Dear Ajay,

What do you mean "nominal form"? Generally, panel data that we deal with is quantitative data. Do you mean that the data you have is nominal, i.e. yes = 1 and No = 0? or is it that the term "nominal" used here has non-technical meaning but a substitute for "general form".

Cheers.

Hello Dr. Paul,

     Here I mean that  I have data in a raw form like GDP in million US$ - time series. I heard for OLS, time series data should be checked for Stationarity. But, what in case of Panel Data? Should the data be stationary in order to run  Panel Data Analysis? 

One more doubt is that I had run ADF test and I found the data is stationary in case of 1st difference, but not at level. So, How can I proceed next ?

Thanks for your respond. I think my question is clear now.

Ok, @Jay that 's is clear.

STATIONARITY OF DATA: in time series, the common model used in autoregressive type and its variations. in autoregressive time series, we are regressing Yt against its own value in the last period Yt-1; thus:

Yt = B0 + B1Xt-1

The value of Yt throughout the period when plotted will not be smooth; there will be some period when there will be spikes (up and down). Let's call this volatility (up and down) the effect of shock. the idea of testing for stationarity is to verify whether the effect of shock is permanent or transitory. if the effect of shock is transient (temporary), the value of Yt in subsequent period will return to its long-run equilibrium. If Yt return to its long-run equilibrium, we say that the data set is stationary, i.e. meaning that the data is stable even with the effect of shock, Yt still goes back to its long-run mean (mean reverting). However, if after the shock, the subsequent Yt does not go back to its long-run equilibrium, its means that the effect of the shock is absorbed into the system and becomes part of the system. This type of data set is called integrated time series. This is one rationale for checking data stationarity.

AFTER ADF TEST, WHAT 'S NEXT? If the ADF test shows that is stationary at first difference---most cases are--it means that the data is considered stable when lag one period. in general, if the data is stationary after I(1), i.e. after first difference, it means that the data set is stationary. This means that the still retains its memory in mean reverting. In such a case, the data set is predictable. There is no need for error correction mechanism. if the data set lost its mean reverting characteristic, then you would need to implement ECM. What's next? Construct your predictive function (forecast model) and test the model.

REFERENCE: I attach here a reference material that you can use from time to time when doing modeling. I hope it will be helpful.

Thanks Dr. Paul L. You are a good teacher. 

one more doubt: if i want to run Panel OLS or Simple OLS, which value i have to consider- Individual Intercept, Individual intercept and Trend or None. ( In my regression, I took intercept). 

INTERCEPT & TREND: As time lapses with time series, i.e. Yt-1, Yt-2, ... Yt-T, you may notice the value of the intercept B0 or elsewhere the notation may be at may change. this changing is called a drift. recall that the original Dicky-Fuller Test is given as:

ΔYt = B1Yt-1 + et

if there is a constant (a drift), the equation is modified to:

ΔYt = at + B1Yt-1 + et

The notation at here is the same as B0 in my prior notation. There is another adjustment called time trend. With time trend the equation becomes:

ΔYt = at + B1Yt-1 + Bt + et

Thus, in your modeling consider both drift and trend. If there is time trend, report time trend. Test to see the pattern of the drift over time.

Dear Dr. Paul Louangrath

Thank you very much for your above answer. I would like to revisit this topic for a while. I have an unbalanced panel data (time > countries), so I proceeded three unit-root tests to check whether there are some unit roots test in my panel data or not. It turned out there existed some unit roots test in my panel from the results of three unit root tests.

So what should I do next? As far as I am concerned, I should check the integration between dependent variables and independent variables through integration tests, such as Pedroni's panel cointegration tests and KAO Performs Dynamic Ordinary Least Squares for Cointegrated Panel Data with homogeneous covariance structure.

Then if I have integration, what should I do next? Could you please help to guide me? I also would like to change my dependent variable proxy for a robustness check. What should I do following these steps?

Thank you a lot in advance.

Best regards,

Anh

@Paul Louangrath - sir, stationarity is required to be checked in case of ordinal data. Like my dependent variable is credit ratings divided into 3 categories. Whether stationarity to be checked for it if multiple years data to be used ? Please guide

It is important to test for stationarity (unit root) in panel data because many time series models and panel data models require that the underlying data is stationary. Reliable unit root testing is an important step in any time series analysis or panel data analysis.

It enables the researcher to determine the order of integration of variables in a model which then shows at what level each variable must be entered into a regression model to make the model efficient.