# Pesaran cross-sectional dependence test in panel data

I was testing the cross sectional independence test using Pesaran CD test in Stata 10 for the panel data using the N=50 and T=18. After running the fixed effect with time dummies (effects), I got a negative value for the test with the p value >1 (which is not possible). I checked the paper on this: http://www.stata-journal.com/article.html?article=st0113, but they didn't talk about the negative value at all. I would really appreciate if you can help me to interpret the results.

xtreg Y  X1 X2 i.year,fe

Fixed-effects (within) regression               Number of obs      =       900
Group variable: state                           Number of groups   =        50

R-sq:  within  = 0.4336                         Obs per group: min =        18
between = 0.0417                                        avg =        18
overall = 0.3772                                        max =        18

F(19,825)          =     33.24
corr(u_i, Xb)  = -0.0215                        Prob > F           =    0.0000

------------------------------------------------------------------------------
Y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
X1 |  -.0008466   .0005767    -1.47   0.142    -.0019787    .0002854
X2 |    .185078   .0304043     6.09   0.000     .1253991     .244757
|
year |
1993  |  -.0101846   .0029659    -3.43   0.001    -.0160061   -.0043631
1994  |  -.0173621   .0028749    -6.04   0.000     -.023005   -.0117192
1995  |  -.0046886   .0029062    -1.61   0.107     -.010393    .0010159
1996  |  -.0175546   .0028879    -6.08   0.000     -.023223   -.0118862
1997  |   -.009572    .002962    -3.23   0.001     -.015386    -.003758
1998  |   -.012109   .0029123    -4.16   0.000    -.0178254   -.0063926
1999  |  -.0097348   .0029043    -3.35   0.001    -.0154356   -.0040341
2000  |  -.0137918   .0028784    -4.79   0.000    -.0194416   -.0081419
2001  |    .004144   .0029323     1.41   0.158    -.0016116    .0098996
2002  |   .0188509   .0028925     6.52   0.000     .0131733    .0245285
2003  |   .0058601   .0028772     2.04   0.042     .0002127    .0115076
2004  |  -.0005801   .0028731    -0.20   0.840    -.0062195    .0050594
2005  |  -.0085907   .0029534    -2.91   0.004    -.0143877   -.0027937
2006  |   -.018118   .0028702    -6.31   0.000    -.0237516   -.0124843
2007  |  -.0164648   .0028771    -5.72   0.000    -.0221121   -.0108174
2008  |  -.0352191   .0028805   -12.23   0.000    -.0408731   -.0295652
2009  |   .0094679   .0032904     2.88   0.004     .0030094    .0159265
|
_cons |   .0467515   .0024088    19.41   0.000     .0420234    .0514797
-------------+----------------------------------------------------------------
sigma_u |  .00686051
sigma_e |  .01433916
rho |   .1862708   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0:     F(49, 825) =     4.02             Prob > F = 0.0000

xtcsd, pesaran abs
Pesaran's test of cross sectional independence =    -2.673, Pr = 1.9925
Average absolute value of the off-diagonal elements =     0.215


The relevant lines in the code file xtcsd.ado, to view which type

viewsource xtcsd.ado


are 163-165, which read

    di in gr "Pesaran's test of cross sectional independence = "/*
*/in ye %9.3f pesaran' in gr ", Pr = " %6.4f /*
*/ in ye 2*(1-norm(abs(pesaran')))


The last line of code is the one that produces the p-value, and it behaves as expected under version control, with the value of the statistic that you get

. version 9: di 2*(1-norm(abs(-2.673)))
.00751763


So, there is no ostensible reason why your computed statistic should result in an abnormal p-value. I suggest you set trace on and check what is going on, or show us the output.

By the way, you should check what version of the xtcsd package you have. You can check using

. which xtcsd
*! version 1.1.1        R.E. De Hoyos and V. Sarafidis 16may2006

• Thanks nu for the insight. I checked the version and it is version 1.1.0 (how do I have the new version?; stata says it is the latest). As to the code in the line 165, I figure out (by googling) that stata 11 doesn't have norm (stata.com/statalist/archive/2011-08/msg00761.html). Is it possible for us to change that content? – Metrics Nov 9 '12 at 18:27
• In order to get the latest version of the xtcsd package, type ssc install xtcsd, replace at the prompt. Also, since xtcsd runs under version control (version 6), norm should be okay. However, if you do run into trouble relating to the use of the norm function, then starting Stata 10.1, there was a reorganization of the density functions, and the norm function was replaced by the normal function. See help density_functions##normal. – tchakravarty Nov 10 '12 at 2:43
• Thanks a lot!. The problem occurred because of using the old version. Now, I got the correct answer Pr = 0.0075. – Metrics Nov 10 '12 at 3:02
• It doesn't allow me to vote for the answer; i don't have enough reputation. Is there alternative way to do that? – Metrics Nov 10 '12 at 3:08
• You don't need to vote -- you can simply accept it by clicking the check mark underneath the downvote button. See the end of the "How do I ask questions here?" section here. – tchakravarty Nov 10 '12 at 3:10