Results of three cross-sectional depedence (CSD) tests - Pesaran, Frees, and Friedman: Does the panel data have CSD?

[Andy Oh]

Dear Stata users,

I obtained the results of three cross-sectional depedence (CSD) tests - Pesaran, Frees, and Friedman. Pesaran test and Friedman test show no CSD, but Frees test shows CSD. Does the panel data have CSD?


. xtreg lnFDIkrj L.lnFDIkrj L.lnODAkrj L.lnGDPj L.c_GDPpcGAPkrj L.c_GDPpcGAPkrj2 L.WGIj L.KOAFECj year_trend, fe

Fixed-effects (within) regression Number of obs = 510
Group variable: cid Number of groups = 30

R-sq: Obs per group:
within = 0.2515 min = 17
between = 0.1630 avg = 17.0
overall = 0.1869 max = 17

F(8,472) = 19.83
corr(u_i, Xb) = -0.3426 Prob > F = 0.0000

--------------------------------------------------------------------------------
lnFDIkrj | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------------+----------------------------------------------------------------
lnFDIkrj |
L1. | .483017 .0404235 11.95 0.000 .4035847 .5624493
|
lnODAkrj |
L1. | -.0056871 .0714747 -0.08 0.937 -.1461351 .1347609
|
lnGDPj |
L1. | -1.017686 2.57222 -0.40 0.693 -6.072105 4.036732
|
c_GDPpcGAPkrj |
L1. | -2.247599 2.808771 -0.80 0.424 -7.766843 3.271644
|
c_GDPpcGAPkrj2 |
L1. | .1559566 .3374765 0.46 0.644 -.5071857 .8190989
|
WGIj |
L1. | -.1002665 .2580883 -0.39 0.698 -.6074106 .4068776
|
KOAFECj |
L1. | -.2352726 .2591522 -0.91 0.364 -.7445074 .2739621
|
year_trend | .0356637 .1276293 0.28 0.780 -.2151282 .2864557
_cons | 20.15579 42.97641 0.47 0.639 -64.29296 104.6045
---------------+----------------------------------------------------------------
sigma_u | 2.6624541
sigma_e | 2.556644
rho | .5202653 (fraction of variance due to u_i)
--------------------------------------------------------------------------------
F test that all u_i=0: F(29, 472) = 1.88 Prob > F = 0.0043

. xtcsd, pesaran abs


Pesaran's test of cross sectional independence = -0.383, Pr = 0.7014

Average absolute value of the off-diagonal elements = 0.201

. xtcsd, frees


Frees' test of cross sectional independence = 0.244
|--------------------------------------------------------|
Critical values from Frees' Q distribution
alpha = 0.10 : 0.1521
alpha = 0.05 : 0.1996
alpha = 0.01 : 0.2928

. xtcsd, friedman


Friedman's test of cross sectional independence = 18.146, Pr = 0.9412

[Manh Hoang Ba]

Pesaran and Friedman statistics may perform poorly in cases where the cross-sectional correlation coefficients have opposite signs, in which case the Frees statistic will provide more accurate information. And that is the case with your data.
Both Pesaran and Friedman have large p-values, but the Frees statistic is larger than the critical value Q at the 5% significance level => reject H0 at the 5% significance level (Do not reject H0 at the 1% significance level). The overall conclusion is that there is cross-sectional dependence.
You can test whether cross-sectional dependence is strong or weak using the xtcd2 command. With the results from xtcsd, I would expect the cross-sectional dependence to be weak.

[Andy Oh]

Thanks a lot for your advice.