Cross-sectional dependence for panel data with T=2: is it possible and relevant to test?

[Hanna Murina]

I have a panel of N=80 and T=2 describing countries with results from two surveys and a set of control variables. I progressed from xtreg, fe to xtreg, re vce (cluster id) and pooled OLS by reg vce (cluster id) based on (1) detected group-wise heterogeneity (significant xttest3 after xtreg fe), insignificant Mundlak test and insignificant xttest0 after xtreg, re vce (cluster id). I tried to test serial correlation for T=2 with a correlation estimate for idiosyncratic error and its lagged value after xtreg, re vce(cluster id) - low and insignificant. And I am puzzled by cross-sectional dependency test. xtcsd, pesaran in Stata is not working for T=2. I looked for the formulas of the test in Pesaran 2004 and applied them to exported errors in Excel. It was possible to calculate. But does it have meaning and should be trusted? The CD test may justify xtpcse with correction for cross-section dependency

[George Ford]

I think you need at least 3, but it would have very little power at that.

[Carlo Lazzaro]

Hanna:
welcome to this forum.
Why not posting what you typed and what Stata gave you back (as per FAQ)? Thanks.

[Hanna Murina]

Hi Carlo! Yes, I am using Stata BE 18.5 and here are the estimation results:

[Hanna Murina]

FE with vce (cluster ID)

[Hanna Murina]

Re with vce (cluster ID)

[Hanna Murina]

Mundlak and xttest0 after RE vce(cluster ID)

[Hanna Murina]

Pooled OLS with vce(cluster ID)

[Hanna Murina]

vif and ovtest after pooled OLS with vce(cluster ID)

[Hanna Murina]

the summary table with estimation results of several method, where 4-6 are xtpcse: (4) xtpcse, correlation(independent) hetonly (correcting for heteroskedasticity only), (5) xtpcse, correlation(ar1) hetonly (correcting for heteroskedasticity and serial correlation), (6) xtpcse, correlation(psar1) hetonly (correcting for heteroskedasticity, serial correlation and cross-sectional dependence - the main concern to test). Note how different are R2 and some of the coefficients after correcting for cross-sectional dependence, and how similar are 2-5 methods.

[Carlo Lazzaro]

Hanna:
given what above, I would stick with -xtreg,fe- with cluster-robust SE.
In addition, please consider that your sample size is pretty limited, while you imposed a too demanding specification in the right-hand side of your regression equation.
Are you sure that you need so many predictors?

[Hanna Murina]

Thank you for your opinion. xtreg, fe tells too little and its results are used in the analysis for the changes between the periods. I also did robust OLS cross-section for the two periods, which gave meaningful results despite small sample challenges (here I discovered the issue of misleadingness of the conventional significance levels). I have test-based justification for xtreg, re and pooled OLS with results complementary to one-period OLSs but with more significance, likely, due to more observations (NxT).
I consider that I do need all the variables by the theoretical justification, which extends the traditional macroprudential approach of macro variables with indexes on institutional development. In the estimation est IC was used to verify the variables' relevance, the insignificant were confirmed