Negative Value of Pesaran cross sectional Test

[Soliman Rakha]

Dear there at Statalist Could anybody help to find answer for this Question?

After regress the following model:
xtreg BTD0 LSA00 TAN00 PRF0 TBQ00 DEFM0, fe

I did Pesaran's test and I have got negative value??? How could interpret such NEGATIVE VALUE and over unity P-Value as bellow:

. xtcsd, pesaran
Pesaran's test of cross sectional independence = -0.742, Pr = 1.5416

Furthermore, Frees' Q test value indicated the presence of contemporaneous correlation

. xtcsd, frees
Frees' test of cross sectional independence = 5.139
Critical values from Frees' Q distribution
alpha = 0.10 : 0.2136
alpha = 0.05 : 0.2838
alpha = 0.01 : 0.4252

Appreciate help,,,

[Jesse Wursten]

What do you get when you use xtcdf/xtcd/xtcd2 instead of xtcsd?

[Soliman Rakha]

Dear Jesse
Thanks so much for response, hereby you find the outputs of xtcd and xtcdf

xtcsd, pesaran
Pesaran's test of cross sectional independence = -0.742, Pr = 1.5416


. xtcsd, frees
Frees' test of cross sectional independence = 5.139
|--------------------------------------------------------|
Critical values from Frees' Q distribution
alpha = 0.10 : 0.2136
alpha = 0.05 : 0.2838
alpha = 0.01 : 0.4252


. xtcd BTD0 LSA00 TAN00 PRF0 TBQ00 DEFM0
Average correlation coefficients & Pesaran (2004) CD test
Variables series tested: BTD0 LSA00 TAN00 PRF0 TBQ00 DEFM0
Group variable: FirmID
Number of groups: 59
Average # of observations: 12.21
Panel is: unbalanced

---------------------------------------------------------
Variable | CD-test p-value corr abs(corr)
-------------+-------------------------------------------
BTD0 | . . . .
-------------+-------------------------------------------
LSA00 | 108.35 0.000 0.756 0.807
-------------+-------------------------------------------
TAN00 | 10.74 0.000 0.075 0.370
-------------+-------------------------------------------
PRF0 | 7.91 0.000 0.055 0.306
-------------+-------------------------------------------
TBQ00 | 40.96 0.000 0.286 0.387
-------------+-------------------------------------------
DEFM0 | 16.29 0.000 0.114 0.283
---------------------------------------------------------
Notes: Under the null hypothesis of cross-section
independence CD ~ N(0,1)


. xtcdf BTD0 LSA00 TAN00 PRF0 TBQ00 DEFM0
xtcd test on variables BTD0 LSA00 TAN00 PRF0 TBQ00 DEFM0
Panelvar: FirmID
Timevar: Year
------------------------------------------------------------------------------+
Variable | CD-test p-value average joint T | mean ρ mean abs(ρ) |
----------------+--------------------------------------+----------------------|
BTD0 + 20.714 0.000 12.00 + 0.14 0.36 |
LSA00 + 108.35 0.000 12.00 + 0.76 0.81 |
TAN00 + 10.742 0.000 12.00 + 0.07 0.37 |
PRF0 + 7.914 0.000 12.00 + 0.06 0.31 |
TBQ00 + 40.956 0.000 12.00 + 0.29 0.39 |
DEFM0 + 16.29 0.000 12.00 + 0.11 0.28 |
------------------------------------------------------------------------------+
Notes: Under the null hypothesis of cross-section independence, CD ~ N(0,1)
P-values close to zero indicate data are correlated across panel groups.

[Jesse Wursten]

You have to predict your residuals first - you're not testing the same variables in the various tests.

[Soliman Rakha]

Is it the right case now?

. xtcd r

Average correlation coefficients & Pesaran (2004) CD test

Variables series tested: r
Group variable: FirmID
Number of groups: 59
Average # of observations: 12.21
Panel is: unbalanced

---------------------------------------------------------
Variable | CD-test p-value corr abs(corr)
-------------+-------------------------------------------
r | 78.56 0.000 0.548 0.593
---------------------------------------------------------
Notes: Under the null hypothesis of cross-section
independence CD ~ N(0,1)


. xtcdf r

xtcd test on variables r
Panelvar: FirmID
Timevar: Year
------------------------------------------------------------------------------+
Variable | CD-test p-value average joint T | mean ρ mean abs(ρ) |
----------------+--------------------------------------+----------------------|
r + 78.562 0.000 12.00 + 0.55 0.59 |
------------------------------------------------------------------------------+
Notes: Under the null hypothesis of cross-section independence, CD ~ N(0,1)
P-values close to zero indicate data are correlated across panel groups.

[Jesse Wursten]

I have no idea unless you show me the code used to generate r... also, Stata output is a lot more readable if you enclode it in code brackets (the hashtag in the editor bar).

[Soliman Rakha]

Dear Jesse,,, Sorry for inconvenience

I did this model
[reg BTD0 LSA00 TAN00 PRF0 TBQ00 DEFM0]

Then I did
[predict r]

Then I did the above mentioned tests for r
[xtcd r] and [xtcdf r]

[Jesse Wursten]

Now you use two different models? The first one was a fixed effects panel regression, this one just standard OLS? To predict residuals after xtreg, use predict residuals, e

[Soliman Rakha]

Really thanks
I did this model
[xtreg BTD0 LSA00 TAN00 PRF0 TBQ00 DEFM0, fe]

Then I did as you mentioned
[predict residuals, e]

Therefore, the outputs are as bellow: Values are negative like as original Pesaran test

[. xtcd residuals]

Average correlation coefficients & Pesaran (2004) CD test
Variables series tested: residuals
Group variable: FirmID
Number of groups: 59
Average # of observations: 12.21
Panel is: unbalanced

---------------------------------------------------------
Variable | CD-test p-value corr abs(corr)
-------------+-------------------------------------------
residuals | -0.74 0.458 -0.005 0.373
---------------------------------------------------------
Notes: Under the null hypothesis of cross-section
independence CD ~ N(0,1)


[. xtcdf residuals]

xtcd test on variables residuals
Panelvar: FirmID
Timevar: Year
------------------------------------------------------------------------------+
Variable | CD-test p-value average joint T | mean ρ mean abs(ρ) |
----------------+--------------------------------------+----------------------|
residuals + -.742 0.458 12.00 + -0.01 0.37 |
------------------------------------------------------------------------------+
Notes: Under the null hypothesis of cross-section independence, CD ~ N(0,1)
P-values close to zero indicate data are correlated across panel groups.

[Jesse Wursten]

Ah, now we're there. The CD-statistic is basically a mean of pairwise correlations (= all the possible correlations between the firms in your sample). In your case there's relatively many negative correlations, which leads to a negative CD statistic. This is fine. The CD-statistic is standardnormally distributed, which means you'd expect negative values half the time (if the null hypothesis of cross sectional independence is true). The value you end up with (-0.742) is not abnormally far from zero, meaning you can conclude that your residuals are free from cross sectional dependence (to the extent you can conclude anything from tests).

PS: This is one of the first times I've seen the CD test accept the null hypothesis, so congratulations!

[Soliman Rakha]

Dear Jesse
So, I don't have CD in this sample,,,

My Deepest Thanks, appreciate your time and efforts,
all my best wishes