Cross section dependence - The Economist

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Friday, 3 March 2017

Cross section dependence

cross sectional dependence and independence :
Professor Saeed Khan Meo
Ade Kutu When applying the Pesaran CD (cross-sectional dependence) test, what you are looking for is to test whether the residuals are correlated across entities. The benchmark null hypotheses that are tested for the cross-sectional dependence are: Ho:α=1, there is no correlation of the residual.
H1:뱭1, there is correlation of the residual.
or
It is like people are getting confused as to the right meaning of cross-sectional dependence. In a simple language, cross-sectional dependence means for instance, Ade Kutu who is a Nigerian, he is based in South Africa and working in South Africa. He earns income in South Africa and send money to his family every month in Nigeria. Now, if Ade Kutu who is working in South Africa should lost his job, it means his family in Nigeria will be affected as he will no longer be able to send money to his family again every month. This means that there has been a cross-sectional dependence across entity between Ade Kutu in South Africa and his family in Nigeria. This simple analysis can be expanded to macro level. That is why the Pesaran CD (cross-sectional dependence) test is a test for the correlation of the residual.
or 
Abu Subhi Suborno is right Cross-sectional correlation and serial correlation are two different things. We can confirm that by taking an excerpt from a paper written by Frees (1995):

"there may exist important correlations between [cross-sectional] units ... These are called ‘cross-sectional’ correlations to distinguish them from auto-correlations, or correlations through time" (p. 394).

I tried to find the exact definition of cross-sectional correlation or dependence in my econometric texts but found nothing. However, in a recent article published in the Stata Journal, cross-sectional dependence can be defined as:

"some correlation structure in the error term between [cross-sectional] units” (Burdisso & Sangiácomo, 2016, p. 424).

This definition is different from the definition of serial correlation or autocorrelation. In Wooldridge's textbook, autocorrelation refers to "correlation between the errors in different time periods" (Wooldridge, 2013, p. 857).

References

Burdisso, T., & Sangiácomo, M. (2016). Panel time series. Review of the methodological evolution. The Stata Journal, 16(2), 424–442.

Frees, E. W. (1995). Assessing cross-sectional correlation in panel data. Journal of Econometrics, 69(2), 393-414.

Wooldridge, J. M. (2015). Introductory econometric: A modern approach. Nelson Education.
Endogenous and Exogenous Variable:
If you need to solve the system of equation to find the value of variable, this variable is endogenous. Otherwise, it will be exogenous which means the value of variables will be determined outside the system of equations.

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