# Is unit root test in panel data required?

I have 212 countries for 16 years of data. (Y=Export, X1= Export Credit, X2= GDP, X3...... X7=Some Dummies).

I understand that F test is required to decide if the model is OLS or fixed effect and LM test is required if the model is OLS or random effect.

To decide between fixed and random effect, the Hausman test is required.

Of course, theory and the literature are also indicative to choose the best modeling. My question is that applied research do not start with unit root test to see if the variables are stationary or not. So, what is the benefit of deciding whether OLS, fixed effect or random effect if the variables are not stationary? I looked export and export credit for my data and found that they are not stationary at level. As the theory and applied research insist using the log values of these variables I tested the logs for unit root and found that they are now stationary by Levin-Lin-Chu unit-root test and Harris-Tzavalis unit-root test . Why is the applied research missing the unit root tests in panel data analysis? Does unit root test be about IV or DP or both? Is there anything I missed?

There are 3 main methods of regression for panel data. Pooled OLS, Fixed and Random Effects.

Mainly to select Pooled OLS you'll need to test for individual effects in the error, this mean that Var(u) differs from 0 and E(u) is also different from 0. So there is presence of individual/ Heterogeneous effects in your OLS regression and your estimators will be biased. You can confirm this Breush-Pagan LM test. So you need a futher method of regression.

If such thing happen. then you'll need to select a fixed/random effect above your OLS estimation. and you do that with Hausmann test.

Under these conditions, Modelling data panel analysis has different points about the considerations of unitroots and cointegration. But I like to take what Park (2011) and similars say about the Modelling. That there is no test of unitroots, cointegration needed to model under the fixed/random effects.

However under different estimation methods, I believe it's better to test the unitroot/stationarity of the variables, morelikely if T tends to equal N. In this case spurios regression may outcome. A formal test of unitroot rejected means your data is stational, but if this hypthesis is not rejected, cointegration should be tested. And then regression methods would be a bit more accuracy.

The idea behind the testing of unitroots and cointegration derives from the assumptions of the regression model. Random effects for example according to Woolridge has 3 core assumptions, but noone of them are related to the time series unit root. except for the one where (u_i) shall not be correlate with (u_j) for any time period inclidung i=j, the cross sectional dependence may lead to biased estimators, so the common correlated effects method of regression would be better and there unitroot and cointegration should be tested.

As you see the Panel Data Analysys without including the time regression pattern of test is well detailed. So papers don't bother about including the stationarity or the unitroots presence over the random/fixed effects methods, not even Pooled OLS.

I'd like to stay with the basics from what Park says about modelling.