, February 26, 2009 2:20 pm
> Subject: st: Panel Data-FIXED, RANDOM EFFECTS and Hausman Test
> To: [email protected]
>
>
> > I am having some problems with my econometrics based dissertation. I
> > doing a panel data on 12 sub-saharan african nations, with
> 6 variables
> > over a 17 year time period.
> >
> > I am using a simple log log model to test to see if one of my
> > variables lx2 (tourism receipts) has a positive affect on
> GDP. I have
> > run a pooled regression, then fixed effects between and within, and
> > finally a random effects. I have then carried out a Hausman test and
> > achieved a negative value, which has confused me more. I
> was wondering
> > what do I do, as in what model shall I choose? I have attached my
> > STATA output so you can see if I have gone through the right steps.
> >
> > I will really appreciate if you can help me,
> >
> > Kind Regards,
> >
> > Mohammud
> >
> >
> > Carrying out a pooled data regression
> > . regress ly lx1 lx2 lx3 lx4 lx5 lx6
> >
> > Source | SS df MS
> Number of obs =
> > 57
> > -------------+------------------------------ F(
> 6, 50) =
> > 52.04
> > Model | 59.1406489 6 9.85677481 Prob
> > F =
> > 0.0000
> > Residual | 9.47031674 50 .189406335
> R-squared =
> > 0.8620
> > -------------+------------------------------ Adj
> R-squared =
> > 0.8454
> > Total | 68.6109656 56 1.22519581 Root
> MSE =
> > .43521
> >
> >
> --------------------------------------------------------------
> ----------------
> > ly | Coef. Std. Err. t P>|t|
> [95% Conf. Interval]
> >
> -------------+------------------------------------------------
> ----------------
> > lx1 | .173204 .0545574 3.17 0.003
> .0636223
> > .2827857
> > lx2 | .0816157 .0737985 1.11 0.274
> -.0666129
> > .2298442
> > lx3 | 1.207415 .7336368 1.65 0.106
> -.2661382
> > 2.680968
> > lx4 | .8167941 .0985049 8.29 0.000
> .6189412
> > 1.014647
> > lx5 | 4.014936 1.263028 3.18 0.003
> 1.478069
> > 6.551803
> > lx6 | .2619006 .2371792 1.10 0.275
> -.2144879
> > .738289
> > _cons | -20.5465 5.498655 -3.74 0.000
> -31.59087 -9.502123
> >
> --------------------------------------------------------------
> ----------------
> >
> > . gen country = region
> > Setting up a panel
> > . tsset country year, yearly
> > panel variable: country (strongly balanced)
> > time variable: year, 1990 to 2006
> >
> > Carrying out a fixed effects within regression on panel data
> > . xtreg ly lx1 lx2 lx3 lx4 lx5 lx6, fe
> >
> > Fixed-effects (within) regression Number of
> obs =
> > 57
> > Group variable (i): country Number of
> groups =
> > 10
> >
> > R-sq: within = 0.7640 Obs per
> group: min =
> > 2
> > between = 0.5507
> avg =
> > 5.7
> > overall = 0.5374
> max =
> > 8
> >
> > F(6,41)
> =
> > 22.12
> > corr(u_i, Xb) = 0.5835 Prob > F
> =
> > 0.0000
> >
> >
> --------------------------------------------------------------
> ----------------
> > ly | Coef. Std. Err. t P>|t|
> [95% Conf. Interval]
> >
> -------------+------------------------------------------------
> ----------------
> > lx1 | -.0075411 .0061342 -1.23 0.226
> -.0199293
> > .0048472
> > lx2 | .1397473 .0208394 6.71 0.000
> .0976612
> > .1818334
> > lx3 | -.0471179 .0766965 -0.61 0.542
> -.2020095
> > .1077738
> > lx4 | .0883038 .0510516 1.73 0.091
> -.0147971
> > .1914046
> > lx5 | .4423916 .1609951 2.75 0.009
> .1172554
> > .7675278
> > lx6 | -.0635172 .0380633 -1.67 0.103
> -.1403876
> > .0133532
> > _cons | 2.404044 .8235133 2.92 0.006
> .7409252
> > 4.067163
> >
> -------------+------------------------------------------------
> ----------------
> > sigma_u | .95115353
> > sigma_e | .03719725
> > rho | .99847294 (fraction of variance due to u_i)
> >
> --------------------------------------------------------------
> ----------------
> > F test that all u_i=0: F(9, 41) = 755.95
> Prob > F
> > = 0.0000
> >
> > . xtreg ly lx1 lx2 lx3 lx4 lx5 lx6, be
> >
> > Carrying out a fixed effects between regression on panel data
> >
> >
> > Between regression (regression on group means) Number of
> obs =
> > 57
> > Group variable (i): country Number of
> groups =
> > 10
> >
> > R-sq: within = 0.0790 Obs per
> group: min =
> > 2
> > between = 0.9488
> avg =
> > 5.7
> > overall = 0.7682
> max =
> > 8
> >
> > F(6,3)
> =
> > 9.26
> > sd(u_i + avg(e_i.))= .4441503 Prob > F
> =
> > 0.0477
> >
> >
> --------------------------------------------------------------
> ----------------
> > ly | Coef. Std. Err. t P>|t|
> [95% Conf. Interval]
> >
> -------------+------------------------------------------------
> ----------------
> > lx1 | .5188441 .2315068 2.24 0.111
> -.2179138
> > 1.255602
> > lx2 | -.0061883 .4172493 -0.01 0.989
> -1.334062
> > 1.321685
> > lx3 | .1313838 4.684306 0.03 0.979
> -14.77617
> > 15.03894
> > lx4 | .9508895 .2441334 3.89 0.030
> .173948
> > 1.727831
> > lx5 | 7.621178 7.059213 1.08 0.359
> -14.84439
> > 30.08674
> > lx6 | -.672947 1.417266 -0.47 0.667
> -5.183319
> > 3.837425
> > _cons | -26.37744 19.85242 -1.33 0.276
> -89.5567
> > 36.80181
> >
> --------------------------------------------------------------
> ----------------
> >
> > . xtreg ly lx1 lx2 lx3 lx4 lx5 lx6, re
> >
> > Carrying out a random effects regression on panel data
> >
> >
> > Random-effects GLS regression Number of
> obs =
> > 57
> > Group variable (i): country Number of
> groups =
> > 10
> >
> > R-sq: within = 0.7556 Obs per
> group: min =
> > 2
> > between = 0.6683
> avg =
> > 5.7
> > overall = 0.6327
> max =
> > 8
> >
> > Random effects u_i ~ Gaussian Wald
> chi2(6) =
> > 94.90
> > corr(u_i, X) = 0 (assumed) Prob > chi2
> =
> > 0.0000
> >
> >
> --------------------------------------------------------------
> ----------------
> > ly | Coef. Std. Err. z P>|z|
> [95% Conf. Interval]
> >
> -------------+------------------------------------------------
> ----------------
> > lx1 | -.0065896 .0077505 -0.85 0.395
> -.0217803
> > .0086011
> > lx2 | .1253869 .0257565 4.87 0.000
> .0749051
> > .1758687
> > lx3 | -.0363082 .0969763 -0.37 0.708
> -.2263783
> > .1537619
> > lx4 | .1554292 .061983 2.51 0.012
> .0339448
> > .2769135
> > lx5 | .4387479 .2031582 2.16 0.031
> .0405652
> > .8369306
> > lx6 | -.0456517 .0477556 -0.96 0.339
> -.1392509
> > .0479475
> > _cons | 2.241371 1.053202 2.13 0.033
> .1771336
> > 4.305609
> >
> -------------+------------------------------------------------
> ----------------
> > sigma_u | .44383293
> > sigma_e | .03719725
> > rho | .99302502 (fraction of variance due to u_i)
> >
> --------------------------------------------------------------
> ----------------
> > Fixed-effects (within) regression Number of
> obs =
> > 57
> > Group variable (i): country Number of
> groups =
> > 10
> >
> > R-sq: within = 0.7640 Obs per
> group: min =
> > 2
> > between = 0.5507
> avg =
> > 5.7
> > overall = 0.5374
> max =
> > 8
> >
> > F(6,41)
> =
> > 22.12
> > corr(u_i, Xb) = 0.5835 Prob > F
> =
> > 0.0000
> >
> >
> --------------------------------------------------------------
> ----------------
> > ly | Coef. Std. Err. t P>|t|
> [95% Conf. Interval]
> >
> -------------+------------------------------------------------
> ----------------
> > lx1 | -.0075411 .0061342 -1.23 0.226
> -.0199293
> > .0048472
> > lx2 | .1397473 .0208394 6.71 0.000
> .0976612
> > .1818334
> > lx3 | -.0471179 .0766965 -0.61 0.542
> -.2020095
> > .1077738
> > lx4 | .0883038 .0510516 1.73 0.091
> -.0147971
> > .1914046
> > lx5 | .4423916 .1609951 2.75 0.009
> .1172554
> > .7675278
> > lx6 | -.0635172 .0380633 -1.67 0.103
> -.1403876
> > .0133532
> > _cons | 2.404044 .8235133 2.92 0.006
> .7409252
> > 4.067163
> >
> -------------+------------------------------------------------
> ----------------
> > sigma_u | .95115353
> > sigma_e | .03719725
> > rho | .99847294 (fraction of variance due to u_i)
> >
> --------------------------------------------------------------
> ----------------
> > F test that all u_i=0: F(9, 41) = 755.95
> Prob > F
> > = 0.0000
> >
> > . estimates store fixed
> >
> > . xtreg ly lx1 lx2 lx3 lx4 lx5 lx6, re
> >
> > Random-effects GLS regression Number of
> obs =
> > 57
> > Group variable (i): country Number of
> groups =
> > 10
> >
> > R-sq: within = 0.7556 Obs per
> group: min =
> > 2
> > between = 0.6683
> avg =
> > 5.7
> > overall = 0.6327
> max =
> > 8
> >
> > Random effects u_i ~ Gaussian Wald
> chi2(6) =
> > 94.90
> > corr(u_i, X) = 0 (assumed) Prob > chi2
> =
> > 0.0000
> >
> >
> --------------------------------------------------------------
> ----------------
> > ly | Coef. Std. Err. z P>|z|
> [95% Conf. Interval]
> >
> -------------+------------------------------------------------
> ----------------
> > lx1 | -.0065896 .0077505 -0.85 0.395
> -.0217803
> > .0086011
> > lx2 | .1253869 .0257565 4.87 0.000
> .0749051
> > .1758687
> > lx3 | -.0363082 .0969763 -0.37 0.708
> -.2263783
> > .1537619
> > lx4 | .1554292 .061983 2.51 0.012
> .0339448
> > .2769135
> > lx5 | .4387479 .2031582 2.16 0.031
> .0405652
> > .8369306
> > lx6 | -.0456517 .0477556 -0.96 0.339
> -.1392509
> > .0479475
> > _cons | 2.241371 1.053202 2.13 0.033
> .1771336
> > 4.305609
> >
> -------------+------------------------------------------------
> ----------------
> > sigma_u | .44383293
> > sigma_e | .03719725
> > rho | .99302502 (fraction of variance due to u_i)
> >
> --------------------------------------------------------------
> ----------------
> >
> > . estimates store random
> >
> > Carrying out a HAUSMAN TEST
> >
> > . hausman fixed random
> >
> > ---- Coefficients ----
> > | (b) (B) (b-B)
> sqrt(diag(V_b-V_B))
> > | fixed random Difference
> S.E.
> >
> -------------+------------------------------------------------
> ----------------
> > lx1 | -.0075411 -.0065896 -.0009515
>
> > .
> > lx2 | .1397473 .1253869 .0143604
>
> > .
> > lx3 | -.0471179 -.0363082 -.0108097
>
> > .
> > lx4 | .0883038 .1554292 -.0671254
>
> > .
> > lx5 | .4423916 .4387479 .0036437
>
> > .
> > lx6 | -.0635172 -.0456517 -.0178655
>
> > .
> >
> --------------------------------------------------------------
> ----------------
> > 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(6) = (b-B)'[(V_b-V_B)^(-1)](b-B)
> > = -4.12 chi2<0 ==> model
> fitted on these
> > data fails to meet
> the asymptotic
> > assumptions of the
> Hausman test;
> > see suest for a
> generalized test
> >
> > *
> > * For searches and help try:
> > * http://www.stata.com/help.cgi?search
> > * http://www.stata.com/support/statalist/faq
> > * http://www.ats.ucla.edu/stat/stata/
> *
> * For searches and help try:
> * http://www.stata.com/help.cgi?search
> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
>
--
Heriot-Watt University is a Scottish charity
registered under charity number SC000278.
*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/