Pesaran Test

[Nicole Peredo]

Hi guys, I am running a fixed effects regression and wanted to test for cross-sectional dependence. I am not sure how to interpret the results since I am very new to stata and econometrics. I attached a picture of the results and would be happy if someone can help me see if the residuals are correlated with each other. Thanks a lot

[Nicole Peredo]

Carlo Lazzaro Hi Carlo, I saw you responded some questions on this topic and I don't fully know how to interpret this values. Is Pr telling me that there is cross-sectional independence?

[Carlo Lazzaro]

Nicole:
please do not urge potentially interested listers to reply to your queries (we are all busy people, just like you). Thanks.
That said, the help file of the community-contributed programme -xtcsd- (as you're kindly requested to declare as per FAQ) that you're kindly recommened to read just to have an idea of what the module you're interested in can do for you states that:

xtcsd test the hypothesis of cross-sectional independence in panel-data models with small T and large N

It implies that the null of this test is cross-sectional Independence: as the outcome of your test does not show evidence of rejecting the null, your panel are cross-sectional independent.

This results does not mean that the test you picked up is the right one to test cross-sectional Independence of your panels, as you do not specify whether you are dealing with a N>T panel dataset or the other way round.

[JanDitzen]

I am not the author of xtcsd but very familiar with the literature and the author of a similar test (xtcd2). xtcsd offers several tests to test if residuals after xtreg contain (strong) cross-sectional dependence.

First of all I agree with Carlo Lazzaro, you need a large number of observations across the time and cross-section dimension. T can be relatively small to N though.

The null hypothesis of the CD test (Pesaran (2015), Econometric Reviews) is weak cross-sectional dependence, the alternative is strong cross-sectional dependence. There is an important difference between the working paper (Pesaran 2004, funnily the working paper states "do not cite") and the published version of Pesaran (2015), that is that the working paper states the null is cross-section independence. As stated later in the published version, this concept is a very strong assumption for panels with large N and thus weak cross-sectional dependence is more informative. Weak cross-sectional dependence implies that the bias respectively dependence decays if (N,T) -> infinity. Therefore of main interest is if the residuals inhibit strong cross-section dependence. This is also a clear difference to the tests by Friedman (1937) and Frees (1995, 2004), which test the null of no correlation, i.e. cross-section independence.

Nicole Peredo is using the pesaran and absolute options of xtcsd. pesaran indicates that the programs uses the Pesaran (2004,2015) test statistic. To the best of my knowledge, the option abs has no effect on the test statistic results. It only displays the average absolute value of the off-diagonal elements (as a side note: if abs would take the absolute values of the test statistic, the distribution of the test would be different!).
The test has a p-value of 0.0015. This implies that at a level of 1% we can reject the null hypothesis of weak cross sectional dependence and the residuals are likely to inhibit strong cross-section dependence. This implies that your estimates are inconsistent and biased.

[Carlo Lazzaro]

Thanks Jan.
Very enlightening.
I should add that I actually read the wrong lines in Nicole's output and I agree with Jan's diagnosis.
PS: Deliberately off target here: when all this dreadful epidemiological situation will be eventually over, I do recommend foreign listers who're interested in tourist trips to Italy, to visit the town where JanDitzen is based (Bozen/Bolzano, usually really hot in summer) and its modern university.

[Nicole Peredo]

Thank you Jan Ditzen and Carlo for your responses. I am deeply thankful for the time you took! It was very helpful