Conflicting results of cross sectional dependence testing in panel data (PesaranCD, Frees, Friedman tests)

[Elina Kim]

Conflicting results of cross sectional dependence testing in panel data (Pesaran CD, Frees, Friedman tests). Which result should I follow to assure most possible consistent and robust outcomes? Cannot trace what could cause such conflicting results, is there anything that needs to be addressed?
Please, let me know if there is any instructions, recommendations concerning this.

Thank you beforehand

. xtreg lnef lngdp lnurb lnen lnre lntr lngi, fe

Fixed-effects (within) regression               Number of obs     =        308
Group variable: id                              Number of groups  =          7

R-sq:                                           Obs per group:
     within  = 0.6955                                         min =         44
     between = 0.5084                                         avg =       44.0
     overall = 0.5328                                         max =         44

                                                F(6,295)          =     112.31
corr(u_i, Xb)  = -0.5152                        Prob > F          =     0.0000

------------------------------------------------------------------------------
        lnef |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       lngdp |   .2950002   .0505237     5.84   0.000     .1955675    .3944328
       lnurb |   1.214826   .0757327    16.04   0.000     1.065782    1.363871
       lnenu |  -.8183402   .0711855   -11.50   0.000    -.9584359   -.6782445
        lnre |  -.1743426   .0274472    -6.35   0.000    -.2283598   -.1203254
        lntr |   .1272972   .0424765     3.00   0.003     .0437018    .2108926
        lngi |  -.4552396   .1403114    -3.24   0.001    -.7313778   -.1791013
       _cons |   1.020202   .3243207     3.15   0.002     .3819268    1.658478
-------------+----------------------------------------------------------------
     sigma_u |  .37605673
     sigma_e |  .13812131
         rho |  .88113425   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(6, 295) = 135.23                    Prob > F = 0.0000

. xtcsd, pesaran
 
 
Pesaran's test of cross sectional independence =     0.598, Pr = 0.5498

. xtcsd, frees
 
 
Frees' test of cross sectional independence =     1.090, Pr = 0.0000
 
Warning: A normal distribution had been used to approximate Frees' Q distribution

. xtcsd, friedman
 
 
Friedman's test of cross sectional independence =    39.795, Pr = 0.0000

[Rich Goldstein]

these tests (see the help file) are largely for small T, large N - this is not your situation and my guess is that none of these should be relied on in your situation - however, I have not reviewed the unpublished paper by the authors of -xtcsd- to see whether what they say covers your situation; you might want to do that if you can find it (it is cited in the help file); further, the help file does say,

In the
context of large T and small N, the Lagrange multiplier test statistic
proposed by Breusch and Pagan (1980) can be used to test for
cross-sectional dependence (see xttest2).

so you might want to look into that

[Elina Kim]

these tests (see the help file) are largely for small T, large N - this is not your situation and my guess is that none of these should be relied on in your situation - however, I have not reviewed the unpublished paper by the authors of -xtcsd- to see whether what they say covers your situation; you might want to do that if you can find it (it is cited in the help file); further, the help file does say,
so you might want to look into that

Hello, Mr. Rich Goldstein.
Thank you very much for your response. You are completely right, and I noted your advice.

I have chosen these particular methods because according to the descriptive statistics in the panel, N=308 whereas T=44. I stand to be corrected if I overlooked anything.

Also, I'll attach the results of the Breusch and Pagan LM test results below too to present a more complete picture.

And my question now would be: finally, should I reject H0 of cross-sectional independence and run 2nd generation unit root test? Or follow Pesaran CD result and use 1st gen unit root test?

Looking forward to learn from your expertise.
Best regards.

. xtsum ef fdi gdp urb enu re tr gi tech

Variable         |      Mean   Std. Dev.       Min        Max |    Observations
-----------------+--------------------------------------------+----------------
ef       overall |  2.097287   .8649231   .6598417   3.879224 |     N =     308
         between |             .7604621   .8668853   2.916979 |     n =       7
         within  |             .5007887   .9195822   3.654053 |     T =      44
                 |                                            |
fdi      overall |  1.349771   1.361112   -2.75744   6.186882 |     N =     308
         between |             .7062843   .6651596   2.344307 |     n =       7
         within  |             1.193171   -2.30269   5.192346 |     T =      44
                 |                                            |
gdp      overall |  6387.823   5425.159   263.9085   26761.94 |     N =     308
         between |             4622.274    885.419   13330.13 |     n =       7
         within  |              3325.58  -4280.918   19819.63 |     T =      44
                 |                                            |
urb      overall |  52.68966   20.05059       17.4     86.569 |     N =     308
         between |             19.57252    27.2758   76.71477 |     n =       7
         within  |             8.520508   33.48737   77.15057 |     T =      44
                 |                                            |
enu      overall |   1300.64   1087.526   275.9078   5785.563 |     N =     308
         between |             900.5277    425.368   3182.405 |     n =       7
         within  |             696.6703  -1188.426   3903.798 |     T =      44
                 |                                            |
re       overall |  31.75557   20.50185   .4415748   74.37384 |     N =     308
         between |             19.98673    3.21576   53.84452 |     n =       7
         within  |             8.764009   12.04042   52.28488 |     T =      44
                 |                                            |
tr       overall |  40.88807   20.23406   8.384615   110.0001 |     N =     308
         between |             15.82902   21.05438   68.02039 |     n =       7
         within  |             13.92672   11.57606   84.69355 |     T =      44
                 |                                            |
gi       overall |  52.53734    12.8474       24.9   79.50001 |     N =     308
         between |             6.149926   44.39091   61.05455 |     n =       7
         within  |             11.51223   30.98279   71.92825 |     T =      44
                 |                                            |
tech     overall |  53923.77   175551.8         50    1424685 |     N =     308
         between |             88074.72   2305.739   241660.6 |     n =       7
         within  |             155395.6  -179727.8    1236948 |     T =      44

Here are the results from the Breusch Pagan LM test:

. xtreg lnef lnfdi lngdp lnurb lnenu lnre lntr lngi lntech, fe

Fixed-effects (within) regression               Number of obs     =        308
Group variable: id                              Number of groups  =          7

R-sq:                                           Obs per group:
     within  = 0.7235                                         min =         44
     between = 0.4928                                         avg =       44.0
     overall = 0.5463                                         max =         44

                                                F(8,293)          =      95.85
corr(u_i, Xb)  = -0.2315                        Prob > F          =     0.0000

------------------------------------------------------------------------------
        lnef |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       lnfdi |  -.0159813   .0066798    -2.39   0.017    -.0291278   -.0028349
       lngdp |   .2730464   .0493899     5.53   0.000     .1758425    .3702502
       lnurb |   1.217677   .0750835    16.22   0.000     1.069906    1.365448
       lnenu |  -.9493596   .0731223   -12.98   0.000    -1.093271   -.8054482
        lnre |  -.1692652   .0262718    -6.44   0.000    -.2209705   -.1175598
        lntr |   .2145004   .0437457     4.90   0.000     .1284049     .300596
        lngi |  -.7215051   .1468254    -4.91   0.000    -1.010471   -.4325391
      lntech |   .1063388    .023518     4.52   0.000     .0600532    .1526244
       _cons |   1.833698   .4318079     4.25   0.000     .9838598    2.683537
-------------+----------------------------------------------------------------
     sigma_u |  .32865333
     sigma_e |  .13206411
         rho |  .86097744   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(6, 293) = 152.51                    Prob > F = 0.0000

. 
. xttest2
 
Correlation matrix of residuals:

         __e1     __e2     __e3     __e4     __e5     __e6     __e7
__e1   1.0000
__e2   0.6845   1.0000
__e3   0.3381  -0.0139   1.0000
__e4   0.3498   0.3305  -0.3557   1.0000
__e5   0.4397   0.3761   0.6224   0.0187   1.0000
__e6  -0.4571  -0.1450  -0.7716  -0.0028  -0.6280   1.0000
__e7  -0.3452  -0.1531  -0.5228  -0.0144  -0.4165   0.4337   1.0000

Breusch-Pagan LM test of independence: chi2(21) =   161.084, Pr = 0.0000
Based on 44 complete observations over panel units

[Jeff Wooldridge]

Elina: It looks like you have N = 7, T = 44. Hence Rich’s comment.

[Jeff Wooldridge]

I would use the Driscoll-Kraay approach. It’s user-written, xtscc. Don’t even bother testing for cross sectional correlation.

[Elina Kim]

I would use the Driscoll-Kraay approach. It’s user-written, xtscc. Don’t even bother testing for cross sectional correlation.

Thank you very much, Mr. Jeff Wooldbridge, that is very helpful! Have a blessed day!
Best regards.

[Elina Kim]

I would use the Driscoll-Kraay approach. It’s user-written, xtscc. Don’t even bother testing for cross sectional correlation.

Greetings, Mr. Wooldbridge!
In order to provide most consistent results, I'd like to humbly ask for you advice and expertise concerning the following:

In addition to the conditions we discussed above (N=7; T=44; existence of cross sectional dependence in the panel), variables applied in my model have different levels of stationarity. More specifically DV(1), IV(0, 1, mixed)... What would be a suitable methodology applied in this case.

My panel seems to be not large enough to use Dynamic Common Correlated Effect (DCCE; by Jan Ditzen(2018)). Moreover, not sure whether panel ARDL is able to deal with panels that have cross-sectional dependence... Or would Driscoll-Kraay approach suggested be able to deal with DV(1), IV(0, 1, mixed) dataset?

Would be very glad and delighted to hear from you.

Thanks for your consideration.

Best regards.

[Jeff Wooldridge]

Sorry for the delay. Good call on having to deal with I(0), I(1) variables. You should think of this as any time series problems. You can leave I(1) variables in level form if you have cointegrating relationships, but that makes the asymptotic inference tricky -- even for theoretical time series econometricians. The Driscoll-Kraay approach assumes that variables used in their method are I(0). So you should use first differences where necessary.

With such a small N, you can allow for dynamic models.

[Elina Kim]

Sorry for the delay. Good call on having to deal with I(0), I(1) variables. You should think of this as any time series problems. You can leave I(1) variables in level form if you have cointegrating relationships, but that makes the asymptotic inference tricky -- even for theoretical time series econometricians. The Driscoll-Kraay approach assumes that variables used in their method are I(0). So you should use first differences where necessary.

With such a small N, you can allow for dynamic models.

You are right on time, sir. Thank you very much! That is very insightful and right on point. Really appreciate your recommendations. Glad to learn from your expertise, Dr. Wooldridge.

Best regards.

[Duong Chi]

Dear Statalist,
I have a problem with the result of testing cross sectional dependence in panel data, with model t=4,n=189. Please, let me know in this case:

. xtcsd, pesaran abs


Pesaran's test of cross sectional independence = 8.710, Pr = 0.0000

Average absolute value of the off-diagonal elements = 0.515

.
. xtcsd, friedman


Friedman's test of cross sectional independence = 32.359, Pr = 1.0000

.
. xtcsd, frees


Frees' test of cross sectional independence = 1.831
--------------------------------------------------------
Critical values from Frees' Q distribution
alpha = 0.10 : 0.5822
alpha = 0.05 : 0.8391
alpha = 0.01 : 1.4211