Stationarity of Small size panel data sample

[Tho Nguyen]

Dear all,

I am trying to test stationarity of panel data. My sample size is quite small 13 years and 8 countries. I am told that if the sample size is small (i.e. T<15), then it is not necessary to test because data will be definitely stationary.

Because I could find the reference of this statement, so I am quite confused whether it's true?

Thank you for your help!

[Tho Nguyen]

Is this possible if I use the above statement as a rule of thumb, or it's necessary to do panel unit root test?

Thank you for your time!

[Eric de Souza]

As you say you only have 13 years. The correct formulation is not that the series are stationary, it is that the issue of stationarity does not arise.
Your real problem is that you have only 8 countries and, therefore, you cannot rely on asymptotic results: fixed T but N going to infinity

[Tho Nguyen]

Thank you very much Eric!

So you mean stationarity test is not necessary? but the results are still not reliable? Then which test do I need to do to make the asymptotic results reliable?

[Mateo Zokalj]

Hi Tho,

I believe that there is a chance of non-stationarity issue to arise even when your time dimension is 13 years. It depends on the variables you use and I would apply unit root test, as it is better to confirm your opinion of stationarity than to have spurious regression later in results.

Cheers

[Eric de Souza]

A unit root test with 13 time periods is useless. Even if the series were stochastically trending in the population model, a unit root test with such a small sample wiould have very low power. I repeat, a much more serious problem is the combination of a relatively small time dimension and a very small cross-section dimension.

[Mateo Zokalj]

Dear Eric,

would you consider as a problem panel dataset with N=11 and T=13? Concerning the unit root test, is it because of the fact that the sample is too small, IPS indicates stationarity and LLC indicates non-stationarity for the same variable?

xtunitroot llc ln_socpexp, trend demean
p-value = 0,000 Code:

xtunitroot llc ln_socpexp, trend demean lags(1)
p-value = 0,000
Code:

xtunitroot ips ln_socpexp, trend demean
p-value = 0,34 Code:

xtunitroot ips ln_socpexp, trend demean lags(1)
p-value = 0,69

[Eric de Souza]

It is difficult to draw a fine line between what is a small sample and what is a sufficiently large sample to rely on asymptotic theory. Unit roots tests for panel data are still in the developmental stage, but, as I said with your number of observations I would not rely on them. It is advisable to introduce deterministic time trends in the model (time fixed effects) if you think that the series are non-stationary. Nevertheless, I would treat the panel data results from your sample size with precaution.