Non-stationary variable in panel data

[Emna Trabelsi]

Dear Statalist users,

I am conductiong a panel data analysis on 155 countries under the period 1998-2015. My panel is highly unbalanced. As a preliminary check, I used the Fisher unit root test and I found that only the dependent variable is non-stationary in level, but it is stationary in first difference. Performing a cointegration test afterwards is not feasible in my case because the usual tests by Kao (1999), Pedroni (2004), and Westerlund (2005) require that there’s no gaps in any panel’s series. I tried a log transformation of my dependent variable and I found that it becomes stationary in level.
I would like to know whether trasnforming my variable (in first-difference or in natural log) correctly solves the problem, especially that I am intended to use the two-step system GMM to estimate a dynamic panel model. Thanks a lot for your response.

[Andrew Musau]

You have \(N>T\) and 1998-2015 gives you \(T\)= 18. Therefore, I am not sure why you need a dynamic panel model in this context. Even with a lagged dependent variable, static panel models work well with your data as the lagged dependent variable bias is small. Most economic variables are integrated of order 1, so finding that your variables are \(I(0)\) or \(I(1)\) is nothing to be concerned with. You can proceed and use static panel data models without worrying about stationarity.

[Emna Trabelsi]

Dear Andrew,

Many thanks for your response.

[Emna Trabelsi]

Dear Andrew Musau,

Suppose that I have a strongly panel dataset with N=48 and T=45, shall I test for stationarity in this case? If yes, what kind of test to be run on Stata (LLC, IPS, Breitung)?

Thanks in advance for your reply.
Best,
Emna

[Oscar Ozfidan]

If your data was strictly time series, I would say that you need to work with difference. If you have left of some observations to have strongly balanced panel data set, i strongly advice against that. You have it so use it. Many procedures can handle unbalanced panel data just fine. As for whether to difference or not, I would say it depends on what you want to explain. If you want to find out how independent variables are related to your dependent variable (high-high, high-low, low-high, low-low, or positive or negative relationship) then working with levels should be fine. But if your focus is on whether an independent variable causes the dependent variable to increase or decrease than I would suggest differencing. I think that is the most important consideration in your case from my point of view.

[alessio lombini]

Andrew Musau I tried to look for references supporting the statement that when we have panel data in which N > T and T is not big, non-stationarity is not an issue. Unfortunately, I found nothing, could you please provide references supporting this?

[Andrew Musau]

For static linear panel data models, you are mostly dealing with fixed effects (even if the random effects assumption holds). There are plenty of discussions on the sensitivity of inference to violations of the classical fixed effects assumptions. See, e.g., Chapter 14 of Introductory Econometrics : a Modern Approach by Jeff Wooldridge - 5th Edition (Advanced Panel Data Methods). I will have to check later if it is the same chapter number in the latest edition, as the book is somewhere in my office.

[alessio lombini]

Thank you very much Andrew! In case it might be useful to future readers, also in Econometric Analysis of Panel Data, Third edition (Badi H. Baltagi), the author supports the idea that in micro panels (large N and small T) nonstationarity is not a source of concern.