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st: Panel Data-FIXED, RANDOM EFFECTS and Hausman Test
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
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