First, you can observe your data through summary statistics, correlation matrix, box plots, scatter plots, detect extreme outliers, perform variable transformation if necessary, take into consideration the size of time dimension and number of cross-section units in your panel dataset, also whether your panel is balanced or unbalanced, etc. If your panel data is unbalanced, you can generate missing values through multiple imputations or some other methods (personally I prefer multiple imputations or just leave missing values as it is if it is not a lot). If you go with generating missing values, take care if it is missing at random or not, and some other details when you specify the options for estimation in your software.

Second, before stationarity check, observe cross-sectional dependence in your panels (usually Pesaran CD “Cross-Sectional Dependence Test”).

Third, if you have cross-sectional dependence in your variables, you will apply 2nd generation unit root tests like Breitung, Pesaran CIPS (Cross-sectional Augmented Im-Pesaran-Shin), and/or CADF (Cross-section Augmented Dickey-Fuller). If the variables do not suffer from cross-sectional dependence, you can proceed with 1st generation unit root tests like LLC (Levin, Lin, and the Chu), Hadri, IPS (Im-Pesaran-Shin), Fisher type ADF and/or PP, etc. You will need to read about each unit root test if it is appropriate for your data. You should also select an appropriate lag length for preferred unit root tests (If the software you are using lets you to choose the lag length according to information criteria (e.g. Akaike, Schwarz, Hannan-Quinn, etc.) then go with it; if there is no option for information criteria, you can choose the lag length according to the average lag length for each cross-section unit in your panel (it is just one option), or follow Schwert (1989)’s pmax formula). Perform multiple unit root tests and if the majority of the tests show stationarity/non-stationarity of the variables then that is it. No single unit root test can have superior power and precision so use a couple of them.

Fourth, if you get stationary variables, you can estimate Fixed/Random/Pooled OLS models and decide between the models according to Hausman and Lagrange Multiplier (LM) test results. After you can check the violation of estimated regression assumptions (e.g. heteroskedasticity, autocorrelation, normality of residuals, endogeneity, multicollinearity). Usually, you get autocorrelation and heteroskedasticity problems that can be dealt with by estimating the regression with robust standard errors (e.g. Prais-Winston regression model with panel corrected standard errors (PCSE), pooled OLS with Driscoll-Kraay standard errors, GLS estimators, and/or simply clustering standard errors). If you get non-stationary variables I(1) (integrated of order 1), you can proceed with cointegration estimators like Pedroni and/or Kao (Engle-Granger based), Johansen (Fisher), and Westerlund panel cointegration (for cross-sectionally dependent panels). After you will estimate coefficients (e.g. through Fully Modified OLS (FMOLS) and/or VECM). If you get mixed stationarity of variables (both stationary and non-stationary), you can employ ARDL for panels, MG/PMG (pooled) mean group estimator (take care of stationarity of dependent variable, it should be non-stationary for MG/PMG ARDL).

Fifth, after all, you can check causality through the Panel Granger causality test.

P.S. It is just a couple of ways to analyse your data. There are plenty of models and tests to apply depending on the exact data specification. I hope it will help a bit, at least for a general guideline. Wish you all the best.

Dear Davit,

Hello,

I hope all is well for you.

Thank you for your detailed answer. I really appreciate that.

In fact, for the descriptive statistics, my study is on panel data, I have all the data for all the variables except for 2 variables for one it is missing the data for a single year and for another variable it is missing the data for three years. But I used "individuals samples" to get the descriptive statistics table. Is it right ?

Otherwise, I observed the data by the scatter plots and as you can see on the image it is the dependent variable with one of the independent variables, and most of them had the same result with the descending regression line but I don't know if it's good or bad! (picture 1).

For stationarity, I did the Persaran CD test and the results were: (knowing that H0 = no cross section dependence = correlation)

For the dependent variable (Pesaran CD test result) is : 0.1041

Using other tests: Breusch-Pagan: 0.1041

Pesaran scaled LM: 0.2457

Bias-corrected scaled LM: 0.2720

For independent variables (using pesaran CD):

- 0.5717

- 0.4525

- 0.5225

- 0.0001

- 0.6943

- 0.1700

- 0.2490

- 0.9867

- 0.8283

- 0.2876

Is this means that i should use first generation Unit root or second?

Otherwise to apply stationarity, I used "summary" and I chosed: Schwarz in info criterion but most of the variables were not stationary at level, but all are stationary at first difference. So, as they all are stationary at first difference i first used fixed effect model using in panel option for coef covariance method: "white cross-section" and also choosed: no d.f. correction. And I had good results. Then after that I did Pooled OLS using same panel option, i mean : "white cross-section" and also choosed: no d.f. correction, and I also had good results, so I decided to use pooled OLS for robustness. I would like to know if what I have just done is correct or not? When we have all stationary data at first difference for panel model can we use the fixed effect? Because that's what I did as explained above.

For my estimate using Pooled OLS I left the option "white cross-section" and also: no d.f. correction. is it right to do it?

Another thing, I don't know if I should do random model too? In fact I tried to do it but it gave me an answer: "Random effects estimation requires number of cross sections> number of coefs for between estimator for estimate of RE innovation variance", and I dont understand why !

Also for stationarity, I chosed Schwarz in info criterion. But I don't know if I should have chosen: "user specified 1"? Knowing that Im using Eviews 11.

Now since I have good results for Fixed and pooled OLS is there no need to do random and hausman test? Otherwise, to choose between pooled and fixed which test should I use? And should i do it ?

You also shared at the end to do the diagnostic tests, just to be sure, by diagnostic tests you meant for residuals? Actually, i tried to do test for heteroskedasticity but also they shared as message: "cross-section effects with period GLS weights not allowed" and when i clik ok they show me the estimation command! I also dont know why?

You said: "Usually, you get autocorrelation and heteroskedasticity problems that can be dealt with by estimating the regression with robust standard errors (eg Prais-Winston regression model with panel corrected standard errors (PCSE), pooled OLS with Driscoll-Kraay standard errors, GLS estimators, and / or simply clustering standard errors) ".

Do you mean that (e.g. Prais-Winston regression model with panel corrected standard errors (PCSE) is used for fixed?

A last thing, while im working using eviews 11 (student version) i always receive as message : "1 table or matrix had a dimension larger than 0 and could not be saved with the workfile". And i dont know why too.

Sorry for asking lot of questions, but i'm new in econometrics. If you can share your responses i would be grateful.

Best regards

You can check the multicollinearity and data stationarity before the estimation and do Hausman Test for Model Selection (weather you should go for Fixed effect or Random Effect model)

Dear Md Humayun,

I tried to do random on eviews but as i wrote, eviews didnt allow me to do it,"as i shared in my previous message" and they share as message (see picture in attachment).

I'm stuck and don't know what to do! Is ir because im using student version ?

I am not sure how you organised your data, but the way it works is - i) quick estimation ii) select panel data option iii) select random effect and then iv) do the Hausman Test. reject or accept the model depending on the significance level. I did it like this and it worked for me. I am not sure about the student version, I use the other one.

Thank you for your reponse Md Humayun but what do you mean by "the other one" ?

The one bought by the universities

Thank you. But if i already had good results using fixed effect and Pooled OLS. There is no need to do random ? because i already got good results? im asking you in general i mean if it was the case.

You must need Hausman test for the model selection or some other test like this. There are some Videos on Youtube for fixed effect model, which might help you.

Yes i know all this, but eviews is not allowing me because my cross sections is too small and my study in on 2 countries ! So maybe of problem of degree freedom, but do you know how can i resolve it ? Using eviews of course ?

Dear fatema Matefa,

Please follow these steps during balance panel data analysis:

1. First of all you need to check the Cross-sectional Dependence tests.

2. The second step is to perform the unit root tests.

If you are applying first generation unit root tests, but at the same time the results of Cross-sectional dependence tests shows a strong Cross-sectional dependence it may mislead your results, therefore you need to apply second generation unit root tests.

3. Hence, the third step is to apply the second generation unit root tests.

4. The fourth step is to check the panel cointegration (pedroni, Kao....etc.)

5. In the last step you can apply your proposed model (Panel ARDL, FMOLS, DOLS.....etc.) as per the requirement.

For further clarification you can follow this paper. I hope this paper will be very helpful for you, after reading this article you will be able to apply and interpret the results easily.

Please click on the following link:

https://www.researchgate.net/publication/342607411_Determinants_of_CO2_emissions_in_upper_middle-income_group_countries_an_empirical_investigation

Thank you Mr. Mujtaba for your response.